**Graduate Seminar**Song Shi will speak on "

**Note on Laplace Operators and Homologies**" at 2:00p.m. in N638 Ross.ABSTRACT:

*In this seminar we will talking about some positive self-adjoint operators and their actions. Also we will conclude with some useful equations.*

**Graduate Seminar - 2nd Talk**Song Shi will speak on "

**Classical Theta Functions and Quantum Tori**" at 3:00p.m. in N638 Ross.ABSTRACT:

*The Schwartz kernel of the multiplication operation on a quantum torus is shown to be the distributional boundary value of a classical multivariate theta function. The kernel satisfies a Schr¨odinger equation in which the role of time is played by the deformation parameter h and the role of the hamiltonian by a Poisson structure. At least in some special cases, the kernel can be written as a sum of products of single variable theta functions.*

**Survey Paper**Shahriar Shams will speak on "

**Recent Development in Empirical Likelihood Based Variable Selection Approach**" at 10:00a.m. in N638 Ross.ABSTRACT:

*In statistical analysis information criteria form an important class of model/variable selection methods which is based on parametric likelihood. But insituations where parametric family assumption for the data is not plausible or when the model is specified using set of estimating equations, the likelihood is no longer available. To overcome this problem, information criterion under empirical likelihood was introduced. Also when a serious computational problem was found in empirical likelihood based variable selection approach, adjusted empirical likelihood was proposed. In this survey paper we have analyzed the performance of this approach. A simulation study was conducted and also this approach was applied on a real life data set. Adjusted empirical likelihood was found to be consistent when the parametric family assumption is not available and also when it's available.*

**Graduate Seminar - 2nd Talk**Dorota Mazur will speak on "

**G-m-Quasi-Invariants in Light of the Theory of Orbit Harmonics**" at 9:00a.m. in N638 Ross.ABSTRACT:

*This seminar is an extension of my previous talk on 'Orbit Harmonics'. It is based on 2005 article of A. M. Garsia and N. Wallach 'Some New Applications of Orbit Harmonics'. I will define m-Quasi-Invariants of a Coxeter group.I will also state some basic results for the degree-graded G-invariant subalgebra of a ring of polynomials Q[X], and then show that the ring of G-m-Quasi-Invariant polynomials satisfies them.*

**Graduate Seminar**Li Wang will speak on "

**Modeling of Drug Treatment of Influenza In Vitro**" at 2:00p.m. in N638 Ross.ABSTRACT:

*The objective of this seminar is an extension of the first one. We will focus on the evolution of the drug resistance in influnenza A in vitro. Specifically speaking, modeling the infection process in HF system of experiments and drug effect in the models.In this seminar we will refer to the main paper, Catherine A.A. Beauchemin, James J. McSharry, George L. Drusano,J ack T. Nguyen, Gregory T. Went, Ruy M. Ribeiro,and Alan S. Perelson, Modeling amantadine treatment of influenza A virus in vitro,Journal of Theoretical Biology 254(2008) 439-451.*

**Survey Paper Presentation**Mario Soster, Mathematics Education, will speak on "

**The Changing Landscape of Teaching Mathematics in Ontario and the Evolution of the Mathematics Curriculum at the Intermediate and Senior Level from 1937-2007**" at 9:00a.m. in N627 Ross.ABSTRACT:

*Titled ‘The Intellectual Chameleon' my research explores the changes in the mathematics curriculum in Ontario at the intermediate and senior level (grades 7 through 13) focusing on the history of and the philosophy behind the changes made during the last eight decades. Each curriculum change is briefly analyzed with a historical backdrop studying the evolution of the mathematics curriculum in Ontario through the examination and utilization of key documents and primary source materials. During my talk I will outline when the changes occurred and discuss under what premise and direction the Ministry was taking when it came to mathematics instruction. Highlights include specific aspects of the changes such as: math course pathways, terminal math courses, standardized testing, and streaming/de-streaming.*

**Graduate Colloquium**Han Qiuzi Wen will speak on "

**A Hybrid-domain Approach on Modeling Nonstationary Time Series with Multiple Time-varying Deterministic Component**" from 1:00p.m. to 3:00p.m. in N638 Ross.ABSTRACT:

*In this thesis, an innovative hybrid-domain approach is developed to model nonstationary time series with multiple time-varying deterministic components, such as periodicities, trend and shifts in mean. The proposed frequency domain approach and a time domain approach are combined together through an iterative procedure analogue to the backfitting algorithm. The performance of the proposed method is evaluated by Monte Carlo Simulations and its power is further illustrated through applications in climate research.*

**Graduate Seminar – 1st Talk**Jessica Tsang Kwai Kew will speak on "

**Asset Allocation and Efficient Frontiers for Mortality Linked Securities**" at 11:00a.m. in N638 Ross.ABSTRACT:

*Investment in mortality-linked securities such as baskets of life settlements offer investors returns that are largely uncorrelated with other asset classes. The absence of academic work on the investment characteristics of such baskets is an obstacle to institutional investors entering this market. A Monte Carlo approach is used to quantify the diversification benefits in incorporating life settlement policies in a portfolio. The efficient frontier as well as questions concerning an optimum asset allocation when we combine these securities with equities and bonds in a portfolio is examined. In this presentation, I will introduce life settlement which is a financial arrangement when a third party buys the rights to the benefits of a life insurance policy from an insured individual or policyholder. I will also present some simulation results on how I model the behavior of a portfolio over a period of 10 years when we vary the initial allocation of equities/bonds and life settlements in the portfolio.*

**Graduate Seminar**Marc Cassagnol will speak on "

**Introduction to Implied Levy Volatility**" at 10:00a.m. in N638 Ross.ABSTRACT:

*Historical stock price data shows that log-stock returns are rarely normally distributed, and as a result, the Black-Scholes pricing model is inadequate for computing implied volatility. This is apparent in the "smile" or "smirk" shape that is often seen when plotting implied volatility versus strike price. By generalizing the concept to include more realistic Levy models, we obtain a more consistent estimate of implied volatility. In this seminar we discuss implied Levy space and time volatility, and how they perform in several applications.*

**Graduate Seminar – 2nd Talk**Kaijie Cui will speak on "

**High Dimensional Polynomial Interpolation on Sparse Grids**" at 12:30p.m. in N638 Ross.ABSTRACT:

*By using least solution at sparse grids with the Chebyshev polynomials, we study the polynomial interpolation on d-dimentional cube for large d. The method is shown to be optimal for many function spaces. We will also consider the polynomial exactness, error bounds and order of convergence of the method.*

**Survey Paper**Li Wang will speak on "

**Implementation of Rapidly Convergent Representations for the Green's Function on Periodic Structure**" at 2:00p.m. in N638 Ross.ABSTRACT:

*Numerical methods to evaluate the kernel function of PDE,our topic is to evaluate the performance of five important representation for Green's function of Helmholtz equation on periodic domain and the objective of this survey paper is to study and implement the efficient representation methods for Green's function for a Helmholtz equation with periodic structure.Thorough an experiment of electromagnetic(EM) problem to analyze, verify facts in objected main paper and understand the strength and weakness of each method.*

**Graduate Seminar**Dorota Mazur will speak on "

**Characteristic Properties of Reflection Groups**" at 12:00p.m. in N638 Ross.ABSTRACT:

*An invertible linear transformation of a finite dimensional vector space V over a field K will be called a reflection if it is of order two and leaves a hyperplane pointwise fixed. A group G of linear transformations of V is a finite reflection group if it is a finite group generated by reflections. --Claude Chevalley, "Invariants of Finite Groups Generated by Reflections, http://www.jstor.org/pss/2372597," American Journal of Mathematics, Vol. 77, No. 4 (Oct., 1955), pp. 778-782**The aim of this talk is to introduce some interesting characteristics of finite groups generated by reflections, particularly the connection between quite different algebraic objects: the invariants and the harmonics of these groups. The theorems and propositions will be illustrated by a classical example, a permutation group S_3.*

**Survey Paper**Douglas Tsang will speak on "

**Generalized Estimating Equations in Longitudinal Data Analysis**" at 10:30a.m. in N638 Ross.ABSTRACT:

*The Generalized Estimating Equations (GEE) method is an essential and often used method in handling correlated longitudinal data, especially in the field of epidemiology. This survey paper will discuss the use of the GEE method in various contexts of longitudinal data analysis. When longitudinal data are dependent, an extension of the Generalized Linear Model (GLM), namely the subject-specific and population-averaged models cater for heterogeneity across subjects. Statistical inference for these models can be based on the corresponding GEE methods. Under the context of having incomplete covariates or missing data which are missing at random, the Inverse Probability Weighted Generalized Estimating Equations (IPWGEE) method deems to be an effective one. GEE methods do not require distributional assumptions but only specifications of the first two moments. GEE estimates are consistent and asymptotically normal under suitable conditions even if the variance-covariance structure (i.e., the second moments) is mis-specified, as long as the mean structure is correctly specified. In addition, this paper presents ideas of missingness in data as well as various correlation structures within a subject's observations, and illustrates with an example how to implement the GEE method in R.*

**Graduate Seminar**Anton Tenyakov will speak on "

**Pricing European Options in a Levy Model Using Fast Fourier Transform**" at 11:00a.m. in N638 Ross.ABSTRACT:

*European Options are the foundations of the options universe. Presenting itself as the most basic type of option contract, these options give the holder or seller of the option the ability to exercise the option at the expiry of the option.**In this talk we describe how to price European options where characteristic function of return is known analytically. We introduce Generalized Tempered Stable and Variance Gamma processes and explain how to calculate the price of European option using Fourier transform following by derivation of implied volatility surface for the above mentioning models with an additional optimization of the algorithm.*

**Survey Paper**Kaijie Cui will speak on "

**Static Hedging of Barrier Options**" at 3:30p.m. in N638 Ross.ABSTRACT:

*Put-call symmetry relates the prices of puts and calls struck at different values, and provides static hedges for many exotic options by the way of standard European-style options. We mainly surveyed the works done by Peter Carr and Roger Lee and Peter Carr, Kartina Ellis, and Vishal Gupta, reviewed the definitions and conditions of put-call symmetry, then used the theoretical support to value and hedge various barrier options. Also, we considered hedging techniques for asymmetric dynamics.*

**Graduate Seminar**Shicheng Wu will speak on "

**Introduction to Economic Capital**" at 10:00a.m. in N638 Ross.ABSTRACT:

*Economic Capital ("EC" or Risk Capital) is a financial concept in risk management, which is the reserve required to absorb unexpected losses, in this case due to derivative counterparty defaults. Specifically it is the 99.95% unexpected loss due to counterparty default: ECONOMIC CAPITAL = Unexpected Loss – Average Loss. This seminar would introduce the methodology and computing process of Economic Capital at banking level.*

**Dissertation Subject Oral**Adnan Sljoka will speak on "

**Counting for Rigidity and Flexibility—Algorithms and Applications**" at 10:30a.m. in N627 Ross.ABSTRACT:

*In rigidity theory, specifically combinatorial rigidity, one can simply count vertices and edges (constraints) in a graph and its subgraphs to determine the rigidity and flexibility of a corresponding framework. The 6|V|–6 counting condition for 3-dimensional body-hinge structures (modulo molecular conjecture), and a fast `pebble game' algorithm which tracks the underlying count in the multigraph, have led to the development of the program FIRST, for rapid analysis of the rigidity and flexibility of proteins. We will give a brief description and illustration of the 6|V| – 6 pebble game algorithm. We have extended the pebble game algorithm to quantify the relative degrees of freedom of a specified region (core) in the multigraph and identify the regions that are relevant as constraints with respect to the core and those regions that are irrelevant. Our recent work has extended this basic model and the pebble game algorithm to predict hinge motions of proteins, as well as some preliminary predictions for 'allostery' in models - where binding on one portion of a large molecule changes the shape or binding at a distance 'active site' of the molecule. We also present a new approach and guidance on how to use the pebble game/FIRST to give a prediction on rigidity/flexibility and hydrogen-deuterium exchange rates of structural protein ensembles.*

**Dissertation Subject Oral**Anouk Bergeron-Brlek will defend her PhD Dissertation entitled "

**Words and Noncommutative Invariants of Finite Groups**" at 11:00a.m. in Stedman Lecture Hall 120E.

**Graduate Seminar**Mitra Ghoncheh Arghavan will speak on "

**Evaluation of Target Date Funds**" at 10:00a.m. in N638 Ross.ABSTRACT:

*Target date funds are an emerging class of investment products, designed for retirement savings, diversified across stocks, bonds, and cash. We want to illustrate methodologies for ranking such funds through two their phases pre-retirement (contribution) and post-retirement (consumption). We will outline such an approach and provide preliminary numerical results.*

**Graduate Seminar**Mitra Ghoncheh Arghavan will speak on "

**H1N1: Media Coverage and Waves of Infection**" at 11:00a.m. in N638 Ross.ABSTRACT:

*The World Health Organization declared the new strain of swine-origin H1N1 as a pandemic which is the most common cause of influenza in humans. We develop a three dimensional compartmental model to investigate the impact of media coverage to the spread and control of H1N1 in a given region/area. Stability analysis of the model will be discussed in terms of the basic reproduction number (R0). The existence of unique endemic equilibrium point and a Hopf bifurcation which causes oscillatory shape will be considered. We figure out that when R0 >1 and the media impact is stronger enough, the model exhibits endemic equilibria which poses challenge to the prediction and control of the outbreaks of infectious diseases.*

**Graduate Seminar**Kaijie Cui will speak on "

**Numerical Integration using Sparse Grid**" at 3:00p.m. in N638 Ross.ABSTRACT:

*We reviewed various constructions for numerical integration of multivariate functions on sparse grids, these formulas are Trapezoidal, Clenshaw-Curtis, Gauss and Gauss-Patterson formulas. The algorithms are constructed by combinations of tensor products of one-dimensional cases. And within these formulas, Gauss-Patterson quadrature formula shows the superiority in comparison to others, so, the Gauss-patterson formula is considered as the one-dimensional basis of the multivariate construction.*

**Dissertation Subject Oral**Cheng Liu will speak on "

**Non-stationary Time Series Analysis using the Generalized Stockwell Transforms**" at 10:00a.m. in N638 Ross.ABSTRACT:

*In time series analysis, the coherence function measures the linear interaction between two time series and the phase-locking statistics evaluate the nonlinear interrelation based on the phase synchronization. However, these measures are defined under the assumption that the time series are stationary. For non-stationary time series analysis, evolutionary spectrum theory was established for locally stationary time series. Time-frequency representations are commonly used to derive the estimators of the evolutionary spectrum, which provide descriptions of the time-varying characteristics of non-stationary time series. In this thesis, we first propose a generalized Stockwell transform that produces adaptive frequency-dependent resolution. We then use it to define various measures in the time-frequency domain that can more accurately reveal the time-varying interrelations between multiple time series. Finally, we apply the proposed measures to study the brain functional networks under the multi-source interference task. Our findings provides valuable insight about how human brains deal with interference stimuli and contribute to the understanding and treatment of attention deficit hyperactivity disorder.*

**PhD Defence**Philippe Choquette will defend his PhD Dissertation entitled "

**Species of Type B and Related Graded Hopf Algebras**" at 1:00p.m. in N638 Ross.

**Dissertation Colloquium**Marija Zivkovic Gojovic, will speak on "

**Age Structured Pertussis Models: Transmission Dynamics, Vaccination and Resurgence**" at 10:30a.m. in N638 Ross.ABSTRACT:

*Since the first pertussis vaccine was introduced in the mid 1940s, there have been several changes in the pertussis vaccine structures and vaccination policy. During the same time period, the pertussis incidence rate varied. A drastic 90% drop is observed immediately after the vaccination in 1940s and in 1950s, followed by a steady decrease until 1988, and then by a slow but consistent increase in the beginning of 1990s that continues until today. Along with the changes in the pertussis incidence rate, the significant shift in the demographic structure of the pertussis infection can also be observed. In this thesis, we developed an age-structured mathematical model to analyze the influence of the vaccination on the demographic structural change of the infected population, and we formulated and analyzed a delay differential equations model to explore the oscillatory behavior of pertussis transmission dynamics. To conduct numerical simulations based on our structured models, we designed a novel discretization technique that replaces the usual change rates with survival probabilities. We analyzed the vaccine administration in two different time periods: the whole cell vaccine administrated in the 1943, and the acellular vaccine administrated since 1997. We additionally used the model to estimate the acellular vaccine characteristics, to analyze the potential changes in the vaccination schedule and to estimate the underreporting level of pertussis incidence. Oscillatory behavior of pertussis infection was illustrated by same numerical simulations and same theoretical analysis based on the Hopf bifurcation theory. We showed that repeated pertussis outbreaks may be attributed to the waning but partially present immunity after the pertussis infection.*

**Dissertation Colloquium**Anouk Bergeron-Brlek will speak on "

**Words and Noncommutative Invariants of Finite Groups**" at 10:00a.m. in N638 Ross.ABSTRACT:

*Let G be a finite group and V a complex vector space with basis {x_1,x_2,...,x_n} and a G-module structure. Then the tensor algebra T(V) over the field of complex numbers, which is isomorphic to the polynomials in the non-commutative variables x_1, x_2, ..., x_n with complex coefficients, is also a G-module. In this talk, we give a combinatorial interpretation for the decomposition of T(V) into simple G-modules. More specifically, we give a general method for decomposing the space T(V) in terms of words in a particular Cayley graph of the group G and we study the graded space of invariants in T(V) with respect to the action of G. To apply the method to a particular group, we require a surjective algebra momorphism from a special subalgebra of the group algebra into the algebra of characters.**We present the cases of the symmetric group, the hyperoctahedral group, the dihedral group and the cyclic group. For the symmetric group, we give an example of this homomorphism from Solomon's descent algebra. When we consider the hyperoctahedral group, the required homomorphism, due to Bonnaf‚ and Hohlweg, is from the Mantaci-Reutenauer algebra. In those two cases, we can give an explicit decomposition of the tensor algebra only on certain modules, via some words in a particular Cayley graph.**As a consequence we have an interpretation for the graded dimensions and the number of free generators of the algebra of invariants in terms of those words. For the dihedral group and the cyclic group, we have a realization of the algebra of characters as a subalgebra of the group algebra, hence the combinatorial technique presented permits to decompose the tensor algebra on any module.*

**Dissertation Subject Oral**Zhi Chen will give a talk on "

**Basis of Diagonally Alternating Harmonic Polynomials for Low Degree**" at 10:30a.m. in N638 Ross.

**Dissertation Subject Oral**Xiaoping Shi will speak on "

**Some Problems in Change Points Analysis**" at 1:30p.m. in N638 Ross.ABSTRACT:

*A change point refers to a location or time in which the observations or data satisfy two different models before and after it. There are many important applications of change point analysis in many fields including finance, environment, quality control, medicine, geology, etc. After reviewing some relevant literature on change point analysis, we propose a general framework for improving current testing procedures for change points.*

**Dissertation Colloquium**Pengfei Guo will speak on "

**Robust Inference and Weighted Likelihood Estimation**" at 9:30a.m. in N638 Ross.ABSTRACT:

*Hu and Zidek (1997) proposed a very general method for using all relevant information in statistical inference. We extend their method to generalized linear models when the covariates are generated from different populations. Furthermore, we propose a unified and effective method to choose the weights using the estimated probability of membership through the expectation-maximization algorithm when memberships are unknown.**Robust techniques, such as M-estimation, are used to control the possible model violation on the response direction. We also consider the weighted likelihood when the memberships of observations are known.*

**Graduate Seminar**Navjot Thind will speak on "

**Introduction to the Study of Mathematical Immunology and its Application to HIV**" at 10:30a.m. in N638 Ross.ABSTRACT:

*Differential equations can be used to model the spread of viruses from cell to cell. There are basic laws that govern the spread of infectious agents within individuals, their interactions with the immune system and their responses to treatments. The basic model of virus dynamics will be introduced. Furthermore, I will discuss basic topics and definitions in immunology.*

**Graduate Seminar**-- CANCELLEDNavjot Thind will speak on "

**Introduction to the Study of Mathematical Immunology and its Application to HIV**" at 3:30p.m. in N638 Ross.ABSTRACT:

*Differential equations can be used to model the spread of viruses from cell to cell. There are basic laws that govern the sprad of infectious agents within indiviudals, their interactions with the immune system and their responses to treatments. The basic model of virus dynamics will be introduced. Furthermore, I will discuss basic topics and definitions in immunology.*

**Dissertation Subject Oral**Shahla Molahajloo will speak on "

**Heat Semigroups of Hermite Operators and Twisted Laplacians**" at 10:00a.m. in N627 Ross.ABSTRACT:

*The heat semigroup of a partial differential operator is the solution of the initial value problem of the heat equation governed by the partial differential operator. Using techniques from Harmonic Analysis and Quantum Theory such as Wigner transforms, Weyl transforms and their variants, we compute explicit formulas for the heat semigroups of time-dependent Hermite operators, multiscale twisted Laplacians, and Hierachical twisted Laplacians.**In the case of the time-dependent Hermite operators and the multiscale twisted Laplacians, the heat kernels, i.e., the kernels of the integral operators for the semigroups are computed. Applications of the heat kernels of the multiscale twisted Laplacians to the Green functions and global hypoellipticity of the multiscale twisted Laplacians are given.*

**Dissertation Colloquium**Daniel Oancea will speak on "

**The Andrews-Curtis Conjecture and the Recalcitrance of Groups**at 3:30p.m. in N638 Ross.ABSTRACT:

*In 1924, Nielsen defined certain automorphisms of the free group F of rank n, and showed that they generate the automorphism group of F. These "elementary" automorphisms are given by so-called "elementary Nielsen transformations" of generating n-tuples of F; Nielsen showed that any two generating n-tuples of F are transformable into one another by means of a finite sequence of such transformations.**In 1965, Andrews and Curtis introduced the extended Nielsen transformations, obtained by supplementing the original elementary Nielsen transformations by conjugations. They conjectured that any two normal generating n-tuples of F are equivalent under these extended transformations.**In this work we focus on the generalization of this conjecture to the class of all finitely generated groups. Thus, we consider the question as to whether the normal generating n-tuples of any group of rank n can be transformed by means of extended Nielsen transformations into generating n-tuples.**We begin by investigating the Nielsen classes of abelian groups, and we generalize an existing classification from finite to finitely generated abelian groups. We then use this result to establish a property of the abelianization homomorphism of finitely generated groups, relating the Nielsen classes of the abelianized group to the Andrews-Curtis classes of the group.**In 1993, Burns and Macedonska introduced so-called "M-transformations", and showed that they are, in a certain specific sense, equivalent to extended Nielsen transformations. The supremum of the numbers of M-transformations needed to transform normal generating n-tuples of a group G of rank n into generating n-tuples is called the recalcitrance of G.**Our main results give upper bounds on the recalcitrance of several classes of groups, chiefly solvable groups, finite groups, and finitely generated infinite groups with a principal series.**We also investigate certain possible counterexamples to the conjecture, bound the recalcitrance of a family of annihilating pairs in a free group of rank 2 from below, and consider so-called "weak" Andrews-Curtis equivalence in this context.**Finally, we examine briefly the connections between the group-theoretic and topological aspects of the Andrews-Curtis conjecture.*

**Dissertation Subject Oral**Fang Chang will speak on "

**Third Order Likelihood Inference on Stationary Time Series Analysis**" at 10:00a.m. in N620 Ross.ABSTRACT:

*For tail probability approximation, Lugananni and Rice (1980), and Barndorff-Nielsen (1986) derived formulas through modifying tail area and signed likelihood root, respectively. Fraser (1990), and Fraser and Reid (1995) proposed another formula to make Lugananni and Rice and Barndorff-Nielsen formulas reparametrization invariant. The proposed method, which is referred to as the third order method, also takes into consdideration of a broader distribution family. The aim of my research is to derive the methods for testing any scalar quantities of interest in two widely used stationary time series models, second order autoregressive model and first order moving average model, based on third order method and further investigating their performance.*The syllabus will available for perusal in N519 Ross.

**Thesis Defense**Ljiljana Mrdjenovic will defend her MSc Thesis entitled "

**Digital Watermarking in the Generalized Discrete Cosine Transform Domain**" at 2:00p.m. in N638 Ross.

**Dissertation Subject Oral**Natasha May will speak on "

**Noetherian Bases**" at 10:30a.m. in N638 Ross.ABSTRACT:

*A collection of sets is Noetherian if it contains no infinite strictly increasing chain. We are interested in topological spaces which have or do not have a base with this property. We will provide examples of such spaces and state facts and some open problems about topological spaces and Noetherian bases.*

**Dissertation Subject Oral**Hsiao-Hsuan Wang will speak on "

**Empirical Likelihood Method and its Applications**" at 11:00a.m. in N638 Ross.ABSTRACT:

*The empirical likelihood (EL), which was first introduced by Owen (1988), is a nonparametric method of inference based on a data-driven likelihood ratio function. The EL combines the reliability of the nonparametric methods with the efficiency of the likelihood approach. It has become one of the most popular statistical methods in the past twenty years or so. Qin and Lawless (1994) has shown that the EL and estimating equation are well suited for each other. We propose to link various moment estimating equations through the EL to provide more efficient estimation in mixture models. We also propose to use the EL method to avoid the controversy of the process of determining the likelihood weight in the weighted likelihood method.*

**Graduate Seminar**Seyed Tavalla will speak on "

**Eigenvalues of Stochastic Matrices**" at 2:30p.m. in N501 Ross.ABSTRACT:

*In this seminar I am going to summarize the study which has been done on geometric description of the location of characteristic roots of a stochastic matrix of order n. This question was first posed by A.N.Kolmogorov during a study on Markov Chains in mid nineteen forties. Later in 1945 and 1946, Dmitriev and Dynkin could partially solve this question.**In fact they solved the problem completely for all n <=5 and partially for n>5.**In 1951, F.I. Karpelevich could solve the question completely by deriving the parametric equations of the curvilinear arcs of the boundary of this region. Finally Hishashi Ito, in 1997 modified these equations and found a simplified form of them by means of Fary sequences and their properties.*

**Thesis Colloquium -- 2nd Talk**Ljiljana Mrdjenovic will speak on "

**Digital Watermarking in the Generalized Discrete Cosine Transform Domain**" at 3:00p.m. in N638 Ross.ABSTRACT:

*In recent years, advances in digital technologies have created significant changes in the way we reproduce, distribute, and market intellectual property (IP). However, with the lowered cost of reproduction, storage, and distribution motivation for large-scale commercial violation becomes a problem. In a world where piracy is growing, the rights of the IP owners need to be protected. As a result, digital watermarking is a commonly used method of protecting the ownership of someone's intellectual property. Digital watermarking can be generally defined as embedding additional information, called a watermark or signature, into an original digital object (often called a cover object) that can be detected and extracted later to make an assertion about the object. The most interest for us is digital watermarking used for protection of digital images. In this thesis, we explore digital watermarking in the generalized discrete cosine transform (GDCT) domain and compare the results with the well explored technique in the discrete cosine transform (DCT) domain.**In this talk, we will present the GDCT-based scheme for watermarking digital images as well as the modified DCT-based scheme. Performance of these two algorithms will be illustrated and compared using numerical simulations.*

**Thesis Defence**Yimin Du will defend his MSc Thesis "

**Global Stability of Tb Models: Heterogeneous Populations and Resistance**" at 10:30a.m. in N620 Ross.

**Survey Paper**Sulin Shakya will speak on "

**Integration of Microarray Data and its Applications**" at 1:00p.m. in N638 Ross.ABSTRACT:

*The rapid accumulation of microarray datasets demands for new method capable of combining microarray data obtained from different studies. This has been shown to be a useful way to increase sample size and thereby predicting a more reliable robust markers. The functional interpretation of microarray datasets represents a time-consuming and challenging task. The integration of Gene Ontology (GO) annotations in correspondence analysis is considered to ease interpretation of microarray datasets. In the endeavour of Inferring protein networks from biological data, integration of multiple biological data is preceded for supervised network inference. A kernel-based method has been proposed in literature for supervised graph inference based on multiple types of biological datasets such as gene expression, phylogenetic profiles and amino acid sequences. In this survey paper, the existing methods proposed by Lie Xu, et al. (2005), Christian H.B. et al. (2005) and Tsuyoshi, K. et al. (2005) are briefly reviewed and its applications are studied.*

**Survey Paper**Heather Krause will speak on "

**Semiparametric Mixed Model: A Best of Both Worlds Approach**" at 2:00p.m. in N638 Ross.ABSTRACT:

*The presentation will provide a brief overview of modern nonparametric techniques and a short summary of current linear mixed model theory. The focus of the presentation will be the fusion of these two techniques resulting in semiparametric mixed models. The presentation will focus on a survey of the work of Ruppert, Wand, and Carroll (2003). We will look at several recent examples of applications and developments in a wide range of fields including an examination of spinal bone mineral density in women, factors influencing the use of the death penalty in Britain and the effect of air quality on the growth of spruce trees. As much as possible, emphasis will be on the application and implementation of this type of model R.*

**Dissertation Subject Oral**Yan Yan Wu will speak on "

**Higher-order Inference in the Linear Mixed Model and Gaussian Graphical Model**" at 2:00p.m. in N638 Ross.ABSTRACT:

*Higher-order methods provide accurate results for approximating the p-values for testing both scalar and high dimensional parameter of interest. We propose likelihood based third-order method testing the random effects and fixed effects in the Linear Mixed Model where the parameter of interest is a scalar. Saddlepoint approximation method is proposed to test the equality of several covariance matrices that belong to Gaussian Graphical Model family.*

**PhD Oral Exam**Beatriz Zamora-Aviles will defend her PhD Dissertation entitled "

" at 10:30a.m. in N638 Ross.The Structure of Order Ideals and Gaps in teh Calkin Algebra

**MSc Thesis Defence**Sheel Chopra will defend his MSc Thesis entitled "

**Study of Extra Tropical and Higher Latitude Cyclone Tracks in the Northern Hemisphere**" at 12:30p.m. in N638 Ross.

**Thesis Defense**Rory Lucyshyn-Wright will defend his MSc Thesis entitled "

**Monoidal Domain-theoretic Topology**" at 10:00a.m. in N501 Ross.

**MA Oral Exam**Holly Heglin will defend her Master's Thesis entitled "

**The Plancherel Measure fo the Symmetric Group and the Limit Form of Young Diagrams**" at 10:00a.m. in N638 Ross.

**Graduate Seminar - 2nd Talk**Lucian Savin will speak on "

**Coarse Smith Theory**" at 4:00p.m. in N638 Ross.ABSTRACT:

*The talk defines the notion of bounded fixed set and shows that Smith's result (that relates the homology of the fixed set to that of the total space) holds for coarse geometry. Representative examples will be discussed.*

**Graduate Seminar - 2nd Talk**Francis McMullan will speak on "

**Conditional Expectations of Random Sets**" at 1:00p.m. in N638 Ross.ABSTRACT:

*The conditional expectation of a random subset of Euclidean space can be defined based on the conditional expectations of random variables. An application is defining martingales for random sets.*

**Graduate Seminar**Seyed Tavalla will speak on "

**Spectral Theory**" at 12:00p.m. in N638 Ross.ABSTRACT:

*In this talk I review basic definitions and theorems about Normal Operators and their Spectrum as well as C*-algebra and the space of all Bounded Borel functions over a (locally)compact space(SP(T)) for a Normal Operator T over a Hilbert space H.*

**Survey Paper**Hong Xu will speak on "

**Tuning Parameter Selection for Penalized Likelihood Estimation of Inverse Covariance Matrix**" at 2:00p.m. in N638 Ross.ABSTRACT:

*In a Gaussian graphical model, the conditional independence between two variables are characterized by the corresponding zero entries in the inverse covariance matrix. Maximum likelihood method using the smoothly clipped absolute deviation (SCAD) penalty and the adaptive LASSO penalty have been proposed in literature. The method leads to a sparse and shrinkage estimator of the inverse covariance matrix. In this project, we establish the result that using BIC in penalized likelihood framework with both types of penalties can lead to consistent graphical model selection. We compare the empirical performance of BIC with cross validation method and demonstrate the advantageous performance of BIC criterion for tuning parameter selection. A simulation study was conducted to demonstrate the competitive performance of the proposed method.*

**Dissertation Colloquium**Beatriz Zamora-Aviles will speak on "

**The Structure of Order Ideals and Gaps in the Calkin Algebra**" at 3:00p.m. in N638 Ross.ABSTRACT :

*Let $\omega$ denote the set of natural numbers. In 1997 S. Solecki proved that an ideal $I$ on $\omega$ is an analytic P-ideal iff it can be determined by a lower semicontinuous submeasure $\phi$ on $\omega$, i.e., $I=Exh(\phi)=\{x\in 2^{\omega}: \displaystyle\lim_{n}\phi(X\smallsetminus n)=0\}$. We consider the set of positive bounded operators of norm at most one on a separable infinite dimensional complex Hilbert space. This set can be naturally regarded as a partial order, it is also a Polish space with respect to the weak operator topology. We define analytic P-ideals on this set and prove a non commutative version of Solecki's Theorem. We also see that Solecki's result can be deduced from it.**In this dissertation we also study the gap structure of the partial order of projections of the Calkin algebra. We prove the existence of an analytic Hausdorff gap in this partial order. As a consequence we obtain that under Todorcevic's Axiom and Martin's Axiom the gap spectrum of the poset of projections of the Calkin algebra is strictly bigger than the gap spectrum of $P(\omega)/Fin$.*

**Graduate Seminar**Lucian Savin will speak on "

**Introduction to Coarse Geometry**" at 4:00p.m. in N638 Ross.ABSTRACT:

*The aim of the talk is to introduce all the notions necessary to define coarse homology. The notion of asymptotic dimension is also introduced. This talk provides the backgroung for the second talk that deals with Coarse Smith Theory.*

**Graduate Seminar**Majid Nabipoor Sanjebad, will speak on "

**Simulation of Hyper-inverse Wihart Distribution in Graphical Models**" at 10:00a.m. in N638 Ross.ABSTRACT:

*For direct sampling from hyper-inverse Wishart distribution an efficient method is introduced. The method is based on junction-tree representation of graphs. Theory and computational algorithm for both decomposable and decomposable graphical models is described.*

**Survey Paper**Jaiwei Li will speak on "

**Pricing Credit Default Swaps**" at 11:00a.m. in N638 Ross.ABSTRACT:

*This survey paper provides a methodology of pricing plain vanilla Credit Default swaps when the payoff is contigent on default of the reference entity. The stochastic valuations of the interest rate and the probability of default are implemented by using the one-factor Vasicek model and the one-factor model of non-default probability. This paper employs Monte Carlo Simulations and the Crank-Nicolson method in the valuation and the CDS premium calculated by two methods are compared.*

**Financial Engineering Diploma**Jiawei Li will speak on "

**Talk on Internship**" at 12:00p.m. in N638 Ross.ABSTRACT:

*I will give a talk on my experience as an investment research assistant. My responsibilities are to monitor the financial markets and collect market data. Using the information I collect to develop market observation reports.*

**Survey Paper**Sabria Khan will speak on "

**Testing Correlated Correlation**" at 2:00p.m. in N638 Ross.ABSTRACT:

*Correlational analysis is an important method in statistical analysis especially in the area of psychonometric, finance, sociology, etc. In order to test whether independent or dependent correlation coefficients are equal, several methods have been proposed during the past few decades. Whenever testing this kind of hypothesis arrives, extensive computational work makes finding goals difficult. In the survey paper, the existing methods proposed by Olkin & Finn (1990) and Cheung & Chan (2002) are briefly reviewed and its applications are studied.*

**Graduate Seminar**Majid Nabipoor Sanjebad will speak on "

**The EM Algorithm for Graphical Association Models with Missing Data**" at 10:00a.m. in N638 Ross.ABSTRACT:

*Log-linear models is considered for contingency tables in the case of multinomial sampling. The related notation and basic estimates are performed. In presence of missing data the traditional mle estimator does not work, then EM algorithm is used to estimate marginal probability. E-step calculation is based on and the procedure of Lauritzen and Spiegelhalter is exploited to estimate it.*

**Thesis Colloquium**Rory Lucyshyn-Wright will speak on "

**Monoidal Domain-Theoretic Topology**" at 10:00a.m. in N638 Ross.ABSTRACT:

*It has been shown that topological spaces and other topological objects may be described via formally simple axioms expressed in terms of monads and lax monads (Manes 1969; Barr 1970; Gaehler 1992; Clementino and Hofmann, 2003; Clementino and Tholen, 2003; Clementino, Hofmann, and Tholen, 2004; Pisani, 1999; Hofmann and Tholen, 2006; Seal, 2005, 2009).**Recent reseach to be presented shows that basic objects of domain theory (in the sense that arose in the study of programming language semantics), such as the continuous directed-complete partial orders (continuous DCPOs), also arise in their topological form via similar axiomatizations.**In providing an exposition of this research, the thesis first discusses the basic notion of a topological space and some of its various axiomatizations in terms of interior operators, neighbourhood systems, and convergence, studying the relationships between these formulations and showing how they yield axiomatizations in terms of monads and lax monads of filters on the powerset of a set.**Upon this foundation, the thesis then examines the basic topological nature of the objects of domain theory, and a particular associated notion of convergence. A particular class of topological spaces is identified and captures an essential notion underlying domain theory. These spaces support a notion of internal convergence of filters on the specialization order, and it is shown that this class of spaces may be described via several interconnected axiomatizations, including formulations in terms of monads and lax monads which bear a striking formal connection to the related axiomatizations of topological spaces in general. It is shown that among the topological spaces in this class, those that are sober are precisely the continuous DCPOs -- so that the category of continuous DCPOs embeds reflectively into the identified subcategory of Top. Finally, the relationship of these spaces to the algebraic category of continuous lattices -- which are the Eilenberg-Moore algebras of the filter monad (Day, 1975) -- is examined, and we expose new connections between the continuous lattices and the basic notion of a topological space.*References: Barr, M. (1970) Relational algebras. Lecture Notes in Math. 137 39{55).

