1996 Calendar of Events

December 1996

Wednesday, December 18

• Chris Henville will give a talk entitled "Axiom Systems of a Matroid" at 9:00a.m. in N638 Ross, York University
  ABSTRACT: Will present three axiom systems of a matroid.

  Seminar Requirement for MA Degree
  Master's Mathematics students are expected to attend the talk.

Tuesday, December 17

• Ph.D. Oral: Elliott Pearl will defend his PhD Dissertation: "Some Results in General Topology and Applications to Dynamical Systems: Homogeneity and Monotone Semiflows" at 3:00p.m. in 1158 Vari Hall

Monday December 16

• Topology Seminar: Gary Gruenhage (Auburn University) will give a talk entitled: "The Baire property in function spaces with the compact-open topology" at 4:00p.m. in N638 Ross

Monday, December 16

• Statistics Seminar: Liqun Wang (University of Basel, Switzerland) and Cheng Hsiao (University of Southern California, Los Angeles) will speak on "A Simulated Semiparametric Estimation of Nonlinear Errors-in-Variables Models" on Dec. 16, Monday, 1-2pm at N638R, York University
  ABSTRACT: This paper deals with a nonlinear errors-in-variables model where the error distributions are nonparametric and a prediction equation for unobserved covariates is available. Consistent and asymptotically normally distributed estimator is constructed using the combined approach of the method of nonparametric estimation and the method of simulated moments (MSM) of McFadden (1989) or Pakes and Pollard (1989). This semiparametric McFadden (1989) or Pakes and Pollard (1989). This semiparametric estimator achieves the root-T rate of convergence. Necessary and sufficient conditions of identifiability of the model are derived by using the Fourier deconvolution method.

  Keywords: Measurement Errors, Nonparametric Estimation, Method of Simulated Moments, Identification, Fourier Deconvolution.

Friday, December 13, 1996

• Ph. D. Oral: Qingning Zeng (York University) will defend her Ph.D. Dissertation entitled "Third Order Asymptotic Approach to the Generalized Behrens-Fisher Problem" on Friday, December 13, 3:00 p.m. in 1158 Vari Hall.

Friday, December 6, 1996

• Statistics Seminar: Dr. F. Hu (Singapore National University) will speak on "The Estimating Function Bootstrap" on Friday, December 6, 10:30 a.m. in N638 Ross York University
  ABSTRACT: Graphical statistical models have proven to be very useful in the analysis of multivariate dependencies, and can provide transparent representations of quite complex models. estimating function itself can be approximated, a confidence distribution for $\theta$ is induced and confidence regions can be simply defined. The procedure is termed the EF (Estimating Function) Bootstrap and, under fairly general conditions, can be shown to yield confidence intervals whose coefficients are accurate to first order. A simple studentized version is also defined and, in many instances, gives a second order approximation. In a number of examples, the method is shown to compare very well with classical bootstrap procedures. The intervals produced are more accurate, the method is more stable, and it has considerable computational advantage when compared to classical approach. A number of comments and suggestions for future research are also given.

Wednesday, December 4, 1996

• Category Seminar: Mr. Tran Kim Quang (York University) will speak on "Operads in Some Symmetric Monoidal Categories" on Wednesday, December 4, 4:00pm in N638 Ross York University
  ABSTRACT: Operads are one of the most powerful algebraic structures. Operads are described by explicit formulae. They are also viewed as monoids in symmetric monoidal categories. From this point of view, operads in some monoidal categories can be defined by common formulae.

Tuesday, December 3

• Dissertation Colloquium: Elliott Pearl will speak on "Some results in General Topology and applications to Dynamical Systems: Homogeneity and Monotone Semiflows" at 3:30 p.m. in N638 Ross.
  ABSTRACT: This thesis contains four chapters on unrelated topics from the fields of General Topology and Dynamical Systems.
  It is proven that the omega power of a first-countable zero-dimensional space is homogeneous. This answers a question of G. Gruenhage, posed as a New Classic Problem in Topology in 1990.
  The Baire property is examined in the case of finite products of a space and its dense subspace.
  The Theory of Monotone Semiflows is developed under weak order-preserving properties. This theory has already been developed by others under powerful montonicity conditions. Monotone Semiflows model an important class of continuous time dynamical systems. Set-theoretic examples are provided to show that these new order-preserving conditions are significantly weaker than the montonicity conditions previously known.
  A new class of Denjoy homeomorphisms is introduced. Denjoy homeomorphisms can be considered as the only interesting iterative dynamical systems on the open disk. This new class generalizes previous constructions.

November 1996

Friday, November 29, 1996

• Statistics Seminar: Dr. David Tritchler (Ontario Cancer Institute) will speak on "Reasoning about data with graphical representations" on Friday, November 29, 10:30 a.m. in N638 Ross York University
  ABSTRACT: Graphical statistical models have proven to be very useful in the analysis of multivariate dependencies, and can provide transparent representations of quite complex models. The graphs clearly depict the primary aspects of models by displaying assumptions and hypotheses of statistical dependence and independence. We will discuss graphical representations of some important problems in biostatistics: the scientific interpretation of interventions, the evaluation of candidate surrogate endpoints, and aspects of confounding in clinical trials.

Thursday, November 28, 1996

• Colloquium: Professor Claudio Albanese (University of Toronto) will speak on "TWO PROBLEMS IN MATHEMATICAL FINANCE: VALUE AT RISK AND DYNAMIC CALIBRATION" on Thursday, November 28, 4:00p.m. in 3006 Vari Hall, York University
  ABSTRACT: Finance and risk management are nowadays a rich source of challenging mathematical problems. After a review of the subject, this talk addresses two recent results in this area. The problem of Value at Risk can be formulated as a problem of Gaussian integration on the exterior of a quadric. This is an old problem first considered by Ruben in the '60s. Risk management makes one look at it in a new light and motivates the development of new elegant applications of harmonic analysis techniques. The problem of calibration risk is also a subject of high industrial interest. In this case, homogenization techniques for stochastic differential equations developed by Papanicolaou in the '70s are helpful and lead to new and more stable calibration techniques.
  Refreshments will be served at 3:30p.m. in the Departmental Common Room--N620R
  Everyone is Welcome!

Tuesday, November 26, 1996

• Probability Seminar: Douglas Blount (Arizona State University) will speak on "Sobolev Space Regularity for Super Brownian Motion and Some Related Processes" for surveys with a complex design" on Tuesday, November 26, 11:00 a.m. in N638 Ross York University
  ABSTRACT: This talk will discuss the use of Fourier transform techniques to obtain pathwise Sobolev space smoothness results for the $(\alpha, d, 1)$ superprocess on $R^d$. The main tool is a maximal inequality which may be of independent interest. The Sobolev space regularity of the occupation time processes of Brownian motion and Super Brownian motion will also be examined with simple proofs given for the existence of densities in certain cases.

Friday, November 22, 1996

• Statistics Seminar: Dr. W. Sun (BSMD, Statistics Canada) will speak on "Frequency valid multiple imputation for surveys with a complex design" on Friday, November 22, 10:30 a.m. in N638 Ross York University
  ABSTRACT: General conditions required for valid design-based inference when using multiple imputation for dealing with missing values are considered. We focus on the means or totals and the estimation of their variances. We study multiple and proper imputation under a general setting, concentrating on the mathematical and statistical conditions required for valid design-based inference, assuming the nonresponse mechanism is an additional phase of sampling.

Wednesday, November 20, 1996

• Category Seminar: Mr. Sandro Fusco (York University) will give the first of two talks on "Stable functors and the Grothendieck construction" on Wednesday, November 20, at 4 pm in N638 Ross. The second talk will be given on November 27, at 4 pm in N638 Ross.

Friday, November 15, 1996

• Statistics Seminar: Ms Xia Pan (York University) will speak on "Retrieve Snow Depth from Special Scanning Microwave Imager (SSM/I) Data" on Friday, November 15, 10:30 a.m. in N638 Ross York University
  ABSTRACT: Passive microwave remote sensing data were available to environmental monitoring. One of interesting problems is to retrieve snow depth from the remote sensing data. Traditionally, the linear retrieval algorithm was used. This project is to investigate statistical characteristics regarding temporal and spatial variability of snow depth as well as of remote sensing data. Principal component analysis and canonical correlation analysis were applied to develop a more efficient retrieval algorithm. Crude analysis results will be shown during the talk.