Clementino, M.M. and Hofmann, D. (2003) Topological features of lax algebras. Appl. Categ. Structures 11 267-286

Clementino, M.M., Hofmann, D. and Tholen, W. (2004) One setting for all: metric, topology, uniformity, approach structure. Appl. Categ. Structures 12 127-154.

Clementino, M.M. and Tholen, W. (2003) Metric, topology and multicategory: a common approach. J. Pure Appl. Algebra 179 13-47.

Day, A. (1975) Filter monads, continuous lattices and closure systems. Canad. J. Math. 27 50-59.

Gaehler, W. (1992) Monadic topology . a new concept of generalized topology. In: Recent Developments of General Topology and its Applications. Mathematical Research, vol. 67, pp. 136.149. Akademie-Verlag, Berlin.

Hofmann, D. and Tholen, W. (2006) Kleisli compositions for topological spaces. Topology Appl. 153 2952-2961.

Manes, E. (1969) A triple theoretic construction of compact algebras. Lecture Notes in Math. 80 91-118.

Pisani, C. (1999) Convergence in exponentiable spaces. Theory Appl. Categ. 5 148{162. Seal, G.J. (2005) Canonical and op-canonical lax algebras. Theory Appl. Categ. 14 221-243.

Seal, G.J. (2009) A Kleisli-based approach to lax algebras. Appl. Categ. Structures 17 75-89.

**Graduate Seminar**Majid Nabipoor will speak on "

**The EM Algorithm for Graphical Association Models with Missing Data**" at 12:30p.m. in N638 Ross.ABSTRACT:

*Log-linear models is considered for contingency tables in the case of multinomial sampling. The related notation and basic estimates are performed. In presence of missing data the traditional mle estimator does not work, then EM algorithm is used to estimate marginal probability. E-step calculation is based on and the procedure of Lauritzen and Spiegelhalter is exploited to estimate it.*

**MSc Thesis Defense**Yimin Du will defend his MSc Thesis entitled "

**Global Stability of TB Models: Heterogeneous Populations and Resistance**" at 10:30a.m. in N638 Ross.

**Graduate Seminar**Xi Yang will speak on "

**A Fast Algorithm for Computing Integrals in Function Spaces: Financial Applications**" at 11:00a.m. in N638 Ross.ABSTRACT:

*I will describe in my talk a fast and general numerical algorithm for computing path integrals in function spaces. Efficiency is ensured by use of FFT-based procedures as the primary element of the algorithm. The total number of operations required by the algorithm can be shown to be proportional to the total number of discretization nodes. Some financial applications of the algorithm are considered.*

**Thesis Colloquium -- 2nd Talk**Yimin Du will speak on "

**Global Stability of Tb Models: Heterogeneous Populations and Resistance**" at 1:30p.m. in N627 Ross.ABSTRACT:

*In this thesis, we first formulate a two-group tuberculosis model involving the interaction between a homeless group and the general community. We investigate the global stability of the disease-free and disease endemic equilibria using a Lyapunov function. In the second part, we develop a two-train tuberculosis model with drug-sensitive strain and drug-resistant strain, and describe the transmission dynamics of such a model. Finally, we present some numerical simulation results based on our models parameterized in terms of Canadian population.*

**Graduate Seminar**Francis McMullan will speak on "

**Convergence of Random Sets**" at 3:00p.m. in N627 Ross.ABSTRACT:

*Random sets take values which are subsets of some space, for example the space of real numbers or vectors. I will talk about how they can be related to random variables/vectors including a possible definition of expectation. This definition leads to various convergence theorems including central limit theorems.*

**Dissertation Subject Oral**Han Quizi Wen will speak on "

**Innovative Statistical Approaches to Homogenization of Climate Data Series**" at 9:00a.m. in N638 Ross.ABSTRACT:

*As has been widely recognized in recent climate research, climate data time series often contain discontinuities (sudden changes or shifts) due to inevitable changes in instruments, observing practices, station location/environment, etc., during the period of data record; and non-climatic shifts shall be eliminated, to the extent possible, from the data time series prior to its application, especially its application in climate trend assessment. Such climate data homogenization process involves statistical testing for homogeneity (or lack of it) and estimation of the shift magnitude to adjust the series to make it homogeneous. One common characteristic of most climate variables is that they have various periodicities (e.g., annual cycle, decadal and inter-decadal oscillations…). Also, some climate variables (e.g., daily precipitation) have non-normal distributions. The presence of periodicity and non-normality make classical statistical testing methods not directly applicable to climate data series. This thesis proposes two innovative statistical approaches to deal with the homogeneity test problem for periodic and non-normal climate data series, respectively.*

**Graduate Seminar**Xi Yang, will speak on "

**Robust Hedging of Barrier Options**" at 1:00p.m. in N638 Ross.ABSTRACT:

*The standard approach to the hedging of a barrier options is to postulate a model for the behavior of the underlying asset. This requires the model precisely describes the real world. This assumption is normally very unlikely to be satisfied. My talk will give a way to find hedging strategies for options which are robust to a misspecifiction of the model for the underlying asset and gives the numerical results of this method.*

**Thesis Colloquium -- 1st Talk**Yimin Du will speak on "

**Global Stability of Tb Models: Heterogeneous Populations and Resistance**" at 1:30p.m. in N627 Ross.ABSTRACT:

*In this thesis, we first formulate a two-group tuberculosis model involving the interaction between a homeless group and the general community. We investigate the global stability of the disease-free and disease endemic equilibria using a Lyapunov function. In the second part, we develop a two-train tuberculosis model with drug-sensitive strain and drug-resistant strain, and describe the transmission dynamics of such a model. Finally, we present some numerical simulation results based on our models parameterized in terms of Canadian population.**In this talk, I will give the brief introduction of TB and then discuss the model formulation. In the second talk, I will present the main results of global stability for equilibria using lyapunov functions.*

**Thesis Colloquium**Holly Heglin will speak on "

**The Plancherel Measure and the Limit Form of Young Tableaux**" at 2:00p.m. in N638 Ross.ABSTRACT:

*In this paper I reconstruct proofs of the results shown by Vershik and Kerov and independently Logan and Shepp pertaining to the Plancherel measure and the symmetric group. The intent of this exposition is to rigor- ously prove the main theorems and provide detailed motivation for the ideas involved. Further to reproducing the original results, I intend to provide de- tailed proofs and discussion of all results and preliminary information crucial to proving the main theorems. Hence, my work will expand upon the un- derstanding of the results by examining details not contained in the original work. A group representation can be associated with a Young diagram which in turn can be associated with a continuous function. This allows study of the limit forms of the functions associated with arbitrarily large Young tableaux. Moreover, it is shown through analysis of the hook integral that the Plancherel measure of the set of functions arbitrarily close to the limit form is 1.*

**MA Thesis Colloquium**Rory Lucyshyn-Wright will speak on "

**Continuous Domains as Algebras of a Lax Monad**" at 11:30a.m. in N638 Ross.ABSTRACT:

*Day (1975) showed that the continuous lattices of Dana Scott may be described as the Eilenberg-Moore algebras of a filter monad, from which it follows that these ordered sets may be described equationally via (infinitary) algebraic operations. Earlier, Manes (1969) had shown that the compact Hausdorff spaces may be described via convergence as the algebras of an ultrafilter monad, and then Barr (1970) found that by moving to a relational setting and relaxing to inequations the two simple equational axioms which govern the description of a compact Hausdorff space via the ultrafilter monad, we obtain a description of the category Top of all topological spaces via ultrafilter convergence. A similar description of Top as a category of lax algebras of the filter monad has also been established (Pisani, 1999; Hofmann and Tholen, 2006; Seal, 2005).**I have found that those topological spaces whose associated lax algebras of the filter monad satisfy the lax axioms up to strict equality are those which possess a natural domain-theoretic approximation property, such that the sober spaces among these constitute the most prominent general category of domain-theoretic objects - the continuous DCPOs. Thus, the continuous DCPOs are those strict algebras of the lax filter monad which are sober as topological spaces.**Moreover, the category of continuous DCPOs and Scott-continuous maps reflects the structure of the encompassing category of strict algebras, which we call the continuous spaces, since in fact it occurs therein as a reflective subcategory. Further, the continuous spaces are exponentiable and closed under finite products and arbitrary coproducts in Top, from which it follows by a theorem of Brian Day (1972) that the category of topological quotients of continuous spaces is cartesian closed.*

**Thesis Colloquium -- 2nd Talk**Sheel Kumar Chopra will speak on "

**Study of Extra Tropical and Higher Latitude Cyclone Tracks in the Northern Hemisphere**" at 1:00p.m. in N638 Ross.ABSTRACT:

*Extra tropical cyclones (also sometimes called middle-latitudes cyclones outside of tropics) in the Northern Hemisphere are generally generated between 30 -60 degree North Latitudes. Higher latitudes cyclones, also called Arctic cyclones, are generally generated from 60-90 degree North latitudes. It has been felt that there seems to be a trend of cyclones moving North over time especially in North America during their movements from starting latitudes to the ending latitudes.**In this research, we attempt to investigate the following problem based on the data called ERA40 North Hemispheric cyclone tracking data provided to us by Environment Canada for 44 years (1958-2001). Firstly, we propose to detect if there is a trend of cyclones moving North over time by comparing individual cyclone tracks in one year with cyclone tracks in subsequent years. This is intended to be done by defining a function to calculate a test statistic based on criteria such as mean latitudes/starting latitudes/ending latitudes/curvature of tracks of randomly selected pairs of cyclones in two different years. Subsequently, non parametric statistical tests, such as permutation tests, are to be conducted to see if there is a trend of the cyclones moving North over time. We are concentrating our study in the North American Region.**In the second talk, which is further continuation of the first talk, some more observations regarding uptrend over time based on other criteria such as start/end/mean latitudes, system intensity, etc will be presented.*

**Graduate Seminar**Xiangqian Cui, will speak on "

**Consistent Model Selection and Data-driven Smooth Tests for Longitudinal Data in the Estimating Equations Approach**" at 2:00p.m. in N627 Ross.ABSTRACT:

*Model selection for marginal regression analysis of longitudinal data is challenging owing to the presence of correlation and the difficulty of specifying the full likelihood, particularly for correlated categorical data.The paper introduces a novel Bayesian information criterion type model selection procedure based on the quadratic inference function, which does not require the full likelihood or quasi-likelihood. With probability approaching 1, the criterion selects the most parsimonious correct model. Although a working correlation matrix is assumed, there is no need to estimate the nuisance parameters in the working correlation matrix; moreover, the model selection procedure is robust against the misspecification of the working correlation matrix.**The criterion proposed can also be used to construct a data-driven Neyman smooth test for checking the goodness of fit of a postulated model.This test is especially useful and often yields much higher power in situations where the classical directional test behaves poorly. The finite sample performance of the model selection and model checking procedures is demonstrated through Monte Carlo studies and analysis of a clinical trial data set.*

**Thesis Colloquium**Sheel Kumar Chopra will speak on "

**Study of Extra Tropical and Higher Latitude Cyclone Tracks in the Northern Hemisphere**" at 2:00p.m. in N638 Ross.ABSTRACT:

*Extra tropical cyclones (also sometimes called middle-latitudes cyclones outside of tropics) in the Northern Hemisphere are generally generated between 30 -60 degree North Latitudes. Higher latitudes cyclones, also called Arctic cyclones, are generally generated from 60-90 degree North latitudes. It has been felt that there seems to be a trend of cyclones moving North over time especially in North America during their movements from starting latitudes to the ending latitudes.**In this research, we attempt to investigate the following problem based on the data called ERA40 North Hemispheric cyclone tracking data provided to us by Environment Canada for 44 years (1958-2001). Firstly, we propose to detect if there is a trend of cyclones moving North over time by comparing individual cyclone tracks in one year with cyclone tracks in subsequent years. This is intended to be done by defining a function to calculate a test statistic based on criteria such as mean latitudes/starting latitudes/ending latitudes/curvature of tracks of randomly selected pairs of cyclones in two different years. Subsequently, non parametric Statistical tests, such as permutation tests, are to be conducted to see if there is a trend of the cyclones moving North over time. We are concentrating our study in The North American Region.*

**Dissertation Subject Oral**Elissa Ross will speak on "

**Periodic Rigidity**" at 1:00p.m. in N638 Ross.ABSTRACT:

*Zeolites are a type of molecule with a sieve-like structure where the"holes of the sieve expand and contract. Using this as motivation, we study the rigidity properties of in ?nite periodic frameworks. We can think of such a framework in dimensions as a multigraph embedded on an n-dimensional torus, where the torus may be of ?xed or variable dimensions. In this talk we describe a characterization of in ?nitesimal rigidity for 2-dimensional frameworks on a ?xed torus, and outlinewhat is known for periodic frameworks in higher dimensions.*

**Graduate Seminar**Xiangqian Cui will speak on "

**A Formula for the Tail Probability of a Multivariate Normal Distribution and its Applications**" at 10:30a.m. in N638 Ross.ABSTRACT:

*An exact asymptotic formula for the tail probability of a multivariate normal distribution is derived. This formula is applied to establish two asymptotic results for the maximum deviation from the mean: the weak convergence to the Gumbel distribution of a normalized maximum deviation and the precise almost sure rate of growth of the maximum deviation. The latter result gives rise to a diagnostic tool for checking multivariate normality by a simple graph in the plane. Some simulation results are presented.*

**PhD Defence**Bernd Schulze, will defend his PhD Dissertation entitled "

**Combinatorial and Geometric Rigidity with Symmetry Constraints**" at 1:00p.m. in N638 Ross.

**Dissertation Colloquium**Daniel (Qiang) Pu will speak on "

**Dependency Network in Multivariate Analysis**" at 2:00p.m. in N627 Ross.ABSTRACT:

*In biological science, biological process in the cell such as biochemical interactions and regulatory activities constitute complicated dependency among genes. Statisticians apply statistical methods to pinpoint complex gene interactions and map gene regulatory network that may be critical for understanding and treating cancer and other diseases.**In order to investigate the gene dependency network, statisticians measure thousands of genes' expression level and apply multivariate analysis to evaluate the structure and select model for gene network. In the area of multivariate analysis, various methods and procedures have been proposed and their properties have been examined. In the dissertation, we emphasize a diagrammatic representation of the variable relations and propose graphical modeling methods to investigate gene dependency network in multivariate analysis.*

**Thesis Colloquium -- 2nd Talk**Qiang Yuan will speak on "

**The Multiple Sub-domains RS-HDMR Approach and its Application**" at 11:30a.m. in N627 Ross.ABSTRACT:

*Many problems in science and engineering involve the interaction of a large number of input variables. One important objective is to explore the relation between high dimensional inputs and outputs. Recently, the High Dimensional Model Representation (HDMR) was proposed as an efficient tool to capture the input-output relationships in high-dimensional systems.**In this thesis, we develop the Multiple Sub-domains Random Sampling HDMR methods (MSD-RS-HDMR) for general high dimensional input-output systems. The domain splitting technique is applied to divide the whole domain into multiple sub-domains and a set of weighted functions are introduced for obtaining the approximations near the interfaces. The outputs of prediction are evaluated by the RS-HDMR on sub-domains. The sample points of high dimensional inputs are generated in a quasirandom sequence by a stochastic algorithm. Numerical tests are carried out by the MSD-RS-HDMR for given high dimensional functions and one actual application problem. This application is to efficiently compute the important problem of the Tropospheric Alkane Photochemistry model, which describes the species concentration in troposphere in environmental science. Moreover, we propose a modified RS-HDMR method for sub-domain predictions by applying the objective function's coefficient adjustment in variance reduction.*

**Dissertation Subject Oral**Tianshu Ma will give a talk on "

**Application of Bayesian Techniques to Climate Change Analysis and Covariance Estimation in Graphical Gaussian Models**" at 1:00p.m. in N638 Ross.ABSTRACT:

*Human influence on climate is measured by comparing the observed values of certain climate variables with the values obtained from model simulation under external forcing, using a generalized linear regression technique. Current detection methods are able to detect external forcing influence on climate one forcing signal produced from one global Climate Model (GCMs) at a time, only. In the first part of our work, we propose a Bayesian technique to combine signals which are simulated from multiple GCMs to detect anthropogenic changes on climate.**In the second part of our work, we are concerned with covariance estimation for high-dimensional data. Graphical Gaussian Models, also known as "covariance selection model", have proven to be very useful tools in the analysis of such data. Numerous papers have proposed Bayesian estimators of the covariance-parameter. Dawid and Lauritzen (1993) defined tow distributions, namely, the hyper Wishart distribution as the distribution of the maximum likelihood estimator of the covariance parameter and the hyper inverse wishart distribution as the standard conjugate prior distribution for the same parameter. Letac and Massam (2007) generalized these two distributions, which each have only one shape parameter, to two more flexible families of Wishart distribution with k+1 shape parameters in each family where k is the number of cliques in the graph G. These distributions are called the WQG and WPG Wishart family of distributions respectively. Subsequently, Rajaratnam, Massam and Carvalho (2008) use the WPG distribution as a prior on the inverse covariance parameter to obtain better estimators of the covariance.**In this proposal, we aim to extend the calculation of Bayes estimators found in Rajaratnam et al (2008) to the class of homogeneous graphs. This will necessitate in particular the construction of a new reference prior for homogeneous graphs reflecting the special character of these graphs.*

**Dissertation Colloquium**Bernd Schulze will speak on "

**Combinatorial and Geometric Rigidity with Symmetry Constraints**" at 11:00a.m. in N638 Ross.ABSTRACT:

*In this talk, we investigate the rigidity and flexibility properties of frameworks consisting of rigid bars and flexible joints that possess non-trivial symmetries. First, using techniques from group representation theory, we show that a symmetric isostatic (i.e., minimal infinitesimally rigid) framework must obey some very simply stated restrictions on the number of joints and bars that are `fixed' by various symmetry operations of the framework. In particular, it turns out that a 2-dimensional isostatic framework must belong to one of only six possible point groups. For 3-dimensional isostatic frameworks, all point groups are possible, although restrictions on the placement of structural components still apply.**For the symmetry groups C_2, C_3, and C_s in dimension 2 generated by a 2-fold rotation, a 3-fold rotation, and a reflection, respectively, we present symmetric versions of Laman's Theorem, i.e., we show that the conditions concerning the number of fixed structural components, together with the Laman conditions, are also sufficient for a framework whose joints are positioned as generically as possible subject to the given symmetry conditions to be isostatic. Symmetric versions of Henneberg's Theorem and Crapo's Theorem for these groups are also considered. Finally, we derive sufficient conditions for the existence of a finite flex of a symmetric framework. Finite flexes detected with these results have the nice property that they preserve all of the symmetries of the given framework.*

**Dissertation Subject Oral**Marija Zivkovic Gojovic will speak on "

**Pertussis -- The Effect of the Vaccine Introduction on Change in Demographic Structure of Infected Population. Resurgence Analysis -- Causes and Consequences**" at 12:00p.m. in N638 Ross.ABSTRACT:

*Pertussis is a bacterial infection caused by the bacterium Bordetella pertussis. It belongs to a group of childhood diseases, and is considered to be a vaccine preventable disease. In Canada, the strict vaccination program is applied, starting at two months of children?s age. Before the vaccine was developed, the pertussis was a disease of very high morbidity and mortality rates in children. The massive vaccination, in mid 40?, decreased the pertussis incidence rate drastically; up to an 80% in the subsequent 10 years. However, despite the extremely high vaccination rate today, the number of pertussis cases in Canada recently started to rise again. The greatest incidence has been noticed among infants <1 year of age, and the second highest rate, at present, is among children 10-14 years of age. In this work, we develop an age-structured mathematical model to capture the dynamics of pertussis spread in Canada. The focus of this work is the analysis of the impact of changes of the vaccine programs on the demographic structure of the infected population, and the analysis of mechanisms to the appearance of recurrent outbreaks.*

**Thesis Colloquium, First Talk**Qiang Yuan will speak on "

**Multiple sub-Domains RS-HDMR Approach and Applications**" at 2:30p.m. in N638 Ross.ABSTRACT:

*Many problems in science and engineering involve the interaction of a large number of input variables. One important objective is to explore the relation between high dimensional inputs and outputs. Recently, the High Dimensional Model Representation (HDMR) was proposed as an efficient tool to capture the input-output relationships in high-dimensional systems.**In this thesis, we develop the Multiple Sub-domains Random Sampling HDMR methods (MSD-RS-HDMR) for general high dimensional input-output systems. The domain splitting technique is applied to divide the whole domain into multiple sub-domains and a set of weighted functions are introduced for obtaining the approximations near the interfaces. The outputs of prediction are evaluated by the RS-HDMR on sub-domains. The sample points of high dimensional inputs are generated in a quasirandom sequence by a stochastic algorithm. Numerical tests are carried out by the MSD-RS-HDMR for given high dimensional functions and one actual application problem. This application is to efficiently compute the important problem of the Tropospheric Alkane Photochemistry model, which describes the species concentration in troposphere in environmental science. Moreover, we propose a modified RS-HDMR method for sub-domain predictions by applying the objective function's coefficient adjustment in variance reduction.*

**Graduate Seminar**Yurong Cao will give a talk on "

**An Application of Dea Window Analysis with the Malmquist Index in Large Canadian Schedule I Banks**" at 10:30a.m. in N638 Ross.ABSTRACT:

*This seminar is the main focus on the application of the DEA analysis of 7 largest Canadian Schedule ² banks. Combined with DEA window analysis, the efficiency scores of 10-year period from 1998-2007 were obtained. The Malmquist Productivity Index was used to calculate the productivity changes. The data from the DEA model was analyzed and compared with economy development in Canada within the study period. A good agreement between the model result and real economic situation was shown.*

**Dissertation Subject Oral**Neil Roger will speak on "

**s-Versions Of Standard Notions For Transversing Families Of Sets**" at 11:00a.m. in N638 Ross.ABSTRACT:

*Given a family of sets A, we can say that a set X splits the sets in A if for every a 2 A, X \ a is nonempty but small. It is natural to consider notions of smallness that include cardinality, small in measure, topologically small and others. For example, a Bernstein set X R is a set that splits the family of perfect subsets of R, where "small" means "is not equal to". A series of papers by people such as Hajnal, Juhász, and Shelah and others have looked at various kinds of transversals of families of sets under various conditions. We look at s-versions of these concepts. Instead of considering a single set X intersecting a family of sets A, we look at a countable collection of sets fXn : n 2 !g, so that each a 2 A is split or has small intersection with some Xn. This is a weakening of the original concept, but may allow us to prove that a s-version exists in cases where the original version either didn't exist or was unknown. In particular, we look at transversals of families of "strongly almost disjoint" sets (infinite sets that have finite intersection with each other).*

**Dissertation Subject Oral**Qiang Guo will speak on "

**Wavelet and Adaptive Methods for Time Dependent Problems and Applications in Aerosol Dynamics**" at 12:00p.m. in N638 Ross.ABSTRACT:

*Aerosol science is a subject of growing importance worldwide due to its effect on global environment. Atmospheric aerosol modeling is very important to study the behavior of aerosol dynamics. The general aerosol dynamic equations are the nonlinear integro-differential equations on time, particle size and space, which describe different processes of atmospheric aerosols including condensation, nucleation, coagulation, deposition, sources as well as turbulent mixing. It is an important and challenging task to develop efficient numerical methods to solve the general aerosol dynamic equations.**In my thesis, we will develop and analyze efficient wavelet and adaptive methods for time dependent problems and applications in aerosol dynamics. Aerosol distribution varies strongly along the particle size direction and wavelets have the great advantage of simulating the sharp distribution problems. In the first part of the thesis, we develop the wavelet-Galerkin method to solve the homogeneous aerosol dynamic equations by applying the advantage of wavelets. At the second step, we propose a new characteristic-based adaptive multi-resolution numerical scheme for solving the aerosol dynamic equations, which combines the attractive advantages of the adaptive multi-resolution technique and the characteristics method. On the aspect of theoretical analysis, we will analyze the existence, convergence and error estimates of wavelet methods. Moreover, we will study the reliable and efficient posteriori error estimate for linear parabolic equations based on stable multi-scale bases. In the last part, we will develop efficient numerical methods by combining the wavelet methods proposed in the previous parts and the splitting technique to solve the inhomogeneous aerosol dynamic equations on time, particle size as well as space. Numerical experiments will be taken for both the homogeneous and inhomogeneous aerosol dynamic systems.*

**PhD Oral**Aparajita Dasgupta will defend her PhD Dissertation entitled "

**The Twisted Laplacian, The Laplacians on the Heisenberg Group and SG-Pseudo-Differential Operators**" at 2:30p.m. in N627 Ross.

**PhD Oral**Michael Moras will defend his PhD Dissertation entitled "

**SBM Conditioned on Non-Extinction in Denjoy Domains and Perforated Strips**" at 1:00p.m. in N638 Ross.

**Dissertation Colloquium**Aparajita Dasgupta will speak on "

**The Twisted Laplacian, the Laplacians on the Heisenberg Group and Sg Pseudo-differential Operators**" at 11:00a.m. in N638 Ross.ABSTRACT:

*This thesis is a study of the twisted Laplacian, the sub-Laplacian and the Laplacian on the Heisenberg group. The last part of the thesis deals with the spectral properties of SG pseudo-dierential operators.**Using the heat kernel and Green function, the twisted Laplacian has been shown to be globally hypoelliptic in the Schwartz space. In the thesis we prove that the same is true in Gelfand-Shilov spaces. A scale of Sobolev spaces is introduced to measure the global hypoellipticity of the twisted Laplacian. The essential self-adjointness of the twisted Laplacian is established and the domain of the unique self-adjoint extension is determined in terms of a Sobolev space.**Another important operator is the sub-Laplacian which is a nowhere elliptic partial differential operator on R3. By decomposing the sub-Laplacian on the Heisenberg group into a family of twisted Laplacians parameterized by Planck's constant and by defining new Weyl transforms depending also on Planck's constant, we give new formulas for the inverse and the strongly continuous one-parameter semigroup generated by the sub-Laplacian. New Sobolev spaces are introduced to obtain norm estimates for the inverse and the semigroup. Using the Fourier-Wigner transform so parameterized, the global hypoellipticity the twisted Laplacians on the Schwartz space is then proved. The result on the global hypoellipticity is then used to obtain Liouville's theorems for harmonic functions for the sub-Laplacian. Using the same techniques as in the case of the sub-Laplacian, Liouville's theorems for the Laplacian on the Heisenberg group are presented.**The final part of the thesis deals with SG pseudo-dierential operators or pseudo-differential operators with symbols of global type. After a recapitulation of the basic properties of these operators, the spectral theory on L^p(R^n), 1 < p infinity, is given in the context of minimal and maximal operators, the domains of elliptic operators, Fredholm operators and essential spectra. Finally the result on the ellipticity of Fredholm pseudo-differential operators with symbols in S0 is presented and is generalized to arbitrary symbol classes.*

**Graduate Seminar**Sadaf Naveed will speak on "

**The Spectral Theorem I**" at 2:00p.m. in N638 Ross.ABSTRACT:

*We will discuss spectral theory for Normal element of special Banach algebras (C*-Algebra). En route we pass through Gelfands theory of commutative Banach algebras and the proof of spectral theorem I.*

**MA Oral Exam**Andrei Akhvlediani will defend his Master's Thesis entitled "

**Hausdorff and Gromov Distances in Quantale-enriched Categories**" at 12:30p.m. in N638 Ross.

**Thesis Colloquium**Bo Zhou will speak on "

**Vaccination and Immigrant Affect Pertussis Model**" at 11:00a.m. in N638 Ross.ABSTRACT:

*Pertussis (whooping cough) is a highly contagious infection of airborne transmission. It is a common disease of infants and children. Outbreaks of pertussis in adolescents and adults have rarely been documented, because they are often not recognized as pertussis outbreaks. Before the vaccination program began, pertussis was one of the main causes of infant morbidity and mortality. After the introduction of mass vaccination, the incidence and severity of pertussis decreased drastically. In my thesis, the mathematics model in discrete time is based on the partial differential equations. The epidemiologic-demographic model developed here for pertussis is a simplified approximation of pertussis transmission and vaccination, but it retains the essential aspects of pertussis epidemiology in an age-structured population. In this talk, I will introduce the background, the mathematic model system and the data which I choice to run the simulation.*

**PhD Oral Exam**Sandeep Bhargava will defend his PhD Dissertation entitled "

**Realization of BC_r-Graded Intersection Matrix Algebras with Grading Subalgebras of Type B, r >=3**" at 10:00a.m. in N638 Ross.