Friday, November 8, 1996

• Statistics Seminar: Professor C. Czado (York University) will speak on "Bayesian Analysis of Multivariate Categorical Response Data" on Friday, November 8, 10:30 a.m. in N638 Ross York University
  ABSTRACT: The development of adequate models for multivariate categorical response data with covariate adjustment has been an active research area in the last years. In the case, where interest is focused on marginal and association parameters, generalized estimating equations (GEE) (see for example Lipsitz, Laird and Harrington (1991) and Liang, Zeger and Qaqish (1992)) and likelihood (see for example Fitzmaurice and Laird (1993) and Molenberghs and Lesaffre (1994)) based methods have been proposed. The number of parameters required for the full specification of these models grows exponentially with the length of the response vecror Therefore, the analysis is often focused on marginal and first order parameters. In this case, the multivariate probit model (Ashford and Sowden (1970)) becomes an attractive alternative to the above models. The application of the multivariate probit model has been hampered by the intractability of the maximum likelihood estimator, when the length of the response vector is large. This paper shows that this difficulty can be over come by the use of Markov Chain Monte Carlo methods. This analysis also allows for valid point and interval estimates of the parameters in small samples. In addition, the analysis is adopted to handle the case of missing at random responses. Two examples will be presented. The first one involves binary responses measured at unequally spaced time points and is compared to a GEE analysis given in Fitzmaurice and Lipsitz (1995). The second example assumes ordered categorical responses.

  References:

  • Ashford, J.R. and Sowdon, R.R. (1970) Multivariate probit analysis, Biometrics, 26, 535-546.
  • Fitzmaurice, G.M. and Laird, N.M. (1993). A likelihood-based method for analysing longitudinal binary responses, Biometrika, 80, 1, 141-151.
  • Fitzmaurice, G.M. and Lipsitz, S.R. (1995). A model for binary time series data with serial odds ratio patterns. Appl. Statist., 44, No. 1, 51-61.
  • Liang, K.-Y, Zeger,S.L. and Qaqish, B. (1992). Multivariate regression analyses for categorical data (with discussion). J.R. Statist. Soc. B, 54, 3-40.
  • Lipsitz, S.R., Laird, N.M. and Harrington, D.P. (1991). Generalized estimating equations for correlated binary data: using the odds ratio as a measure of association, Biometrika, 78, 153-160.
  • Molenberghs, G. and Lesaffre, E. (1994). Marginal Modeling of Correlated Ordinal Data Using a Multivariate Plackett Distribution. J. Amer. Statist. Soc. , 89, No. 426, 633-644.
• Algebra/Statistics Seminar: Professor Yuri Medvedeev (York University) will give an introduction to Jordan Algebras on Friday, November 8, 2:00p.m. in N638 Ross York University
  

Thursday, November 7, 1996

• Colloquium: Professor Terry Gannon (York University) will speak on "Monstrous Moonshine" on Thursday, November 7, 4:00p.m. in 3006 Vari Hall, York University
  ABSTRACT: John McKay noticed in 1978 that 196884 nearly equals 196883: the former is the first nontrivial coefficient of the j-function, which generates all functions invariant under the modular group PSL(2,Z); the latter is the dimension of the first nontrivial irreducible representation of the Monster, which is the largest of the sporadic finite simple groups. Soon after that Conway and Norton proposed a number of conjectures, called Monstrous Moonshine, generalizing and exploring McKay's observation. Though most of these conjectures are now proven, these connections between finite groups and modular functions remain very mysterious, and connections with other algebraic structures are being made. In this elementary talk I will describe the Conway-Norton conjectures, their proof by Borcherds and Frenkel-Lepowsky-Meurman, and my own contribution to the subject.
  Refreshments will be served at 3:30p.m. in the Departmental Common Room N620R.

Wednesday, 6, 1996

• Category Seminar: Professor Joan Wick Pelletier (York University) will give the second talk of a two-talk series on "Simple Involutive Quantales" on Wednesday, November 6, 1996 at 4:00p.m. in N638 Ross York University.

  Future talks: On November 13 and 20, S. Fusco will speak on "Stable functors and the Grothendieck construction".

Tuesday, November 5, 1996

• Awards Ceremony: The annual Awards Ceremony for presenting our best students with awards recogning their academic achievements will be held on Tuesday, November 5 at 5:30 in Vari Hall Lecture Hall A, and will be followed by a reception in Room N620.

Monday, November 4, 1996

• Econometrics Seminar: Xiaohong Chen (University of Chicago) will speak on "Asymptotic properties of sieve extremism estimates" on November 4 (Monday), 4:00-5:00pm 1063 VARI HALL, York University.

Friday, November 1, 1996

• Statistics Seminar: Mr. Pflueger (University of Gottingen, Germany) will speak on "Bioequivalence testing in a parametric multivariate setting" on November 1 (Friday), 10:30am -11:30 at Room N638 Ross, York University
  ABSTRACT: The general problem is testing $\mbox{H}_0: \mu \notin \Gamma$ versus $\mbox{H}_1: \mu \in \Gamma$ with observed $X_1,\ldots, X_n$ i.i.d. $N_p(\mu, \Sigma)$. I consider the practical relevant case of unknown $\Sigma$. In such a general setting testing is only possible by estimation of confidence regions for $\mu$ and to compare them with $\Gamma$. I take as example two estimates, one based on Hotelling's $T^2$-test and another developed recently by Brown et al. (1995, JASA).

  Restricting $\Gamma$ to the reasonable form of $\left\{\mu: \mu'A\mu > \delta \right\}$ with $A$ positive definite and $\delta$, without loss of generality, equals to 1, one can then consider testing with the quadratic form $\overline{X}'A\overline{X}$. To do so, approximations and asymptotic results for its distribution have to be used.

  At the end I compare the achieved test in power in a simulation study.

• Seminar in history & philosophy of mathematics and math education: Mr. Hugh McCague (Faculty of Environmental Studies, York University) will speak on "GOD the geometer during the middle ages" on Friday, November 1, 1996 at 4:00-5:00 p.m. in N638 Ross Bldg. York University
  ABSTRACT: God was seen as the quanifier, orderer, and geometer of the universe. This took a dramatic, visual form, in the more than forty extant medieval manuscripts that depict God the Creator wielding a large compass. Earlier sources of this idea and imagery appear in the Platonic and Judaic-Christian traditions. This notion was central to the theology and philosophy underlying medieval mathematics, and practical geometry. There is a continuance of this conception and metaphor in some philosophical interpretations of twentieth-century mathematics and science.
• Analysis Seminar: Mr. G. Mihai Iancu (Department of Mathematics and Statistics, (York University) will speak on "Spectral Mapping Theorems for Semigroups and Semilinear Heat Equations in Hilbert Spaces" on Friday, November 1, 1996 at 4:00 p.m in 1022 Vari Hall, York University
  ABSTRACT: New spectral mapping theorems for strongly continuous one-parameter semigroups of bounded linear operators on Hilbert spaces are presented. We describe how these theorems can be used to obtain new results on the asymptotic properties of global solutions (in time) of semilinear heat equations in Hilbert spaces. Semilinear heat equations modelled by pseudo-differential operators, i.e., observables in relativistic quantum mechanics, are shown to best fit these functional analytic results. (Joint work with M. W. Wong)

October 1996

Wednesday, October 30, 1996

• Algebra Seminar: Dr. David Doniz (University of Leeds) will speak on "Residual properties of groups" on Wednesday, October 30, 1996 at 2:30pm in Room N638 Ross, York University.
  (This will be a general talk, suitable for a general algebraic audience.)

Monday, October 28, 1996

• Applied Mathematics Seminar: Professor Jeff Edmonds (Computer Science, York University) will speak on "Multiprocessor scheduling with no information" on Monday, October 28, 1996 at 4:00p.m. in S175 Ross, York University.
  ABSTRACT: There is pressure, at least in the Computer Science department, to be more practical. As a theory person, this is a little scary. However, I am finding that computer science is filled with many practical problems that can be posed as quite elegant and interesting math problems. I am going to present one such problem. I have a solution to part of it. The systems people seem happy, and it only took a little calculus. The problem is not completely solved, and I thought perhaps someone in the math department would like to think about it.

  We consider schedules of parallel jobs where:

  • goal is to minimize average completion time of jobs
  • preemption is allowed (i.e. changing # processors allocated)
  • all jobs arrive at time zero
  • each job has an arbitrary number of phases. each phase has an amount of work and an arbitrary (non-decreasing, sub-linear) speed up curve (i.e. with b processors, S(b) work gets done per time unit.

  Optimal schedule is hard to find.

  Equal partition (round robin) is a schedule that gives P/n processors to each job when there are P processors and n jobs remaining in the system.

  • It requires no information about the jobs.
  • Rescheduling need only be done log n times (with small adjustment)
  • Very little computation time required.

  We prove (the surprising) result that Average completion time for EQUI is within 3.7 of optimal.

  The next step is to consider jobs arriving at arbitrary times.

Wednesday, October 23, 1996

• Category Seminar: Professor Joan Wick Pelletier (York University) will speak on "Simple Involutive Quantales" on Wednesday, October 23, 1996 at 4:00p.m. in N638 Ross York University, as part of a two-talk series. The second talk will be given on November 6.
  Future talks: On November 13 and 20, S. Fusco will speak on "Stable functors and the Grothendieck construction".

Friday, October 18, 1996

• Algebra/Statistics Seminar: Professor Helene Massam (York University) will speak on "The Wishart family of distributions as an exponential dispersion model'' on Friday, October 18, 1996 at 2:00p.m. in N638 Ross York University
  ABSTRACT: Statisticians who have missed the first two lectures should have no trouble following this. Indeed in the first lecture, we basically introduced the Wishart distribution as the distribution of the sum of squares of independent centered normals and the second lecture was devoted to a quick review of basic probability concepts.

Thursday, October 17, 1996

• Colloquium: Professor Jeremy Gray (Faculty of Mathematics and Computing, Open University, Milton Keynes, England and Dibner Institute for the History of Science and Technology, Cambridge, Massachusetts) will speak on "Poincare's Discovery of Fuchsian Functions, and Hadamard's Commentary'' on Thursday October 17, 1996 at 4:00p.m. in 3006 Vari Hall York University
  ABSTRACT: In 1880 Poincare wrote an essay for a prize competition on differential equations. He followed this essay with three supplements that document his path to the discovery of automorphic functions. They have never been published, and they shed an interesting light on his way of working, and the importance non-Eculidean geometry had for him. In the 1920s Jacques Hadamard wrote a monograph for a Russian; it seems that the French original is lost. This fascinating commentary is now being translated by Abe Shenitzer, and it forms the subject of the second part of the talk.
  Refreshments will be served at 3:30p.m. in the Departmental Common Room--N620.
• Category Seminar: Professor Walter Tholen (York University) will speak on "Presentation of relations by partial maps" on Thursday, October 17, 1996 at 4:00p.m. in N638 Ross, York University
  ABSTRACT: It is known from topos theory that the presentation of relations by multivalued functions establishes a universal description of power sets; in fact it can be take to be the defining property of a topos, i.e. of any generalized mathematical universe. We shall present an improved version of a theorem given in X. Dong's thesis, which deals with the categorical presentation of relations as multivalued maps with NON-EMPTY values, and with the role of the "pierced power set".

Saturday, October 5, 1996

• Conference: Mathematics and its History in celebration of the 75th birthday of Abe Shenitzer. Speakers include Ed Barbeau, Harold Edwards, Peter Hilton, Walter Littman, and Helena Pycior. See announcement. Contact Israel Kleiner or Martin Muldoon, coorganizers of the conference.

September 1996

Friday, September 27, 1996

• Analysis Seminar: Ryuichi Ashino (College of Industrial Engineering, Japan) will speak on "Multiwavelets" on September 27, 1996 at 4:00 p.m. in V. H. 1022, York University
  ABSTRACT: Multiwavelets are generalizations of orthonormal wavelet bases. A class of r-regular multiwavelets, depending on the smoothness of the multiwavelet functions, is introduced. A class of split-type multiwavelets is defined and some examples are given. It is shown that for some multiwavelets, the support or width of a wavelet is shorter than the support or width of the scaling function, but the regularity and vanishing moments are the same. It is also shown that, in the case of unbounded support, symmetry and anti-symmetry are preserved.

Thursday, September 26, 1996

• Graduate Seminar: Richard Baldwin will speak on "Some knot invariants" on September 26, 1996 at 2:30 p.m. N638 Ross, York University
  ABSTRACT: The paper surveys some old and new invariants of classical knots (tame embeddings of the one-sphere in the three-sphere), from the knot complement to knot energies.

Friday, September 20, 1996

• Ph.D. Oral: Xiaomin Dong will defend his Ph.D. Dissertation entitled "Representation of Partial Maps and Relations, and the Span-Map Adjunction" on Friday September 20, 1996 at 2:30 p.m. in 1154 Vari Hall.

Tuesday, September 17, 1996

• Probability Seminar: Remco van der Hofstad (Utrecht, visiting McMaster) will speak on "Probabilistic polymer models" on September 17, 1996 at 1:30 p.m. in N638 Ross, York University
  ABSTRACT: This talk will discuss models for polymers based on Brownian motion and random walks. I will begin with an introduction to these models, explaining why they model polymers, what conjectures there are, etc. Then I will go deeper into the one-dimensional models and the results there.

Monday, September 16, 1996

• Ph.D. Oral: Xiaojin Yuan will defend her Ph.D. Dissertation entitled "The Box and Cox Problem: Asymptotic Significance Levels" on Monday, September 16, 1996 at 4:00 p.m. in N627 Ross.

Friday, September 13, 1996

• M.A. Oral: Constanze Pumpluen will defend her M.A. Thesis entitled "A General Riesz Decomposition Theorem for Charges" on Friday September 13, 1996 at 2:30 p.m. in 1154 Vari Hall.
• Probability Seminar: Krishna B. Athreya (Iowa State University) will speak on "Change of measures for Markov chains and the LLOGL theorem for general state space branching processes" on September 13, 1996 at 2:30 p.m. in 1152 Vari Hall, York University
  ABSTRACT: Let P be a transition function with a strictly positive eigenfunction V and let Q be the V-biased transform of P. The absolute continuity of the measures on the Markov chains corresponding to P and Q but with the same initial measure is studied via a natural martingale. It is applied to derive the Kesten Stigum LLOGL theorem for general state space branching processes following the methods of Pemantle, Peres and Lyons.
• Dissertation Colloquium: Xiaojin Yuan will speak on "Asymptotic Inference in the Box & Cox Problem" on September 13, 1996 at 3:00 p.m. in N638 Ross, York University
  ABSTRACT: In many applications a transformation of the response variable is required to make a normal-theory linear model plausible. Box and Cox (1964) recommend that, having chosen a suitable transformation, we should estimate and interpret effects on this transformed scale, ignoring the fact that the transformation was estimated from the data. In the same paper, they developed the Bayesian and first order likelihood procedures.
  Recent asymptotic theory has produced highly accurate third order tests in the case where the variable and parameter are of the same dimension. In order to reduce the general model to the preceding special case, attempts have been made to determine the third order ancillary, or the information needed from it for third order ancillary, or the information needed from it for third order inference. In this thesis, the third order procedure for testing the transformation parameter in the Box & Cox model is developed, for normal and nonnormal errors, the appropriate approximate ancillary is derived, and simulation is performed to determine the accuracy of the procedure. Comparisons with Bayesian and first order methods are also made.

Wednesday, September 11, 1996

• Thesis Colloquium: Constanze Pumpluen will speak on "A General Riesz Decomposition Theorem for Charges" on September 11, 1996 at 4:00 p.m. in N638 Ross, York University
  ABSTRACT: Finitely additive real- or complex valued set functions on a Boolean algebra of sets, called charges, are important in many parts of mathematics. Charges, which are sigma-additive, are the well-known measures playing a central role in measure theory, integration and probability theory. In order to see if a charge that is not a measure can be "approximated" by a measure or by another charge having special properties, one is interested in finding unique representations of charges permitting an answer to these questions.
  In this thesis a general Riesz decomposition theorem is proved giving a unique representation for every positive charge as a sum of two elements, one belonging to a fixed set M of positive charges and the other one to its orthogonal complement. By specializing the set M, one gets several famous representation theorems as easy corollaries.
• Graduate Seminar: Clara Auyeung will speak on "Binary Convolutional Codes" on September 11, 1996 at 4:00 p.m. 1016 Vari Hall, York University
  ABSTRACT: This seminar will deal with the encoding and decoding of binary convolutional codes. These codes differ from block codes in that the encoder must possess a memory element. The truncated viterbi decoding algorithm will be briefly discussed.