**Graduate Seminar**Barbara Perez will give a talk entitled "

**Comparison of Numerical Integrating Algorithms by Trapezoidal, Lagrange, and Spline Approximation with Some Applications**" at 11:00a.m. in N638 Ross.ABSTRACT:

*The main focus is on applications using data sets from biopharmaceutics and doing concentration-area calculations by numerical methods. Also, some time will be spent on examining the cubic spline approximation. The purpose is to find which algorithms are appropiate for different data sets, and provide some intuition to selecting the proper method for the given data set. The article choosen is from K.C. Yeh and K. C. Kwan titled "A Comparison of Numerical Integrating Algorithms by Trapezoidal, Lagrange, and Spline Approximation".*

**PhD Defense**Qingwen Hu will speak on "

**Differential Equations with State-dependent Delay: Global Hopf Bifurcation and Smoothness Dependence on Parameters**" at 2:30p.m. in N638 Ross.ABSTRACT:

*This thesis is devoted to a few important issues in the qualitative theory of delay differential equations with state-dependent delay. We first develop a global Hopf bifurcation theory, based on an application of the homotopy invariance of $S^1$-equivariant degree using the formal linearization of the system at a stationary solution. Our results show that under a set of mild technical conditions the information about the characteristic equation of the formal linearization with frozen delay can be utilized to detect the local Hopf bifurcation and to describe the global Hopf continuation of periodic solutions.**We then apply our global Hopf bifurcation theory to investigate the global continuation with respect to parameters for periodic solutions. We give sufficient geometric conditions to ensure uniform boundedness of periodic solutions and obtain an upper bound of the period of periodic solutions in a connected bifurcation branch in the Fuller space. This permits to establish the existence of fast oscillating periodic solutions.**We also study the second order differentiability of solutions with respect to parameters. We introduce the notion of a locally complete triple-normed linear space and obtain an extension of the well-known Uniform Contraction Principle in such a space. We then apply this principle and obtain the second order differentiability of solutions with respect to parameters in the $W^{1,p}$-norm ($1 \leq p<\infty$).*

**Graduate Seminar**Edmund Lee will give a talk on "

**A Financial Engineering Diploma Internship at RBC Dexia**" at 10:30a.m. in N638 Ross.ABSTRACT:

*This talk will describe my experience at RBC Dexia on the financial reporting team. I had two main responsibilities. The first was preparing statements of investments (SOI) using net asset values (NAV) of mutual funds. The second was to assist in developing new financial reporting criteria based on CICA 3862. This refers to a new accounting standard of the Canadian Institute of Chartered Accountants related to Disclosures for Financial Instruments. This policy now requires mutual funds to calculate how much they are exposed to 5 different risks (interest rate risk, currency risk, credit risk, market risk and liquidity risk).*

**Student Colloquium**Tao Sun will speak on "

**Spatial Modeling of Multivariate Data with Autocorrelated Discrete-continuous Mixture Margins Using Copulas**" at 2:00p.m. in CTL 120E.ABSTRACT:

*The issue of climate change is receiving increased public attention. It has a great potential impact on the natural environment and on socioeconomic systems. A lot of current scientific research concerns building models to detect and attribute of climate change in the extreme weather conditions. As the major input to climate models, daily climate observations taken at point locations are often limited in spatial coverage, incomplete and short in length. Simulating and interpolating multi-site daily precipitation series is a challenging task in view of their discrete-continuous mixed margins.**A copula-based approach is developed to address the problem of multivariate data modeling given autocorrelated discrete-continuous mixture margins. Copulas generated from the elliptical family are compared. Studies on real precipitation data show that the proposed methodology performs very well in capturing the spatial dependence of the aucorrelated discrete-continuous mixed series. A multivariate inversion method is proposed to generate truncated or bounded multivariate random vectors with a known cumulative distribution function.*

**Dissertation Subject Oral**Pengfei Guo will speak on "

**Robust Inference in Generalized Linear Model**" at 1:30p.m. in N638 Ross.ABSTRACT:

*Generalized linear models have been widely used in practice. Although the classical generalized linear models are quite powerful and enjoy many desirable asymptotic properties, they rely explicitly or implicitly on the model assumptions. Markatou, Basu and Lindsay (1998) proposed weighted likelihood estimating equations (WLEE) to modify the classical maximum likelihood when the covariates follow a mixture distribution. In this proposal, we aim to extend the WLEE to the linear and generalized linear model when the covariates follow a finite mixture model. More importantly, we hope to propose a unified approach to choose weights for linear and generalized linear models. The weights are based on the estimated probabilities of the memberships of covariates. Finally, with our proposed weights, we should be able to apply the WLEE proposed by Markatou et al. (1997, 1998) in a general regression setting without any difficulties.*

**Survey Paper**Hugh McCague will speak on "

**Graphical Models and Directional Statistics: The Bivariate von Mises Distribution, Dynamic Bayesian Networks and Local Protein Structure**" at 10:00a.m. in N638 Ross.ABSTRACT:

*Directional statistics have been recently introduced into graphical models for applications in bioinformatics. More specifically, the TorusDBN model, a Dynamic Bayesian Network or a Hidden Markov Model with multiple outputs, efficiently and accurately samples and predicts the backbone geometry of proteins. Mixture models and the Cosine variant of the bivariate von Mises distribution on the torus are incorporated into the TorusDBN model. The stochastic expectation-maximization algorithm, Gibbs sampling and other algorithms have been applied in an Open Source software implementation of the model. The TorusDBN model is an important step towards solving the protein folding problem in bioinformatics, and shows how directional statistics can be readily employed in graphical models.*

**Graduate Seminar**Lindsay Jamieson, York University , will speak on "" at 3:00p.m. in N638 Ross.Experience as a Business Analyst at TD Securities ABSTRACT:

*This talk will be about my experience at TD on a project team developing an in-house derivative pricing product. The talk will cover the scope and intent of the project in general, the businesses involved in development, and my role as an analyst on the project. It is intended to give some insight into day-to-day business workings on the project, and the application of both qualitative and quantitative skills put to use there.*

**Graduate Seminar**Mayra Montalvo will give a talk on "

**The continuum Hypotesis**" at 12:30p.m. in N638 Ross.ABSTRACT:

*Arguably the most famous formally unsolvable problem of mathematics is The Continuum Hypothesis. Posed first by Cantor on the IX century, this problem belongs to an ever-increasing list of problems known to be unsolvable from the usual axioms of set theory. The answer to the continuum problem lies on undestanding the structure H(w_2), but, in order to solve the problem, mathematicians take an incremental approach trying to undestand H(w_1)(the standard structure of Second Order Number Theory). In this seminar I will talk about what the continuum problem is and what do we need to know to "completely" undestand H(w_1): the axiom of Projective Determinacy.*

**Graduate Seminar**Francois-Alexis Ouegnin will give a talk entitled "

**Linear Bi-level Programming and Optimal Allocation Problem**" at 11:00a.m. in N638 Ross.ABSTRACT:

*Bi-level Programming Problem (B. P. P) is usually used to model decentralized planning problems involving a decision process with a hierarchical structure. Although much research has been carried out on congestion management, networks and engineering, we could not find in the existing literature some applications related to finance. This talk will mainly introduce Bi-level programming problem, some solution techniques and an application to finance.*

**PhD Oral**Nikolai Slobodianik, York Univerity , will defend his PhD Dissertation entitled "" at 2:00p.m. in N638 Ross.Model Selection for Bayesian Networks and Other Quantitative Approaches in Stem Cell Research

**Graduate Seminar**Barbara Perez, York University , will speak on ‘" at 3:30p.m. in N638 Ross.Numerical Treatment of Stochastic Differential Equations with Applications ABSTRACT:

*My talk will consist of a friendly introduction to stochastic differential equations with applications in geophysics. Issues such as why numerical 'noise' is added to the differential equations and how it differs from regular differential equations will be addressed. These concepts can be extended to geophysics problems and finance problems. Also, basic terminology will be explored. How to treat stochastic differential equations numerically using the Runge-Kutta scheme will be the main focus of my presentation.*

**PhD Oral**Jianfu Ma, York University , will defend his PhD Dissertation entitled "" at 1:30p.m. in N638 Ross.Multistability in Neural Networks with Delayed Feedback: Theory and Applications

**Survey Paper**Roman Khaykin will speak on "

**The Dynamics of Hepatitis B**" at 10:00a.m. in N627 Ross.ABSTRACT:

*This is a review of several in-host Hepatitis B Virus (HBV) models combined to make a more realistic ODE model. Sensitivity analysis is then tested on each of the variables in the model to show that varying life time distributions yields convergence to the same value in the same time frame. Also, the basic reproductive ratio of HBV is derived using the Jacobian method, Survivor method, and the Next Generation method. This number is then used to predict the nature of HBV and its probability of clearing or becoming a chronic infection depending on the parameters. This value shows that a system being infected with one virion would infect the system with probability of 0.0076; whereas, a system that starts off with an infected cell would become infected with a probability near to 99.9%. Lastly, a Monte Carlo (MC) simulation (an individual based model) is constructed and compared to the ODE to show variability in HBV infection.*

**Graduate Seminar**Mayra Montalvo will speak on "

**Hilbert C*-modules and Kasparov's Stabilization Theorem**" at 10:30a.m. in N638 Ross.ABSTRACT:

*Hilbert C*-modules are objects like Hilbert spaces except that the inner product, instead of being complex valued, takes its values in a C*-algebra. The theory of these modules together with their bounded and unbounded operators is not only rich and attractive in its own right but forms an infrastructure for some of the most important research topics in operator algebras. The Kasparov's Stabilization Theorem is one of the main results in this theory.*

**Graduate Seminar**Roman Khaykin will speak on "

**The Modeling of Cellular Electrical Activity**" at 10:00a.m. in N638 Ross.ABSTRACT:

*Electro-diffusion of ions, both inside and outside of biological cells, are highly important to proper cellular functions. A series of partial differential equations will be derived that takes into account cellular electrical activity and discuss its biological significance. The models derived can be termed as cable models which are based on an ohmic current continuity relation on a branched one dimensional electrical cable.*

**Survey Paper**Mohamed Abdelghani will speak on "

**Stochastic Filtering Theory and Application to Finance**" at 12:00p.m. in N638 Ross.ABSTRACT:

*Filtering theory is concerned with the estimation of unobserved variables from related observed quantities. It is a blend of statistics, stochastic and numerical methods. I survey thedevelopment of filtering theory from its inception at the hands of Kolmogorov and Wiener to its current form; the work of Kalman on linear filters; and the development of nonlinear filter theory by Stratonovich, Kushner, Zakai and others. Also, I discuss computational approximation methods such as the extended Kalman filter, particle filters and spectral decomposition for solving stochastic partial differential equations arising in nonlinear filtering. Furthermore, I discuss the application of filtering theory to finance; the estimation of volatility and risk premium; and optimal hedging strategy under imprecise knowledge of asset price.*

**Thesis Colloquium**Andrei Akhvlediani will speak on "

**An Introduction to Gromov Distance**" at 1:00p.m. in N638 Ross.ABSTRACT:

*The talk will introduce Gromov distance on the category of metric spaces and non-expansive maps. We will discuss formulations of Gromov distance in terms of correspondences and $\epsilon$-isometries. We shall see that the category of compact metric space is itself a metric space; furthermore, it is complete with respect to the Gromov distance. Important examples of convergence with respect to the Gromov distance will be given. If time permits, we will briefly mention Gromov distance in the $\V$-categorical setting.*

**Graduate Seminar**Fady Daoud will speak on "

**Some Uses of Analysis in Number Theory**" at 2:00p.m. on N638 Ross.ABSTRACT:

*Some number theoretic topics will be covered including the classical theorems, how analysis was introduced to number theory, the Riemann zeta function, and the prime number theorem. Additionally, there will be a presentation of some proofs in Transcendental Number Theory, and a discussion of the classical inquiries regarding the distribution of the prime numbers. The Riemann Hypothesis will be one of the key ideas discussed which covers its statement and, if proved true, how it can influence mathematics. This seminar is a combination of history, proofs, and discussions of famous number theoritic problems and ideas that every mathematician should be aware of.*

**PhD Oral Exam**Chuanbin Du will defend his PhD Dissertation entitled "

**Efficient Splitting Domain Decomposition Methods for Time Dependent Problems and Applications in Porous Media**" at 10:00a.m. in N638 Ross.

**Dissertation Colloquium**Michael Moras will speak on "

**Conditioned Sbm in Denjoy Domains and Perforated Strips**" at 1:00p.m. in N638 Ross.ABSTRACT:

*Super Brownian motion is a measure valued process that by construction suffers extinction almost surely. We look at various schemes for conditioning SBM on non-extiction in Denjoy domains and in perforated strips. We give explicitly the Martingale change of measure and backbone representation for these processes. Related results have been obtained in other contexts, but the nature of the domains that we're working in yield to some interesting and counterintuitive results. Moreover we give an integral test that separates the qualitatively different behaviour that can exist in these domains. This work is motivated by Benedicks (1980), Evans (1993) and in particular Salisbury and Verzani (1999).*

**Graduate Seminar**Tak Hong Leung will speak on "

**The Optimal Time to Initiate HIV Therapy Under Ordered Health States**" at 10:00a.m. in N638 Ross.ABSTRACT:

*The question of when to initiate HIV treatment is the most important question in HIV care today. Benefits of delaying therapy include avoiding the negative side effects and toxicities associated with the drugs, and development of resistant strains of the virus. However, the risk of delaying therapy include the possibility of irreversible damage to the immune system,development of AIDS and death. We use the Markov Decision Process to developthe first HIV optimization models that aim to maximize the expected lifetime or quality-adjusted lifetime of a patient.*

**PhD Oral Exam**Naveen Vaidya will defend his PhD Dissertation entitled "

**Membrane Fusion Between an Influenza Virus and a Host Cell: Mathematical Models**" at 9:00a.m. in N638 Ross.

**Thesis Colloquium -- 1st Talk**Andrei Akhvlediani will speak on "

**Hausdorff Distance Categorically**" at 1:00p.m. in N638 Ross.ABSTRACT:

*The Hausdorff distance was introduced by Dimitrie Pompeiu in the beginning of the 20th century. We shall introduce the classical Hausdorff distance and state major results about it. Next we introduce the Hausdorff distance into the V-category setting. We define the Hausdorff functor, the Hausdorff monad and find the Eilenberg--Moore algebras for this monad.*

**Dissertation Colloquium**Nikolai Slobodianik, will give a talk on "

**Model Selection for Bayesian Networks and Other Quantitative Approaches in Stem Cell Research**" at 2:00p.m. in N638 Ross.ABSTRACT:

*In modern biological science, computational methods occupy an important, ever-expanding niche. Biological scientific computing is concerned with building mathematical and statistical models to address a wide range of questions originated from biological research and applications. Motivated by actual problems in stem cell research we propose a branching process model to study stem cell fate decisions. Further, we investigate the machinery of stem cell signaling processes by building an appropriate Bayesian network model. Questions of computational efficiency and effectiveness in Bayesian networks model selection as well as strong consistency of Bayesian scoring criterion are addressed.*

**Survey Paper**Haohan Huang will speak on "

**Gaussian Copula in Finance**" at 11:00a.m. in N638 Ross.ABSTRACT:

*Copulas are tools for modeling dependence of several random variables. And in the financial industry, gaussian copula is by far the most popular copula used in default dependency modeling. In my survey paper, I will present with the basic knowledge of copulas method and how the gaussian copula is used in two cases of financial industry. One is CDO pricing and the other is hedge fund strategies choosing.*

**Graduate Seminar**Sadaf Naveed will talk on "

**The Double Commutant Theorem**" at 11:00a.m. in N638 Ross.ABSTRACT:

*For an infinite dimentional Hilbert space H,the operator algebra B(H) has many interesting topologies.We will define Strong and weak operator topology on B(H), commutant of a subset of B(H), Von Neumann algebras, and we will prove The double commutant theorem by Von Neumann,which is the fundamental result in operator algebra theory.*

**Graduate Seminar**John Chak will speak on "

**Experience of a Rate Analyst at TD Securities**" at 1:00p.m. in N638 Ross.ABSTRACT:

*My major responsibility at TD Securities is to retrieve data of Foreign Exchange, Fixed income & Future from Reuters and Bloomberg and then upload to various systems to perform analysis. My colleagues in the Front office and Middle office will then work on the P&L based on the rates/prices that I upload daily.*

**Dissertation Colloquium**Sandeep Bhargava, will speak on "

**Realizations of $BC_r$-graded intersection matrix algebras with grading subalgebras of type $B_r$, $r \geq 3$**" at 2:00p.m. in N638 Ross.ABSTRACT:

*Peter Slodowy, in the early to mid 1980s introduced a generalization of Kac-Moody Lie algebras called generalized intersection matrix (gim) algebras. We construct such an algebra by multiply affinizing a Cartan matrix of type $B_r$ with arbitrary long roots. We then define the radical of this gim algebra to be the ideal generated by all root spaces that do not belong to a root system of type $BC$. The resulting quotient algebra, called the intersection matrix (im) algebra, is $BC_r$-graded with a grading subalgebra of type $B_r$. The ``Recognition Theorem'' of Allison, Benkart, and Gao establish a link between our im algebra and a special orthogonal Lie algebra $so_{2r+1}(a,\eta,C,\chi)$ where $a$ is an associative algebra with involution $\eta$, and $C$ is a right $a$-module with a $1$-hermitian form $\chi$. We proceed to develop an explicit understanding of this ``coordinate'' algebra $a$ and module $C$. We also establish that our im algebra is in fact a universal central cover of $so_{2r+1}(a,\eta,C,\chi)$, hence justifying the title of the thesis.*

**Financial Engineering**Haohan Huang, will give a talk on "

**Non-negative Matrix Factorization in Value at Risk Calculation**" at 10:00a.m. in N638 Ross.ABSTRACT:

*Value at Risk (VaR) is a very important methodology for measuring portfolio risk in finance. Normally when calculating VaR, we require the valuation of complex instruments over a large set of scenarios. As complex derivatives use computationally expensive methods for pricing purposes, full valuation of these instruments on every scenario is not a viable solution. In this tall, I will describe a method to approximate expensive pricing functions that allows for fast and accurate VaR calculations, it is the Non-negative Matrix Factorization method(NNMF). NNMF has previously been shown to be a useful decomposition for multivariate data. Then this tool can be used to deal with the data of the portfolio and reduce the complexity of estimating VaR in a similar way compared to Principal Component Analysis.*

**Dissertation Subject Oral**Lily Moshe will speak on "

**How Mathematicians Use Visual Reasoning: Background for an Investigation**" at 3:00p.m. in N638 Ross.ABSTRACT:

*What is visual reasoning in higher level mathematics? Chalk drawings on the board, physical models, dynamic computer diagrams, or even visualizing in one's head can all be used by mathematicians in their research. But how are they used? The choice of a visual and the way it is used have a direct impact on one's reasoning. And what convinces mathematicians that their visual reasoning is "correct"? Is there such thing as a proof that is done visually, or does it always need to be verified with non-visual, logical/symbolic techniques? These are some of the questions I hope to answer as part of my dissertation thesis, through grounded theory research methods. The key components of my research method will comprise of interviewing mathematics and statistics professors and graduate students, observing them while they are doing mathematics, and analyzing their publications and presentations. In this talk, I will provide the background for this research, discuss its implications, and describe the methodology that I've chosen to follow.*

**Dissertation Colloquium**Jianfu Ma will speak on "

**Multistability in Neural Networks with Delayed Feedback: Theory and Applications**" at 1:30p.m. in N638 Ross.ABSTRACT:

*In this dissertation, we study the coexistence of multiple stable patterns (multistability) in recurrent neural networks with delayed feedback. We first investigate the impact of the effective timing of a delayed feedback on multistability in a recurrent inhibitory loop when biological realities of firing and absolute refractory period are incorporated into an integrate-and-fire neuron model. Our analysis shows that the interaction of the delay, the inhibitory feedback and the absolute refractoriness can generate four basic types of oscillations which give the basic building blocks of possible periodic patterns. We then show how these basic oscillations can be pinned together to form four types of periodic patterns, such as self-inhibitory patterns and nearest-neighborhood-inhibitory patterns.**Second, we examine the effect of non-monotonic activation functions on the network's capacity for memory storage and retrieval. We first show how supercritical pitch-fork bifurcations and saddle-node bifurcations lead to the coexistence of multiple stable equilibria in the instantaneous updating network. We then study the effect of time delay on the local stability of these equilibria and show that four equilibria lose their stability at a certain critical value of time delay, and a Hopf bifurcation of four periodic solutions occurs simultaneously, leading to multiple coexisting periodic orbits. We apply the center manifold theory and the normal form theory to determine the direction of this Hopf bifurcation and the stability of bifurcated periodic orbits.*

**Graduate Seminar**Avideh Sabeti will speak on "

**The Establishment of Causal Effects in Generalized Linear Model**" at 11:30a.m. in N638 Ross.ABSTRACT:

*This paper presents a method to establish the causal effects in generalized linear model. Chapter 1 presents the structure of the studies for causal effects. Moreover, this chapter contains the work of Cochran and Chambers (1965) on the planning of observational studies of human populations and introduces the difficulties in observational studies. Chapter 2 presents the estimating causal effects of treatments, finding unbiased estimation over the randomization set, considering additional variable and generalizing the results to other trials. Chapter 3 presents balancing scores, propensity score methods and its three applications (matched sampling, sub-classification, and covariance adjustment) with an example to illustrate the reducing bias using sub-classification on the propensity score. Also explains the situation where there are two treatment conditions, defines strongly ignorable treatment assignment, and contains large-sample and small-sample theories by Rosenbaum and Rubin, 1983. Moreover, illustrates the case where response has a nonlinear regression on covariate x in the treated and control groups. In chapter 4 the work of Jinyong Hahn (1998) is presented which is about the role of the propensity score in efficient semi-parametric estimation of average treatment effects. Chapter 5 presents the work of Rosenbaum and Rubin (1984) to estimate propensity score with missing covariate data and define a "generalized" propensity score and using a "pattern mixture" model (Little 1992, Rubin 1986). Also describes the work of Little and Rubin (1978, chap. 10) on the fundamental method to find estimates of the parameters of the general location model in the case of having ignorable missing data on the basis of the EM algorithm (Dempster et al. 1977) and ECM algorithm (Meng and Rubin 1993).*

**PhD Defence**Yumin Wang will defend her PhD Dissertation entitled "

**Matheamtical Finance Related to Insurance Contracts--Quantile Hedging and Efficient Hedging for GMDB**" at 10:00a.m. in N638 Ross.

**Dissertation Colloquium**Ghuanbin Du will speak on "

**Efficient Splitting Domain Decomposition Methods for Time-dependent Problems and Applications in Porous Media**" at 2:00p.m. in N638 Ross.ABSTRACT:

*Time dependent partial differential equations (PDEs) are widely used as mathematical models of computational simulations in science and engineering, e.g., oil recovery, groundwater contamination, seawater intrusion in coastal aquifers, environment prediction, hazardous waste deposition, etc. These models are characterized by the coupling, nonlinearity, convection dominance, moving sharp fronts, heterogeneity of porous medium, large scale field and long term prediction. Therefore, it is very important and difficult to develop efficient solution techniques for solving time-dependent PDEs in porous media.**In this thesis, we develop efficient splitting domain decomposition methods for time-dependent problems and applications in compressible fluid flows in porous media. By combining the non-overlapping domain decomposition and the splitting technique, we propose a splitting domain decomposition method (S-DDM) over multiblock subdomains in which the interface values of solution are solved by a local multilevel explicit scheme while the interior solutions of subdomains are solved by the splitting implicit scheme. On the theoretical aspect, we prove the stability and convergence of the method and obtain the optimal error estimation theorem for parabolic problems. We also propose a splitting Eulerian-Lagrangian localized adjoint method (S-ELLAM) for time-dependent convection diffusion problems where numerical approximation appears serious difficulty due to the convection dominance. The developed S-ELLAM effectively eliminates non-physical oscillation or excessive numerical dispersion and treats boundary conditions well and in a natural way. It also reduces temporal errors and generates accurate numerical solutions even if large time and coarse spatial step sizes are used in computation. We further develop the S-DDM linearized iterative approach to compressible fluid flows in porous media. The developed S-DDM approach is an efficient explicit-implicit domain decomposition method over multiple block-divided subdomains, which overcomes the limitation of the stripe-divided subdomains in previous research work. It keeps the excellent advantages of the non-overlapping domain decomposition and the splitting technique. It reduces computational complexities, large memory requirements, and long computation durations. Numerical experiments show that the S-DDM approach can accurately and efficiently simulate the time-dependent problems and the fluid flows in porous media*

**Dissertation Colloquium**Naveen Vaidya will speak on "

**Membrane Fusion Between an Influenza Virus and a Healthy Cell: Mathematical Models**" at 9:30a.m. in N638 Ross.ABSTRACT:

*A crucial step for an influenza virus to invade a healthy cell is the fusion of the membranes (merging of lipid bilayers) mediated by hemagglutinin (HA) protein anchored in the viral membrane. We present a mathematical model for pre-fusion interaction between an influenza virus and a healthy cell. Our model describes the role played by hemagglutinin (HA) protein clusters in bringing the viral membrane into close contact with the host cell membrane. We discuss analytical and numerical results for two experimentally observed HA protein clusters: linear cluster and axi-symmetric ring-like cluster. Our results support the hypothesis of dimple formation in the fusion site proposed in the literature. The asymmetric nature of the protein molecules due to various reasons such as tilting is the primary cause for the dimple formation. We discuss the effects of the protein cluster radius, fusion-site size and the bending moment exerted by the protein cluster. We also examine the effects of membrane tension and the presence of a host cell on the dimple shape. Our results support previous experimental observations.**Furthermore, for fusion process, the microscopic level interaction between HA fusion-peptide and lipid bilayer membrane is important. We use a coarse-grained molecular dynamics simulation (CGMD) method to study the interaction between HA fusion-peptide and phospholipid bilayer membrane. With CGMD, we have been able to simulate a relatively large piece of membrane for a sufficiently long time period and with more than one peptide embedded in the membrane, which is necessary for the detail understanding of the fusion process. We obtained the kinked-shaped conformation of the peptide with the kink at the level of phosphate group, consistent with NMR study. The N-terminal segment of the peptide inserts more deeply into the membrane bilayer, compared to the C-terminal segment as observed in experiments. The presence of fusion peptides inside a membrane may cause bilyer thinning and lipid molecule disorder, which are required for fusion activity. The peptides tend to come close to each other, which is a very good indication of the tendency of peptides to form clusters for performing concerted action required for fusion as seen in many experiments.*

**Dissertation Subject Oral**Qingling Zeng will speak on "

**Febrile Respiratory Illnesses in Health Care Setting: Mathematical Modeling, Analysis, Prediction & Control**" at 10:30a.m. in N638 Ross.ABSTRACT:

*Febrile Respiratory Illnesses (FRIs) are increasingly recognized as a growing concern for healthcare workers (HCWs) and patients. The recent hospital-based outbreak of Severe Acute Respiratory Syndrome (SARS) has once again highlighted the vulnerability of HCWs due to the impact of the disease on morbidity, mortality and the economy. In this thesis, we studied some of respiratory pathogens that are well-known to cause nosocomial outbreaks, such as Influenza and SARS. The deterministic compartmental models are developed to focus on the management of patients and HCWs in health care setting, who are potentially at risk of nosocomial infection. The models are also used to explore various preventive strategies of respiratory illnesses in health care settings, in particular, vaccination and prophylaxis programs. Based on the mathematical analyses (basic reproduction number, final size relationship, equilibrium points, etc.), some analytic expressions can be yielded for epidemic potential and outcomes in terms of parameters which related to control strategies. These expressions facilitate sensitivity and uncertainty analysis. Although our models are parameterized for Influenza and SARS, they can be relevant to other emerging infectious respiratory diseases during a respiratory season.*

**Dissertation Subject Oral**Daniel Oancea will speak on "

**The Andrews-Curtis Conjecture and the Recalcitrance of Groups**" at 1:00p.m. in N638 Ross.ABSTRACT:

*In 1924, Nielsen defined certain automorphisms of a free group F of rank n, and showed that they generate the automorphism group of F, Aut(F). These elementary automorphisms correspond to elementary Nielsen transformations (of rank n), which can be seen as permutations of the set of generating n-tuples of elements of F. The Nielsen group, generated by the elementary Nielsen transformations, is isomorphic to Aut(F), and acts on the set of n-tuples of elements of F. The action is faithful and transitive on the set of generating n-tuples.**Inspired by Nielsen's results and by certain questions in topology, Andrews and Curtis introduced in 1965 the extended Nielsen transformations (of rank n), which generate the AC group (of rank n). This group also acts on n-tuples of elements of F, and moreover, the set of annihilating n-tuples is closed with respect to this action. (An n-tuple of elements of F is called annihilating if the normal subgroup it generates in F is F.) The AC group of rank n is isomorphic to a subgroup of Aut(F*F). The Andrews-Curtis (AC) Conjecture states that the action of the AC group is transitive on the set of annihilating n-tuples of F.**The conjecture, formulated in the language of combinatorial group theory, has important connections to low dimensional topology. These connections originate mainly from the correspondence between group presentations and 2-dimensional CW complexes, and between extended Nielsen transformations (including stabilization moves) and formal deformations of CW complexes. Under this correspondence, using the language of simple homotopy theory, the conjecture states that a contractible 2-dimensional CW complex can be transformed into a point by using a finite sequence of elementary expansions and collapses with cells of dimension at most three.**Several generalizations of the AC conjecture have been proposed. In this work we investigate one of the most natural and immediate generalizations to the class of all finitely generated groups, namely the possibility of transforming annihilating n-tuples into generating n-tuples in a group of rank n, by using extended Nielsen transformations. We show that finite groups satisfy the AC conjecture in this formulation.**In 1993, Burns and Macedo'nska introduced M-transformations and showed that they are equivalent to the extended Nielsen transformations. The investigation of M-transformations has led to the concept of recalcitrance. The recalcitrance of a group G of rank n is an upper bound on the number of M-transformations necessary to transform an annihilating n-tuple of G into a generating n-tuple. We show that finite groups have finite recalcitrance.**We have three directions for further work. The first one is to find bounds on the recalcitrance of finite groups in terms of their rank. We have some partial results in this respect. Another direction is to find other classes of groups which satisfy the AC conjecture and to calculate their recalcitrance (e.g., the class of solvable groups). Finally, the third direction of study is to investigate the intriguing connections between the AC conjecture, the classification of the splitting epimorphisms of free groups, and the Zeeman conjecture for CW complexes.*

**Dissertation Colloquium**Yumin Wang will speak on "

**Mathematical Finance Related to Insurance Contracts--Quantile Hedging and Efficient Hedging for GMDBs**" at 10:30a.m. in N638 Ross.ABSTRACT:

*Quantile hedging and efficient hedging for contingent claims are active topics of research in mathematical finance. They play a role in incomplete markets, or when perfect hedging is not possible. Guaranteed minimum death benefits (GMDBs) are present in various annuity contracts, and act as a form of portfolio insurance. They cannot be perfectly hedged due to the mortality component, except in the limit as the number of contracts becomes infinitely large. In my thesis I apply ideas from finance to derive quantile or efficient hedges for these products.**The talk will covers history review, literature notation, model structures, closed form solutions, theoretical parts and numerical results.*

**Survey Paper Presentation**Louis Lim will speak on "

" at 4:00p.m. in N638 Ross.Implementing Reading Strategies in a Grade 9 Applied Mathematics Class: the Effects on Student Learning and a Teacher's Successes and Challenges ABSTRACT:

*This survey paper reports on a qualitative study that documents the teacher- researcher's implementation of a reading-intensive programme in a self-contained grade 9 applied mathematics class with students identified with communication disability. Vocabulary development, informational texts, and reflection were incorporated to determine their effects on students' learning of mathematics. Students' views of the reading strategies as well as the teacher-researcher's successes and challenges were documented.**The study was conducted during the second semester of the school year 2005/06 using a variety of data-collection techniques: observations, fieldwork journal, questionnaires, and students' work samples. Through on-going analysis, the action research study revealed how reading strategies help students acquire the mathematical vocabulary and access the informational texts. Students' attitudes to the reading strategies were difficult to glean from the questionnaires as many responses were left blank. The researcher's successes include assembling a collection of reading strategies that can be used in future courses and addressing the needs of the students who were all identified with communication disability. Challenges include the increased teacher workload to plan such learning episodes as well as the additional time needed during class to implement the strategies.**Research has shown that explicit attention to reading strategies impact mathematics achievement and learning, yet teachers feel uncomfortable implementing reading strategies due to lack of formal literacy training. This study serves as professional development for teachers to learn from a teacher's journey with incorporating reading strategies. The opportunity to critically reflect on one's practice is an implication for the teacher-researcher. For educational research, this study provides a glimpse into the successes and challenges experienced by one teacher of a province-wide initiative with all educators are teachers of literacy.*

**Dissertation Subject Oral**Qiange Pu will speak on "

**Model Selection in Gaussian Graphical Model**" at 2:30p.m. in N638 Ross.ABSTRACT:

*Recently there has been increasing interest in the study of Gaussian graphical models. Various penalized likelihood methods have been proposed for estimating the concentration matrix in the Gaussian graphical model. In this proposal, to improve the recent existing L1 penalty function, we aim to develop a penalized likelihood estimation method for covariance selection with smoothly clipped absolute deviation penalty (SCAD) by Fan and Li (2001), which has been successfully used in the context of linear regression and generalized linear models. It is advantageous to investigate to employ such penalty function for the estimation of concentration matrix in the Gaussian graphical model.*

**PhD Defence**Vera Fischer will defend her PhD Dissertation "

**The Consistency of Arbitrarily Large Spread Between the Bounding and the Splitting Numbers**" at 2:00p.m. in N638 Ross.

**Dissertation Subject Oral**Aparajita Dasgupta will speak on "

**Twisted Laplacians, the Sub-Laplacian on the Heisenberg Group And SG Pseudo-differential Operators**" at 10:00a.m. in N638 Ross.ABSTRACT:

*Using the heat kernel and Green function, the twisted Laplacian has been shown to be globally hypoelliptic in the Schwartz space. We prove that the same is true in Gelfand-Shilov spaces. Essential self-adjointness of the twisted Laplacian is established and the domain of the unique self-adjoint extension can be described in terms of a Sobolev space. By decomposing the sub-Laplacian on the Heisenberg group into a family of twisted Laplacians parametrized by Planck's constant, we give new formulas for the inverse and the strongly continuous one-parameter semigroup generated by the twisted sub-Laplacian. New Sobolev spaces are introduced to obtain norm estimates for the inverse and the semigroup. Using the global hypoellipticity of the twisted Laplacians on the Schwart space, Liouville's theorems for harmonic functions for the sub-Laplacian are presented. The final part of the presentation is on SG pseudo-differential operators or pseudo-differential operators with symbols of global type. After a recapitulation of the basic properties of these operators, the spectral theory on $L^p(\mathbb{R}^n),\, 1 < p <\infty,$ is given in the context of minimal and maximal operators, the domains of elliptic operators, Fredholm operators and essential spectra. The culmination is the result that for SG pseudo-differential operators, Fredholmness on $L^p(\mathbb{R}^n)$ for one value of $p$ in $(1,\infty)$ and ellipticity are equivalent.*

**Dissertation Subject Oral**Yu Liu will speak on "

**Time-frequency Spectra and Localization Operators**" at 10:00a.m. in N638 Ross.ABSTRACT:

*After a review of some basic notions in time-frequency analysis using the Gabor transforms, wavelet transforms and Stockwell transforms, the notion of a polar wavelet transform is introduced. The underlying non-unimodular Lie group, the associated square-integrable representations and admissible wavelets are presented. The resolution of the identity formula for the polar wavelet transform is then formulated. Localization operators corresponding to the polar wavelet transforms are then defined and shown to be in the Schatten-von Neumann class S_p when the corresponding symbols are in L^p. Under suitable conditions on the symbols, these localization operators are shown to be paracommutators, paraproducts and Fourier multipliers. A related, but not identical, program is to study two-dimensional Stockwell transforms. The most general form of a two-dimensional Stockwell transform is introduced. Then the two-dimensional non-isotropic Stockwell transforms and the two-dimensional polar Stockwell transforms are singled out. Two sets of reconstruction formulas are given. Localization operators corresponding to these Stockwell transforms are introduced and their Schatten-von Neumann properties invetigated. Under suitable conditions on the symbols, they are given explicit formulas as paracommutators, paraproducts and Fourier multipliers.*

**PhD Defence**Jinnan Liu will defend her PhD Dissertation entitled "

**Non-decomposable Discrete Graphical Models**" at 1:00p.m. in N638 Ross.

**Dissertation Colloquium**Vera Fischer, will speak on "

**The Consistency of Arbitrarily Large Spread Between the Bounding and Splitting Numbers**" at 1:00p.m. in N638 Ross.ABSTRACT:

*Let $f$ and $g$ be infinite sequences of natural numbers. Then $f <^* g$ if there is $n$ such that for every $k\geq n$ $f(k)\leq g(k)$. A family $H$ of infinite sequences of natural numbers is said to be unbounded if there is no single sequence $g$ such that for every $h\in H(h <^* g)$. Given an unbounded $<^*$-directed family $H$ of size $\kappa$, for $\kappa$ arbitrary regular uncountable cardinal, we obtain a ccc forcing notion which preserves $H$ unbounded and adds a real "independent" of the ground model reals. Thus under a suitable finite support iteration we obtain the consistency of $\mathfrak{b}=\kappa < \mathfrak{s}=\kappa^+$.*

**Dissertation Subject Oral**Jianfu Ma will speak on "

**Multistability Analysis in Neural Networks with Delayed Feedback**" at 2:00p.m. in N638 Ross.ABSTRACT:

*This dissertation focuses on investigating the coexistence of multiple stable patterns (multistability) including equilibria and periodic orbits in delayed recurrent inhibitory loops, which is the basis for associative content-addressable memory storage and retrieval in dynamical neural systems. Our investigation addresses the questions of how we can efficiently increase the network's capacity for memory storage and retrieval, and what kind of mechanisms enable neural networks to generate a large number of coexisting stable oscillatory patterns. To achieve our objectives, two efficient methods are applied to the simple phenomenological neuron models: 1) the incorporation of two important biological features of neurons --- the firing procedure and the absolute refractoriness 2) the introduction of a non-monotonic activation function. Our results showed that the interaction of the time lag, the inhibitory feedback, the firing procedure and the absolute refractoriness leads to a large number of stable periodic solutions with predictable patterns of oscillations, via interesting pattern transition procedures or through a mode interaction of fold and Hopf bifurcations.**First, we incorporate two important biological features of neurons into simple phenomenological spiking neuron models of recurrent inhibitory loops --- the firing procedure and the absolute refractoriness, which determines whether an inhibitory feedback has impact on the excitatory neuron in recurrent inhibitory loops. We then develop a creative approach to rigorously and systematically analyze the mechanism for generating a large number of coexisting stable periodic patterns in delayed recurrent inhibitory loops. The interaction of the delay, the inhibitory feedback and the absolute refractoriness can generate three basic types of oscillations and one type of more complicated oscillations, which consists of a possible solution for any initial condition. The inhibition delivered by the feedbacks finally stabilizes this solution to a limit stable periodic solution with predictable pattern of oscillations. The combination of different numbers of these oscillations leads to multiple coexisting stable periodic patterns. Moreover, interesting pattern transitions occur as the time delay passes through certain critical values. These pattern transitions play a similar role to the standard bifurcation theory in terms of the birth and continuation of multiple periodic patterns. Using our analytic approach, we are able to identify each periodic pattern with the classification of rhythms and to estimate the average time of convergence to the pattern for a given condition. The recognition time of a periodic pattern represented by the convergence time helps us to find the potential periodic patterns used for neural information transmission.**Second, the work provides the importance of interneuron synaptic connection for multistability in terms of dynamical bifurcation theory. We use non-monotonic activation functions to describe the synaptic connection between neurons in coupled networks with a discrete time delay. For the instantaneous feedback, supercritical pitch-fork bifurcations and a saddle-node bifurcation lead to the coexistence of multiple stable equilibria. On the other hand, as the delay increases to a certain critical value, the neuronal system undergoes a Hopf bifurcation, which results in the appearance of coexisting stable periodic orbits. We then apply the center manifold and the norm form theory to study the properties of the Hopf bifurcation and stability of bifurcated periodic orbits. Furthermore, the interaction of periodic orbits and other equilibria yields very interesting global continuation patterns that lead to the creation of butterfly phenomena through the gluing bifurcation.*