Tuesday, September 10, 1996

• Dissertation Colloquium: Xiaomin Dong will speak on "Representations of Partial Maps and Relations, and the Span-Map adjunction" on September 10, 1996 at 4:00 p.m. in N638 Ross, York University
  ABSTRACT: In this dissertation, we investigate partial maps in poset-enriched categories. Based on the theory of partial products and pullback complements developed by R. Dyckhoff and W. Tholen, we study the chain C --> Par(C) --> Rel(C) --> Span(C) for a poset-enriched category C, and establish an adjunction at each stage.
  We also consider map factorizations in preorder-enriched categories, generalize these notions from a 2-categorical environment to a pseudo context and construct the Span-Map adjunction.

Thursday, September 5, 1996

• Graduate seminar: Ioulia Ioffe will speak on "Distributions and partitions" on Thursday, September 5, 1996 at 4:00 p.m. in N638 Ross, York University
  ABSTRACT: Many problems in real life involve the separation of a series of elements into a series of classes. The number of ways in which this can be done is of great interest. In this talk a few types of problems of this kind will be discussed and their solutions will be presented.

August 1996

Wednesday, August 23, 1996

• Geometry seminar: Ludwig Danzer, University of Dortmund, will speak on "Species of aperiodic but strictly ordered tilings" on Wednesday, August 21 at 2 p.m. in Seminar Room, N638 Ross Building, York University

January 1996

Thursday, January 4, 1996

• Restructuring Committee: Retreat to discuss: "THE FUTURE OF MATHEMATICS AND STATISTICS AT YORK" from 9:30 am to 4:OO pm, Room 305 York Lanes. See agenda.

Monday, January 8, 1996

• Classes: first day.

Wednesday, January 10, 1996

• Meeting of Statistics Section: There will be a meeting of the Statistics Section from 12:30 to 1:30 p.m. in N627R. See agenda.
• Graduate Seminar: Matthew Elmslie will speak on "Ramsey Numbers" at 2:30 p.m. in N638 Ross. See abstract.

Thursday, January 11, 1996

• Colloquium: Professor John C. Stillwell of the Department of Mathematics, Monash University, Australia, will speak on "WHAT IS CALCULUS?" at 4:00 p.m. in N203 Ross Building. See abstract.

Friday, January 12, 1996

• Graduate Seminar: Christopher Benson will give a talk entitled "A Proof of Brown's Algorithm for Solving a Two-Person Game" at 2:00 p.m. in N638 Ross See abstract.
• Analysis Seminar: Man Wah Wong will speak on sampling theorems and signal analysis at 4:00 pm in N638 Ross. See proposal for seminar.

Friday, January 19, 1996

• Statistics Seminar: Professor Eli Posner, Department of Statistics, University of Toronto, will speak on "Nonparametric Regression for Arbitrary Random Processes with Applications to Nonlinear System Output Prediction," at 10:30 a.m. in N638 Ross. See abstract.
• Topology Seminar: Xiao-Qiang Zhao, Institute of Applied Mathematics, Academia Sinica, Beijing, China, will talk on "The Theory of Monotone Dynamical Systems," at 12:30 p.m. in N638 Ross. See abstract
• Seminar in History & Philosophy of Mathematics and Math Education: Professor John Stillwell, Department of Mathematics, Monash University, Melbourne, Australia, will give a talk entitled "From Pythagorean Triples to Eulerian Quadruples," at 2:45 (PLEASE NOTE TIME CHANGE) in N638 Ross. See abstract.
• Analysis Seminar: Professor Man Wah Wong, York University, will continue to talk on "Signals, Wavelets and Localization Operators," (joint work with Zhiping He) in N638 Ross. See abstract

Saturday, January 20, 1996

• Classes: Last day for registered students to enrol in Term W courses without the approval of the course director.

Tuesday, January 23, 1996

• Department meeting: will be held at 4 p.m. in S173 Ross. See Council Home Page for agenda and minutes of last meeting.

Wednesday, January 24, 1996

• NEW Algebra and Topology Seminar: First meeting on "compact groups," will take place at 2:30 in N638 Ross. See organizational message.

Friday, January 26, 1996

• Graduate Social: At 1 p.m. in N620 Ross. See poem.

  There will be cards, drink (and not just your regular kind) and food to spare, so bring the kids and have some fun. We are looking forward to seeing as many of you as possible! We go till we drop -- so come and join in!

• Classes: Last day to enrol in Term W courses with the approval of the course director.
• Statistics Seminar: Professor S.R. Chamberlin, York University, will speak on "The Third Property of Mathematical Likelihood" at 10:30 a.m. in N638 Ross. See abstract.
• Topology Seminar: Alexander V. Arhangelskii, Ohio University and Moscow State University, will speak on "Relative topological properties: some results and problems" at 12:30 p.m. in N638 Ross.
• Ph.D. Defense: George Delistathis will defend his Ph.D. dissertation entitled "A Regular Space with a Countable Network and Different Dimensions - Compact Spaces with Few Regular Open Baire Subsets," at 2:15 p.m. in S130 Ross. Anyone interested is welcome to attend.

Tuesday, January 30, 1996

• Fourth Dynamical Systems Day: Professor Raymond Kapral, University of Toronto, will talk on "Chaotic Chemical Fronts," at 10:10 a.m. in N638 Ross. See abstract.
• Fourth Dynamical Systems Day: Professor Kaijun Zhan, University of Guelph, will talk on "Generalized Hopf Bifurcations and Vortex-induced Vibration Problems," at 11:10 a.m. in N638 Ross. See abstract.

February 1996

Thursday, February 1, 1996

• Computer Announcement: The Mathstat machines will go down briefly around 5 p.m. to allow the installation of a new CD-ROM.

Friday, February 2, 1996

• Topology Seminar: Jianping Zhu will speak on "Q-points and composants of $H^*$". at 12:30 p.m. in N638 Ross.
• Computer Science Distinguished Lecture Series: Bart Selman, AT&T Bell Laboratories, will give a talk entitled "Stochastic Search and Phase Transitions: Artificial Intelligence Meets Physics," at 1:30 p.m. in CCB115. See abstract.
• Graduate Seminar: Eng Ong will give a talk entitled "Lidstone's Theorem" at 2:00 p.m. in S536 Ross. See abstract.
• Pure Math Curriculum Committee: will meet at 2:30 p.m. in N627 Ross.See agenda.
• Seminar in History & Philosophy of Mathematics & Math. Educ: Professor P Rajagopal, Department of Mathematics & Computer Science, Atkinson College, York University, will give a talk on "Indian Mathematics in the 1850s," at 2:45 in N638 Ross. See abstract.
• Colloquium: Professor Mark A. Kon, Department of Mathematics, Boston University, will give a talk entitled "Can we recover a function from the maxima of its wavelet expansion?" at 4 p.m. in N638 Ross. See abstract.

Tuesday, February 6, 1996

• Applied Math/Probability Seminar: Chris Soteros, University of Saskatchewan, will talk about "Collapsing Lattice Animals" at 1:30 p.m. in N638 Ross. See abstract.

Thursday, February 8, 1996

• Colloquium: Professor H. Freedman of the University of Alberta will speak on "Mathematical Models describing interactions between Agriculture, Industry and Environment," at 4:00 p.m. in N203R. See abstract.

Friday, February 9, 1996

• Topology Seminar: Jianping Zhu will continue to speak on "Q-points and composants of H^*" at 12:30 p.m. in N638 Ross.
• Graduate Seminar: Tina Haller will talk on "Clinical Trials" at 2:00 p.m. in S536 Ross. See abstract.
• Algebra/Category Seminar: Walter Tholen will give a talk entitled "Separation versus Connectedness," at 2:30 p.m. in N637 Ross. See abstract.
• Analysis Seminar: Zhiping He of York University will give the first of a series of lectures entitled "An Introduction to the Continuous Wavelet Transform" at 4:00 p.m. in N638 Ross. See abstract.

Saturday, February 10, 1996

• Classes: Last day to withdraw from Term Y courses without receiving a grade.

Wednesday, February 14, 1996

• Executive Committee: meets from 12:30 to 2:00 in N627 Ross.

Friday, February 16, 1996

• Graduate Social: celebrating "Valentine's Day" at 1:00 pm in N620 Ross. Refreshments will be served.
• Topology Seminar: Xiao-Qiang Zhao will resume a series of talks on "The Theory of Monotone Dynamical Systems," at 12:30 p.m. in N638 Ross. See abstract
• Algebra/Category Seminar: Walter Tholen will give part II of a talk entitled "Separation versus Connectedness" at 2:30 pm in N638 Ross. See abstract.
• Analysis Seminar: Zhiping He of York University will give the second of the lecture series entitled "An Introduction to the Continuous Wavelet Transform" at 4:00 p.m. in N638 Ross Building.

Monday, February 19, 1996

• Visit: Prof. David Brillinger visits from Berkeley as an appraiser for the OCGS review of the graduate programmes. He will stay two days. See message for further information or contact the Director of the Graduate Programme, David.Promislow@mathstat.yorku.ca.

Tuesday, February 20, 1996

• Department meeting: *** postponed possibly to March 5 ***. See message.

Thursday, February 22, 1996

• Colloquium:Krzysztof Ciesielski (West Virginia University) will give a talk on "Set Theoretic Analysis" at 4:00 p.m. in N203 Ross. See abstract. Cookies and coffee will be available from 3:30 in the lounge.

Friday, February 23, 1996

• Topology Seminar: Xiao-Qiang Zhao will continue a series of talks on "The Theory of Monotone Dynamical Systems," at 12:30 p.m. in N638 Ross. See abstract
• Algebra Seminar:Professor Trueman Machenry will speak on "A subgroup of the group of multiplicative arithmetic functions," at 2:30 pm in N638 Ross. See abstract.
• Analysis Seminar:Zhiping He of York University will give the third (also the last) of the first series of lectures entitled "An Introduction to the Continuous Wavelet Transform" at 4:00 p.m. in N638 Ross Building.

Monday, February 26, 1996

• First day of Reading Week

March 1996

Friday, March 1, 1996

• Last day of Reading Week

Monday, March 4, 1996

• Statistics Seminar: Dr. Yodit Seifu will give a talk entitled "Local Lyapunov Exponents: Results and Applications," at 11:30 in N 638 Ross. (Dr. Seifu is a candidate for a position in Statistics) See abstract.

Tuesday, March 5, 1996

• Probability Seminar: John Verzani (York University) will give a talk entitled "Some Path Properties of the Planar Brownian Snake," at 1:30 p.m. in N638 Ross. See abstract.
• Physics and Astronomy Seminar: E. J. Janse van Rensburg will give a talk entitled " Monte Carlo Study of the Theta Point in Collapsing Trees" at 3:30 in Room 317, Petrie. (Refreshments will be served in Petrie 315 at 3:00 p.m.) See abstract.
• Department meeting: will be held in S173 Ross from 4 pm to 6 pm. See agenda and minutes.

Wednesday, March 6, 1996

• Graduate appraisal: First day of a two day visit by Professor Angelo Mingarelli of Carleton. See announcement.
• Statistics Seminar: Mr. Peter Xue-Kun Song will give a talk entitled "Stationary Time-Series Models With Exponential Dispersion Model Margins," at 11:30 in N 638 Ross. (Mr. Song is a candidate for a position in Statistics) See abstract.

Friday, March 8, 1996

• Statistics Seminar: Dr. Michael Xiaopeng Dong will give a talk entitled "Estimating Density Functions: A Constrained Maximum Likelihood Approach," at 11:30 in N 638 Ross. (Dr. Dong is a candidate for a position in Statistics). See abstract
• Algebra Seminar: Professor Trueman Machenry will give a second talk entitled "On a subgroup of the group of multiplicative arithmetic functions," at 1:45 pm in N638Ross. See abstract.
• History and Philosophy of Math. and Math. Education: Professor V. Tikhomirov, Moscow State University & Mathematical College of Moscow Independent University, will give a talk on "The History of Functional Analysis" at 2:45 pm in N638 Ross. See abstract.
• Dissertation subject oral: Ying Zhang will speak on "Resonance problems for semilinear pseudo-differential operators," at 3 p.m. in Room 1154 Vari Hall.

Saturday, March 9, 1996

• Classes: Last day to withdraw from Term W courses without receiving a grade.

Monday, March 11, 1996

• Statistics Seminar: Dr. Joan Xiaoquiong Hu will give a talk entitled "Analyses of Data from Post-Market Studies," at 11:30 in N 638 Ross. (Dr. Hu is a candidate for a position in Statistics). See abstract.

Friday, March 15, 1996

• Graduate Seminar: Tilaye Teshager will give a talk entitled "An application of the Principle of Maximum Entropy to the study of an M/M/1 queueing system." at 11:15 a.m. in N638 Ross.
• Topology Semianar: Xiao-Qiang Zhao will continue a series of talks on "The Theory of Monotone Dynamical Systems," at 12:30 p.m. in N638 Ross. See abstract
• Social: The departmental graduate student association will host a social in the departmental lounge from 1 p.m. All are invited.
• Graduate Seminar: Constanze Pumpluen will give a talk entitled "Complete Valuation Rings and P-adic Numbers" at 3:30 in 1154 Vari. Masters Mathematics students are expected to attend this talk.

Tuesday, March 19, 1996

• Probability Seminar Vladimair S. Korolyuk (Institute of Mathematics, National Academy of Science of Ukraine, Kiev) will speak on "Ruin problems: Explicit and asymptotic approaches" at 1:30 p.m. in N638 Ross. See abstract.

Wednesday, March 20, 1996

• Statistics Seminar: Dr. Kalyanee Viraswami of the Department of Statistics at Oxford University will speak on Higher order results on some robust test statistics under model misspecification at 11:30 a.m. in N638 Ross.

Thursday, March 21, 1996

Probability Seminar: Neil O'Connell (BRIMS, Hewlett Packard Labs, Bristol, U.K.) will speak on "Large deviations for sample paths indexed by the half line" at 11:30 a.m. in N638 Ross. See abstract.

Friday, March 22, 1996

• Topology Seminar: Vl. Todorov of the University of Sofia, Bulgaria will speak on transitive shift operators at 12:30 p.m. in N638 Ross. Abstract to follow.
• SEMINAR IN HISTORY &PHILOSOPHY OF MATH AND MATH EDUCATION: Professor Guenther Frei of the Department of Mathematics and Statistics, University of Laval will give a talk on "EULER'S CONVENIENT NUMBERS" at 2:45 p.m. in N638 Ross. See abstract.
• Graduate Seminar: Eng Ong will speak on "MODELS IN MULTIPLE DECREMENT THEORY" at 3:30 p.m. in 1154 Vari Hall.
• Graduate Seminar Constanze Pumpluen will give a talk entitled "HENSEL'S LEMMA" at 4 p.m. in Ross S175.
• Departmental Colloquium: Prof. Rongqing Jia of the Department of Mathematical Sciences, University of Alberta will speak on "Approximation and Smoothness Properties of Wavelets" in N638 at 4:00 p.m. Refreshments will be served in N620 Ross at 3:30 p.m. See abstract.

Friday, March 29, 1996

• Party: The YGMA hosts a social in the lounge N620 between 1 p.m. and 5 p.m..
• Topology Seminar: Jianping Zhu will speak on "+Ramsey filters and \alpha_i spaces" at 12:30 p.m. in N638 Ross. See abstract.
• Topology Seminar: Prof. Franya Franek (McMaster) will speak on "Structural Properties Of Universal Minimal Dynamical Systems For Discrete Semigroups - the last chapter". at 1:30 p.m. in N638 Ross. See abstract.
• Seminar in History & Philosophy of Mathematics & Math. Educ: Hardy Grant (Emeritus Professor, York University) will give a talk on "SOME THOUGHTS ON THE HISTORY OF BEAUTY IN MATHEMATICS" at 2:45 p.m. in N638 Ross.
• Graduate Seminar: Maurice Tsang will give a talk entitled "Stationary Population Model" at 3:00 p.m. in 1154 Vari Hall. Masters students are expected to attend the talk. See abstract way below.