**Dissertation Colloquium**Jinnan Liu will speak on "

**Non-decomposable Discrete Graphical Models**" at 2:30p.m. in N638 Ross.ABSTRACT:

*In the Bayesian analysis of contingency tables, the choice of a prior distribution for either the log-linear parameters or the cell probabilities is a major challenge.**In this paper, we define a flexible family of conjugate prior distributions for the wide class of graphical models, including both decomposable and non-decomposable graphical models.**These priors are first defined as the Diaconis-Ylvisaker (1979) conjugate priors on the log-linear parameters subject to the baseline constraints. We show that they have several desirable properties: the mathematical convenience of a conjugate prior, the flexibility of having as many hyper parameters as there are free cell probabilities in the model, and the ability to reflect some prior knowledge.**We then obtain the induced priors on the cell probabilities and give, for decomposable models, the correspondence with the hyper Dirichlet distribution as defined in Dawid \& Lauritzen(1993).**Finally, we show how the new prior can be used to compute the normalizing constant and do model selection for a simulated example within the classes of both decomposable and non-decomposable graphical models with four vertices.*

**Dissertation Colloquium**Isabel Hubard will speak on "

**Two-Orbit Polytopes**" at 12:00p.m. in N638 Ross.ABSTRACT:

*An (abstract) polytope is called a two-orbit polytope if its automorphism group has exactly two orbits on the flags. Two-orbit polytopes are highly symmetric polytopes; as an example, chiral polytopes are two-orbits polytopes. In this talk we classify two-orbit polytopes into disjoint classes, depending on the local configuration of its flags, and find generators for the automorphism group of polytopes in each class. In particular, there are 6 different classes of two-orbit polyhedra (3-polytopes) that are not chiral. An idea of how to construct two-orbit polyhedra, starting from a group will also be given.*

**Dissertation Subject Oral**Sandeep Bhargava will speak on "

**Realizations of Root-graded Generalized Intersection Matrix Algebras**" at 3:00p.m. in N638 Ross.ABSTRACT:

*Generalized intersection matrix (g.i.m.) algebras arise from weakening the condition that the off-diagonal entries be non-positive in a generalized Cartan matrix. We look at g.i.m. algebras that result from multiply affinizing a Cartan matrix of type C_n. We show that these g.i.m. algebras have a root-grading and are central extensions of some symplectic Lie algebras.*

**MSc Thesis Defence**Kenji Suzuki will defend his thesis "

**Multi-stage Influenza Models for Containment of a Pandemic**" at 3:00p.m. in N638 Ross.

**Graduate Seminar**Mehnaz Rahman will speak on "

**Random Graphs with Arbitrary Degree Distribution and Contact Network Epidemiology**" at 2:00p.m. in N638 Ross.ABSTRACT:

*Random graphs have been employed extensively as models of real world networks of various types, particularly in epidemiology. Other than that, recent studies on the structure of social networks have focused attention on graphs with distributions of vertex degree that are significantly different from the Poisson degree distribution. In this talk, the structure and properties of random graphs will be introduced. Then applying these concepts we will develop the contact network epidemiology model which aims to find out the reproductive number R 0, the distribution of disease outbreak and the size of an epidemic.*

**Graduate Seminar**Ka Ho Lee will speak on "

**Measuring Value-at-risk by Historical and Monte Carlo Simulation**" at 1:15p.m. in N638 Ross.ABSTRACT :

*In the past, portfolio managers have used various techniques to capture risk. In recent years, risk management has experienced a revolution. This was started by Value-at-Risk (VaR), a new method to measure financial market risk. In brief, Value-at-Risk measures the worst expected loss over a given time period under normal market conditions at a given confidence level. This talk will present two different methods to calculate VaR: the Historical Simulation and Monte Carlo Simulation.*

**Graduate Seminar**Meng Han will speak on "

**Introduction to the Model Vetting Management System**" at 4:00p.m. in N638 Ross.ABSTRACT:

*This talk is related to my work for the summer internship at Royal Bank of Canada. In order to facilitate managing models inventory and vetting activities, a web-based information management system named Model Vetting Management System (MVMS) is designed and developed for the Group Risk Management at RBC. In this talk, the structure, functionality and feature of the system, as well as technologies involved in this project such as .NET 2.0 environment, Ajax, JavaScript, etc. will be introduced.*

**PhD Dissertation**Ye Sun will defend her PhD Dissertation entitled "

**Higher Order Likelihood Inference for a General Statistical Model**" at 11:00a.m. in N638 Ross.ABSTRACT:

*For an exponential model or a transformation model, a third order confidence interval for a parameter can be obtained very easily. When a model not in the natural exponential form, I use both observed likelihood and the tangent of pivotal statistics at the observed data to obtain a locally defined canonical parameter such that third order likelihood inference for any scaler parameter can be obtained. In my thesis, I discussed several cases depending on the availability of the explicit form of canonical parameters or the explicit form of of nuisance parameter.**Simulation studies show that the proposed methodology is very accurate even when sample size is very small. It outperforms almost all the existing asymptotic methods except for the exact methods. In most cases, it can be easily implemented into R, Splus or Matlab.*

**Graduate Seminar**Fang Chang will speak on "

**Smoothing Functional Data via B-Spline Basis**" at 10:30a.m. in N638 Ross.ABSTRACT:

*Many data collected from the real world can be considered as functional, such as height of a person observed in different occasions of his life. Actually this type of data are usually generated from smooth processes which possess one or more derivatives, that is a salient feature that we should take good advantage of. New methods of analyzing this kind of data are ongoing and we mainly introduce the weighted least square method with roughness penalty to smooth the curve and then retrieve it through a linear differential operator. Principle component analysis can be also extended to the functional data butwe interpret this method from a different point of view.*

**Survey Paper Presentation**Xiaofeng Zhou will speak on "

**Multi-way Data Analysis**" at 11:30a.m. in N638 Ross.ABSTRACT:

*This survey paper describe some useful methods (PCA, SVD, and PARAFAC) used in Multi-way analysis, provide a good understanding especially about the PARAFAC which is developed independently by Harshman [Harshman 1970] in 1970. The name of PARAFAC is standing for Parallel factor analysis. The basic idea of this model is to use the same factors to describe the variation in several matrices simultaneously with different weighting coefficients for each matrix, this is exactly the idea behind 'parallel proportional profiles' of Cattell. This report is emphasize on the understanding of the PARAFAC in the case of three-way array. The comparison between those methods used in two-way array and three-way array is made in this report.*

**Survey Paper Presentation**Jinling Gao will speak on "

**Model Selection of Microarray Analysis**" at 3:30p.m. in N638 Ross.ABSTRACT:

*This paper presents several model selection methods in microarray analysis. First a new distance metric is introduced in which whether or not the two genes have a common gene function is being taken consideration. Second learning causal networks from time course data via a model selection approach for a vector autoregressive process is introduced. A shrinkage approach is used to improve estimation of VAR regression coefficients and the model is selected by testing the associated partial correlations. Third two new normalization methods were developed which are based on iterative local regression and optimization of model parameters by generalized cross-validation. Fourth Bayesian model averaging (BMA) method for gene selection and classification of microarray data accounts for the uncertainty about the best set to choose by averaging over multiple models.*

**Survey Paper Presentation**Mehnaz Rahman will speak on "

**Contact Network Epidemiology and AIDS**" at 1:00p.m. in N638 Ross.ABSTRACT:

*We begin with a brief overview of the compartmental model framework including its applications and limitations. Then a discussion about the new analytical approach called the contact network epidemiology which models the spread of infectious disease by applying the bond percolation on random graphs. Using the later approach we will try to explain the impact of concurrent partnership on epidemic spread for AIDS. An index of concurrency based on graph theoretical considerations is introduced and the way in which it is related to the degree distribution of the contact graph is demonstrated.*

**Graduate Seminar**Bobby Babak Pourziaei will speak on "

**Hodgkin-Huxley Model**" at 10:00a.m. in N638 Ross.ABSTRACT:

*In 1952 Alan Hodgkin and Andrew Huxley developed a model to explain the ionic mechanisms underlying the initiation and propagation of action potentials in the giant squid axon. Their work provided the foundation for the all of the current work on voltage-sensitive membrane channels, which are responsible for the functioning of animal nervous systems. In 1963, Hodgkin and Huxley were awarded the Nobel Prize in Physiology or Medicine for their work.**In this talk we build the Hodgkin-Huxley model from the ground up. We describe the biology, chemistry and physics behind the mathematical model. We are able to analyze the behavior of the Hodgkin-Huxley model by reducing its dimension.*

**PhD Oral Defence**Mihai Beligan will defend his PhD Dissertation entitled "

**Insertaion for Tableaux of Transpositions (A Generalization of Schensted's Algorithm**" at 2:30p.m. in N638 Ross.ABSTRACT:

*We consider intervals $[u,w]_k,$ in the $k$-Bruhat order on permutations, where $w,u \in S_n$ satisfy certain criteria Maximal chains in these intervals can be represented as tableaux of transpositions. We provide an algorithm for the insertion of a pair of integers $(x,y)$ into a strict tableau of transpositions $T,$ similar to Schensted insertion. The algorithm leads to a rectification procedure on these tableaux, and we explore some of the subsequent combinatorial properties. We point out two applications: one is concerning structure constants in the multiplication of Schubert polynomials by Schur symmetric polynomials; the other is the partitioning of an interval in the Grassmanian Bruhat order satisfying what we call the no-nesting criteria, into cells indexed by some strict tableaux of transpositions.*

**Graduate Seminar**Fang Chang will give a talk entitled "

**Asymptotic Behavior of Maximum Likelihood Estimators in Generalized Linear Models**" at 12:00p.m. in N638 Ross.ABSTRACT:

*Most statistical inferences are based on the asymptotic behavior of the Maximum Like-lihood Estimator. As we know, the choice of the link function have a strong effect on the asymptotic properties of the MLE. Here we mainly deal with the case for natural link function and introduce some useful results, but the conditions in those results can vary due todifferent models according to different link functions since each link function has its own property. The conditions do not involve in the unknown parameter are our special interest in practical use.*

**Graduate Seminar**Chen Xu will give a talk on "

**Interpreting Statistical Evidence by Using Imperfect Models: Robust Adjusted Likelihood Functions**" at 1:30p.m. in N638 Ross.ABSTRACT:

*The strength of statistical evidence is measured by the likelihood ratio. Two key performance properties of this measure are the probability of observing strong misleading evidence and the probability of observing weak evidence. For the likelihood function associated with a parametric statistical model, these probabilities have a simple large sample structure when the model is correct. Here we examine how that structure changes when the model fails. This lead criteria for determining whether a given likelihood function is robust, and to a simple technique for adjusting both likelihoods and profile likelihoods to make them robust.*

**MSc Defence**Qi Zhou will speak on "

**General Hull-White One factor Model and Calibration**" at 2:30p.m. in N638 Ross.ABSTRACT:

*In financial mathematics, the Hull-White model is a model of future interest rates. It is relatively straight-forward to translate the mathematical description of the evolution of future interest rates onto a tree or lattice and so interest rate derivatives such as swaptions can be valued in the model. This presentation will overview the Hull-White one factor model and illustrate an example on how to use this model to price derivatives.*

**Graduate Seminar**Tao Lei will give a talk entitled "

**Elements of Free Probability Theory**" at 1:00p.m. in N638 Ross.ABSTRACT:

*We will briefly review the basic notions of non-commutative probability space and the concept of free independence which refines "non-commutative probability theory" to "free probability theory". We will use a combinatorial view to introduce the theory.*

**Graduate Seminar**Chen Xu will speak on "

**Empirical Likelihood Confidence Intervals for the Mean of a Population Containing Many Zero Values**" at 2:00p.m. in N638 Ross.ABSTRACT:

*If a population contains many zero values and the sample size is not very large, the traditional normal approximation-based confidence intervals for the population mean may have poor coverage probabilities. This problem is substantially reduced by constructing parametric likelihood ratio intervals when an appropriate mixture model can be found. In the context of survey sampling, however, there is a general preference for making minimal assumptions about the population under study. The authors have therefore investigated the coverage properties of nonparametric empirical likelihood confidence intervals for the population mean.*

**MSc Defence**Qi Zhou will speak on "

**Introduction to Interest Rate Derivatives**" at 2:30p.m. in N638 Ross.ABSTRACT:

*Interest rate derivatives are instruments whose payoffs are dependent in some way on the level of interest rates. In the 1980s and 1990s, the volume of trading in interest rate derivatives in both the over-the-counter and exchange-traded markets increased very quickly. Many new products were developed to meet particular needs of end users. A key challenge for derivatives traders is to find good, robust procedures for pricing and hedging these products. This presentation will introduce the basic concepts or ideas about interest rate derivatives and overview some popular interest rate models in financial industry.*

**Survey Paper**Yan Yan Wu will speak on "

**Higher Order Likelihood Inference for Two-sample Test When One Variance Is Known and the Other Is Unknown**" at 11:00a.m. in N638 Ross.ABSTRACT:

*It's known that Behrens-Fisher problem (both the variances of are unknown and unequal in the two-sample t-test) does not has an exact t-distribution Satterthwaite(1941,1946) approxmated the degree of freedom using the method of moment matching. When one variance is known and the other is unknown, the inference is more difficult to obtain. In 2005, Maity & Sherman (2005) applied Satterthwait's tool and achieved approximated t-distribution result.**In this paper, a likelihood based method is introduced to obtained the confidence intervals and p-value for the difference in means. The simulation shows that the methods gives extremely accurate result.*

**MSc Thesis Defence**Wensheng Liu will defend his MSc thesis entitled "

**Supervised Projective Adaptive Resonance Theory**" at 10:00a.m. in N638 Ross.

**Thesis Colloquium**Wensheng Liu will speak on "

**Supervised Projective Adaptive Resonance Theory**" at 3:30p.m. in N638 Ross.ABSTRACT:

*Projective Adaptive Resonance Theory (PART) has been shown to be a powerful gene screening tool for prognostic prediction as it is capable of constructing predictors consisting of only a small subset from a large group of genes in a given collection of samples. PART however is a unsupervised clustering algorithm, and its direct application to a training data set usually ignores the useful annotations coming with the data and sometimes may not work well. It is therefore necessary to improve PART algorithm in order to achieve the supervised clustering of the training data, and to incorporate the functions of model calibration and validation, so that predictors based on adaptively identified subgroup of genes perform very well for the training data, and that the construction of these predictors can be automatically modified when more data sets and information become available.**New modules Data Marking, Model Calibration, Predictor Construction, and Predictor Validation are incorporated into PART so that the new neural network architecture, called Supervised Projective Adaptive Resonance Theory (SPART), can perform supervised learning from a training data and construct predictors based on small subset of automatically identified genes, in addition to its ability to learn from the testing data and newly available information in order to update the predictors.*

**Dissertation Colloquium**Ye Sun will give a talk on "

**Higher Order Likelihood Inference for a General Statistical Model**" at 2:00p.m. in N627 Ross.ABSTRACT:

*For an exponential model or a transformation model, a third order confidence interval for a parameter can be obtained very easily. When a model not in the natural exponential form, I use both observed likelihood and the tangent of pivotal statistics at the observed data to obtain a locally defined canonical parameter such that third order likelihood inference for any scaler parameter can be obtained. In my thesis, I discussed several cases depending on the availability of the explicit form of canonical parameters or the explicit form of of nuisance parameter.**Simulation studies show that the proposed methodology is very accurate even when sample size is very small. It outperforms almost all the existing asymptotic methods except for the exact methods. In most cases, it can be easily implemented into R, Splus or Matlab.*

**Dissertation Subject Oral**Beatriz Zamora-Aviles will speak on "

**Set Theoretic Properties of the Calkin Algebra**" at 3:00p.m. in N638 Ross.ABSTRACT:

*Let H be a separable infinite dimensional Hilbert space, If B(H) is the algebra of bounded operators and K(H) the ideal of compact operators, the Calkin algebra C(K) is the quotient C*-algebra. Let P(C(H)) be the partially order set of projections in the Calkin algebra. We can regard C(H) and P(C(H)) as the the quantum versions of the remainder of the Stone-Cech compactification and the power set of the natural numbers modulo finite sets respectively. We intend to study the set theoretic properties of these structures.*

**Graduate Seminar**Babak Pourziaei will speak on "

**Non Linear Neurodynamics & Bifurcation**" at 9:30a.m. in N627 Ross.ABSTRACT:

*In this talk, we introduce and analyze simple neural networks in terms of the stability of their equilibrium states. Mutual excitation in short-term memory and mutual inhibition in neural decision making will be discussed. It will be shown that neural adaptation will lead to memory loss, a topic that will introduce bifurcation theory.*

**Graduate Seminar**Jian Li will speak on "

**The Role of Learning in Dynamic Portfolio Decision**" at 10:30a.m. in N627 Ross.ABSTRACT:

*This paper analyzes the effect of uncertainty about the mean return on the risky asset on the portfolio decisions of an investor who has a long investment horizon. Building on the earlier work of Detemple (1986), Dothan and Feldman (1986), and Gennotte (1986), it is shown that the possibility of future learning about the mean return on the risky asset induces the investor to take a larger or smaller position in the risky asset than she would if there were no learning, the direction of the effect depending on whether the investor is more or less risk tolerant than the logarithmic investor whose portfolio decisions are unaffected by the possibility of future learning. Numerical calculations show that uncertainty about the mean return on the market portfolio has a significant effect on the portfolio decision of an investor with a 20 year horizon if her assessment of the market risk premium is based solely on the Ibbotson and Sinquefield (1995) data.*

**Survey Paper**Hao Bai will speak on "

**Statistical Analysis of Time Course Microarray Experiments**" at 11:00a.m. in N627 Ross.ABSTRACT:

*Time-course microarray experiments are useful approaches for exploring biological systems. In this type of experiments, the researcher is frequently interested in studying gene expression changes along time and in evaluating trend differences between the various experimental groups. The high dimensionality of genes, multi-collinearity amonggenes and high correlations among experimental conditions in the temporal fashions pose the great challenges to data analysis. In this paper we will introduce several popular statistical analysis methods applied in this topic.*

**Thesis Colloquium -- 2nd Talk**Kenji Suzuki will speak on "

**Multi-stage Influenza Models for Containment of a Pandemic**" at 2:30p.m. in N638 Ross.ABSTRACT:

*Several studies have discussed the containment of influenza virus using mathematical models, however the previous studies have some limitations for dealing with influenza infection and containment. In this talk, first I will propose new discrete models with multiple infection stages. Then I will study the dynamical properties, such as disease free equilibrium, basic reproduction number, local and global stability of the basic model. A cost-effective study will be carried out numerically to discuss the efficiency of containment measure, such as prophylaxis and treatment.*

**PhD Defence**Qian Tong will defend her PhD Dissertation entitled "

**Combining Current and Historical Survival Data Using the Weighted Likelihood**" at 10:00a.m. in N638 Ross.

**PhD Defence**Huilan Li will defend her PhD Dissertation entitled "

**Algebraic Structure on Grothendieck Groups of a Tower of Algebras**" at 2:00p.m. in N638 Ross.

**Dissertation Subject Oral**Bernd Schulze will speak on "

**Combinatorial and Geometric Rigidity with Symmetry Constraints**" at 12:00p.m. in N638 Ross.ABSTRACT:

*We consider various results in rigidity theory and extend these results to frameworks that possess symmetry. Maxwell's rule from 1864 says that if a framework (G,p) with G=(V,E) is minimal infinitesimally rigid (isostatic) in n-space, then we must have |E|=n|V|-n(n+1)/2. Using group representation theory to exploit the full symmetry of (G,p), it is possible to derive further necessary conditions for (G,p) to be isostatic. In particular, it turns out that a symmetric isostatic framework (G,p) must obey some very simply stated restrictions on the number of structural components that are ‘fixed' by the symmetry operations of (G,p). Care must be taken whenever the configuration p of (G,p) is not injective since in this case the definition of ‘fixed' must take into account not only the geometric but also the combinatorial properties of the joints and bars of (G,p).**Furthermore we introduce a symmetry adapted notion of a generic framework and present some related results. Finally, we state a conjecture that gives sufficient conditions for a 2-dimensional framework which is generic within a given symmetry group to be isostatic.*

**PhD Defence**Guojun Gan will defend his PhD Dissertation entitled "

**Subspace Clustering Based on Fuzzy Models and Mean Shifts**" at 1:30p.m. in N627 Ross.

**Dissertation Colloquium**Qian Tong will speak on "

**Combine Current and Historical Data using Weighted likelihood with Application into Survival Analysis**" at 11:00a.m. in N638 Ross.ABSTRACT:

*The weighted likelihood approach could make effective use of related information from other populations to yield a more accurate estimator than the classical maximum likelihood estimator (MLE). The central issue of the weighted likelihood method is to choose the likelihood weights adaptively and effectively. There are several methods proposed in the literature about choosing adaptive weights. However, the proposed adaptive weights might have some limitations, being too difficult to apply.**We propose a new approach to choose the weights based on the shortest Euclidean distance. The goal of this research is to further improve the classical likelihood estimator using the proposed likelihood weights for the weighted likelihood. The asymptotic properties of the proposed likelihood weights will be discussed. Future work also includes applying the proposed method to cure rate models by combining the current data with the historical data.*

**Thesis Colloquium (1st Talk)**Kenji Suzuki will speak on "

**Influenza Compartmental Models with Multiple Infection Stages**" at 10:00a.m. in N638 Ross.ABSTRACT:

*The 20th century witnessed several influenza outbreaks. Recently there is a risk of the prevalence of new influenza strain such as Bird Flu, therefore it still draws much attention. In this talk, first I will recall and summarize previous studies about mathematical models of influenza and comment on these models. Then, by improving previous models, I propose the new discrete model with multiple infection stages. We will study the basic properties of this model, and conclude with preliminary simulated results.*

**Dissertation Subject Oral**Ye Sun will speak on "

**Higher Order Likelihood Inference for a General Statistical Model**" at 1:00p.m. in N638 Ross.ABSTRACT:

*Recent higher order likelihood asymptotic inference procedures start to be implemented in standard softwares because of its accuracy. Andrews, Fraser \& Wong (2005) showed that any statistical model can be approximated locally by a tangent exponential model. In my thesis, I use both observed likelihood and the tangent of pivotal statistics at the observed data to obtain a tangent exponential model and the locally defined canonical parameter. Hence third order likelihood inference for any scaler parameter can be obtained. This third order method is very accurate even for small sample size. In most cases, it can be easily implemented into R, Splus or Matlab. In my thesis, I will apply the proposed theories to a variety of problems. Highly accurate performances are expected. The talk will describe the third order likelihood theories and several problems I am going to investigate on.*

**MSc Thesis Defence**Jack Greogory Pitt will defend his MSc thesis entitled "

**Three-species Model for the Transmission Dymanics of the West Nile Virus**" at 2:00p.m. in N627 Ross.

**Dissertation Colloquium**Guojun Gan will give a talk on "

**Subspace Clustering Based on Fuzzy Models and Mean Shifts**" at 12:30p.m. in N627 Ross.ABSTRACT:

*Cluster analysis, also called segmentation analysis or taxonomy analysis, is a way to create groups of objects, or clusters, in such a way that objects in one cluster are very similar and objects in different clusters are quite distinct. Cluster analysis is a very complex task and faces many challenges due to the curse of dimensionality and the unknown number of clusters. In this colloquium, we start with some existing algorithms and then introduce two novel approaches to overcome the curse of dimensionality and determine the number of clusters in clustering high dimensional data sets. In particular, we introduce two main algorithms, the fuzzy subspace clustering (FSC) algorithm and the mean shift for subspace clustering (MSSC) algorithm, and present their experimental evaluation using a variety of synthetic data sets. In addition, the convergence of the FSC algorithm is established theoretically and the critical value of a parameter of the MSSC algorithm when the first phase transition occurs is approximated.*

**Dissertation Subject Oral**Yumin Wang will speak on "

**Mathematical Finance Related to Insurance Contracts**" at 10:30a.m. in 1154 Vari Hall.ABSTRACT:

*Quantile hedging and efficient hedging for contingent claims are active topics of research in mathematical finance. They play a role in incomplete markets, or when perfect hedging is not possible. Guaranteed minimum death benefits (GMDBs) are present in various annuity contracts, and act as a form of portfolio insurance. They cannot be perfectly hedged due to the mortality component, except in the limit as the number of contracts becomes infinitely large. In my thesis I hope to apply ideas from finance to derive quantile or efficient hedges for these products.**The talk will describe quantile hedging, efficient hedging, and GMDBs. I will describe some initial results that have been derived in special cases.*

**Dissertation Colloquium**Huilan Li, will speak on "

**Algebraic Structures on Grothendieck Groups of a Tower of Algebras**" at 1:30p.m. in N638 Ross.ABSTRACT:

*The Grothendieck group of the tower of symmetric group algebras has a self-dual graded Hopf algebra structure. Inspired by this, we introduce by way of axioms, a general notion of a tower of algebras and study two Grothendieck groups on this tower linked by a natural paring. Using representation theory, we show that our axioms give a structure of graded Hopf algebras on each Grothendieck groups and these structures are dual to each other. We give some examples to indicate why these axioms are necessary. We also give auxiliary results that are helpful to verify the axioms. We conclude with some remarks on generalized towers of algebras leading to a structure of generalized bialgebras (in the sense of Loday) on their Grothendieck groups.*

**Dissertation Subject Oral**-- Rescheduled TalkMichael Moras will speak on "

**Super Brownian Motion and Martin Boundaries**" at 2:30p.m. in N638 Ross.ABSTRACT:

*After a short introduction to superprocesses and Martin boundaries, we'll talk about Salisbury and Verzani's description of a conditioned exit measure for super Browian motion and Cranston and Salisbury's integral test for Martin boundaries of sectorial domains with the ultimate goal in mind to combine these papers to describe qualitatively different ways for a super Brownian motion to exit a 'perforated' and unbounded domain.*

**Dissertation Subject Oral**Michael Moras will speak on "

**Super Brownian Motion and Martin Boundaries**" at 10:00a.m. in N638 Ross.ABSTRACT

*After a short introduction to superprocesses and Martin boundaries, we'll talk about Salisbury and Verzani's description of a conditioned exit measure for super Browian motion and Cranston and Salisbury's integral test for Martin boundaries of sectorial domains with the ultimate goal in mind to combine these papers to describe qualitatively different ways for a super Brownian motion to exit a 'perforated' and unbounded domain.*

**Graduate Seminar**Morteza Safar-Ali will speak on "

**Finite Fields for Coding**" at 3:00p.m. in N638 Ross.ABSTRACT:

*Hocquenghem (1959) and Bose and Ray-Chaudhuri (1960) independently proved a remarkable theorem which enables us to systematically construct one of the most powerful multiple error-correcting codes for random independent errors. We will present these so called BCH codes and explain their foundation in finite field theory.*

**Thesis Colloquium**Greg Pitt will give his second talk on "

**Three-Species Model for the Transmission Dynamics of the West Nile Virus**" at 2:30p.m. in N638 Ross.ABSTRACT:

*The transmission dynamics of the West Nile Virus (WNv) are summarized using a large ODE model which features two species of bird (robin and crow) and one species of mosquito. Corvids (e.g., crows) have high WNv mortality rates. They are considered alongside non-corvids (e.g., robins), with low WNv mortality, making it easier to compare the reservoir and sentinel roles that birds play in the study of WNv epidemiology. Analysis of the model is supported by numerical simulations.*

**Dissertation Subject Oral**Anouk Bergeron-Brlek, York University , will speak on "" at 4:00p.m. in N627 Ross.Non-Commutative Invarient Theory ABSTRACT:

*Let V be a vector space of dimension n over the rationals Q. We consider finite subgroups G of GL(V) that act on the algebra Q[X_n] of polynomials in commuting variables x_1,x_2,..., x_n with rational coefficients. The coinvariant space of G is the quotient Q[X_n] / I_G, where I_G is the ideal generated by G-invariants of Q[X_n] of positive degree. An interesting question is to understand the structure of coinvariants of those groups in the non-commutative version. In particular, we will be investigating the non-commutative version of a theorem which gives a characterization of all group actions on polynomials such that the dimension of the space of coinvariants is equal to the order of the group (generally referred to as Chevalley's theorem).*

**Thesis Defence**Oulu Xu will defend her MSc thesis "

**Interest Rate Modelling: The Market Models Approach**" at 2:00p.m. in N638 Ross.

**Dissertation Subject Oral**Naveen Vaidya will speak on "

**Membrane Fusion: An Influenza Virus and a Host Cell**" at 1:30p.m. in N638 Ross.ABSTRACT:

*Membrane fusion is the first step for the invasion of an influenza virus into a healthy cell. Understanding the pre-fusion and the fusion mechanisms mediated by Hemagglutinin (HA) protein is important for various purposes such as disease control and drug design. We discuss the role of HA-protein in fusion process. We present a mathematical model for pre-fusion interaction between an influenza virus and a healthy cell. After a brief discussion of some results, we point out the possible techniques to model the functional motion of HA-protein, intermediate stage of membrane fusion and dynamics of the fusion pore.*

**Dissertation Subject Oral**Philippe Choquette will speak on "

**A Braided Category of Hopf Algebras**" at 2:00p.m. in N638 Ross.ABSTRACT:

*We discuss a special braided monoidal category C of combinatorial Hopf algebras. The objects of C are functors from the category Set to the category Vect. The functors r-Q ? in C can be mapped to the well known ordinary Hopf algebras r-QSym, for r > 0. These r-Q ? are of great interest, in particular since 1-Q ? is the terminal object of C. We want to calculate odd and even subalgebras of r-Q ? and study quotients and operators in C.*

**MSc Thesis Defence**Marija Zivkovic Gojovic will defend her MSc thesis "

**Structured Influenza Model for Metapopulation**" at 10:00a.m. in N638 Ross.

**Dissertation Colloquium**Mihai Beligan will give a talk on "

**Insertion for Tableaux of Transpositions: A Generalization of Schensted's Algorithm**" at 4:00p.m. in N638 Ross.ABSTRACT:

*We consider intervals $[u,w]_k,$ in the $k$-Bruhat order on permutations, where $w,u \in S_n$ satisfy certain criteria. Maximal chains in these intervals can be represented as tableaux of transpositions. We provide an algorithm for the insertion of a pair of integers $(x,y)$ into a strict tableau of transpositions $T,$ similar to Schensted insertion. The algorithm leads to a rectification procedure on these tableaux, and we explore some of the subsequent combinatorial properties. We point out two applications: one is concerning structure constants in the multiplication of Schubert polynomials by Schur symmetric polynomials; the other is the partitioning of an interval in the Grassmanian Bruhat order satisfying what we call the no-nesting criteria, into cells indexed by some strict tableaux of transpositions.*

**Thesis Defence**Leda Weiss will defend her MSc thesis entitled "

" at 3:00p.m. in N638 Ross.Effect of Migration on the Transmission Dynamics of HIV in India

**Thesis Colloquium**Oulu Xu will speak on "

**Interest Rate Modelling: The Market Models Approach**" at 10:00a.m. in N627 Ross.ABSTRACT:

*In this talk, I will present the market models, the calibration procedure of the LIBOR market model and some numerical results of the calibration. Moreover, I will present the implentation of the model by Monte Carlo simulation and then show the performance of the calibraiton.*

**Graduate Seminar**Jian Li will give a talk entitled "

**Minimizing the Probability of Lifetime Ruin under Borrowing Constraints**" at 10:00a.m. in N638 Ross.ABSTRACT:

*We determine the optimal investment strategy of an individual who targets a given rate of consumption and who seeks to minimize the probability of going bankrupt before she dies, also known as lifetime ruin. We impose two types of borrowing constraints: First, we do not allow the individual to borrow money to invest in the risky asset nor to sell the risky asset short. However, the latter is not a real restriction because in the unconstrained case, the individual does not sell the risky asset short. Second, we allow the individual to borrow money but only at a rate that is higher than the rate earned on the riskless asset. We consider two forms of the consumption function: (1) The individual consumes at a constant (real) dollar rate, and (2) the individual consumes a constant proportion of her wealth. The first is arguably more realistic, but the second is closely connected with Merton's model of optimal consumption and investment under power utility. We demonstrate that connection in this paper, as well as include a numerical example to illustrate our results. Keywords: Self-annuitization, optimal investment, stochastic optimal control, probability of ruin, borrowing constraints, lending rate borrowing.*

**Thesis Defence**Adnan Sljoka will defend his MSc thesis entitled "

**Counting for Rigidity, Flexibility and Extensions Via the Pebble Game Algorithm**at 1:00p.m. in N638 Ross.

**Survey Paper**Yun Qiao will speak on "

**General Principles of Indifference Pricing in Incomplete Market**" at 10:30a.m. in N638 Ross.ABSTRACT:

*In this presentation I'd like to introduce the general principle of indifference pricing and it's applications in incomplete market. Some latest work using this approach will be discussed as well.*

**Thesis Colloquium--First Talk**Wensheng Liu will speak on "

**Suprevised Projective Adaptive Resonance Theory (SPART)**" at 1:00p.m. in ICES (Linton Boardroom, Insititue for Clinical Evaluative Sciences), Sunnybrook Hospital.ABSTRACT:

*Supervised Projective Adaptive Resonance Theory (SPART) is a newly developed neural network model based on another neural network model PART (Projective Adaptive Resonance Theory). PART has been a powerful gene-screening tool in dealing with high dimension gene data. However, due to its unsupervised clustering property, it is usually difficult for PART to select a suitable pair of vigilance parameter and distance parameter, which is important for PART to achieve an ideal clustering result. Therefore, it is helpful to improve PART model and incorporate new modules including Data Marking, Model Calibration, Predictor Construction, and Predictor Validation to perform supervised neural network learning. A predictor is constructed and calibrated by learning the training data set and validated by the testing data set. In the talk, the structure and components of SPART will be introduced by demonstrating an application of SPART on the ALL-AML data sets (First introduced on the journal 'Science' by Golub et al in 1991). In addition, the ideas about calibration and validation will also be applied to a Diabetes Incidence Risk Prediction Algorithm.*

**Thesis Colloquium -- First Talk**Oulu Xu will speak on "

**Interest Rate Modelling: The Market Models**" at 1:00p.m. in N638 Ross.ABSTRACT:

*In this talk, I will briefly review interest rate models and introduce the recent popular market models: the LIBOR market model and swap-rate market model. Furthermore, I wil introduce the industrial formula and involve this formula to calibrate the LIBOR market model.*

**Graduate Seminar**Natasha May will speak on "

**Applications of the Amalgams of L^p and 1^q**" at 10:00a.m. in N627 Ross.ABSTRACT:

*This talk will focus on spaces called the amalgams of L^p and l^q. The amalgam of L^p and l^q on the real line consists of functions which are locally in L^p and whose L^p norms over the intervals [n, n+1], for every integer n, form an l^q sequence. Amalgams of L^p and l^q are defined similarly on groups, and we will list some properties of these spaces. We will then focus on applications of amalgams to other areas of mathematics. Specifically, the application to almost periodic functions, product-convolution operators and extending the domain of the Fourier transform.*

**Thesis Colloquium**Leda Weiss will speak on "

**Effect of Migration on the Transmission Dynamics of HIV in India**" at 10:30a.m. in N638 Ross.ABSTRACT: Our model characterizes the transmission dynamics of HIV in India. It is a system of differential equations and includes migration between the north and south. A one patch model was used to describe each geographic area (south and north), while a two patch model was used for the entire country including migration. The basic reproductive number, Ro, was found by using second generation matrices. The Ro of the entire country was found as a function of each regional Ro and also was found as a function of the migration parameters. We investigated these relationships numerically and graphically. The results have both epidemiological and mathematical implications.