April 1996

Thursday, April 4, 1996

• First day of Passover No examinations will be scheduled on the evenings prior to, nor during this day. However, classes will be held, and university offices will be open normal hours.

Friday, April 5, 1996

• Second day of Passover
• Good Friday: University closed.

Wednesday, April 10, 1996

• Seventh day of Passover No examinations will be scheduled on the evenings prior to, nor during this day. However, classes will be held, and university offices will be open normal hours.

Thursday, April 11, 1996

• Eighth day of Passover No examinations will be scheduled on the evenings prior to, nor during this day. However, classes will be held, and university offices will be open normal hours.
• Colloquium: Professor Donald St. P. Richards, of the Department of Statistics at the University of Virginia will speak on "Algebraic Methods towards Higher-Order Probability Inequalities" at 4 p.m. in N638 Ross. See abstract.

Friday, April 12, 1996

• Classes: Terms Y, W classes end.
• Statistics Seminar: Professor Ka-Sing Lau of the Department of Mathematics and Statistics at the University of Pittsburgh will speak on "The Discount Sum of Bernoulli Random Variables" at 10:30 a.m. in N638 Ross. See abstract.
• Graduate Seminar: Kam Cheung Ko will give a talk entitled "SOME MATHEMATICAL MODELS FOR THE UNCERTAINTY INDUCED BY FUZZINESS" 12:00 p.m. in S176 Ross. See abstract.
• Social: The YGMA hosts an end of term party in the lounge N620, from 1 p.m. to 4 p.m.. All are welcome to attend.
• Seminar in History & Philosophy of Mathematics and Mathematics Education Professor Trueman MacHenry (York University) will speak on "COUNTING REVISITED" at 2:45 p.m. in N638 Ross.

Saturday, April 13, 1996

TORONTO SPRING MEETING
A Weekend Meeting on Category Theory and Its Applications
YORK UNIVERSITY, North York (Metropolitan Toronto)
Saturday/Sunday, April 13/14, 1996
Announcement and Information

Monday, April 15, 1996

• Examinations: First day. (Last day to submit term work).

Tuesday, April 16, 1996

• M.A. Thesis Defense G. Mihai Iancu will speak on "GLOBAL SOLUTIONS OF SEMILINEAR EVOLUTION EQUATIONS IN HILBERT SPACES" at 3:00 p.m. in 1158 Vari Hall.

Thursday, April 18, 1996

• Category Theory Seminar: Professor Maria Cristina Pedicchio (University of Trieste, Italy) will give a lecture on "Grids and topological systems" at 2:30pm in N638Ross.
• Category Theory Seminar: Walter Tholen will give a talk on "Separated and connected maps" at 3:30pm in N638Ross.
• Category Theory Seminar: Dr. Dorette Pronk (Rijksuniversitet Utrecht and Dalhousie University) will speak on "Etendues and Stacks" at 4:30 in N638Ross.

Tuesday, April 23, 1996

• Probability Seminar: George L. O'Brien will speak on "Loosening Tightness" at 1:30 p.m. in N638 Ross.
  Abstract:
  Conditions are given which are equivalent to uniform tightness in the weak convergence context and exponential tightness in the large deviation context. It is shown both by general considerations and by virtue of examples that these conditions can be much easier to verify than tightness itself. In one example, Donsker's funtional central limit theorem in D[0,1] is shown to be a simple consequence of the corresponding theorem for C[0,1] and that in particular, no detailed consideration of compact sets in D[0,1] is required. In a second example, a relatively simple tightness argument is provided for a large deviation principle for a class of processes including all spectrally positive stable processes.
• Council Meeting: There will be a meeting of departmental council at 4:00 p.m. in S173R. Please submit any other agenda items as soon as possible.
  Agenda:
  
  • Restructuring

Thursday, April 25, 1996

• Graduate Seminar: Qunsheng Zhou will give a talk entitled "CONSISTENT ESTIMATES OF SUPER IMPOSED EXPONENTIAL SIGNALS WHEN SOME OBSERVATIONS ARE MISSING" at 10:00 a.m. in N638 Ross. This is a seminar requirement for the M.A. degree of the speaker. All other M.A. Statistics students are required to attend.
  Abstract:
  Methods are proposed for estimating the parameters of undamped exponential signals when observations are missing. Some consistency results have been established. The finite sample behavior of the proposed methods have been studied by Monte Carlo simulation.
• Graduate Seminar: Guojie Liu will give a talk entitled "Sinusoidal Signals With Random Amplitude: Least-Square Estimators and Their Statistical Analysis" at 11:00 a.m. in 638 Ross. This is a seminar requirement for the M.A. degree of the speaker. All other M.A. Statistics students are required to attend.
  Abstract:
  The asymptotic properties of constrained and unconstrained least-squares estimate of the parameters of a random amplitude sinusoid are analyzed. An explicit formula for the asymptotic covariance matrix of the estimation errors is derived for both the constrained and unconstrained estimators. Accuarcy aspects are investigated with the following main results. For a certain weighing matrix, which is shown to be the same for the constrained and unconstrained methods, the estimation errors acheive their lower bounds. It is proven that in the optimal case, the constrained method always outperforms the unconstrained method. It is also proven that the accuarcy of the optimal estimators improve as the number of least-squares equations increases.
• Category Theory Seminar: Professor Christopher Gilmour (University of Cape Town) will give a talk on "Realcompactifications, Lindelo"fications and cozero bases" at 2:30 p.m. in N638 Ross.
  Abstract:
  Every Lindelo"f topological space is realcompact and it is well known that the converse is false. However in the setting of frames, ie. lattice theoretic generalisations of topologies, there is good evidence that, at least in some respects, the two concepts should coincide. We discuss various notions of realcompactness for frames and the relationships between them. Of particular importance is the role of the cozero elements. The appropriate setting for spaces is provided by the Alexandroff spaces and, for frames, their counterpart the regular sigma-frames. We will indicate some new proofs in frames which extend classical topological results that relate compactifications, realcompactifications, pseudocompactness and properties of cozero-bases.
• Category Theory Seminar: Walter Tholen will speak on "Separated and connected maps" at 3:30 p.m. in N638 Ross. This talk is rescheduled from last week.

Friday, April 26, 1996

• The Seventh Annual York-McMaster Probability Day
  See program.
• Statistics Seminar: Dr. R. Moeanaddin, of Shiraz University, will speak on "Conditional Mean and Conditional Variance of Bilinear Models" at 11:30 a.m. in N638 Ross.
  Abstract:
  In this article we consider the problem of evaluating the conditional mean and the conditional variance of some classes of bilinear time series models. We show that for some simple models the non-parametric estimates of the conditional mean and the conditional variance can be used as a graphical tool for distinguishing ARMA and bilinear model and identifying the adequate bilinear model. It may be mentioned that in the context of linear model (AR, MA, ARMA) the conditional mean shows a straight line pattern.
  \[ E( Z(t) | Z(t-j) = x ) = a + b x, \hspace{0.5in} j=1,2, \ldots. \]
  Some theoretical results are also included.

Monday, April 29, 1996

• Graduate Seminar: Yun Yi will give a talk entitled "A GENERAL AKAIKE-TYPE CRITERION FOR MODEL SELECTION IN ROBUST REGRESSION" at 9:00 a.m. in N638 Ross.
  Abstract:
  Akaike's procedure (1970) for selecting a model minimises an estimate of the expected squared error in predicting new, independent observations. This selection criterion was designed for models fitted by least squares. A different model-fitting technique, such as least absolute deviation regression, requires an appropriate model selection procedure. This paper presents a general Akaike-type criterion applicable to a wide variety of loss functions for model fitting. It requires only that the function be convex with a unique minimum, and twice differentiable in expectation. Simulations show that the estimators proposed here well approximate their respective prediction errors.

Tuesday, April 30, 1996

• Examinations: Last day.

May 1996

Wednesday, May 1, 1996

• Graduate Seminar: Tilaye Teshager will give a talk entitled "GRADUATION (THE REVISION OF ESTIMATES)" at 2:30 p.m. in N638 Ross. This talk has been rescheduled from April 26.
  Abstract:
  Graduation is an exercise in statistical estimation, specifically in a situation where a sequence of estimates is to be produced, such as mortality rates by age. The graduation process must take into account the presumed relationship that exists among the elements in the sequence under consideration, and called this prior opinion about the data.

Thursday, May 2, 1996

• Graduate Seminar: Wenbiao Zhang will give a talk entitled "Analysis of Ordinal Paired Comparison Data" at 11:00 a.m. in N638 Ross.
  Abstract:
  The method of paired comparisons is used primarily in cases when the objects to be compared can be judged only subjectively: that is to say, when it is impossible or impracticable to make relevant measurements in order to decide which of two objects is preferable.
  Two types of models are dicussed for paired comparisons of several treatments using ordinal scales such as (A < < < B, A < < B, A < B, A=B, A > B, A > > B, A > > > B), where A < < < B denotes strong preference for treatments B over treatment A, A < < B denotes moderate preference for B, A < B denotes weak preference for B, A=B denotes no preference, and so forth. For the Binary scale ( A, B, A > B), special cases of the models using logit transforms simplify to the Bradley-Terry model.
  When the same raters compare each pair of treatments, one can allow within-rater dependence by fitting the models with constrained maximum likelihood.

Tuesday, May 7, 1996

• Meeting: There will be a meeting of the Pure Math section at 10:00 a.m. in N638 Ross.
  Agenda: Hiring (due to retirement there is a possibility of hiring)

Wednesday, May 8, 1996

• Analysis Seminar: Professor Mioljub Niki\'c (University of Belgrade) will speak on "Certain classes of analytic functions and some inequalities in the algebra C(T)" at 3:00 p.m. in 1154 Vari Hall.
  Abstract:
  The object is to generalize certain classes of the holomorphic functions in the algebra C(T) concerning the Frechet derivative and to prove some inequalities in this algebra.

Friday, May 10, 1996

• Graduate Seminar: Maurice Tsang will give a talk entitled "Measurement of Equity" at 10:00 a.m in N638 Ross.
  Abstract:
  When insurers set rates, they have to classify risks according to certain criteria. However, when only certain factors are considered and others ignored, inequity may result. With ideas used by economists to measure income inequality, Promislow proposed a method of measuring this enquity. The concept of riskiness is introduced to explain it and the method is illustrated in a simple situation.
• Graduate Seminar: Christopher Benson will give a talk entitled "THE KOLMOGOROV-SMIRNOV STATISTICS" at 11:00 a.m. in N638 Ross. Rescheduled from Thursday.
  Abstract:
  The Kolmogorov-Smirnov statistics can be used for testing the fit of a model. These will be discussed, and an outline of their derviation will be given using the empirical distribution, the Brownian bridge, the Glivenko-Cantelli theorem, and the central limit and weak convergence theorems for random functions.

Wednesday, May 22, 1996

• Probability Seminar: Vladimir V. Korolyuk (Landford International Ltd.) will speak on "Diffusion approximation of Markov systems and networks" (joint work with Nicholas Derzko, University of Toronto) at 11:00 a.m. in N638 Ross. Lunch to follow.

Friday, May 24, 1996

• Analysis Seminar: Professor Sid Scull will give the first of a series of two or three lectures entitled "Spectra of Localization Operators" at 4:00 p.m. in N638 Ross.

Friday, May 31, 1996

• Analysis Seminar: Professor Sid Scull will continue a series of lectures entitled "Spectra of Localization Operators" at 4:00 p.m. in N638 Ross.

June 1996

Friday, June 7, 1996

• Analysis Seminar: Professor Sid Scull will continue a series of lectures entitled "Spectra of Localization Operators" at 4:00 p.m. in N638 Ross.

Friday, June 14, 1996

• Probability/Statistics/Combinatorics Seminar: Mike Mosca (Oxford University): "Expected number of colours in a proper colouring of a graph". 10:30 a.m. in N638 Ross (lunch to follow).
  Abstract:
  For a graph $G$ on $n$ vertices, let $\Omega$ be the set of all proper $n$-colourings of the vertices of $G$ (ie. using up to $n$ available colours, and such that no adjacent vertices are the same colour). Define $\mu(G)$ to be the average number of colours used in a proper $n$-colouring of $G$. It is $\#P$-$hard$ to compute $\mu(G)$ exactly, thus it is believed that there is no efficient algorithm for doing so for a general graph $G$. However fast randomised approximation may be possible.

  One method that often works in approximating $\#P$-hard quantities is approximately uniform random generation. A rapidly mixing Markov chain on the set $\Omega$ can be used to do this. Some bounds on $\mu(G)$ would be useful, and in attempting to find some, the effect of adding and deleting edges is investigated.

Wednesday, June 19, 1996

• Graduate Student Seminar: Clara Auyeung will give a talk entitled "THE BROUWER DEGREE IN FINITE DIMENSIONAL SPACES" at 2:30 p.m. in N638 Ross.
  Abstract:
  The seminar is an introduction to the Brouwer degree. The Brouwer degree is a map from a specific set and function to an integer value. Its main purpose is to aid in finding the zeros of a function. In this seminar, basic properties of the degree will be derived from its fundamental axioms. The computation of the degree will be briefly discussed.

Thursday, June 20, 1996

• Graduate Seminar: Ya-Ping Chen will give a talk entitled "ON THE MEAN LENGTH OF THE ENTROPIC ALGORITHM OF PATTERN-RECOGNITION" at 9:30 a.m. in N638 Ross.
  Abstract:
  Problem of recognition occur in practically every field of human activity, e.g., in medical diagnosis, in chemical analysis, in the recognition of a failure in a complicated mechanism or and entity in archaeology, in classification problems, and so on. The entropic algorithm of recognition is a strategy of recognition. The entropic algorithm of L.N. Landa for pattern-recognition is improved for the case when the auxiliary experiments are incompletely determined by the main global experiment. The minimization of the mean length of the final graph is analysed.

Friday, June 21, 1996

• Probability Seminar: George O'Brien (York University) will speak on "Large deviations for spectrally positive stable and related processes" at 10:30 a.m. in N638 Ross.
• Analysis Seminar: Professor Sid Scull will continue a series of lectures entitled "Spectra of Localization Operators" at 4:00 p.m. in N638 Ross.

Tuesday, June 25, 1996

• Probability Seminar: Tom Salisbury (York University) will speak on "Conditioned superprocesses" at 10:30 a.m. in N638 Ross.
• Applied Mathematics Seminar: Dr. Jurgen Burzlaff, Dublin City University will speak on "Existence theorems for vortex-vortex scattering" at 3:00 p.m. in N638 Ross
  Abstract:
  We formulate a Cauchy problem, first for the nonlinear partial differential equations of the Abelian Higgs model, and then for those of the CP^2 model. The problems describe the scattering of two vortices. It is shown that the problems have a unique finite-energy solution. The symmetry of the solutions is studied. It is shown that a local analytic solution exists near the origin, and that the vortices scatter at right angle.

Wednesday, June 26, 1996

• Graduate Seminar: A. Jabashvili will give a talk entitled "THE NET DIAGRAM OPTIMIZATION" at 12:00 p.m. in N638 Ross.
  Abstract:
  A problem of reduction of task accomplishment mean time is considered (the task is paralleled along branches). Organizing the iterational process of finding the optimal regime it is necessary to have some mode of evaluation of task accomplishment mean time. One method of this is also considered.

Friday, June 28, 1996

• Graduate Seminar: Sanjana Kapoor will give a talk entitled "REACHING A VERDICT BY WEIGHTING EVIDENCE" at 10:00 a.m. in N638 Ross.
  Abstract:
  Discussion of Mathematical model describing the process of reaching a verdict by probabilistically weighting the available evidence. The classical decision making rules from decision theory proposed by Hooper, Dempster, Bayes, and Jeffrey prove to be special cases of such a weighting process. The evidence induced by a fuzzy set will be discussed.