**Graduate Seminar**Innocent Mberabagabo will speak on "

**Configurations and Maps**" at 3:00p.m. in N638 Ross.ABSTRACT:

*During this presentation, we will review Menger?s idea of representing a configuration of points and lines by a graph. We will focus on regular compound polytopes in 2, 3, 4 and higher dimension, and deduct some of their core properties.*

**Survey Paper**Jing Sun will speak on "

**Parallel Computing and Statistics**" at 10:00a.m. in N627 Ross.ABSTRACT:

*Over the last decades, parallel computing become accessible to researchers and it has been used for solving a wide range of problems that arise in diverse applications areas. However, the development of parallel computing for general use in statistics has been comparatively neglected. This survey paper presents an overview of parallel computing, and describes how to apply subroutines in the current parallel numerical libraries to general linear model and singular value decomposition computing from a statistical computing standpoint.*

**Thesis Colloquium -- Second Talk**Marija Zivkovic Gojovic will speak on "

**Structured Influenza Model for Metapopulation**" at 10:30a.m. in N638 Ross.ABSTRACT:

*Influenza remains to be one of the most important public health problems in today's industrial and modern world. There have been several pandemics recorded in the history, followed by tremendous number of infected population, numerous influenza related deaths and significant economic loss. In this work, we will present an age structured influenza model for matapopulation, where the age represents the time elapsed since the infection. The model will be parameterized using the data from 1918/19 pandemic, but also modified to account for today's achievements in medical care and technology, so the model with carefully selected parameters can be used to analyze and simulate different scenarios in a new changing environment. The aim of this work is to evaluate the influence of a different control measures on a temporal patterns of a pandemic and to consider the impact of structured population movement on spatial spread.*

**Graduate Seminar**Zhun Han will speak on "

**Delay Differential Equation and Predator-Prey Model**" at 2:00p.m. in N638 Ross.ABSTRACT:

*The theory of Delay Differential Equation (DDE) has been widely applied in both mathematics and other subjects. So far, dozens of DDEs occured from biological systems.**This talk will give an introduction on basic ideas of DDE and analyze a predator-prey model with a single discrete delay.*

**Survey Paper Presentation**Kirandeep Bumraw will speak on "

**Classification Using Support Vector Machines**" at 9:00a.m. in N638 Ross.ABSTRACT:

*Support Vector Machines (SVM) are Machine Learning techniques and have been gaining popularity among the scientific community due to many attractive features, and promising empirical performance. This survey paper presents an overview of the theory behind support vector machines and discusses its importance, usefulness and effectiveness in classification. The results have been presented by implementing support vector machines using R software (LIBSVM). SVMs based on various kernels were tested for classifying data from various domains.*

**Survey Paper Presentation**Natasha May will speak on "

**A Survey of the Existence of Cech Functions**" at 10:00a.m. in N627 Ross.ABSTRACT:

*In 1947, E. Cech asked whether there exists a surjective closure operator that is not the identity, an operator known as a Cech function. This question posed by Cech remained an open problem until very recently; it was unknown whether Cech functions existed assuming only the axioms of ZFC. However, in the 1980s some results proved by Roderick A. Price and Fred Galvin were published. We will survey what these mathematicians discovered about the existence of Cech functions, as well as what is known about Cech functions in general, and include a proof that Cech functions exist in ZFC.*

**PhD Defence**Rong-Song Liu will defend her PhD Dissertation entitled "

**Transmission Dynamics and Spatial Spread of Vector Borne Diseases: Modelling, Prediction and Control**" at 2:00p.m. in N638 Ross.

**Graduate Seminar**Konstantin Zukker will speak on "

**Quasi-Monte Carlo and Low-Discrepancy Sequences**" at 2:00p.m. in N638 Ross.ABSTRACT:

*Quasi-Monte Carlo methods differ from Monte Carlo in that for simulations they use deterministic sequences instead of pseudorandom. This brings in a number of benefits such as better accuracy. Quality of the Quasi-Monte Carlo methods depends on how uniform the deterministic sequence is. In the seminar I talk about discrepancy, which is a measure of uniformity, its link with the methods' error bounds and describe some ways to generate uniform sequences.*

**Graduate Seminar**Cheng Liu will speak on "

**The Kernel Approach to Study the Quadratic Time-Frequency Distribution**" at 9:00a.m. in N638 Ross.ABSTRACT:

*All the time-frequency distributions can be represented by the gerenel Cohen class with different kernels. And the properties of the time-frequency distributions can be stuied by the kernel instead. This talk will give a basic introduction about the common useful properties of the time-frequency distribution and all of them will be considered in the kernel method either.*

**Survey Paper Presentation**Rabih Saab will speak on "

**Spatio-temporal Designs**" at 10:00a.m. in N638 Ross.

**Graduate Seminar**Cheng Liu will give a talk entitled "

**The Mathematical Model for the HIV/AIDS**" at 2:00p.m. in N638 Ross.ABSTRACT:

*The Mathematical Model for the sexual transmission of HIV/AIDS that incorporate changes in behaviour as well as the effects associated with HIV is considered in the talk. The wquilibrium point and reproductive number are also discussed.*

**MSc Colloquium**J.G. Pitt will speak on "

**Three-species Model for the Transmission Dynamics of the West Nile Virus**" at 11:00a.m. in N638 Ross.ABSTRACT:

*The transmission dynamics of the West Nile Virus (WNv) are summarized using an ODE model which features two species of bird and one species of mosquito. Corvids (e.g., crows) are known to have high WNv mortality rates. By considering them alongside non-corvids with low WNv mortality, it is easier to compare the reservoir and sentinel roles that birds play in the study of WNv epidemiology. Analysis of the model is supported by numerical simulations.*

**Survey Paper Presentation**Weiming Hong will give a talk on "

**Quantile Regression in Selected Financial Applications**" at 10:30a.m. in N638 Ross.

**Graduate Seminar**Josephine Ke Fei Tang will give a talk entitled "

**Modeling on West Nile Virus**" at 2:00p.m. in N638 Ross.

**Survey Paper Presentation**Cheng Liu will give a talk on "

**Instantaneous Frequency Estimation with Time Frequency Distribution**" at 10:00a.m. in N638 Ross.

**Survey Paper**Li Kang will present the survey paper, "

**A Survey of Degree Theory in the Differential Topology of Manifolds**" at 2:00p.m. in N638 Ross.

**Dissertation Colloquium**Ronsong Liu will speak on "

**Transmission Dynamics and Spatial Spread of Vector Borne Diseases: Modelling, Prediction and Control**" at 11:00a.m. in N638 Ross.ABSTRACT:

*In this thesis, we study the transmission dynamics and spatial spread of vector borne diseases using mathematical models incorporating different factors, contributing to the complicated transmission dynamics and spatiotemporal spread patterns of vector borne diseases. We focus on the demographic and disease ages on hosts, the age structured culling on vector, the spatial movement of the disease hosts, and the heterogeneity in host populations. We address the above issues and the relevant modeling and analysis techniques via a detailed case studying about the invasion and spread of West Nile virus in North America. Models involved and developed include patchy models with both long-range and short-range dispersal, delay differential systems, non-local delayed reaction diffusion equations and impulsive differential equations. We develop necessary mathematical techniques, and carry out qualitative analysis and numerical simulations to describe the transmission dynamics and spatiotemporal patterns of disease spread.*

**PhD Oral**Jin Wang will defend her PhD Dissertation entitled "

**Numerical PDE Techniques for Personal Finance and Insurance Problems**" at 10:00a.m. in N638 Ross.

**Graduate Seminar**Kagba Kousse will speak on "

**Modeling the Term Structure of Credit Risk Spreads: The jarrow-Lando-Turnbull Model**" at 9:00a.m. in N638 Ross.ABSTRACT:

*The Jarrow-Lando-Turnbull model, is a Markov model that describes the term structure of credit risk spreads. Based on the Jarrow-Turnbull model for the pricing of derivatives securities involving credit risk (cf. seminar 1), it uses a discrete state space Markov chain in credit ratings for the bankruptcy process.**After birefly revisiting the original Jarrow-Turnbull model, the present model will be derived and computations algorithms will be presented as well.*

**Graduate Seminar**Kagba Kousse will speak on "

**Pricing Derivatives Securities Invovlving Credit Risk: The Jarrow-Turnbull Approach**" at 11:00a.m. in N638 Ross.ABSTRACT:

*The Jarrow-Turnbull model, by applying the foreign currency analogy to decompose the dollar payoff from a risky security into a payoff of a default-free security and a ‘spot exchange rate' and using arbitrage-free valuations techniques conditioned by some assumptions, gives a methodology to price and hedge derivatives securities involving credit risk.**After revisiting the discrete case of the model, the continuous-time version will be derived. Then the pricing of such derivatives securities will be illustrated with the use of martingale properties.*

**Survey Paper Presentation**Martin Merener will speak on "

**A Survey in Broadcast Encryption**" at 2:00p.m. in N638 Ross.

**Survey Paper Presentation**Ming Chen will give a talk entitled "

**Neural Networks Applications for Statistical Classification**" at 10:00a.m. in N638 Ross.

**Graduate Seminar**Zhun Han will speak on "

**An Introduction to Curvelet and its Applications**" at 2:00p.m. in N638 Ross.ABSTRACT:

*Curvelet is a newly developed transform. Though it was first introduced in late 1990's, it has been applied to various subjects. This talk will mainly focus on the definition of Continuous Curvelet Transform (CCT) and some basic theorems. With these concepts and principles, we will analyze some single singularities of functions on R2. Some real applications and the comparison of CCT and classical wavelet transform will also be involved.*

**Graduate Seminar**Natasha May will speak on "

**Applications of Maximal Topologies**" at 2:00p.m. in N638 Ross.ABSTRACT:

*This talk will focus on applications of maximal topologies. We will begin with an overview, including the importance of maximal topologies, where they appear in mathematics and all related definitions. This will lead to the construction of a countable crowded perfectly disconnected regular space.**An interesting result exists concerning the space N*, the remainder of the Stone-Cech compactification of the natural numbers N. We know that if there is a countable crowded perfectly disconnected regular space, then N* can be mapped into a separable space by a continuous <= 2-to-one function.*

**Graduate Seminar**Leonid Sharster will speak on "

**The Non Negative Inverse Eigen Value Problem (NIEP)**" at 2:00p.m. in N638 Ross.ABSTRACT:

*This is an introductory talk on the the non negative inverse eigenvalue problem (NIEP). The NIEP is a problem to find necessary and sufficient conditions on a multi set S={a_1,...,a_n} of complex numbers to be the spectrum (=set of eigenvalues) of a n by n matrix P with real non negative entries. Even though, the problem can be formulated very easily it remains unsolved up to this day. The goal of the talk is to pose the problem, to discuss different approaches and to present some technique. The fundamental concepts in the theory of non negative matrices will be introduced. Some necessary conditions and illustrations in low dimensions will be presented as well.*

**Graduate Seminar**Martin Merener will speak on "

**Lower Bounds in Broadcast Encryption**" at 2:00p.m. in N638 Ross.ABSTRACT:

*Solutions of the problem of broadcast encryption are evaluated in terms of two variables: the number of private keys held by each user and the number of communications between the center and the users needed to allocate a new broadcast key. There is an inherent trade-off between these variables -we cannot make both arbitrarily small.**After introducing the general setting we define the class of consistent protocols and show for these two explicit relationships between the two variables using the finite delta-system lemma.*

**Graduate Seminar**Innocent Mberabagabo will speak on "

**The Golden Section, Phyllotaxis, and Wythoff's Game**" at 2:00p.m. in N638 Ross.ABSTRACT:

*Geometry has two great treasures: One is the Theorem of Pythagoras; the other, the division of a line into extreme and mean ratio. The first we may compare to a measure of Gold; the second we may name a precious jewel. J. KEPLER (1571-1630) We will be talking about the Golden Ratio and proving how this ratio can be seen as a common link between Nature (specifically with Botanic) , Fibonacci numbers, some geometrical graphs and Whythoff?s Game.*

**Graduate Seminar**Meng Han will speak on "

**Introduction to Parallel Computing and Its Applications in Option Pricing**" at 3:00p.m. in N638 Ross.ABSTRACT:

*Parallel computing is being seen as one of powerful tools for the fast solution of computationally large and data-intensive problems. This seminar will first introduce some basic concepts and methods of parallel computing. Further, after exploring SHARCNET environment and Message Passing Interface (MPI) , we will turn to applications in option pricing by utilizing parallel algorithms based on Monte Carlo method and Lattice method, respectively. The performance charateristics of these algorithms will be presented, and an experimental study of implementations of these algorithms on SHARCNET is also undertaken to examine the efficiency.*

**Graduate Seminar**Martin Merener will speak on "

**Subset-Cover Algorithms in Broadcast Encryption**" at 2:00p.m. in N638 Ross.ABSTRACT:

*Broadcast Encryption deals with the problem of a center transmitting data to a large group of users, in such a way that only qualified users can decrypt the content. In this talk we will describe a general algorithm which is based on a subset cover of the set of users. Particular implementations of this algorithm are evaluated in terms of the length of the encrypted message, the size of the private information of the users and the processing time. We will analyze two implementations with subset-cover defined in terms of a tree that has the set of users as leaves.*

**Graduate Seminar**Josephine Tang will speak on "

**A Variational Multiscale Finite Element Method for Multiphase Flow in Porous Media**" at 1:00p.m. in N638 Ross.ABSTRACT:

*We present a stabilized finite element method for the numerical solution of multiphase flow in porous media, based on a multiscale decomposition of pressures and fluid saturations into resolved (or grid) scales and unresolved (or subgrid) scales. The multiscale split is invoked in a variational setting, which leads to a precise definition of a grid scale problem and a subgrid scale problem. The subgrid problem is modeled using an algebraic approximation. This model requires the definition of a matrix of intrinsic time scales, which we design based on stability considerations.**We illustrate the performance of the method with simulations of a waterflood in a heterogeneous oil reservoir. The proposed method yields stable, highly accurate solutions on very coarse grids, which we compare with those obtained by the classical Galerkin method or the upstream finite difference method.*

**Survey Paper Presentation**Ying Li will speak on "

**Numerical Methods for Stochastic Control Problems**" at 1:30p.m. in N638 Ross.ABSTRACT:

*In the report, we review a class of stochastic control problems, examine its application in finance industry, evaluate and compare the numerical methods such as discrete and polynomial approximations as well as numerical techniques in the context of computational Stochastic Dynamic Programming.*

**Dissertation Subject Oral**Ghuanbin Du will speak on "

**Efficient Splitting and Domain Decomposition Methods for Time-Dependent Problems and Applications**" at 10:30a.m. in N638 Ross.ABSTRACT:

*Many industrial problems require large scale computations and simulations in science and engineering, e.g., groundwater modelling, petroleum reservoir simulation and environment prediction. Domain decomposition methods (DDMs) and splitting techniques have been studied in rich literature and applications for reducing the complexities and computational cost in realistic long term, large scale problems. In this thesis, we propose an efficient splitting domain decomposition method (SDDM) for solving parabolic equations. We will study the theoretical properties including convergence of the SDDM scheme. Numerical experiments will be performed to illustrate its accuracy and efficiency. Then, we will further develop the SDDM scheme combining the modified upstream methods to simulate the groundwater contaminant transport in porous media, which is modeled by a coupled system of nonlinear PDEs, one of parabolic equation for water head and the other of convection-diffusion equation for concentration of the contaminant. Meanwhile, we will also study a splitting ELLAM (S-ELLAM) for convection-dominated diffusion problems in high dimensions. The method takes the advantages of the ELLAM and splitting technique. It is able to generate accurate numerical solutions even if a large time step and coarse spatial step sizes are used in simulation.*

**Thesis Colloquium -- 1st Talk**Marija Zivkovic Gojovic will speak on "

**Structured Influenza Models for Metapopulations**" at 1:00p.m. in N638 Ross.ABSTRACT:

*Recent appearance of avian flu among human population has again raised the fear of a pandemic influenza. In last century, there were several pandemics of which 1918/19 was the deadliest one. We will present the models parameterized using available data from the 1918/19 pandemic. The model considers structured population moving between two patches, in which we have in mind a possible application of modeling the impact of cross-board between Canada and USA, and we tie the structured model to the duration of illness and the rate and length of visit.*

**Graduate Seminar**Yun Qiao will speak on "

**Portfolio Optimization**" at 3:30p.m. in N638 Ross.ABSTRACT:

*Examines the optimal annuitization as well as the usual investment and consumption strategies of a utility-maximizing retiree facing a stochastic time of death under a variety of institutional pension and annuity arrangements.*

**Graduate Seminar**Yun Qiao will speak on "

**Using Hull-White Interest Rate Trees**" at 4:00p.m. in N638 Ross.ABSTRACT:

*Provide detailed procedures of building up the Hull-White tree and how it can be used. Further, we are going to discuss about the generalized Hull-White model and how to build up a recombining trinomial tree. Some examples of implementation of the model using market data would be provided.*

**Dissertation Subject Oral**Jinnan Liu will speak on "

**The Normalizing Constant for Discrete Graphical Models**" at 2:30p.m. in N638 Ross.ABSTRACT:

*We consider discrete graphical models represented by an undirected graph and assume that the sampling scheme for the contingency table is the multinomial distribution. We will be concerned with model selection within a Bayesian framework among the class of graphical models Markov with respect to an undirected graph G. We will see that finding the values of the posterior distribution for different graphs reduces to computing the normalizing constant of the posterior distribution.**It is well known that when the graph is non-decomposable, this normalizing constant has no closed form. The aim of our work is to give a Monte Carlo method to compute the normalizing constant for non-decomposable graphs.**With just 10 variables, there are total 245 possible graphs, and only less than 1 percent of them, i.e. approximately 12*1011 are decomposable models, the rest, more than 99% of them, are non-decomposable models. So it is easy to see that our method is important both for theoretical and practical reasons.*

**Dissertation Colloquium**Jin Wang will speak on "

**Numerical PDE Techniques for Personal Finance and Insurance Problems**" at 11:00a.m. in N627 Ross.ABSTRACT:

*In recent years, quantitative analysis has become an important tool for financial companies and financial institutions. Many problems in finance are modeled using stochastic differential equations (SDEs), which are solved by simulation techniques or converted into partial differential equations (PDEs). Under the framework of stochastic optimal control, some of these problems can be represented by the Hamilton-Jacobi-Bellman (HJB) equation, a highly nonlinear PDEs. Under special circumstances, analytical (closed form) solutions can be found. In some cases, approximate solutions are available. In general, however, it is difficult or impossible to find exact or approximate solutions in closed form and numerical methods become the only viable alternative.**This dissertation focuses on two problems related to personal finance. The first issue concerns the probability of s retired person exhausting his or her personal wealth, as known in the insurance literature the ruin probability. The second problem is closely related to the first one but viewed from a different angle; we are interested in the financial well being of an individual family with stochastic non-capital gain income using the optimal asset allocation and consumption approach. Both problems are formulated using the PDE representation.*

**PhD Defence**Ziting Zeng, York University , will defend her PhD Dissertation entitled "**Free Fields and Hermitian Representations of the Extended Affine Lie Algebra of Type A**" at 2:00p.m. in N627 Ross.

**Dissertation Subject Oral**Qian Tong will give a talk entitled "

**On Weighted Likelihood**" at 3:00p.m. in N627 Ross.ABSRACT:

*The proposal discusses motivation for developing adaptive weights approach. We will present a general framework in which a rough idea with regard to the thesis research is proposed. Relevant literature concerning adaptive weights is reviewed.*

**Dissertation Subject Oral**Tao Sun will speak on "

**Spatial-Temporal Modeling of Precipitation**" at 11:30a.m. in N638 Ross.ABSTRACT:

*Models of observed daily/weekly precipitation sequences are frequently used in climate change simulations because observed ground-based precipitation data are often inadequate in terms of its length, completeness or spatial coverage. Analyzing an attribute measured in both space and time is challenging work. More specifically, precipitation assumes non-negative values with a significant mass of probability at zero so that traditional spatial-temporal models are not valid. In this talk I will review historical approaches and speak about recent trends including Bayesian space-time model for multi-site precipitation simulation.*

**The Fundamental Series**Vera Fischer will give a talk on "

**The Husdorff Gap**" at 4:00p.m. in N638 Ross.ABSTRACT:

*In this talk we will see the construction of a Hausdorff gap, and discuss some applications to measure theory and analysis.*

**The Fundamental Series**Konstantin Zukker will give a talk on "

**Independent Component Analysis**" at 4:00p.m. in N638 Ross.ABSTRACT:

*Independent Component Analysis is a powerful tool for data and signal analysis. In this talk I introduce this technique and demostrate its application to the weak market efficiency hypothesis.*

**Dissertation Subject Oral**Vera Fischer will speak on "

**Cardinal Invariants of the Continuum. Bounding and Splitting Numbers**" at 3:30p.m. in N627 Ross.ABSTRACT:

*In 1874 Georg Cantor conjectured that every set of reals is either equipotent with the real line or is countable. Many other properties of the real line can be expressed in terms of size of families of sets. For example countably many meager sets do not cover the real line (Baire's category theorem); a countable family of sequences of natural numbers is eventually dominated by a single sequence. In each instance, there is a family equipotent with the continuum for which the respective property fails. Thus if CH does not hold, one may ask what is the minimal size of a family of meager sets that covers the real line, respectively what is the minimal size of a family of sequences which is not dominated by a single sequence.**In this talk I will consider these as well as other cardinal characteristics of the real line, and speak about the consistency of the bounding number , < the splitting number.*

**Dissertation Colloquium**Ziting Zeng will speak on "

**Free Fields and Hermitian Representations of the Extended Affine Lie Algebra of Type $A$**" at 10:30a.m. in N638 Ross.ABSTRACT:

*We use the idea of free fields to obtain highest weight representations for the extended affine Lie algebra $\widetilde{\frak{gl}_{2}(\bc_q)}$ and $\widetilde{\frak{gl}_{3}(\bc_q)}$, coordinatized by the quantum torus $\bc_q$ and go on to construct a contravariant hermitian form. We further give a necessary and sufficient condition such that the contravariant hermitian form is positive definite.*

**The Fundamental Series**Chuanbin Du, York University, will give a talk on "

**The Fractional Step Methods for Two-Dimensional Convection-Diffusion Equation**" at 4:00p.m. in N638 Ross.ABSTRACT:

*It is well known that the fractional step methods reduce multidimensional problems to a series of uncoupled one-dimensional problems which results in very low execution times and storage. In this talk, some fractional step methods are developed for solving two dimensional conveciton diffusion equation. Numerical experiments and simulations indicate the accuracy and efficiency of these methods.*

**The Fundamental Series**Qiang Guo, York University, will give a talk on "

**Wavelet Numerical Methods for Aerosol Dynamic Modelling**" at 4:00p.m. in N638 Ross.ABSTRACT:

*Aerosol modelling is very important in the atmosphere. The general aerosol dynamic equation describes the spatial-temporal evolution of the aerosol distribution on size, time and space, which is a nonlinear integro-partial differential equation including different processes. A splitting wavelet-Galerkin method is proposed for solving the general aerosol dynamic equation. The class of Daubechies wavelets is adopted in the Galerkin scheme. Numerical experiments and simulations are taken for both spatially homogeneous and inhomogeneous aerosol dynamics. Numerical tests indicate the developed method to be accurate and effective.*

**The Fundamental Series**Ghulam Anjum, Economics, York University, will speak on "

**Invoicing Strategies of Exporting Firms**" in N638 Ross.ABSTRACT:

*A monopolistic firm charges price in a way to maximize its profits. Profit maximizing objective needs to be addressed carefully if the firm is selling in international market. Selling in a foreign country is different from selling in the domestic market due to a number of factors. One of those factors is the exchange rate. Exporting firm sets price in any (own, importer's or a third country's) currency before the exchange rate is revealed. Choice of currency in the face of exchange rate uncertainty has repercussion on firm's profit. We shall look into invoicing strategies given the exchange rate uncertainty. Also the role of transportation cost and market share will be explored.*

**The Fundamental Series**Lily Moshe, York University, will speak on "

**Mathematics and Art: A case of Linear Perspective**" in N638 Ross.ABSTRACT:

*A fascinating fact about linear perspective is that given a picture with a one-point perspective, using geometry of similar triangles, one can easily locate a point in space, such that looking at the picture from that point will make the picture "pop out" in space and appear 3-dimensional! Being able to look at a painting or a photograph and to see it in 3-d - the way it was meant to be looked at - is powerful and changes one's appreciation of art and mathematics behind it. Using Grade 9 mathematics, I will derive the location of the "viewpoint". After that, we will look at posters in order to practise and appreciate the newly acquired skill.*This talk is based on a workshop entitled VIEWPOINTS 2005 which Ms Moshe attended last summer.

**PhD Dissertation**Shuqing Liang will defend his PhD Dissertation entitled "

**Thermal Stress Reduction inside InSb Crystal grown by Czochralski Method**" at 9:00a.m. in N638 Ross.

**Dissertation Subject Oral**Isabel Hubard will speak on "

**Twisting Operations and Chiral Polytopes**" at 10:00a.m. in N638 Ross.ABSTRACT:

*A chiral polytope is a non-reflexible polytope with maximal symmetry by rotation. Self-dual chiral polytopes can be properly or improperly. Properly self-dual chiral 4-polytopes can be twisted to obtain regular maps. A similar operation can be done for improperly self-dual chiral 4-polytopes which will give us chiral quotients of the Petrie-Coxeter polyhedra.*

**The Fundamental Series**Asrat Gashaw, York University, will give a talk entitled "

**Basic Concept and Application of Artificial Neural Network**" at 4:00p.m. in S205 Ross.ABSTRACT:

*Artificial Neural Network(ANN) is biologically inspired information processing machine that is designed to model the way in which human brain process information. The computing power of Neural Network drives from its massively parallel distributed structure and its capability to learn from experience. These training and learning features make ANN suitable for applications like pattern recognition, prediction, data mining, and many others. This presentation introduce the basic mathematical model of various types of ANNs and their learning algorithms with examples.*

**The Fundamental Series**Beatriz Zamora, York University, will speak on "

**Countable Dense Homogeneity with Lipschitz Functions**" at 4:30p.m. in S205 Ross.ABSTRACT:

*A separable topological space is said to be Countably Dense Homogeneous (CDH) if given any two countable dense subsets of the space, there exists a homeomorphism of the space which sends one onto the other. We consider two metric variants, namely iso-CDH and LCDH. We show that every separable Banach space is LCDH.*

**The Fundamental Series**David Brooke, Univerity of Toronto, will speak on "

**Quasicrystal Lie Algebras**" at 4:00p.m. in N638 Ross.ABSTRACT:

*I will discuss the ideas in a paper by J. Patera and R. Twarock about a class of infinite dimensional Lie algebras. The basis elements of such Lie algebras are in a 1-1 correspondence with the points of a quasicrystal. I will begin with a mathematical description of quasicrystals (aperiodic sets) and describe the Quasicrystal Lie algebras. I will discuss some of their properties and if time allows talk about some alternative definitions of Quasicrystal Lie algebras, which give slightly different properties. The talk is geared towards a general audience of mathematics graduates, although some general knowledge of Lie algebras may be useful.*

**The Fundamental Series**Naveen Vaidya will speak on "

**The Phase-field Method and Parallel Computation**" at 4:30p.m. in S205 Ross.ABSTRACT:

*We give an introduction to the phase-field method of solidification. Obtained equations are solved by the numerical method. A basic technique of parallel computation will be discussed with examples of three and nine processors. Results will be summarized and we will conclude with some directions for future work.*

**Dissertation Subject Oral**Guojun Gan will speak on "

**Dynamics of the Iterative Mean Clustering Model**" at 2:30p.m. in N627 Ross.ABSTRACT:

*Iterative Mean Clustering(IMC) algorithm is a very simple and incremental clustering algorithm. In this study, we investigate the IMC algorithm from a nonlinear dynamics point of view. Especially, we interested in using the bifurcation theory from dynamic systems to analyze the relations between the parameter $\sigma$ and the number of clusters of a data set.*

**MSc Thesis Defence**Yuanyi Pan will defend his Thesis entitled "

**From Scenario Association to Categorical Data Clustering**" at 3:30p.m. in N627 Ross.

**Dissertation Colloquium**Shuqing Liang will give speak on "

**Thermal Stress Reduction Inside InSb Crystal Grown by Czochralski Method**" at 10:00a.m. in N638 Ross.ABSTRACT:

*The industry's demand for large diameter and high quality single crystals grown by Czochralski (Cz) method has led to the extensive research for understanding the growth process and defects formation. Duo to the difficulty and the cost of experimental investigations, crystal growth modeling using computer simulation has attracted more attention in research and development of the Cz crystal growth community. This dissertation focuses on the growth of indium antimonide (InSb) crystals by the Cz method.**Based on previous work, we derive a semi-analytical model for predicting the temperature field and the thermal stress inside the InSb single crystals grown by the Cz method. A perturbation method for the temperature field is used for an arbitrary crystal shape using the Boit number, characterizing the lateral heat flux, as a expansion parameter. As a result, an explicit formula for calculating the thermal stress is obtained and its magnitude is shown to be dependent of the Boit number. Using the semi-analytical model, we identify the lateral heat flux and the crystal shape as two key factors in reducing the thermal stress inside the crystal. An optimal control approach for thermal stress reduction is proposed. Using the lateral heat flux as a control variable, we derive an optimal control formulation for minimizing thermal stress with a given crystal shape. Since thermal stress is also affected by the lateral shape of crystals during growth, the level of the stress can be reduced by growing crystals into a suitable shape. Using the lateral shape as a control variable, we derive a similar optimal control formulation for stress reduction. In both cases, von Mises stress is used as an objective function for the constrained optimization problem. Euler-Lagrange equations are derived using calculus of variations and the method of Lagrange multipliers. Various stress reduction strategies are explored by solving the Euler-Lagrange equations numerically. The comparison between the semi-analytical solution and the full two dimensional solution is given which shows that the semi-analytical model can be used to provide valuable insights.*

**The Fundamental Series**Rongsong Liu, York University, will speak on "

**Basic reproduction numbers for compartmental models of disease transmission**" at 4:00p.m. in S205 Ross.

**Thesis Colloquium**Yuanyi Pan will give his second talk on "

**From Scenario Association to Categorical Data Clustering**" at 1:00p.m. in N638 Ross.ABSTRACT:

*Most categorical clustering algorithms have no dependent variable and do not consider the decisive rule between variables when choosing the distance or dissimilarity function. In this thesis, we develop an algorithm that starts from the association rule between the dependent and the independent scenario. We define dissimilarity measure between independent scenarios based on this association and apply this measure to provide a simple and effective one-dimensional categorical clustering.*

**The Fundamental Series, Math Graduate Seminars**Lindsey Shorser, University of Toronto, will give a talk on "

**An Introduction to Lie Algebras**" at 4:00p.m. in S205 Ross.ABSTRACT:

*In this talk we will reconcile the algebraic and geometric notions of a Lie algebra. This will be accompanied by a look at root systems, some other structural aspects, and the connection between Lie groups and Lie algebras.*

**Dissertation Subject Oral**Qingwen Hu will give a talk entitled "

**On Second Order Differentiability w.r.t Parameters of Solutions to Delay Differential Equations with Adaptive Delays**" at 2:30p.m. in N627 Ross.ABSTRACT:

*In this paper we study second order differentiability of solutions w.r.t the parameters in a class of state-dependent delay differential equations, where the evolution of the delay is governed by a differential equation involving the state variable and the parameters. Using an extended version of the Uniform Contraction Principle for quasi-Banach spaces, we give a set of sufficient conditions for the second order differentiability of solutions w.r.t parameters in the space $W^{2,\infty}$ equipped with $W^{2, p}$ norm.*

**The Fundamental Series**Qingwen Hu will give a talk entitled "

**On Second Differentiability with Respect to Parameters of Solutions to Delay Differential Equations with Adaptive Delays**" at 4:30p.m. in S205 Ross.