July 1996

Wednesday, July 3, 1996

• Graduate Seminar: Ying Liu will give a talk entitled "ASYMPTOTICS AND LIKELIHOOD INFERENCE" at 2:00 p.m. in N638 Ross.
  Abstract:
  For the purpose of making inferences for a one-dimensional interest parameter, the directed likelihood can be adjusted so that the resulting modified directed likelihood is under ordinary repeated sampling approximately standard normal with error of third order, conditional on a suitable ancillary statistic and hence unconditionally. In general, suitable specification of the ancillary statistic may be difficult. Two stable and invariant adjusted directed likelihoods were introduced by Barndorff-Nielsen & Chamberlin (1994), and a modified profile likelihood was introduced by Fraser & Reid (1995) using ancillary direction techniques, which are similar to the modified directed likelihood defined by Barndorff-Nielsen (1983), but do not require the specification of the ancillary statistic.

Thursday, July 4, 1996

• Graduate Seminar: Yun Yi will give a talk entitled "THIRD ORDER ASYMPTOTIC MODEL: EXPONENTIAL AND LOCATION TYPE APPROXIMATION" at 10:00 a.m. in N638 Ross.
  Abstract:
  Recent methods of asymptotic inference including ancillarity and subsequent marginalization or conditioning lead almost universally to the very simple case of a real variable and a real parameter model, to a distribution on the real line with a single parameter. This paper develops some basic asymptotic theory for such a simple statistical model. For this special case we can determine canonical versions of the best approximation at a data point, by an exponential or location type model. We describe a step by step reduction procedure for reducing an initial model to the canonical exponential or location type model. The canonical model in each case has just three parameters, one of which identifies the location or exponential type.

Tuesday, July 9, 1996

• Colloquium: Prof. Gabor Tardos (Mathematical Research Institute, Hungarian Academy of Sciences) will talk on "A survey of interactive proofs in complexity theory" at 1:30 p.m. in room N638 Ross. All welcome: this talk will be of a general nature, for non-experts.

Thursday, July 11, 1996

• Mini conference on Set Theory and Model Theory.

Friday, July 12, 1996

• Analysis Seminar: Dr. Qihong Fan of Peking University and McMaster University will give a lecture entitled "Symbolic Calculus on the Affine Group "ax+b" at 4:00 p.m. in N638 Ross Building.

Monday, July 15, 1996

• Graduate Seminar: Mihaela Iancu will give two consecutive talks at 2:00 p.m. in N638 Ross.
  "Characterizations of normal spaces"
  Abstract:
  Theorems of characterization of normality are proved using extendability of continuous real-valued functions, upper and lower semicontinuous functions and sequences of locally finite families of open sets.

  "Extendability of continuous functions"
  Abstract:
  A theorem that characterizes the extendability of a bounded real-valued continuous function defined on a subset of a topological space is proved. The Tietze-Urysohn Theorem becomes a corollary of this new result.

Wednesday, July 24, 1996

• Graduate Seminar: Kam Cheung Ko will give a talk entitled "METHODS FOR UNCONSTRAINED OPTIMIZATION PROBLEMS" 12:00 p.m. in N638 Ross.
  Abstract:
  The basic idea for the optimization is to find the minimum of a function. The optimization techniques are important not only because they can be applied to sove many problems of considerable practical importance but also because they provide the numerical analyst with a tool for solving a wide range of nonlinear problems. In addition, they form an important complement to analysis of convexity, calculus of variations, optimal control and function approximation. The linear search methods, steepest descent and least squares are basic optimization techniques which will be discussed.

Friday, July 26, 1996

• Graduate Seminar: Kim-Quang Tran will speak on "Operads in some Symmetric Monoidal Categories" at 10:30 a.m. in N638 Ross. This is a survey paper requirement for M.A. degree.
  Abstract:
  In some particular categories, operads are described in explicit formulas. Operads are also viewed as monoids in symmetric monoidal categories and then the general formulas for operads are derived from this point.

Monday, July 29, 1996

• Graduate Seminar: Ioulia Ioffe will give a talk entitled "NUMERICAL SOLUTION OF AN INTEGRAL EQUATION IN FINANCE" at 9:30 a.m. in N638 Ross.
  Abstract:
  An intergral equation describing a model in finance will be presented. Existence of a numerical solution will be shown. Then a numerical algorithm will be presented and the order of the resulting error will be determined. Also some numerical results will be demonstrated.
• Graduate Seminar: Yudong Zhang will give a talk entitled "NUMERICAL SOLUTION FOR CONSTRAINED MINIMIZATION OF OPTIMAL CONTROL PROBLEMS USING LAGRANGE MULTIPLIERS AND PIECEWISE OPTIMIZATION" at 12:00 p.m. in N638 Ross.
• Graduate Seminar: Sanjana Kapoor will give a talk entitled "METHOD FOR CONSTRAINED OPTIMISATION PROBLEM" at 2:30 p.m. in N638 Ross.
  Abstract:
  The conditions for a local optimum are related to the saddle property of the Lagrangain function. Formal Lagrangian Multiplier principal is used to find minimum of f(x) subject to the constraints gi(x)=0. Discuss the finite difference version of Newton method called Quasi Newton method to solve the system of Nonlinear equations resulting from Lagrangian multiplier principal.

Tuesday, July 30, 1996

• Graduate Seminar: Ya-Ping Chen will give a talk entitled "TESTS BASED ON THE GAUSS-NEWTON REGRESSION" at 1:30 p.m. in N638 Ross.
  Abstract:
  There are several tests based on the Gauss-Newton Regression (GNR) that can be highly useful in applied econometric work. These are:
  1. tests for the equality of two (or more)sets of regression parameters;
  2. nonnested hypothesis tests, in which a regression model is tested against the evidence provided by one or more nonnested alternative models;
  3. tests based on comparing two sets of estimates, where generall one set is consistent under weaker conditions than the other; and
  4. tests for heteroskedasticity of known form.

  
  As a result the standard F test for (1) is commonly referred to by economists as the Chow test. J and P tests are asymptotically equivalent instruments under hypothesis for nonnested hypothesis tests, (2). And a class of tests, which we called Durbin-Wu-Hausman, or DWH, tests, that can be used for (3). In my seminar talk, I will focus on testing nonnested regression model by using J-test.

• Graduate Seminar: Ying Liu will give a talk entitled "SIMPLE MODIFICATIONS FOR SIGNED ROOTS OF LIKELIHOOD RATIO STATISTICS" at 3:00 p.m. in N638 Ross.
  Abstract: For the purpose of making inferences for a one-dimensional interest parameter, the directed likelihood can be adjusted so that the resulting modified directed likelihood is under ordinary repeated sampling approximately standard normal with error of third order, conditional on a suitable ancillary statistic A and hence unconditionally. In general, suitable specification of the ancillary statistic A may be difficult. An alternative modification of the directed likelihood is given by DiCiccio and Martin in 1993 using Bayesian point of view, that is available without knowledge of A and the standard normal approximation to its distribution has error of second order.

Wednesday, July 31, 1996

• Graduate Seminar: Avtandil Jabashvili will give a talk entitled "SOME ASPECTS OF ELLIPTIC BOUNDARY PROBLEMS" at 12:00 p.m. in N638 Ross.
  Abstract: The subject of this seminar are essential aspects of the theory of boundary value problems for pseudo differential equations. The starting object is the class G of operators introduced in Boutet de Monvel[1] containing besides the classical elliptic boundary problems their parametrices, too. Thus all the assertions about elliptic operators in the class G are valid especially for classical elliptic boundary problems. An essential point of view in the whole theory is the symbolic calculus for interior and boundary symbols. G is closed under composition and other natural operations which are compatible with corresponding operations on symbolic level.
  [1] Boutet de Monvel, L., Comportement d'un operateur pseudo differential sur une variete a bord J. Anal. Math. 17 (1966) 241-304.
• Statistical Consulting Service Special Colloquium: Kai-Tai Fang (Hong Kong Baptist University and Chinese Academy of Sciences) will speak on "SOME Q-Q PROBABILITY PLOTS FOR TEST MULTIVARIATE NORMALITY SPHERICAL AND ELLIPTICAL SYMMETRY" at 2 p.m. in 3005 Vari Hall.
  Abstract :
  Graphical techniques have been widely used in various branches of statistics. Among various kinds of graphical techniques the normal probability plot has a long history and is one of the most popular methods. In this talk we shall propose some Q-Q plots for multivariate normal distribution as well as for testing spherical and elliptical symmetry.