**MSc Thesis Defence**Qiang Guo will defend her Thesis entitled "

**Wavelet Numerical Methods for Aerosol Dynamic Modelling**" at 1:30p.m. in N627 Ross.ABSTRACT:

*Aerosol modelling is very important to study and simulate the behavior of aerosol dynamics in the atmosphere. In this thesis, we consider the general aerosol dynamic equation which describes the spatial-temporal evolution of the aerosol distribution on size, time and space. A splitting wavelet-Galerkin method is proposed for solving the general aerosol dynamic equation. Numerical experiments and simulations are taken for both spatially homogeneous and inhomogeneous aerosol dynamics. Numerical tests indicate the developed method to be accurate and effective.*

**Dissertation Subject Oral**Rongsong Liu will speak on "

**Transmission Dynamics of Compartmental Models for Infectious Diseases**" at 3:30p.m. in N638 Ross.ABSTRACT:

*In this proposal, we study the transmission dynamics and spreading of vector (mosquito)-borne diseases, such as West Nile virus, with the objective to investigate factors that are responsible for thetransmission and possible outbreaks and to assess the control strategies for controlling of the spreading these diseases.*

**Survey Paper Presentation**Conrad Coleman will speak on "

**Modern Approaches to the Mathematical Modeling of Influenza: Model Formulation, Theory, and Numerical Results**" at 3:30p.m. in N627 Ross.ABSTRACT:

*This survey will introduce the unique characteristics that make modeling influenza a challenge, including its fast evolution rate and cyclical properties. Multiple-strain, evolving strain, and population-structure models will be proposed to deal with these characteristics. Recent advances in traditional compartmental models will also be covered, as well as models that incoporate quarantines and vaccinations. The presentation will focus on model formulation but provide some theoretical and numerical results as well.*

**The Fundamental Series**Jin Wang will give a talk entitled "

**A Model for Pricing the Pension Annuity**" at 4:00p.m. in S205 Ross.ABSTRACT:

*This paper wants to estimate the model parameters for a time-series of pension annuity payouts. The project will use the data provided by CANNEX Financial Exchanges and The IFID Centre-based in Toronto, Canada. The database contains pension annuity quotes for ages 55, 60, 65, 70, 75 and 80 for single males, females and a variety of joint-life scenarios and guarantee periods. We will use the statistics method to estimate all the parameters and then do the simulation to check how good the estimated parameters are.*

**The Fundamental Series**Isabel Hubard will speak on "

**Polytopes and their Symmetries**" at 4:30p.m. in S205 Ross.ABSTRACT:

*Regular polytopes were first studied by the Greeks. Using examples, we will see how the concept of regular polytope has changed over time. We will also examine the notions of convex and abstract polytopes, and consider some properties of regular, chiral, and self-dual polytopes.*

**The Fundamental Series**Qingling Zeng will give a talk entitled "

**Hypothetical Outbreak of Influenza-like Diseases During a Respiratory Season**" at 4:00p.m. in S205 Ross.ABSTRACT:

*We construct a deterministic compartmental model to discuss the importance for managing an emerging respiratory disease during a respiratory season of a key parameter: the total number of individuals who show some common symptoms of respiratory illnesses on the basis of clinical grounds and thus seek care in the health care setting. This parameter is essential for controlling the nosocomial transmission of the disease, and its value can be significantly reduced by vaccination against known respiratory diseases (such as influenza). Our simulation and analysis based on the available data during the 2003 SARS outbreak in Toronto show that without an effective vaccination coverage for Influenza and in the absence of a reliable and rapid test to distinguish such a disease from Influenza, quarantine may be the only feasible way for control, despite its huge societal costs.*

**Thesis Colloquium**Qiang Guo will speak on "

**Wavelet Numerical Methods for Aerosol Dynamic Modelling**" at 10:00a.m. in N638 Ross.ABSTRACT:

*Aerosol modelling is very important to study and simulate the behaviour of aerosol dynamics in the atmosphere. We consider the general aerosol dynamic equation with describes the spatial-temporal evolution of the aerosol distribution on size, time and space. A splitting wavelet-Galerkin method is proposed for solving the general aerosol dynamic equation. We adopt the class of Daubechies wavelets in the Galerkin scheme as the trial and weight functions based on its advantage of both compact support and orthonormality. Numerical experiments and simulations are taken for both spatially homogeneous and inhomogeneous aerosol dynamics.*

**The Fundamental Series**Sandeep Bhargava will give a talk on "

**Semisimple Modules over Associative Algebras**" at 4:00p.m. in S205 Ross.ABSTRACT:

*An associative algebra is a module, over a commutative ring, with an associative, bilinear multiplication. We peek into the category of associative algebras, examining some objects like endomorphism algebras, matrix algebras, and group algebras.**From here, we move to modules over a fixed associative algebra and zoom in on the important class of semisimple modules. Depending on time and interest, we will consider*

* a fundamental characterization of semisimple modules

* a uniqueness theorem on the structure of semisimple modules

* an equivalence of various finiteness conditions for semisimple modules

* semisimple algebras

* the structure theory of semisimple algebras*Knowledge of elementary ring theory and some familiarity with modules will be helpful.*

**MSc Thesis Defence**Jianfu Ma will defend his Thesis entitled "

**Scaling Behaviour of Lattice Vesicles in Three Dimensions**" at 2:00p.m. in N638 Ross.

**Survey Paper Presentation**Carmen Vicol will speak on "

**Independent Component Analysis in Finance**" at 11:00a.m. in N638 Ross.ABSTRACT:

*Independent Component Analysis(ICA) is a statistcal method in which the goal is to find a linear representation of non-Gausian data so that the components are statistically independent, or as independent as posible. After an overview of the method, an application to multivariate financial time series such as a portofolio of stocks will be considered.*

**Graduate Seminar**Yu Liu will speak on "

**Upper Bound Theorem for Convex Polytopes**" at 12:00p.m. in N638 Ross.ABSTRACT:

*Given the number of vertices and the dimension of convex polytopes, we will construct upper bound functions for the number of faces of the polytopes.*

**Survey Paper for Presentation**Mehdi Dadar will speak on "

**Image Smoothing and Edge Detection by Nonlinear Diffusion Equations**" at 11:30a.m. in N638 Ross.ABSTRACT:

*In the past two decades image processing has been a topic of great interest in mathematical society. This survey aims at discussing the main models and methods that are so far introduced in this area. The main focus will be on methods that are based on nonlinear diffusion equations to smooth static images and enhance edges in 2-D and 3-D.*

**Graduate Seminar**Rafael Molina-Rincon will speak on "

**Calculating the Ruin Probability using Path Integrals**" at 12:00p.m. in N638 Ross.ABSTRACT:

*The problem of deriving an analytic expression for the ruin probability is equivalent to solve a PDE of Fokker-Planck type. In my presentation, I will show how this PDE can be solved using Feynman path integrals.*

**Thesis Defence**Haibo Li will defend his Thesis entitled "

**Sequence Analysis in Polyadenylation Site of Human Gene**" at 2:00p.m. in N638 Ross.

**Graduate Seminar**Rafael Molina-Rincon will speak on "

**Calculating Ruin Probabilities using Fast Monte Carlo Simulations**" at 2:30p.m. in N638 Ross.ABSTRACT:

*The ruin probability is the probability that a fixed retirement consumption strategy will lead to financial insolvency, under stochastic investment returns, within a defined time horizon. In my presentation, I will introduce a fast Monte Carlo algorithm for calculating this probability, and discuss some numerical issues related to the calculation of the ruin probability.*

**Graduate Seminar**Nataliya Stoianov will speak on "

**The Picture Matroid for Elementary and General Polyhedral Scenes**" at 1:00p.m. in N638 Ross.ABSTRACT:

*I will present the proofs of theorems that answer the question of whether the given plane pictures of vertices and faces is a projection of a three-dimensional scene with plane faces. This result has a number of applications in computer vision, protein rigidity, parallel redrawing, location in sensor networks and formation control for autonomous agents.*

**Graduate Seminar**Liyi Wei will speak on "

**Waiting for Returns**" at 2:00p.m. in N627 Ross.ABSTRACT:

*In this paper we propose an alternative methodology for testing and calibrating diffusion processes for financial time-serries. The methodology focuses on the duality that exists between time and space for any given stochastic process. More specifically, we use the First Passage Time (FPT) which is the amount of time required by a stochastic process to travel a pre-specified distance. Thus, for example, we demonstrate that testing the hypothesis that (logarithmic) investment returns are independent and normally distributed is equivalent to testing the hypothesis that the FPT is Inverse Gaussian distributed.*

**Survey Paper Presentation**Rui Liu will speak on "

**Statistical Issues in cDNA Microarray Data Analysis**" at 12:30p.m. in N638 Ross.ABSTRACT:

*DNA microarray is part of a new and promising class of biotechnologies that allow the monitoring of expression levels in cells for thousands of genes simultaneously. In my presentation, I will roughly introduce some statistical issues in cDNA Microarray Data Analysis, including Experimental Design, Image Analysis, Graphical Presentation of Slide Data, Normalization, Quality Measures, Selecting Differentially Expressed Genes, and Classification.*

**Thesis Defence**Lu Ye will defend her Thesis entitled "

**Adsorbing Staircase Walks Models of Polmers in the Square Lattice**" at 2:00p.m. in N638 Ross.

**Graduate Seminar**Liyi Wei will speak on "

**Monte Carlo Application in Finance**" at 10:30a.m. in N627 Ross.ABSTRACT:

*When pricing options, stock price forcast via Monte Carlo simulations, precision can be improved by: Performing longer simulations, reducing the variance of the estimators. We also can use Quasi-Monte Carlo method to price the options. In this project, we will one Naive method, one method for variance reduction and quasi method and then compare them.*

**Graduate Seminar**Yu Liu will speak on "

**Standard Monomial**" at 12:30p.m. in N638 Ross.ABSTRACT:

*Using Plucker coordinates to construct a generate set of the polynomial ring over Z, and a Z-basis for the polynomial ring.*

**Thesis Colloquium -- 2nd Talk**Jianfu Ma will speak on "

**Scaling Behaviour of Lattice Vesicles in Three Dimensions**" at 1:30p.m. in N638 Ross.ABSTRACT:

*Biological membrane and polymer have attracted serious attention from mathematician and physicists in past decades. The self-avoiding random walk models not only capture the flexibility and connectivity of membranes and polymer molecule but also model the exclusion of one molecule to other molecules. In the physics literature, the study of models of lattice paths and vesicles were inspired by efforts to understand the entropic nature of polymers. Statistical mechanics enters the models by the definition of a partition function that ultimately gives rise to thermodynamic functions such as energy density, free energy and the specific heat. These quantities usually obey certain scaling laws close to critical points, exhibit through scaling exponents whose universal character connects the combinatorial models to physical phenomena. Lattice vesicles effectively models the entropic part of the free energy, and may describe the phase diagram and scaling behaviour around the critical points encountered in real physical systems.**This thesis is mainly concerned with the scaling behaviour of models of lattice vesicles around their tricritical points. We discuss three models of lattice vesicles : partition vesicles in two dimensions, rectangular vesicles in three dimensions and plane partition vesicles in three dimensions. We will analyze the phase diagram, estimate the asymptotic approximation, determine critical exponent and crossover exponent and prove that three models conform to tricritical scaling theory. Traditionally, perturbation expansion and contour integral methods have been employed in the asymptotic analysis of the generating function of lattice vesicles models. In partition vesicles and three-dimensional rectangular vesicles, we rely on the Euler-MacLaurin formula to approximate the asymptotic form of the generating function. The advantages is that error terms can be controlled and bounded, so that the nature of the approximation is well understood. In the plane partition vesicles, we will use Metropolis Monte Carlo method to simulate the model, employ the maximum likelihood method to fit data and Chi square to test the hypothesized model.*

**Thesis Colloquium -- 2nd talk**Haibo Li will speak on "

**Sequence Analysis in Polyadenylation Site on Human Gene**" at 2:00p.m. in N627 Ross.ABSTRACT:

*With the completion of the Human Genome Project (HGP) in 2003, billions of DNA sequence letters are generated. Also on the internet there are hundreds of RNA and protein databases available. Faster and more powerful analytic tools have to be used to analyze and discover the properties and functions of these DNA, RNA, and protein sequences.**In this talk DNA, RNA and proteins structures and the central rule - DNA -> RNA -> proteins of human genetics will be introduced as well as two elegant computational methods - TEIRESIAS and GENSCAN.**It has been proposed that the tail of human gene which is called 3' untranslated region (3' UTR) plays an important role in translational efficiency and gene expression. In this talk we will give the methods and results of the analysis for human 3' UTR. A Hidden Markov model is made based on the functional regions of 3' UTR.*

**Thesis Colloquium -- 2nd talk**Lu Ye will speak on "

**Absorbing Staircase Walks Models of Polymers in the Square Lattice**" at 3:00p.m. in N627 Ross.ABSTRACT:

*The generating functions of models of Dyck Paths are reviewed. Models of staircase walks are introduced and studied by transfer matrices and recursion relations. We will employ these methods to analyze models of adsorbing and inflating Dyck paths and staircase walks in the square lattice. The phase diagrams of these models contains tricritical points, and we shall consider the generating function close to this point.*

**PhD Defence**Jinman Kim will defend his PhD Dissertation entitled "

**Heat Equations on Lie Groups, Symmetric Spaces and Riemannian Manifolds**" at 2:00p.m. in N638 Ross.

**Graduate Seminar**Ntaliya Stoianov will speak on "

**Metrization Theorems**" at 12:30p.m. in N638 Ross.ABSTRACT:

*I will present the notions of local finiteness and paracompactness and give the proofs of two metrization therems: The Nagata-Smirnov Metrization Theorem and The Smirnov Metrization Theorem.*

**Thesis Colloquium**Qiang Guo will speak on "

**Wavelet Numerical Methods for Aerosol Dynamics**" at 10:30a.m. in N627 Ross.ABSTRACT:

*Atmospheric aerosol modelling is very important in environment science. In this thesis we will develop a wavelet numerical method for the aerosol dynamic PDEs model. We will focus on the study and prediction of the aerosol size distribution in size, time and space. The model involves different chemical and physical processes such as condensation and evaporation, coagulation, nucleation, source and removal as well as space diffusion and advection. Daubechies' wavelets are applied due to the fact that they have important properties of orthogonality and compact support. The wavelet-Galerkin algorithm is proposed, studied and applied for the problem.*

**Dissertation Colloquium**Jinman Kim will give speak on "

**Heat Equations on Lie Groups, Symmetric Spaces and Riemannian Manifolds**" at 2:00 p.m. in N638 Ross.ABSTRACT:

*We prove several existence and uniqueness theorems for Cauchy problems of heat equations on compact connected Lie groups, Heisenberg groups, noncompact Riemannian manifolds and homogeneous spaces of constant curvature.**For compact connected Lie groups, the Cauchy data are in the category of hyperfunctions, and we consider that our results are in the most general form in this kind of theorems.**Furthermore, we show that compactness or noncompactness of the underlying manifold is a crucial condition for uniqueness of the solutions of the heat equations. This provides a new insight on uniqueness of solutions of heat equations.**Finally, as applications, we obtain several results in harmonic analysis including Bochner-Godement type theorems and Schwartz type kernel theorems on compact Lie groups. These results guide us to apply the theory of heat equations to several aspects of harmonic analysis.**For the Heisenberg groups, we have qualitative properties of solutions of the heat equations which generalize some results of Widder for Lie groups.*

**Thesis Colloquium**Lu Ye will speak on "

**Absorbing Staircase Walks Models of Polymers in the Square Lattice**" at 1:30p.m. in N638 Ross.ABSTRACT:

*The generating functions of models of Dyck Paths are reviewed. Models of staircase walks are introduced and studied by transfer matrices and recursion relations. We will employ these methods to analyze models of adsorbing and inflating Dyck paths and staircase walks in the square lattice. The phase diagrams of these models contains tricritical points, and we shall consider the generating function close to this point.*

**Thesis Colloquium**Jainfu Ma will speak on "

**Scaling Behaviour of Lattice Vesicles in Three Dimensions**" at 2:30p.m. in N638 Ross.ABSTRACT:

*Biological membrane and polymer have attracted serious attention from mathematician and physicists in past decades. The self-avoiding random walk models not only capture the flexibility and connectivity of membranes and polymer molecule but also model the exclusion of one molecule to other molecules. In the physics literature, the study of models of lattice paths and vesicles were inspired by efforts to understand the entropic nature of polymers. Statistical mechanics enters the models by the definition of a partition function that ultimately gives rise to thermodynamic functions such as energy density, free energy and the specific heat. These quantities usually obey certain scaling laws close to critical points, exhibit through scaling exponents whose universal character connects the combinatorial models to physical phenomena. Lattice vesicles effectively models the entropic part of the free energy, and may describe the phase diagram and scaling behaviour around the critical points encountered in real physical systems.**This thesis is mainly concerned with the scaling behaviour of models of lattice vesicles around their tricritical points. We discuss three models of lattice vesicles : partition vesicles in two dimensions, rectangular vesicles in three dimensions and plane partition vesicles in three dimensions. We will analyze the phase diagram, estimate the asymptotic approximation, determine critical exponent and crossover exponent and prove that three models conform to tricritical scaling theory. Traditionally, perturbation expansion and contour integral methods have been employed in the asymptotic analysis of the generating function of lattice vesicles models. In partition vesicles and three-dimensional rectangular vesicles, we rely on the Euler-MacLaurin formula to approximate the asymptotic form of the generating function. The advantages is that error terms can be controlled and bounded, so that the nature of the approximation is well understood. In the plane partition vesicles, we will use Metropolis Monte Carlo method to simulate the model, employ the maximum likelihood method to fit data and Chi square to test the hypothesized model.*

**Thesis Colloquium**Haibo Li will speak on "

**Sequence Analysis in Polyadenylation Site of Human Gene**" at 2:30p.m. in 315/317 Petrie.ABSTRACT :

*With the completion of the Human Genome Project (HGP) in 2003, billions of DNA sequence letters are generated. Also on the internet there are hundreds of RNA and protein databases available. Faster and more powerful analytic tools have to be used to analyze and discover the properties and functions of these DNA, RNA, and protein sequences.**In this talk DNA, RNA and proteins structures and the central rule - DNA -> RNA -> proteins of human genetics will be introduced as well as two elegant computational methods - TEIRESIAS and GENSCAN.**It has been proposed that the tail of human gene which is called 3' untranslated region (3' UTR) plays an important role in translational efficiency and gene expression. In this talk we will give the methods and results of the analysis for human 3' UTR. A Hidden Markov model is made based on the functional regions of 3' UTR.*

**Thesis Defence**Francisco Kibedi will defend his Thesis entitled "

**Adding a Binary Modal Operator to Predicate Logic**at 1:00p.m. in N627 Ross.ABSTRACT:

*We define a new axiomatic system of modal logic, BM, by extending classical first order logic with the addition of the binary modal symbol "$\rhd "$ to the formal language (introduced as a definition in terms of a unary modal symbol, "$\Box "$), intended to simulate the informal provability predicate "$\vdash "$ of classical logic. We demonstrate with many examples how BM can be used to extend the capabilities of equational reasoning in first order logic, by proving equationally the BM counterparts of classical theorems. We show that the system is sound and complete with respect to appropriate Kripke semantics. We conclude by showing, using soundness and completeness, that the design intention is met: For any classical formulas $A$ and $B$, BM proves $A\rhd B$ iff $A\vdash B$ can be established classically.*

**Dissertation Subject Oral**Huilan Li will speak on "

**Algebra Structure on Grothendieck Groups of a Tower of Algebras**" at 1:00p.m. in N638 Ross.ABSTRACT:

*It is known that the Grothendieck group of the tower of symmetric group algebras have a self-dual graded Hopf algebra structure. In this work, we define two Grothendieck groups for the more general case where the underlying tower is of finitely dimensional algebras. Using representation theory, we discuss the algebra structure on the Grothendieck groups and show the duality between them.*

**Graduate Seminar**Evren Aydoner will give a talk entitled "

**Liapunov's Method for Autonomous Equations**" at 1:00p.m. in N638 Ross.ABSTRACT:

*I will discuss Liapunov's method for autonomous nonlinear differential equations and show how one can use this method to obtain stabilities without explicitly solving differential equations.*

**Thesis Colloquium**Francisco Kibedi will speak on "

**Adding a Vinary Modal Operator to Predicate Logic**" at 12:30p.m. in N627 Ross.ABSTRACT:

*We define a new axiomatic system of modal logic, BM, by extending classical first order logic with the addition of the binary modal symbol "$\rhd "$ to the formal language (introduced as a definition in terms of a unary modal symbol, ``$\Box "$), intended to simulate the informal provability predicate ``$\vdash "$ of classical logic. We demonstrate with many examples how BM can be used to extend the capabilities of equational reasoning in first order logic, by proving equationally the BM counterparts of classical theorems. We show that the system is sound and complete with respect to appropriate Kripke semantics. We conclude by showing, using soundness and completeness, that the design intention is met: For any classical formulas $A$ and $B$, BM proves $A\rhd B$ iff $A\vdash B$ can be established classically.*

**Graduate Seminar**Evren Aydoner, York University, will give a talk entitled "

**A Hopt Bifurcation in a Predator-Prey Competition Model**" at 1:00p.m. in N638 Ross.ABSTRACT:

*I will analyze a specific predator-prey model, first finding and analyzing the equilibrium points of the system and then determining when a hopt bifurcation occurs in the system.*

**Dissertation Subject Oral**Ziting Zeng will speak on "

**Representations of Lie Algebras Coordinatized by Quantum Tori**" at 2:00p.m. in N627 Ross.ABSTRACT:

*We use the idea of free fields to construct highest weight representations for the extended affine Lie algebra $\widetilde{\frak{gl}_{2}(\bc_q)}$ coordinatized by the quantum torus $\bc_q$ and go on to show that the hermitian form is contravariant. We further give a necessary and sufficient condition so that the contravariant hermitian form is positive definite.*The syllabus of the exam is available for perusal in N519 Ross.

**Dissertation Subject Oral**Mihai Beligan "

**Schubert Polynomials and Generalized Littlewood-Richardson Coefficients**" at 1:30p.m. in N627 Ross.ABSTRACT:

*Indexed by permutations in $S_n$, these polynomials form a homogeneous basis for Z[x_1,x_2, . . .]. Of interest are the Generalized Littlewood-Richardson Coefficients, that is, the coefficients in the expansion of a product of Schubert polynomials in terms of the basis of Schubert polynomials. These coefficients have applications in enumerative geometry--they count the number of points in intersections of certain varieties, and combinatorics--they are conjectured to be counting the number of chains from $w$ to $u$ in the Bruhat order on permutations subject to some restrictions imposed by the permutation $v$. We review partial results that exist for the problem of finding a combinatorial construction for these coefficients and hint at what we try to achieve.*The syllabus of the exam is available for perusal in N519 Ross.

**Dissertation Oral Examination**Yuriy Kazmerchuk will give a talk on "

**Pricing of Derivatives in Security Markets with Delayed Response**" at 10:30a.m. in N627 Ross.ABSTRACT:

*During the last three decades there has been a booming development in modeling of financial security markets, and a large number of models have been introduced following the pioneering work of Black and Scholes in 1973 on option pricing. One of the key assumptions in the Nobel-prize winning work of Black and Scholes is that the parameter of volatility is a constant. This controversial assumption generates a significant development of stochastic volatility models. Unfortunately, most stochastic volatility models constitute incomplete security markets, an inconvenient feature for the purpose of option pricing.**My study of security markets is aimed to develop a more general class of viable stochastic volatility models that constitute complete security markets. We allow a delayed response in the diffusion model for the price of the underlying asset, which may be a stock, an index or any other type of equity. The concept of delayed response is not new and it was introduced in the finance literature as a plausible explanation for abnormal behavior of equity returns. There is also statistical evidence in support of the past-dependence of equity returns.**The subject of this dissertation is a theory of stochastic delay differential equations with applications to finance. In particular, we study stock price modeling and option pricing in the markets with delayed response. We introduce several continuous-time models for stochastic volatility with delay connected with the GARCH model, the widely used econometric model. In these models the time delay is considered constant. We illustrate the viability of the models by looking at the simulated implied volatility structure. We introduce a general option pricing approach for markets with delayed response. For those equations for which it is hard to find analytic solutions, we provide a numerical scheme. We also address the important issue of parameters estimation.**Based on a stock market data, we show that there is a high variability of the estimated delay. In order to explain this, we extend the aforementioned models to include a state-dependent delay. As an essential tool, we derive a discrete-time approximation result for the so-called stochastic state-dependent delay differential equations. We show the influence of state-dependence of the delay on option pricing through a variety of U-shaped implied volatility plots.*

**Dissertation Subject Oral**Jin Wang will speak on "

**Applications of Numerical PDE Techniques in Solving Personal Finance and Insurance Problem**" at 10:00a.m. in N627 Ross.ABSTRACT:

*In this proposal, first of all, a general literature is reviewed, and then we present two applications of numerical PDE solution techniques in solving the finance problem.**The first application is about implementation of numerical PDE solution techniques to compute the \emph{probability of lifetime ruin }which is the probability that a fixed retirement consumption strategy will lead to financial insolvency under stochastic investment returns and lifetime distribution. We compare the estimation results from the PDE to those from various moment matching and other approximation techniques that have been proposed in the literature. Then we change the distribution of outcomes to reduce the lifetime ruin probability, but at a zero financial economic cost. We put it in the section of optimal retirement collars, where we give the PDE representation and simulation results.**The second application is to solve the stochastic optimal control problems in finance by using the numerical PDE method. We mainly discuss the numerical method through the section of investment \& consumption with insurance and human capital: A continuous -time perspective.*

**Dissertation Subject Oral**Shuqing Liang will speak on "

**Control of Thermal Stress inside Crystal for InSb Czochralski Growth**" at 10:00a.m. in N627 Ross.ABSTRACT:

*A semi-analytical model is used to calculate the temperature field and thermal stress inside the crystal. We will talk about how to use the model to investigate the sensitivity of the thermal stress inside the crystal with respect to several control parameters and find the optimal solutions in the sense the index of crystalline defects is minimized for the given crystal shape and heat transfer between the crystal and the gas. Finally we will talk about the models used to calculate the heat fluxes and flow pattern in the melt.*

**Graduate Seminar**Francisco Kibedi will give a talk entitled "

**The Semantics of M3 and the Main Conservation Requirement**" at 1:00p.m. in N638 Ross.ABSTRACT:

*This talk will be a continuation of last week's examination of the modal system of Logic, M3, but this time our focus will shift from the syntax of M3 to its semantics. We have seen how to derive formal M3-proofs of the M3 counterparts of classical formal theorems; we will show that this technique for proving a classical result is indeed valid. Our principal tool will be the "Main Conservation Requirement", the proof of which depends on the semantics (Kripke semantics) of M3 which we outline first. We will state the soundness and completeness of M3 with respect to its semantics and use these connections to prove the Main Conservation Requirement.*

**Graduate Seminar**Francisco Kibedi will give a talk entitled "

**The Syntax of the Modal System of Logic, M3**" at 1:00p.m. in N638 Ross.ABSTRACT:

*The system of logic called M3 is a "modal extension" of classical first-order predicate logic. It is a logic arrived at by adding a new symbol to the language of classical logic -- namely, the modal symbol (drawn as a box) which is intended to simulate the classical metatheoretical provability predicate (drawn as a turnstyle). One of the main purposes of M3 is to extend the capacity of equational reasoning, a technique which has become quite popular and has found application in various areas (e.g., theoretical computer science). Many times in the classical setting, a "formal" equational proof needs to be split into disjoint components connected by "informal" or metatheoretical reasoning--this disconnectedness, apart from detracting from the formal and easy flow of the proof, introduces a source of possible error. We will show how to find "fully connected" equational proofs of classical formal theorems in the modal M3 setting that are counterparts of disconnected equational proofs from the classical setting, after describing more in the detail the syntax of M3. Concrete examples will also be given.*

**Dissertation Colloquium**Yuriy Kazmerchuk, York University, will give speak on "

**Pricing of Derivatives in Security Markets with Delayed Response**" at 2:30p.m. in N627 Ross.ABSTRACT:

*During the last three decades there has been a booming development in modeling of financial security markets, and a large number of models have been introduced following the pioneering work of Black and Scholes in 1973 on option pricing. One of the key assumptions in the Nobel-prize winning work of Black and Scholes is that the parameter of volatility is a constant. This controversial assumption generates a significant development of stochastic volatility models. Unfortunately, most stochastic volatility models constitute incomplete security markets, an inconvenient feature for the purpose of option pricing.**My study of security markets is aimed to develop a more general class of viable stochastic volatility models that constitute complete security markets. We allow a delayed response in the diffusion model for the price of the underlying asset, which may be a stock, an index or any other type of equity. The concept of delayed response is not new and it was introduced in the finance literature as a plausible explanation for abnormal behavior of equity returns. There is also statistical evidence in support of the past-dependence of equity returns.**The subject of this dissertation is a theory of stochastic delay differential equations with applications to finance. In particular, we study stock price modeling and option pricing in the markets with delayed response. We introduce several continuous-time models for stochastic volatility with delay connected with the GARCH model, the widely used econometric model. In these models the time delay is considered constant. We illustrate the viability of the models by looking at the simulated implied volatility structure. We introduce a general option pricing approach for markets with delayed response. For those equations for which it is hard to find analytic solutions, we provide a numerical scheme. We also address the important issue of parameters estimation.**Based on a stock market data, we show that there is a high variability of the estimated delay. In order to explain this, we extend the aforementioned models to include a state-dependent delay. As an essential tool, we derive a discrete-time approximation result for the so-called stochastic state-dependent delay differential equations. We show the influence of state-dependence of the delay on option pricing through a variety of U-shaped implied volatility plots.*

**Survey Paper Presentation**Stephanie Akers will give a talk on "

**Strong Monomorphisms and Strong Epimorphisms in Procategories**" at 12:30p.m. in N638 Ross.ABSTRACT:

*Shape theory is an exciting extension of homotopy theory for general topological spaces. In this talk, some of the foundations of shape theory will be introduced. The notion of a pro-category will be defined and the concept of strong monomorphisms and strong epimorphisms in these pro-categories will be examined. Further characteristics of these strong monomorphisms and strong epimorphisms will then be explored.*

**Survey Paper Presentation**Mark Riczu will give a talk entitled "

**Sphere Packing II: A Survey of Hales' Proof of the Kepler Conjucture on the Optimal Packing of Equal Spheres in 3 Dimensions or What's the Best Way to Stack Oranges?**" at 11:00a.m. in N638 Ross.ABSTRACT:

*This talk will give a general overview of Thomas Hales 1998 proof of the Kepler Conjecture wherein he resolves the 3-demensional sphere packing problem. This result is a veritable tour-de-force of mathematical ingenuity; it includes over 250 pages of mathematics and 3 gigabytes of computer code and data.*

**Dissertation Colloquium**Daniel Beamish will give speak on "

**50 Years Later: A Neurodynamic Explanation of Fitts' Law**" at 11:30a.m. in N627 Ross.ABSTRACT:

*Fitts' law is a robust model of psychomotor behavior developed by applying the information theory of physical communication systems to the human sensory-motor system. However, the information-theoretic development of Fitts' law is incomplete: the experimental observation of non-zero and possibly negative Y-intercepts in the linear relationship between movement time and Index of Difficulty (ID) can not be explained within the theory. Furthermore, this law is known to breakdown when ID is small. We show that both of these phenomenon can be explained as consequences of delay within the nervous system. By introducing delayed feedback into the Vector Integration to Endpoint (VITE) circuit of Bullock and Grossberg, we show that the Shannon formulation of Fitts' law is only an approximation to a more general relationship in which an approximately linear relationship with non-zero Y-intercept holds between movement time and ID when movement times are large relative to the delay. The slope and Y-intercept are determined by two parameters: the delay $\tau$, and the relaxation rate $\alpha$ of the circuit's negative feedback loop. As the movement time approaches the scale of the delay, a non-linear breakdown occurs and the movement time approaches a limiting value of $2\tau$. A re-analysis of data from the literature suggests this model is at least as good as, or better than, linear regression in Shannon Index of Difficulty. Furthermore, it provides an indirect way to measure delay within the nervous system from the speed-accuracy trade-off alone.*

**Dissertation Subject Oral**Daniel Beamish will speak on "

**Neural Network Models of Motor Control**" at 10:00a.m. in N627 Ross.ABSTRACT:

*I will talk about the development of Fitts law from an information-theoretic and experimental point of view, and neuraldynamic models of motor control.*SYLLABUS: Neural Networks; Dynamical Systems and Delay Dynamical Systems; Oscillation Theory of Linear Systems; Information Theory; Fitts Law.

**Graduate Seminar**Gul Oya Ege, York Univeristy, will give a talk entitled "

**Credit Risk Models for Trading Portfolios**" at 1:00p.m. in N638 Ross.ABSTRACT:

*Credit risk arises due to the possibility of a change in the credit quality of a counterparty. In extreme cases it is the risk that a counterparty will be unable to meet its obligations, also called default. Because there are many types of counterparties and many different types of obligations-from auto loans to derivatives transactions-credit risk takes many forms. So there are many ways to manage it. For the purpose of this talk, I will focus on rating-based models in the context of trading derivatives. This presentation explains how to construct the forward distribution of the values, how to use the resulting distribution to estimate risk and how to compare the calculated results with the observed results within a back testing methodology. This work arises from an internship in the financial engineering diploma program.*

**PhD Defense**Baifang Xing, York University, will defend his PhD Dissertation "Best Quadrature Formula, Mixture of Normals Approximation and State-Space Models" at 9:30a.m. in N638 Ross.

**Dissertation Subject Oral**Nikolai Slobodianik will speak on "

**Statistical analysis of stem cell development**" at 10:00a.m. in N638 Ross.ABSTRACT:

*Stem cells have the potential to serve as renewable source of tissue-specific cells in clinical tissue-replacement therapies. The key limitation to the widespread use of stem cells in such applications is the lack of understanding of precise mechanisms driving proliferation and differentiation properties in vitro of the stem cell compartment.**Although a large number of deterministic and stochastic models of stem cell development appeared in the literature over the past 40 years, none remained unquestionable and there is still need for careful modeling addressing particular issues and hypothesizes.**Typical population of stem cells is highly heterogeneous, consisting apart from stem cells of cells passing the differentiation stage as well as differentiated towards various lineages. Biologically, it is fairly difficult to disentangle properties of different cell types in the dynamic mixed population.**We propose a multitype Markov branching process model to imitate temporal development of a general stem cell population. Fundamental parameters such as rates of proliferation and differentiation are obtained by maximum likelihood estimation. Being a relatively crude approximation of real processes, the model could be extended to address intrinsic complexity of a biological system and potentially account for events on molecular level.*The syllabus of the exam is available for perusal in N519 Ross.

**Graduate Seminar**Alena Kabialka will give a talk entitled "

**Combinatorial Species**" at 1:00p.m. in N638 Ross.ABSTRACT:

*I will talk about Species giving main definitions and examples; the structures of species and the way the structures are transported by bijections between their underlying sets; generating function and connection between species and generating functions.*

**Thesis Colloquium**Yuanyi Pan will speak on "

**Gene Expression Data Mining**" at 10:30a.m. in N638 Ross.ABSTRACT:

*I will talk about gene expression data processing from the viewpoint of a graduate student in mathematics: Topics include what gene expression data are, how these data are processed and what the challenges are. The focus of this talk is applications of gene expression data and the relevant methods and literatures, with emphasis on clustering analysis.*

**Dissertation Colloquium**Baifang Xing will speak on "

**Best Quadrature Formula, Mixture of Normals Approximation and State-Space Models**" at 9:30a.m. in N638 Ross.ABSTRACT:

*State-space models have been a powerful tool for modeling and forecasting serially correlated data, because they are based on a structural analysis of the data. The components that contribute tomodeling different aspects of the data, such as trend, seasonal,together with the effects of explanatory variables andinterventions, can be specified separately before being assembledinto one state-space model. Because of the presence of latent (orstate) variables, integration evaluation is generally inevitablein likelihood-based statistical inference. This thesis consistsprimarily two parts: the first concentrating on computationalaspects and the other on statistical aspects.**In the first part, we develop a new numerical approximationmethod, called the Best Quadrature Formula (BQF), for integrationevaluation. Adapted from the BQF to accommodate different featuresof integrands, we propose a smoothed variant of BQF, called Smoothed Best Quadrature Formula (SBQF). Motivated by the SBQF, we further develop an algorithm in the form of mixture of nomalsapproximation (MoNA), which is particularly suitable to deal with the calculation of density functions, such as the Kalman filter density, at different smoothing levels.*

**PhD Dissertation**Qing Shao will defend her PhD Dissertation, "

**Estimating the Number of Clusters in Regression Clustering**" at 10:00a.m. in N638 Ross.ABSTRACT:

*Regression clustering is an important model-based clustering tool with wide applications in a variety of disciplines. It discovers and reconstructs the hidden structure for a data set which is believed to be a random sample from a population comprising of a fixed, but unknown, number of sub-populations each of which is characterized by a class-specific regression hyperplane. A fundamental problem, as well as a preliminary step in most of clustering techniques including regression clustering is to determine the underlying ``true'' number of clusters in the data set.**We attempt to tackle this problem using model selection techniques, in particular the information-based approach. Thus model-selection based procedures are proposed to estimate the number of regression hyperplanes for data with either continuous or binary response variable respectively. And for the former case, we also propose an M-estimator based robust-augmented criterion to deal with abnormality of the data. We present the asymptotic results of the proposed procedures, which are obtained under the framework of classification likelihood approach. Finally their small sample performance is illustrated by examples from simulation studies and data analysis.*

**Survey Paper Presentation**Xingdong Feng will give a talk entitled "

**Survey on Model Averaging Methods**" at 2:00p.m. in N638 Ross.ABSTRACT:

*In classical model selectionn procedure, one "best" model is selected according to some model selection criterion such as MSE or AIC. However, the underlying assumption is that the true model is included in the set of all candidate models. Therefore, the model uncertainty is not addressed. To overcome this, model averaging methods are proposed and studied in the literature.**In this presentation, Bayesian model averaging methods and stacking methods are reviewed. Bayesian model averaging(BMA) is proposed in (Leamer,1978) and several different to realize it will be discussed in the presentation. Compared to BMA, stacking is new and the complete theory has not been established. It is based on cross-validation. We will review the stacking technique in the presentation as well.*

**Graduate Seminar**Alena Kabialka, York University, will give a talk entitled "

**Polya Theory**" at 1:00p.m. in N638 Ross.ABSTRACT:

*Polya Theory is based on a simple idea to count collections of objects possessing some symmetry, for example counting the number of necklaces with n beads of c possible colors. I will speak about group acting on a set, provide necessary definitions and theorem.*

**Graduate Seminar**Sam Cherid will give a talk entitled "

**Mathematical Background in Quantum Mechanical Scattering**" at 10:00a.m. in N638 Ross.ABSTRACT:

*In this study we consider the quantum mechanical problem of scattering of a charged particle by a potential field, we look at the partial wave analysis of scattering by a short-ranged potential and a long-ranged known as Coulomb potential.*

**Graduate Seminar**Sam Cherid will give a talk entitled "

**Green's Functions and Born Approximations**" at 11:00a.m. in N638 Ross.ABSTRACT:

*We look at this integral equation methods which is a general technique used to solve linear partial differential equations in the presence of a source term , and the important approximation that can be made in order to find a solution valid in the asymptotic regime for relatively weak Interactions .*

**Dissertation Colloquim**Qing Shao will give speak on "

**Estimating the Number of Clusters in Regression Clustering**" at 10:00a.m. in N627 Ross.ABSTRACT:

*Regression clustering is an important model-based clustering tool with wide applications in a variety of disciplines. It discovers and reconstructs the hidden structure for a data set which is believed to be a random sample from a population comprising of a fixed, but unknown, number of sub-populations each of which is characterized by a class-specific regression hyperplane. A fundamental problem, as well as a preliminary step in most of clustering techniques including regression clustering is to determine the underlying ``true'' number of clusters in the data set.**We attempt to tackle this problem using model selection techniques, in particular the information-based approach. Thus model-selection based procedures are proposed to estimate the number of regression hyperplanes for data with either continuous or binary response variable respectively. And for the former case, we also propose an M-estimator based robust-augmented criterion to deal with abnormality of the data. We present the asymptotic results of the proposed procedures, which are obtained under the framework of classification likelihood approach. Finally their small sample performance is illustrated by examples from simulation studies and data analysis.*

**Dissertation Oral Examination**Debora Di Caprio, York University, will give a talk entitled "

**Selections, Orderability and Complete Systems**" at 12:30p.m. in N638 Ross.ABSTRACT:

*In 1983, Deutsch and Kenderov give some necessary and sufficient conditions for a convex-valued multifunction to have continuous approximations. Inspired by Deutsch and Kenderov's result, we introduce and characterize coherent multifunctions. We investigate the relationship between lower semicontinuity and coherence, providing several examples. We then interpolate the lemmas behind the well-known Michael results on continuous selections. In doing so, we define a suitable and quite natural convex structure on every topological space, not just on metrizable ones. We produce a selection theorem stronger than Michael's selection theorem, both the convex-valued versions and the zero-dimensional one, in general considered as two independent cases in the literature.**In 1998, Bertacchi and Costantini obtain some conditions equivalent to the existence of continuous selections for the Wijsman hyperspace of ultrametric Polish spaces. We introduce a new class of hyperspace topologies, the macro-topologies. Both the Wijsman topology and the Vietoris topology belong to this class. We show that subject to natural conditions, the base space admits a closed order such that the minimum map is a continuous selection for every macro-topology. In the setting of Polish spaces, these conditions are substantially weaker than Bertacchi and Costantini's ones. In particular, we conclude that Polish spaces satisfying these conditions can be endowed with a compatible order and that the minimum function is a continuous selection for the Wijsman topology, just as it is for [0, 1]. This also solves a problem implicitly raised in Bertacchi and Costantini's paper.**Finally, we introduce and study some completeness properties for systems of open coverings of a given topological space. A Hausdorff space admitting a system of cardinality k satisfying one of these properties is of type G_k.In connection with these properties, we define several new variants of the Cech number and use elementary submodels to determine further results. As an application we give estimates for both the tightness and the Lindelof number of a generic upper hyperspace. Two recent results of Costantini, Hola and Vitolo on the tightness of co-compact hyperspaces follow from ours as corollaries.*

**Presentation**Armando Fabia will speak on "

**A Queueing Application of the Wiener-Hopf Factorization**" at 1:00p.m. in N638 Ross.ABSTRACT:

*The paper shows the close connection between queueing theory and random walks. The most important feature of this connection is the Wiener-Hopf factorization, which led to the simplification of queueing theory. The factorization is applied to the M/M/1 queue.*

**PhD Thesis Defence**Daniel Deaconu, will give a talk entitled "

**On LCA Groups and Epimorphisms of Topological Groups**" at 12:30p.m. in N638 Ross.ABSTRACT:

*A very important class of Hausdorff topological groups is represented by the locally compact abelian groups (LCA). The most important theorem in the theory of LCA groups is Pontryagin's Duality which states that any LCA group is isomorphic in the category of Hausdorff topological groups with its bidual when the dual groups are the groups of continuous group morphisms into the unitary circle with the compact-open topology. Associated to any abelian topological group is the weak topology induced.**By its characters, known as the Bohr topology. Relating an LCA group with its Bohr topology is a very important theorem known as Glicksberg's Theorem that states that the LCA topology and the Bohr topology associated to it determine the same compact subsets of the considered group. Any group topology on an abelian group that determines the same compact subsets of the group as the Bohr topology associated to it will be said to respect compactness. Using Pontrygin's Duality and Glicksberg's Theorem as our main ingredients we look at the following problem: given an abelian group G and a group of morphisms of groups from G into the unitary circle T, when is the considered group of morphisms the group of all characters for an LCA topology on G? The solution to this problem will naturally lead to considering certain types of refinements of topologies. A general study of these refinement will be presentes both in the category of topological spaces and topological groups.**For the refinements considered in the category of topological groups, duality type theorems and Ascoli type theorems will be given. The Duality theorems prezented are satisfied by very important classes of groups that respect duality and satisfy Pontryagin's Duality, among these classes are products of LCA topologies and complete abelian groups that have a neighbourhood base around the identity consisting of open subgroups. Compactness in the category of topological groups is studied and a new proof of a theorem known as Goto's Theorem is given. Also, a topological proof of Glicksberg's Theorem is given. Another important problem discussed is known as the cowellpowerdness problem for Hausdorff topological groups. It is known that epimorphisms in the category of Hausdorff topological groups need not have dense image and the cowellpowerdness problem asks wether the class of extensions of a topological group for which the embeding is epimorphism is a set or a proper class.**We will present new examples of epimorphisms that don't have dense image and generalizations of a few related problems are presented.*

**Dissertation Colloquium**Daniel Deaconu will speak on "

**On LCA Groups and Epimorphisms of Topological Groups**" at 1:30p.m. in 215 Bethune College.ABSTRACT:

*A very important class of Hausdorff topological groups is ~represented by the locally compact abelian groups (LCA). The most important theorem in the theory of LCA groups is Pontryagin's Duality which states that any LCA group is isomorphic in the category of Hausdorff topological groups with its bidual when the dual groups are the groups of continuous group morphisms into the unitary circle with the compact-open topology. Associated to any abelian topological group is the weak topology induced.**By its characters, known as the Bohr topology. Relating an LCA group with its Bohr topology is a very important theorem known as Glicksberg's Theorem that states that the LCA topology and the Bohr topology associated to it determine the same compact subsets of the considered group. Any group topology on an abelian group that determines the same compact subsets of the group as the Bohr topology associated to it will be said to respect compactness. Using Pontrygin's Duality and Glicksberg's Theorem as our main ingredients we look at the following problem: given an abelian group G and a group of morphisms of groups from G into the unitary circle T, when is the considered group of morphisms the group of all characters for an LCA topology on G? The solution to this problem will naturally lead to considering certain types of refinements of topologies. A general study of these refinement will be presentes both in the category of topological spaces and topological groups.**For the refinements considered in the category of topological groups, duality type theorems and Ascoli type theorems will be given. The Duality theorems prezented are satisfied by very important classes of groups that respect duality and satisfy Pontryagin's Duality, among these classes are products of LCA topologies and complete abelian groups that have a neighbourhood base around the identity consisting of open subgroups. Compactness in the category of topological groups is studied and a new proof of a theorem known as Goto's Theorem is given. Also, a topological proof of Glicksberg's Theorem is given. Another important problem discussed is known as the cowellpowerdness problem for Hausdorff topological groups. It is known that epimorphisms in the category of Hausdorff topological groups need not have dense image and the cowellpowerdness problem asks wether the class of extensions of a topological group for which the embeding is epimorphism is a set or a proper class.**We will present new examples of epimorphisms that don't have dense image and generalizations of a few related problems are presented.*

**Dissertation Colloquium**Debora DiCaprio will give speak on "

**Selections, Orderability and Complete Systems Formally Convex-Valued Multifunctions, Minimum Maps and the Tightness of Upper Hyperspaces**" at 12:30p.m. in N638 Ross.ABSTRACT:

*In 1983, Deutsch and Kenderov give some necessary and sufficient conditions for a convex-valued multifunction to have continuous approximations. Inspired by Deutsch and Kenderov's result, we introduce and characterize coherent multifunctions. We investigate the relationship between lower semicontinuity and coherence, providing several examples. We then interpolate the lemmas behind the well-known Michael's results on continuous selections. In doing so, we define a suitable and quite natural convex structure on every topological space, not just on metrizable ones. We produce a selection theorem stronger than Michael's selection theorem, both the convex-valued versions and the zero-dimensional one, in general considered as two independent cases in the literature.**In 1998 Bertacchi and Costantini obtain some conditions equivalent to the existence of continuous selections for the Wijsman hyperspace of ultrametric Polish spaces. We introduce a new class of hyperspace topologies, the macro-topologies. Both the Wijsman topology and the Vietoris topology belong to this class. We show that subject to natural conditions, the base space admits a closed order such that the minimum map is a continuous selection for every macro-topology. In the setting of Polish spaces, these conditions are substantially weaker than the ones given by Bertacchi and Costantini. In particular, we conclude that Polish spaces satisfying these conditions can be endowed with a compatible order and that the minimum function is a continuous selection for the Wijsman topology, just as it is for $[0, 1]$. This also solves a problem implicitely raised in Bertacchi and Costantini's paper.**Finally, we introduce and study some completeness properties for systems of open covering of a given topological space. An Hausdorff space admitting a system of cardinality k satisfying one of these properties is of type G_k. In connection with these properties, we define several new variants of the Cech number and use elementary submodels to determine further results. In particular, we introduce the notions of M-hull and M-network, where M is an elementary submodel. As an application of the results obtained, but again using the technique of elementary submodels, we give estimates for both the tightness and the Lindelof number of a generic upper hyperspace. Two recent results of Costantini, Hola and Vitolo on the tightness of co-compact hyperspaces follow from ours as easy corollaries.*

**Dissertation Subject Oral**Jinman Kim will speak on "

**Harmonic Analysis on Lie Groups and Homogeneous Spaces**" at 10:00a.m. in N501 Ross.ABSTRACT:

*Results on solutions of heat equations, integral representations of distributions and hyperfunctions are given on compact Lie groups, Heisenberg groups, Riemannian manifolds and homogeneous spaces. For compact Lie groups, we have the following results:*

1. Hyperfunctions are boundary values of heat equations satisfying some exponential growth conditions.

2. Solutions of heat equations satisfying some exponetial growth conditions are shown to be unique.

3. Integral representations of positive solutions of heat equations are given.

4. A characterization of central hyperfunctions is given. (This is the analogue of the Schwartz-Godement theorem for compact Lie groups.)

5. An analogue of Schwartz' kernel theorem for bilinear hyperfunctions is established.

6. An integral representation of translation-invariant positive definite bilinear hyperfunctions is obtained.*For Heisenberg groups, we give an integral representation of positive definite solutions of heat equations. Uniqueness of solutions of heat equations on complete Riemannian manifolds with Ricci curvature bounded below, hyperbolic spaces and unit spheres are presented.*A copy of the syllabus of the exam is available in Primrose's office.

**Survey Paper Presentation**Isabel Hubard will give a talk entitled "

**Self-Dual Chiral Polytopes**" at 10:00a.m. in N501 Ross.ABSTRACT: Self-dual regular polytopes posseses a polarity, that is, an involutory duality. We´ll discusse two families of self-dual chiral maps and show that self-dual chiral polytopes of odd rank posseses a polarity. We´ll also give an example of a self-dual chiral 4-polytopes that doesn´t posses a polarity.

**PhD Defense**Fernando Hernandez-Hernandez will defend his PhD Dissertation entitled "

**Topologies on Omega_1 and Guessing Sequences**" at 10:00a.m. in N638 Ross.

**MSc Thesis Defence**Naveen Vaidya will defend his MSc thesis "

**Modeling Grown-in Defects in Indium Antimonide Crystal**" at 2:00p.m. in N638 Ross.

**Graduate Seminar**Morteza Safar-Ali will give a talk entitled "

**The Theory of Braids**" at 1:00p.m. in N638 Ross.ABSTRACT:

*The theory of Braids shows the interplay of two disciplines of pure mathematics. Topology used in the definition of braids, and the theory of groups, used in their treatment. We will show that the system of all braids of order n is a group, and will talk about equality of two braids of the same order.*

**MSc Thesis Defence**Fan Zhang will defend her MSc thesis entitled "

**Mathematical Modeling of Population Dynamics with Delayed Nonlocal Nonlinearities and of a Marine Bacteriophage Infection**" at 2:30p.m. in N627 Ross.

**Dissertation Subject Oral**Yuriy Kazmerchuk will speak on "

**Pricing of Derivatives in Security Markets with Delayed Response**" at 10:30a.m. in N627 Ross.ABSTRACT:

*The following topics will be discussed: Delayed response in stock markets; Stochastic delay differential equations; Black-Scholes model for (B,S)-securities markets; Option pricing in the (B,S)-securities markets; GARCH(1,1) model for volatility; Numerical solution of Black-Scholes problem; Maximum likelihood method for parameters estimation; A proposed model of *B,S)-securities market with delayed response.*

**Graduate Seminar**Armando Fabia will give a talk entitled "

**Employing a Bayesian Network to Loss Forecasting**" at 3:30p.m. in N638 Ross.ABSTRACT:

*Financial institutions must forecast loan losses for the purpose of provisioning; a loss provision is an expense set aside for bad loans. This presentation shows that losses can be tied to a Bayesian network structure involving repayment and delinquency, and how this structure can be used to forecast losses.*

**Graduate Seminar**Daniel Oancea will give a talk entitled "

**Graphs of Groups**" at 1:00p.m. in N638 Ross.ABSTRACT:

*We define two important objects of Combinatorial Group Theory: graphs of groups, and their fundamental groups. We show how graphs of groups can be constructed from group actions on graphs. Conversely, starting with a graph of groups G, one can construct a graph called the universal cover of G. We present the two structure theorems of the Bass-Serre theory: the first one states that the universal cover of a graph of groups is a tree; the second structure theorem shows that a group acting on a tree is isomorphic to the fundamental group of the graph of groups obtained from the action. Applications of the theorems include an easy proof of the Kurosh subgroup theorem for free products of groups.*

**MSc Thesis Defence**Guojun Gan will defend his MSc thesis entitled "

**Subspace Clustering for High Dimensional Categorical Data**" at 2:00p.m. in N627 Ross.

**Graduate Seminar**Romana Danicic, will give a talk entitled "

**Calculating the Liquidity Premium for Fixed Annuities When Interest Rate Follows a Stochastic Process**" at 3:30p.m. in N638 Ross.ABSTRACT:

*Fixed annuities are fairly illiquid financial instruments. Due to its illiquid property, fixed annuities often offer a liquidity premium to compensate for the redemption restrictions. We describe the numerical implementation for calculation of yield when the instantaneous risk-free rate of return follows Vasicek Model. In particular we discuss the benefits and challenges of using Gauss-Hermite quadrature for calculation of two-dimensional integrals.*

**Graduate Seminar**Daniel Oancea will give a talk entitled "Group Actions on Graphs and the Nielsen-Schreier Subgroup Theorem" at 11:00a.m. in N638 Ross.

ABSTRACT:

*We prove a theorem due to Reidemeister and Serre, about groups acting freely on trees. This is the beginning of Bass-Serre theory, which uses group actions on graphs to obtain results on the structure of groups. The theorem leads to an easy proof of the Nielsen-Schreier subgroup theorem, and provides a Schreier basis for subgroups of free groups. The theorem is also used to obtain the Schreier index formula.*

**Graduate Seminar**Isabel Hubard will give a talk entitled "

**Geometric Graph Theory**" at 12:00p.m. in N638 Ross.ABSTRACT:

*We'll talk about planar graph and the Hanani-Tutte theorem about such graph. We'll define what a geometric graph is as well as some of their properties, including the relation between planar and geometric graphs.*

**PhD Oral**Achan Lin will defend her PhD Dissertation entitled "

**Bezier Curves and Surfacts. A New Approach**" at 1:00p.m. in N638 Ross.

**Graduate Seminar**Graham Wells will give a talk entitled "

**Salary and Benefits Projection Model and Risk Management**" at 2:30p.m. in N638 Ross.ABSTRACT:

*Management Board Secretariat's Ministry Salary and Benefits Projection Model will be discussed, which addresses a variety of issues including: annual increases for different groups of staff at different points throughout the fiscal year, staff transitions from one position to another, differing benefit rates for classified versus unclassified staff, etc. Additionally, Risk Management practices in Management Board Submissions and in the government as a whole will be discussed.*

**Graduate Seminar**Karin Prochazka will give a talk entitled "

**Pricing Different Current Products**" at 6:00p.m. in N638 Ross.ABSTRACT:

*We will discuss various products being sold currently. We will look at how they are priced and how we test to make sure the pricing model is properly implemented. In particular we shall look at interest rate derivatives such as GICs with embedded options.*

**Survey Paper Presentation**Sandeep Bhargava will give a talk entitled "

**The Representation Theory of Finite Groups**" at 3:00p.m. in N638 Ross.ABSTRACT:

*We will examine the representation theory of finite groups over the complex field paying particular attention to the associated character theory. If time permits, we will discuss representations of the symmetric group S_n using Specht modules and a recent extension of this approach to the representations of the Rook Monoid.*

**Survey Paper Presentation**Petko Kitanov will give a talk entitled "

**The Mathematical Modelling of Influenza Epidemics**" at 11:00a.m. in N638 Ross.ABSTRACT:

*Different mathematical models for influenza epidemics are presented; deterministic and stochastic. Most of the models are about the spread of influenza. An optimization, a simulation, and a model with corcirculating influenza strains are presented, also.*

**Graduate Seminar**Zhening Li will give a talk entitled "

**Florida Pension Election**" at 2:30p.m. in N638 Ross.ABSTRACT:

*The Florida State Pension plan gives participants the option to switch between Defined Contribution and Defined Benefit Pension plqns. M.A. Milevsky and S.D. Promislow have recently obtained analytical expressions for the optimal switching time to maximize the expected wealth on retirement. When expected wealth is replaced by expected utility of wealth it is no longer possible to derive closed form solutions. This seminar will report on several results for power utility functions obtained by simulation.*

**PhD Oral**Kim-Quang Tran will defend his PhD Dissertation entitled "

**Categorical Approaches to Connectedness and Disconnectedness**" at 10:00a.m. in N638 Ross.

**PhD Oral**Gabor Lukacs will defend his PhD Dissertation entitled "

**c-Compactness and Generalized Dualities of Topological Groups**" at 2:00p.m. in N638 Ross.

**Graduate Seminar**Qingling Zeng will give a talk entitled "

**Modelling of Market Price: Consumer Memory and Storage Policy on Price Fluctuation**" at 2:00p.m in N627 Ross.ABSTRACT:

*We first briefly introduce the model for the dynamics of price adjustment in a single commodity market developed by J.Belair and M.C.Mackey. The model with nonlinearities in both supply and demand functions was discussed in their research. Delays due to production lags and storage policies involved in supply schedule play the key role in the model development. We found the interpretation for the delay, especially on storage time is not reasonable in their discussion, and hence probably produce some problems in the model formulation. As our main work, we introduce penalty functions to improve their method and conclude that under some constraint conditions the storage time can be completely determined by current price. Meanwhile, conditions for the local stability of the equilibrium price are given.*

- Graduate Seminar
Xiaoling Xie will give a talk entitled "

**Pricing American-Style Basket Options by Least Squares Monte-Carlo Simulations**" at 3:00p.m. in N627 Ross.ABSTRACT:

*One of the most important and difficult problems in the option pricing theory is to evaluate and optimally exercise the American-style options on multiple assets. A Basket Option is an option whose payoff is linked to a portfolio or "basket" of several underlying assets. With growing diversification in investor's portfolio, basket options on such portfolios are increasingly demanded.**In this seminar, we will present a Least Squares Monte Carlo (LSM) approach to price American-style basket options. While the Monte Carlo method is applied to simulate trajectories for asset prices, the least-squares regression is used to estimate the continuation values of basket options, which makes this approach readily applicable in path-independent and multifactor situations where traditional techniques can not be used. Simulation examples for spread options, dual options and portfolio options will be given to illustrate the algorithm performance and the detailed numerical analyses will also be provided as well.*

**Dissertation Colloquium**Kim-Quang Tran will give speak on "

**Categorical Approaches to Connectedness and Total Disconnectedness**" at 10:00a.m. in N638 Ross.ABSTRACT:

*The topological theory of connectedness and total disconnectedness has been categorically developed in various ways of approach since the 60s. In this talk we introduce the theory of connectedness by studying two different approaches to the notion of connectedness. The first approach was functionally introduced by R.E. Hoffmann and is used to extend many properties in the category of topological spaces to certain categories. We present a new approach to the notion of connectedness and give a further discussion on its theory. This second approach involves a class F of morphisms in a given category and it then coincides with the first one in a particular class F. We also introduce the categorical concept of total disconnectedness and study its theory so that itself and the connectedness of the forementioned approach have a nice connection. Moreover, by taking advantage of the notion of F-openness which was studied by M. M. Clementino, E. Giuli and W. Tholen, we define the definition of F-local connectedness and derive its properties.*

**Graduate Seminar**Zhening Li will give a talk entitled "

**Florida Pension Election**" from 2:30p.m. to 3:30p.m. in N638 Ross.ABSTRACT:

*The Florida State Pension plan gives participants the option to switch between Defined Contribution and Defined Benefit Pension plans. M.A. Milevsky and S.D. Promislow have recently obtained analytical expressions for the optimal switching time to maximize the expected wealth on retirement. When expected wealth is replaced by expected utility of wealth it is no longer possible to derive closed form solutions. This seminar will report on several results for power utility functions obtained by simulation.*This is in partial fufillment of his seminar requirement for the Master's degree, and all MA students are expected to attend.

**Survey Paper Presentation**Eitan Prisman, York University, will give a talk entitled "

**A Continuous Dynamic Model of Respiration in Humans**" at 3:30p.m. in N638 Ross.ABSTRACT:

*There exist instruments and techniques that produce instantaneous values of CO2 partial pressure in the lung (PACO2) and in associated arterial (PaCO2) and mixed venous blood vessels (PvCO2). However, these techniques are invasive and difficult to carry out. These measurements are very useful in predicting important cardio-respiratory function, as well as in predicting sufficient volumes of an anesthetic to be administered to patients.**I will review the model presented by Chilton and Stacey in 1953. This early model was one of the first to present a broad theoretical attack of the dynamics of carbon dioxide in the lungs during respiration under condition of metabolic equilibrium.**I will construct a continuous dynamic model of the periodic oscillation of PACO2, PaCO2, and PvCO2 as a function of respiratory frequency, cardiac output, fractional residual capacity, and metabolic CO2 production. My formulas will be derived from a mass balance approach to the different compartments of the respiration cycle. I will present simulations of this model under various conditions. I will analyze my results and compare them with results from Chilton and Stacy, and Benallal et al 2000.*Survey paper requirement for Masters students.

Reminder: Master's Mathematics students are expected to attend the talk.

**Graduate Seminar**Elliott Acoose, York University, will give a talk entitled "

**The Fundamental Theorem of Asset Pricing**" at 11:00a.m. in N638 Ross.ABSTRACT:

*A securities market model will first be developed in discrete time. The definitions of arbitrage and equivalent martingale measure in our market model will be given and then it will be shown that the market has no arbitrage opportunities if and only if there exists an equivalent martingale measure. Furthermore the equivalent martingale measure is unique if and only if the market is complete, that is if every security is attainable by some admissible trading strategy. Next the model will be formulated in continuous time and the analagous no arbitrage if and only if there exists an equivalent martingale measure condition will be proven.*Seminar requirement for Masters students.

Reminder: Master's mathematics students are expected to attend the talks of other students. Documented evidence at 6 such talks is expected. Attendance sheets can be picked up from N519 Ross.

**Graduate Seminar**Hanqiuzi Wen will give a talk entitled "

**Application of Statistical Methods on Protein Structure Comparisons**" at 3:00p.m. in N638 Ross.ABSTRACT:

*Protein carries out the majority of the functions for human body. In order to understand the function of proteins, one needs to understand the protein structures first. Due to the large number of known protein structures in Protein Data Bank, protein classification methods are needed to help understanding protein structure-function interaction. In order to effectively classify the proteins, sequence and 3D structure comparison algorithms should be developed first.**This paper focuses on the protein 3D structure comparison methods and can be divided into two parts. In the first part, I present a brief introduction to protein 3D structure, which is necessary for understanding the latter content. A review of existing algorithms is given and the working mechanisms of several popular algorithms are described.**The second part discusses two structure comparison algorithms, which are DALI and VAST. The statistical methods applied in these two algorithms, such as Metropolis algorithm and Gibbs sampler, are introduced. The DALI algorithm was implemented as an example to show how statistical methods can be applied for protein structure comparisons.*Seminar requirement for Masters students

Reminder: Master's Mathematics students are expected to attend the talks of other students. Documented evidence at 6 such talks is expected. Attendance sheets can be picked up from N519 Ross.

**Graduate Seminar**Weihong Dan will give a talk entitled "

**The Discrete Fourier Transform on the Finite Circle Z/nZ**" at 10:00a.m. in N638 Ross.ABSTRACT:

*The discrete Fourier transform has applications in Physics, Statistics, error correcting code, and theoretical problems. We will introduce definitions and the algebra associated to the DFT and attempt to give a "picture" of this operation on the set of functions on the group Z/nZ.*Seminar requirement for Masters students.

Reminder: Master's Mathematics students are expected to attend the talks of other students. Documented evidence at 6 such talks is expected. Attendance sheets can be picked up from N519 Ross.

**Graduate Seminar**Weihong Dan will give a talk entitled "

**Generalized Fundamental Theorem of Galois Theory**" at 1:30p.m. in N638 Ross.ABSTRACT:

*Proof of Generalized Fundentmental Theorem of Galois Group.**Generalized Fundamental Theorem: If F is an algebraic Galois extension field of K, then there is a one-to-one correspondence between the set of all intermediate fields of the extension and the set of all closed subgroups of the Galois group (given by E| Aut_E F ) such that: F is Galois over every intermediate field E, but E is Galois over K if and only if the corresponding subgroup is normal in G=Aut_K F ; In this case G/Aut_E F is (isomorphic to) the Galois group Aut_K E of E over K.*Seminar requirement for masters students.

Reminder: Master's Mathematics students are expected to attend the talks of other students. Documented evidence at 6 such talks is expected. Attendance sheets can be picked up from N519 Ross.

**PhD Dissertation**Dingan Feng will speak on "

**Stochastic Models for High Frequency Financial Time Series**" at 4:10p.m. in N638 Ross.

**Dissertation Colloquium**Achan Lin will give speak on "

**Bézier curves and surfaces**" at 3:15p.m. in N638 Ross.ABSTRACT:

*Based on Grassmann's master piece "Ausdehnungslehre", Ramshow's recent work "On multiplying Points: The paired Algebras of Forms and Sites", and umbral calculus, a new approach to Bézier curves and surfaces is given in the first chapter of the dissertation. Under the new approach a Bézier curve /surface of degree n can be simply denoted as a power of points. Using this new approach, many known results of Bézier curves and surfaces, both the statements and the proofs, can be simplified and many new results can be relatively easier to get.**Some classical problems are studied using this new theory in the second chapter. The geometric Hermite interpolation with the given tangent direction, curvature vector and torsion is studied in detail. A solution of Bézier curve of degree 5 with optimum approximate order is given. The general characterization of singular points, inflection points and torsion vanish points is given for both Bézier curves and Bézier rational curves.**In chapter 3, we first discuss in detail the general case of conversion between triangular Bézier surface and rectangular surface. Under our new theory, the conversion, which is a very important problem in CAGD, becomes much easier and much clearer. Secondly we are able to prove that under some restriction about control points, which is described by a matrix, the condition of Geometric continuity between two triangular Bézier surface patches can be greatly simplified. The matrix itself, we believe, will have an important position to characterize the control points of Bézier patch. Finally the vertex enclosure continuity of n triangular Bézier patches is studied.*

**Dissertation Colloquium**Dingan Feng, York University, will give speak on "

**Stochastic Models for High Frequency Financial Time Series**" at 10:00a.m. in N638 Ross.ABSTRACT:

*This talk focuses on the development of stochastic models for high frequency time series data and related statistical inference procedures. In particular, two classes of models are proposed to analyse stock data. The first one is a class of inter-temporal stochastic conditional duration models that are useful to model the duration process. A duration represents the time difference between consecutive trading times, which is an important financial variable reflecting the activeness of a stock. The statistical inference is developed under the framework of state space models with non-normal marginal errors, in which the Monte Carlo maximum likelihood estimation proposed by Durbin and Koopman (1997) is implemented. Specifically, we consider two heavy tailed distributions, log\-Weibull and log\-gamma random in our analysis of an IBM stock data set. The second one is a class of time deformation return models for the return process. A return process is referred to as the series of differences of two adjacent log-prices of a stock over a certain period of time. The return variable is one of the most interesting and most important financial measurements for both researchers and investors. For the return models, we adopt an inferential strategy based on simulated method of moments (SMM) for parameter estimation, in which simulation studies are conducted to validate certain choice of the number of moments required in the formation of estimating equations. Our numerical results in both simulation studies and data analyses have indicated that this simulation-based inferential approach turns out to work very well for the parameter estimation in the return models. The study presented in the thesis is largely motivated by the analysis of the high frequency IBM stock data.*

**Graduate Seminar**Elliott Acoose, York University, will give a talk entitled "

**The Population Biology of Infectious Diseases**" at 2:30p.m. in N638 Ross.ABSTRACT:

*In this seminar we will present models of microparasitic infections that reproduce within their hosts and transfer from one host to another. The host population is divided into three groups: susceptibles S, infectives I, and removed R who can no longer contract the disease due to immunity or isolation. In the SIR model members of the host population proceed from the S class to the I class and then to the R class. The dynamics of the movement is described by three differential equations in S, I, and R. The SIRS model has the additional feature that members of the host population can move from the R class back to the S class through loss of immunity. The system of differential equations corresponding to this model will be discussed.*Seminar requirement for masters students.

Reminder: Master's Mathematics students are expected to attend the talks of other students. Documented evidence at 6 such talks is expected. Attendance sheets can be picked up from N519 Ross.

**Graduate**Zhening Li will give a talk entitled "

**Entropic Pattern-Recognition Algorithm**" at 1:00p.m. in N620 Ross.ABSTRACT:

*Problems of recognition occur in practically every field of human activity. The talk focuses on the entropic algorithm for pattern-recognition. We will give a brief introduction of Shannon's entropy and its properties, then emphasize the entropic pattern-recognition criterion. A detailed example will be given to illustrate the entropic algorithm for recognition.*Seminar requirement for Masters students

Reminder: Master's Mathematics students are expected to attend the talks of other students. Documented evidence at 6 such talks is expected. Attendance sheets can be picked up from N519 Ross.

**PhD Oral**Zhaohui Zhang defend his PhD Disserttion entitled "

**Localization Operators and Wevelet Multipliers**" at 2:00p.m. in N638 Ross.

**PhD Dissertation**Thorsten Palm will defend his PhD Dissertation entitled "

**Dendroptopic Sets for Weak Infinity-Categories**" at 12:00p.m. in N638 Ross.

**Dissertation Colloquium**Zhaohui Zhang will give a talk entitled "

**Localization Operators and Wavelet Multipliers**" at 11:00a.m. in N638 Ross.ABSTRACT:

*We establish the theory of localization operators with two admissible wavelets on locally compact and Hausdorff groups. The analogue of the resolution of the identity formula, the boundedness of localization operators with symbols in $L^p$, the trace formula and the $S_p$ properties of localization operators are discussed. Moreover, we give the trace class norm inequalities for wavelet multiplers and for wavelet multipliers with two admissible wavelets, we give the trace class norm inequalities and the trace formula.*

**Dissertation Colloquium**Gabor Lukacs will give a talk entitled "

**c-Compactness and Generalized Dualities of Topological Groups**" at 12:00p.m. in N638 Ross.ABSTRACT:

*This work is mainly focused on Hausdorff topological groups. Motivated by the Kuratowski-Mrowka Theorem, a topological group is called c-compact if the projection along any other group of its product with that group maps closed subgroups to closed subgroups. The problem of whether every c-compact topological group is compact has been an open question for over fifteen years.**We obtain three main results on c-compact topological groups. The first one is that every c-compact group that admits a continuous monomorphism into a compact group is actually compact. (As obvious as this result may appear, its proof is fairly non-trivial.) The second states that every c-compact group is compact if every c-compact of a smaller class admits a continuous monomorphism into a compact group, and the third says that every c-compact locally compact group of a certain class is compact if and only if every countable discrete c-compact group admits a continuous monomorphism into a compact group. While the first result is of an affirmative nature, the two latter ones are reduction theorems.**In the course of attempts to solve the problem of c-compactness we construct some dual adjunctions, which in a way generalize several known dualities. Cartesian closedness of the underlying categories of topological spaces turns out to play a crucial role in establishing these dualities. However, the most well-known cartesian closed category of topological spaces (consisting of the Hausdorff k-spaces) is not the most convenient one in the context of topological groups. As a resolution we investigate the categorical properties of Tychonoff spaces with the property that every function on them with Tychonoff codomain and continuous restrictions to compact subsets is continuous. Such spaces are known for over thirty years, and their topological properties of such spaces has been thoroughly studied, but their category does not seem to have not drawn any attention in the past. We prove that this category is cartesian closed, and show that it is equivalent to an epireflective subcategory of Hausdorff k-spaces.**In a category with notions of image and closed subobject an object is called h-closed if its image under every morphism is closed in the codomain. This concept generalizes the notion of h-completeness of topological groups, which is somewhat weaker than the notion of c-compactness. As an addendum we obtain a categorical characterization of C^*-algebras in some larger categories of *-algebras containing it. We show that C^*-algebras are precisely the h-closed objects in these categories.*

**Dissertation Colloquium**Thorsten Palm, York University, will give a talk entitled "

**Dendrotopic set for weak infinity-categories**" at 2:00p.m. in N638 Ross.ABSTRACT:

*An n-category is an n-dimensional geometric object carrying a certain kind of algebraic structure, most notably composition operations. (A 1-category is just an ordinary category.) Several definitions of the notion of n-category have been proposed. The limit case (n tending to infinity) can also be considered, the resulting notion is the most general. This talk chiefly concerns the definition of infinity-categories put forth by Michael Makkai. According to it, an infinity-category is what Makkai calls a multitopic set (a structure built from special oriented polytopes called multitopes; here Makkai's definition is rather involved), and composition is declared by an infinite-dimensional universal property, making additional operations or axioms unnecessary.**After treating the two-dimensional case for motivation, I shall give an improved version of Makkai's definition. The main change lies in the definition of multitopic sets, which in my case is entirely geometric. I call these structures dendrotopic sets. I shall go on to present a different axiomatization of universality in dendrotopic sets and show that it leads to a notion stronger than Makkai's. The crucial part of my proof is a construction that makes use of a rather surprising combinatorial fact concerning dendrotopes.*

**Graduate Seminar**Gang Li will give a talk entitled "

**Discrete Entropy. Properties and the Uniqueness Theorem**" at 9:30a.m. in N638 Ross.ABSTRACT:

*Information theory is a branch of probability theory originated by Dr. Shannon, who proposed a quantative measure of the amount of information supplied by probabilistic experiment and Shannon's entropy. Here we just discuss the basic property of the entropy and the proof of the Unique theorem.*Seminar requirement for Masters students.

Reminder: Master's Mathematics students are expected to attend the talks of other students. Documented evidence at 6 such talks is expected. Attendance sheets can be picked up from N519 Ross.

**Dissertation Subject Oral**Qing Shao, York University, will speak on "

**Robust Model-Based Clustering Analysis**" at 1:00p.m. in N638 Ross.ABSTRACT:

*The proposal discusses motivation for developing a robust model-based clustering approach. We will present a general framework in which a rough idea with regard to the thesis research is proposed. Relevant literature concerning clustering analysis especially statistical model-based clustering techniques is reviewed.*

**Graduate Seminar**Gang Li will give a talk entitled "

**Manufacturing Temperature Control**" at 9:30a.m. in N638 Ross.ABSTRACT:

*Steel bars traveling on a moving belt with an initial temperature of 800C are cooled by water to an target value of 500C within a distance of 100m. The water is provided by shower heads arranged in rows in two groups. The number of the shower heads can be adjusted so that at the exit point the target temperature is reached.**(objective): Derive a mathematical model for the problem; Use numerical simulations (by solving the model equation with C or Matlab) to verify the analysis.*Seminar requirement for Masters students.

Reminder: Master's Mathematics students are expected to attend the talks of other students. Documented evidence at six such talks is expected. Attendance sheets can be picked up from N519 Ross.

**Dissertation Subject Oral**Achan Lin, York University, will speak on "

**Application of Umbral Calculus in Computer Aided Geometric Design"**" at 2:00p.m. in N638 Ross.ABSTRACT:

*Version of Rota and Taylor's classical umbral method is introduced. An generalization of multivariate umbral method on the vector space is given. As an application, the notation and calculation of Bezier curves and surfaces can be greatly simplified. New results can be relatively easier to get. Calculation of Grassmann's weighted points and vectors will also be briefly introduced.*

**Dissertation Subject Oral**Debora Di Caprio, York University, will speak on "

**Orderability and Continuous Selections for Hyperspaces**" at 10:00a.m. in N638 Ross.ABSTRACT:

*Give a topological space X, denote by CL(X) the set of all nonempty closed subsets of X. A "hyperspace" of X is a subfamily H(X) of CL(X) endowed with some "natural topology" such as those of Vietoris, Wijsman or Hausdorff. A continuous selection for a hyperspace H(X) is a continuous function from H(X) into X which assigns to each closed subset C in H(X) a point of C. The idea of selecting a point from each element of the family H(X) is a special case of the more classical one of selecting a point in the image of each C under the multifunction H(X) => X : C -> C. We investigate conditions under which selections and epsilon approximations to these selections exist for the Vietoris and other hyperspace topologies because we can define a suitable linear ordering of the base space; and the possibility that suitable completeness of the base space can allow such orderings to be defined. We thus obtain interpolations for, and strengthenings of, such well-known and classical results as that of Michael on the existence of continuous selections for lower semicontinuous multifunctions.*

**Data Mining / Data Analysis**and**Dissertation Colloquium**Yongqiang Cao, York Unversity, will speak on "

**Neural Networds for Clustering: Theory, Architecture, Algorithm and Neural Dynamics**" from 3:00p.m. to 4:00p.m. in N638 Ross.ABSTRACT:

*Spectacular advances in information technology and large-scale computing are producing huge and very high dimensional data sets. These data sets arise naturally in a variety of contexts such as text/web mining, bioinformatics, imaging for diagnostics and surveillance, astronomy and remote sensing. The dimension of these data is in the hundreds or thousands. The traditional clustering algorithms do not work efficiently for data sets in such high dimensional spaces because of the inherent sparsity of data. This is well known as the curse of dimensionality. This dissertation develops a new neural network architecture PART (Projective Adaptive Resonance Theory) and related algorithms based on the neural dynamics to provide a solution to the difficulties in clustering high-dimensional data. The PART architecture is based on the well known ART developed by Carpenter and Grossberg, and a major modification (selective output signaling mechanism) is provided in order to deal with the inherent sparsity of the data points in high dimensional space from many data-mining applications. We provide a rigorous proof of the regular dynamics of the PART model which is a large scale and singularly perturbed system of differential equations coupled with a reset mechanism. Our simulations and comparisons show that the resulting algorithms based on the PART model are effective and efficient in finding projected clusters in high dimensional data sets. In the second part of this dissertation, we propose a provably correct clustering algorithm IMC (Iterative Mean Clustering) and the related mathematical theory. We provide a rigorous proof of the convergence of this algorithm. In particular, in one-cluster case where the data distribution is unimodal, this algorithm converges to the center of the unique cluster starting from an arbitrary initial value. In multi-clusters case where the data distribution is multimodal, this algorithm converges to the center of a cluster that is close to the initial value. Finally, we develop a neural network implementation of the IMC algorithm, called IMC-ART, and introduce a variation of PART algorithm, called PART-A, which combines PART architecture with IMC algorithm.*

**Survey Paper Presentation**Jian Xiong will give a talk entitled "

**Saddlepoint Approxiamtions to Option Prices**" at 2:30p.m. in N638 Ross.ABSTRACT:

*Much of the recent literature on option valuation has successfully applied Fourier analysis to determine option prices. However, most of these numerical methods can be both slow and inaccurate in computation. We propose a classical statistical technique--saddlepoint approximations method for fast and accurate computation of European option prices. The method is applicable to pricing European options whose returns processes are developed in a general equilibrium model with stochastic volatility and stochastic interest rates. The model is calibrated for the $S\&P$ 500 index, and we show that the saddlepoint approximations methodology is accurate and easily implementation.*Survey Paper requirement for Master's students.

Reminder: Master's Mathematics students are expected to attend the talk.

**Dissertation Subject Oral**Yongqiang Cao will speak on "

**Neural Networks for Clustering: Theory, Architecture, Algorithm and Neural Dynamics**" at 10:30a.m. in N627 Ross.ABSTRACT:

*Data clustering is the unsupervised process of classifying patterns into groups, aiming at discovering structure which is hidden in a data set. Applications in various domains often lead to very high-dimensional data. Clustering such high-dimensional data sets is a contemporary challenge. Successful algorithms must avoid the curse of dimensionality but at the same time should be computationally efficient. The dissertation plans to develop a neural network architecture and related algorithms based on the neural dynamics to provide a solution to the challenging high-dimensional clustering problem.*The syllabus for this exam is available for inspection in N519 Ross.

**Survey Paper Presentation**Renata Kaleta will give a talk entitled "

**Burnside's Theorem on Groups of Order p^a q^b**" at 12:00p.m. in N638 Ross.ABSTRACT:

*In the first edition of his book "The theory of groups of finite order" (1897) Burnside wrote: " No simple group of odd order is at present known to exist. Also there is no known simple group whose order involves fewer than three different primes." These statements were to lead to two of the most important results of the theory of finite groups. The second of these was proved by Burnside--the "p^a q^b theorem": "Every group of order p^a q^b (p,q primes) is solvable" (while the first one, the "odd-order problem", had to wait for another 60 years). The "p^a q^b theorem" together with Burnside's Conjugacy Class Theorem will be presented with full proofs - assuming the theory of characters.*

**Survey Paper Presentation**Milena Kurtinecz will give a talk entitled "

**Multilevel Linear Regression**" at 3:00p.m. in N638 Ross.ABSTRACT:

*Multilevel models are models specifically geared toward the statistical analysis of data that have a hierarchical or clustered structure. Such data arise routinely in various fields, for instance in educational research, where pupils are nested within schools, family studies with children nested within families, medical research with patients nested within physicians or hospitals, and biological research, for instance the analysis of dental anomalies with teeth nested within different persons' mouths. This paper will explain the theory aspects of the two-level regression model, methodology, development, accuracy of the parameters estimates, when a normal distribution is assumed for the dependent variable. Then an illustration of these will be performed.*

**PhD Oral**Stefan Mykytiuk will defend his PhD Dissertation "

**Hopf Algebras of Quasi-Symmetric Functions**" at 2:00p.m. in N638 Ross.

**Dissertation Colloquium**Stefan Mykytiuk will speak on "

**Hopf Algebras of Quasi-Symmetric Functions**" at 11:30a.m. in N638 Ross.ABSTRACT:

*Hopf algebras are a natural setting for the study of many combinatorial problems, while quasi-symmetric functions play an important role as generating functions that encode information about the objects being studied and as a source of Hopf morphisms that translate problems from one area to another.**We introduce quasi-symmetric functions, comparing them to the better-known symmetric functions, and describe three important Hopf algebras which they form. In this we are aided by an association of quasi-symmetric functions with partially ordered sets, which allows us to describe their Hopf algebra structure in terms of operations on partially ordered sets.*

**Graduate Seminar**Shannon Kennedy will give a talk entitled "

**Determining the Liquidity Premium for Fixed Annuities**" at 10:00a.m. in N638 Ross.ABSTRACT:

*When one buys a standard savings bond, it is implicit that the holder may redeem the issue (ie: get their money back) at any time without penalty. Fixed annuities are financial instruments manufactured by U.S.-based insurance companies that are very similar to a typical savings bond (at least in the pre-retirement accumulation phase). However, fixed annuities have liquidity restrictions that prevent their redemption for some period of time. As such, it is expected that a fixed annuity with these restrictions should have a higher guaranteed rate of return than a comparable savings instrument that can be redeemed any time. This talk endeavours to mathematically quantify this yield premium subject to a particular set of liquidity restrictions.*Seminar requirement for Masters students. Reminder: Master's Mathematics students are expected to attend the talks of other students. Documented evidence at 6 such talks is expected. Attendance sheets can be picked up from N519 Ross.

**Survey Paper Presentation**Alina Rivilis will give a talk entitled "

**Application of Bootstrap Methods in Mixed Models**" at 2:00p.m. in N638 Ross.ABSTRACT:

*Mixed-effects models, allow us to model hierarchical data, and flexibly represent the variability structure that is induced by the clustering of the data. First, a mixed model formulation will be presented, followed by some background and historical information on the best linear unbiased predictors (BLUPs) for random effects. The concept of the bootstrap will then be presented and the usefulness of this technique will be discussed in a multilevel setting. The application of the bootstrap techniques to mixed effects models would benefit researchers when model assumptions do not hold (in situations when we don't have normality), or when the sample size is very small and estimation of fixed and random effects is problematic. Since in multilevel data we have a certain hierarchical structure, the bootstrap should produce samples that mimic that hypothetical distribution from which we obtained our observed multilevel data. Different bootstrap methods (parametric, semi-parametric, nonparametric) in multilevel models will be presented followed by applications and simulations of these techniques.*Survey Paper requirement for Master's students. Reminder: Master's Mathematics students are expected to attend the talk.

**Graduate Survey Paper**Joel Culina, York University, will give a talk entitled "

**Stochastic Resonance in Climate Cycles**" at 10:00a.m. in N638 Ross.ABSTRACT:

*I will discuss stochastic resonance, the coupling of noise and periodic forcing, as it occurs in climate cycles. Specifically, I will highlight how it is the driving force behind the 100 000 yr. glacial cycle, the 1500 yr. North Atlantic thermal/circulation cycle and how it factors into the El-Nino/Southern Oscillation (ENSO).*

**Graduate Seminar**Joel Culina will give a talk on "

**Existence of Solutions to the Local Martingale Problem**" from 10:00a.m. to 11:00a.m. in N638 Ross.ABSTRACT:

*I will be discussing existence of solutions to the martingale problem for an elliptic operator in nondivergence form. One of two main theorems shows that continuity of the coefficents and boundedness of the drift of the operator is a sufficient condition for such existence and the other, utilizing the Girsanov theorem, shows that existence of the solution to the martingale problem for a process with drift follows from such existence for a process without drift, if the operator is uniformly elliptic.*Seminar requirement for Masters students. Master's Mathematics students are expected to attend the talks of other students. Documented evidence at 6 such talks is expected. Attendance sheets can be picked up from N519 Ross.

**Graduate Seminar**Claire Sauve will give a talk entitled "

**The Perron-Frobenius Theorem and it's Applications**" at 1:00p.m. in N638 Ross.ABSTRACT:

*We will prove the existence of the Perron-Frobenius eigenvalue in semiprimitive matrices and discuss its applications to the classification of Cartan matrices.*

**Survey Paper Presentation**Yaqing Chen will give a talk entitled "

**Statistical Analysis of Incomplete Quality of Life Data from a Clinical Trial on Breast Cancer**" at 2:30p.m. in N638 Ross.ABSTRACT:

*In this survey paper, we present a data analysis of quality of life study associated with MA.5 clinical trial, which was conducted by the National Cancer Institute of Canada. This trial involved patients with the positive-node breast cancer who were treated by two adjuvant chemotherapies. The objective of this study is to discover statistical evidence regarding whether or not there is a global difference between these two chemotherapies in the aspect of patients' quality of life. Because of patients' dropouts, the collected data is unbalanced with unequal numbers of repeated measures for each patient. This paper discusses three statistical techniques that are suitable for the global comparison under different types of missing patterns. The standard analysis and the growth curve model approach are applied under missing pattern of MAR, and a semi-parametric method approach is employed under informative missing pattern. We find that the three approaches give a consistent conclusion. That it, the two chemotherapies have no statistically significant difference for the benefits of quality of life.*Survey paper requirement for Masters students. Reminder: Master's Mathematics students are expected to attend the talk.

**Graduate Seminar**Tanyi Ojongmboh will speak on "

**Solving Low Degree Polynomial Equations using Circulant Matrices**" at 3:00p.m. in N638 Ross.ABSTRACT:

*I will begin with a brief review of Circulant Matrices, and then show how Circulant Matrices can be used to find the zeros of low degree polynomials. The idea is to construct a Circulant Matrix with a specified characteristic polynomial. The roots of the polynomial thus become the eigenvalues, which are trivially found for circulant matrices.*Seminar requirement for Masters students. Master's Mathematics students are expected to attend the talks of other students. Documented evidence at 6 such talks is expected. Attendance sheets can be picked up from N519 Ross.

**Dissertation Subject Oral**Baifang Xing will speak on "

**Best Quadrature Formulas and their Application for Statistical Inference in State-Space Models**" at 2:30p.m. in N638 Ross.ABSTRACT:

*The proposal discusses motivation for developing a numerical integration method for general nonlinear and non-Gaussian state-space models based on the best quadrature formulas. We review relevant literature concerning especially the Gaussian quadrature approach. We present a general framework in which a rough idea with regard to the thesis research is proposed.*

**Graduate Seminar**Tanyi Ojongmboh will give a talk entitled "

**Circulant Matrices, Permutation Matrices and Fourier Matrices**" at 3:00p.m. in N638 Ross.ABSTRACT:

*Circulant matrices are of the form:*A B C D D A B C C = C D A B B C D A

*where the elements of each row of C are identical to those of the previous row but are moved one position to the right and wrapped around. They have some properties in common with Permutation matrices and Fourier matrices. This talk will be an introduction to these matrices and the relationship between them.*Seminar requirement for Masters students. Master's Mathematics students are expected to attend the talks of other students. Documented evidence at 6 such talks is expected. Attendance sheets can be picked up from N519 Ross.

**Graduate Seminar**Joel Culina will give a talk entitled "

**Existence and Uniqueness of Solutions to Stochastic Differential Equations**" at 11:00a.m. in N638 Ross.ABSTRACT:

*Existence and uniqueness of both strong and weak solutions to stochastic differential equations will be discussed and a proof of strong existence and uniqueness will be detailed. The connection between these solutions to SDEs and the solution to the local martingale problem will be discussed. More specifically, the weak solution will be reformulated as a solution to the local martingale problem and a proof that the strong solution implies a solution to the local martingale problem will be given.*

**Graduate Seminar**Asrat Gashaw will give a talk entitled "

**Credit Risk Measurement**" at 2:00p.m. in N638 Ross.ABSTRACT:

*Recently, credit risk has been attracting a great deal of attention within financial industry. Several models have been proposed to quantify credit risk. This study overviews the three most widely used credit risk models: the credit migration approach(CreditMetrics), the option pricing approach(KMV) and the actuarial approach(CreditRisk+). In addition, detailed analysis is done on simulated data and numerical results discussed to show that how CreditMetrics methodology is used for measuring credit risk at portfolio level.*

**Graduate Seminar**Shelli Pintzov, York University, will give a talk entitled "

**The Dimension of Separable Metric Spaces**" at 12:00p.m. in N638 Ross.ABSTRACT:

*I will be proving the following: For every separable metrizable space X, we have that the small inductive dimension of X = the large inductive dimension of X = the covering dimension of X.*Seminar requirement for Masters students

Reminder: Master's Mathematics students are expected to attend the talks of other students. Documented evidence at 6 such talks is expected. Attendance sheets can be picked up from N519 Ross.

**Graduate Seminar**Dipra Mitra, York University, will give a talk entitled "

**q - Multiplicative Analogues of Weyl Algebras**" at 1:30p.m. in N638 Ross.ABSTRACT:

*Let Q be a n x n matrix over a field of K. Consider the K-algebra**-1 -1 P(Q) = K[x ,x , ...,x , x ] with x x = q x x . Basic properties, including 1 1 n n i j ij j i**the simplicity, of P(Q) will be discussed.*Seminar requirement for Masters students. Reminder: Master's mathematics students are expected to attend the talks of other students. Documented evidence at 6 such talks is expected. Attendance sheets can be picked up from N519 Ross.

**Graduate Seminar**Shelli Pintzov, York University, will give a talk on "

**The Banach-Tarski Paradox**" at 3:00p.m. in N620 Ross.ABSTRACT:

*I will discuss the connection between the Banach-Tarski Parado and measure Theory. I will sketch a proof of the Banach-Tarski Paradox which states the following: If A and B are bounded subsets of R3 with non-void interiors, then A and B are equivalent by finite decomposition.*

Reminder: Master's Mathematics students are expected to attend the talks of other students. Documented evidence at 6 such talks is expected. Attendance sheets can be picked up from N519 Ross.

**Graduate Seminar**Derek Wisniewski, York University, will speak on "

**Penalty Method for Pricing American Options with Stochastic Volatility**" at 10:30a.m. in N638 Ross.ABSTRACT:

*An introduction to derivative securities (specifically, options) will be given before motivating the 2-D analog to the Black-Scholes equation which is used to price derivative securities. The resulting linear convection-diffusion type equation will then be transformed into a PDE with a nonlinear source term in order to implement the penalty method used to handle the early exercise feature of American options. The nonlinear PDE is then solved via a finite element method.*

Reminder: Master's Mathematics students are expected to attend the talks of other students. Documented evidence at 6 such talks is expected. Attendance sheets can be picked up from N519 Ross.

**Graduate Seminar**Selma Kapetanovic, York University, will give a talk entitled "

**A Theorem of Jacobson**" 2:00p.m. in N638 Ross.ABSTRACT:

*Proofs of Wedderburn's Little theorem and Jacobson's Commutativity theorem will be presented.*

Reminder: Master's Mathematics students are expected to attend the talks of other students. Documented evidence at 6 such talks is expected. Attendance sheets can be picked up from N519 Ross.

**PhD Oral**Zehnguo Qiu, York University, will defend his PhD Dissertation entitled "

**Simplex Mixed Models for Longitudinal Proportional Data**" at 10:00a.m. in N638 Ross.

**PhD Oral**Wuwen Guo, York University , will defend his PhD Dissertation entitled "" at 10:00a.m. in N639 Ross.Domain Decomposition Methods for the Solutions of Partial Differential Equations

**Dissertation Subject Oral**Dingan Feng will speak on "

**Stochastic Models for the Analysis of High Frequency Financial Time Series**" at 1:00p.m. in N638 Ross.ABSTRACT:

*In this proposal, we will present two kinds of stochastic models for high frequency time series data and develop statistical approaches to estimation of parameters in these models. The first kind is a class of general stochastic conditional duration (GSCD) models that are useful to model the duration, an important financial variable reflecting the performance of a stock market. This class of models is in nature state space models, and the Monte Carlo maximum likelihood estimation is employed in this framework. The second kind is a class of time deformation return (TDR) models that are useful to model the return (or the difference of log-prices of a stock), one of the most important financial variables largely concerned by practitioners. For this class of models, we aim to develop the generalizedmoment method based on characteristic functions (GMM-CCF) for parameter estimation. Our developments in modelling and estimation are largely driven by our goal of analyzing the IBM stock data that are high frequency time series. This proposal contains 6 sections, including literature review, methodological development and some results of a preliminary analysis of the IBM data using the proposed two models.*

**Graduate Seminar**Yuriy Kazmerchuk, York University, will give a talk entitled "

**Alternatives to Black-Scholes**" at 3:30p.m. in N638 Ross.ABSTRACT:

*The intention of this talk is to discuss different approaches to option pricing model. The first major breakthrough in this subject was made by F. Black and M. Scholes in the early 1970s. One of their assumption is that the process of evolution of stock price has a lognormal disribution. Nowadays, the major part of the stock market has changed and this assumption is far from reality. The real-life distribution of an equity price has a fatter left tail and thinner right tail. As part of this talk we will be introduced to the classical model of Black-Scholes and the number of alternatives to it.*

Reminder: Master's Mathematics students are expected to attend the talks of other students. Documented evidence at 6 such talks is expected. Attendance sheets can be picked up from N519 Ross.

**Graduate Seminar**Neil Roger, York University, will give a talk entitled "

**Measure and Category**" at 3:00p.m. in N638 Ross.ABSTRACT:

*This talk introduces the concepts of measurability, first category and the Continuum Hypothesis, and presents some theorems combining these ideas. In particular, some peculiar sets of real numbers such as the Bernstein, Luzin and Sierpinski sets will be covered.*

Reminder: Master's Mathematics students are expected to attend the talks of other students. Documented evidence at 6 such talks is expected. Attendance sheets can be picked up from N519 Ross.

**Graduate Seminar**Jin Wang will give a talk entitled "

**The Titanic Option: Valuation of the Guaranteed Minimum Death Benefit in Variabel Annutities and Mutual Funds**" at 3:30p.m. in N638 Ross.ABSTRACT:

*The authors use risk-neutral option pricing theory to value the guaranteed minimum death benefit in variable annuities and some recently introduced mutual funds. A variety of death benefits, such as return-of-premium, rising floors, and "ratches," are analyzed. The authors derive analytic option prices for a simplified exponential mortality model and robust numerical estimates in the case of a properly calibrated Gompertz model.*

Reminder: Master's Mathematics students are expected to attend the talks of other students. Documented evidence at 6 such talks is expected. Attendance sheets can be picked up from N519 Ross.

**Graduate Seminar**Jin Wang, will give a talk entitled "

**Travelling Front Soultions of a Nonlocal Fisher Equation**" at 2:00p.m. in N638 Ross.ABSTRACT:

*This paper consider a scalar reaction-diffusion equation containing a nonlocal term of which Fisher's equation is a particular case. The author considers travelling wavefront solutions connecting the two uniform states of the equation. The conlutions is that: (1) If the nonlocality is sufficiently weak in a certain sense then such travelling fronts exist. (2)the main difference between this front and that of Fisher's equation is that the front is non-monotone and has a very prominent hump.*

Reminder: Master's Mathematics students are expected to attend the talks of other students. Documented evidence at 6 such talks is expected. Attendance sheets can be picked up from N519 Ross.

**Survey Paper Presentation**Daniel Beamish will give a talk entitled "

**A Review of Neural Networks in Remote Sensing**" at 3:00p.m. in N638 Ross.ABSTRACT:

*I will discuss remote sensing applications of artificial neural networks. Over the last twenty years neural networks have become an integral tool in the analysis and processing of the large amount of data produced by sensing platforms. The robustness and efficiency with which biological systems are capable of processing information makes them a natural choice for the analysis of multi-spectral and multi-sensor information. The most widely used application of neural networks has been the multi-layer perceptron as a supervised classifier of remotely sensed data. I will discuss recent developments, and review applications of recurrent architectures such as the Hopfield Networks, and Adaptive Resonance Theory, recently appearing in the literature.*Survey paper requirement for Masters students

Reminder: Master's Mathematics students are expected to attend the talk.

- Zenguo Qiu, York University, will speak on "
**Simplex Mixed Models for Longitudinal Proportional Data**" at 12:30p.m. in N638 Ross.ABSTRACT:

*In this thesis, we will present simplex mixed model, a extension of generalized linear mixed model (GLMM), based on the simplex distribution of Barndorff-Nielsen and Jorgensen (1991), which is suitable for modelling longitudinal continuous proportional data. The penalized quasi-likelihood (PQL) proposed by Breslow and Clayton (1993) for the GLMM first is modified for the simplex mixed models, then the parameter estimations for regression coefficients are carried out by the PQL and the estimates of variance parameters for random effects are then obtained by the corresponding restricted maximum likelihood (REML) method based on the PQL. However, the result of simulation study show that such PQL inference may seriously underestimate the variance parameters when the dispersion parameter is large. We then propose a new PQL and REML version for simplex mixed models via the high-order, multivariate Laplace approximation. A simulation study at different levels of dispersion parameters are conducted. The results show that the inference based on the proposed inference methods via high-order, multivariate Laplace approximation to the likelihood reduces the bias of estimations from the original PQL inference. Finally, the proposed methods are illustrated by analyzing some real-life data.*

**Applied and Industrial Mathematics and Graduate Seminar**Yuriy Kazmerchuk, York University, will speak on "

**Internship talk on Principal Component Analysis**" from 1:30p.m. to 2:30p.m. in N638 Ross.ABSTRACT:

*This talk is intended to emphasize different iterative techniques for performing Principal Component Analysis (PCA) with some applications to financial and marketing data. High dimensional data analysis is becoming increasingly common as new industrial problems are placing an ever-growing demand on computing resourses.**There were considered several modern and classical methods for realizing PCA. Results were tested on different data sets. The performance of written C++ codes was compared with performance of SAS routines.*

**Dissertation Colloquium**Wuwen Guo, will speak on "

**A Nonoverlapping Domain Decomposition Methods for Solutions of Partial Differential Equations**" at 3:30p.m. in N638 Ross.ABSTRACT:

*Lions nonoverlapping domain decomposition method is analyzed and explained using an optimal approach for the typical linear model $\-Delta u=f $ in $\Omega$ and $u=0$ on $\partial \Omega$. An optimization-based domain decomposition method for the solutions of partial differential equations is proposed. The crux of the method is solving a minimization problem for which the objective functional measures the interface bias in some sense. Lions iterative method and the proposed iterative procedure are generalized to solve a linear control partial differential equations and a class of nonlinear partial differential equations. Convergence and finite approximations are studied. The results of numerical experiments are given and show that the proposed iterative method generally converges faster than Lions iterative method.*

- Neil Roger, York University, will give a talk entitled "
**The Axiom of Choice**" at 3:00p.m. in N638 Ross.ABSTRACT:

*This talk will provide an introduction to the Axion of Choice, and explain when and why it needs to be invoked. The equivalence of the Axiom of Choice to Tychonoff's Theorem, Zorn's Lemma and Zermelo's Theorem will also be covered.*Seminar requirement for Masters students.

Reminder: Master's Matheamtics students are expected to attend the talks of other students. Documented evidence at 6 such talks is expected. Attendance sheets can be picked up from N519 Ross.

**PhD Oral**Geanine Tudose, York University will defend her PhD Dissertation entitled "

**On the Combinatorics of sl(n)-Fusion Algebra**" at 12:30p.m. in N638 Ross.

**Dissertation Colloquium and Applied Algebra**Geanina Tudose, York University, will speak on "

**On the combinatorics of sl(n)-fusion algebra**" at 12:30p.m. in N638 Ross.ABSTRACT:

*The fusion algebra also known as the Verlinde algebra plays a central role in the 2 dimensional Wess-Zumino-Witten models of conformal field theory. The study of the multiplicative structure of this algebra has received a lot of attention in the past decade due to the fact that it appears in an increasing number of mathematical contexts such as quantum cohomology, representations of quantum groups and Hecke algebras, knot invariants, vertex operator algebras, and others.**The $sl(n)$-fusion algebra can be viewed as a quotient of the ring of symmetric functions in $n$ variables by the ideal generated by Schur functions $S_\lambda$ indexed by partitions of length at most $n$ such that $\lambda_1-\lambda_n \leq k$ and $S_{1^n}-1$.**From representation theoretic arguments it is known that its structure constants N_{\lambda \mu}^{\nu}, called fusion coefficients, are non-negative integers. We will give a combinatorial description for these numbers for $\mu$ two column and hook partitions and a larger family of partitions obtained via fusion invariants. In addition we present a number of applications for these cases including the proof of the conjecture that the fusion coefficients are increasing with respect to the level.*

**M.A. Oral**Sergey Preobrazhensky, York University, will defend his Master's Thesis entitled "

**The Retrieval of Depth of Snow Cover from Remotely Sensed Information: Classification and Estimation**" at 2:00p.m. in N638 Ross.

**Survey Paper Presentation**Romana Danicic, York University, will give a talk entitled "

**One-Way Functions**" at 1:00p.m. in N638 Ross.ABSTRACT:

*Milestones of Modern Cryptography are one-way functions. Loosely speaking, a function is oen-way if it is easy to compute but hard to invert. We will formally define one-way functions and examine two potential candidates. We will also present how one-way functions can be used to implement certain cryptographic models (Secret Key Agreement, Digital Signatures) and state the relation between one-way functions and complexity theory.*Survey Paper requirement for Masters students.

Reminder: Master's Mathematics students are expected to attend the talk.

**Graduate Seminar**Ronit Rosenfield, York University, will give a talk entitled "

**Generating Functions in Combinatorics**" at 3:00p.m. in N638 Ross.ABSTRACT:

*The concept of generating functions will be introduced using ideas formed in George Polya's article "On Picture Writing" (1956). It will be shown how ordinary and exponential generating functions can be used to solve combinatorial problems involving selections, arrangements and partitions. Methods of calculating the coefficients of the terms in generating functions will be discussed, as well as how generating functions can be utilized to solve recurrence relations and to prove useful theorems.*

Reminder: Master's Mathematics students are expected to attend the talks of other students. Documented evidence at 6 such talks is expected. Attendance sheets can be picked up from N519 Ross.

**Thesis Colloquium**Sergey Preobrazhensky, York University, will speak on "

**The retrieval of depth of snow cover from remotely sensed information: classification and estimation**" at 1:30p.m. in N638 Ross.ABSTRACT:

*In this thesis we consider the problem of retrival snow depth from the remotely sensed information, obtained from the Special Sensor Microwave/Imager (SSM/I) and represents the passive microwave emission. 1) to reduce the number of parameters used in snow depth estimation; 2) to substitute the parameters obtained by the ground measurements by those remotely sensed; 3) to find the classification of source variables which provide the best estimation of snow depth. As the result of the research, we find the way to classify the variables which provide the good approximation results. The number of parameters were reduced to 4 from 8. We find possibility to estimate ground measured parameters by satellite measured.*

**PhD Dissertation**Mark Defazio, York University, will defend his PhD Dissertation entitled "

**On the Zeros of Some Quasi-Definite Orthogonal Polynomials**" at 2:00p.m. in N638 Ross.

**Graduate Seminar**Yumin Wang, York University, will give a talk entitled "

**Attractive Periodic Orbits in Nonlinear Discrete-Time Neural Networks with Delayed Feedback**" at 2:00p.m. in N627 Ross.ABSTRACT:

*We consider the discrete-time system describing the dynamic interaction of two identical neurons. We construct explicitely an attractive 2k-periodic orbit in the case where f is a step function(McCulloch-Pitts Model). For the general nonlinear signal transmissions functions, we use a perturbation argument and sharp estimates and apply the contrctive map princible to obtain the existence and attrctivity of a 2k-periodic orbit. This is contrast to the continuous case (a delay differential system) where no stable periodic orbit can occur due to the monotonicity of the associated semiflow.*Seminar Requirement for Masters students.

Reminder: Master's Mathematics students are expected to attend the talks of other students. Documented evidence at 6 such talks is expected. Attendance sheets can be picked up from N519 Ross.

**Dissertation Subject Oral**Zhaohui Zhang, York University, will speak on "

**Two-Wavelet Operator Theory****" at 1:30p.m. in N638 Ross.**