# Seminars and Colloquia - Winter 2009

Dr. Yuming Chen

Wilfrid Laurier University

Departmental Colloquium

Monday, April 20, 2009

2:00p.m., HH-3017

Periodic Solutions and The Global Attractor of A Delayed System Arising From Neural Networks

In this talk, we first give a brief introduction to neural networks. Then we focus on a delayed system describing the dynamics of two identical neurons. The technical tool is the discrete Lyapunov functional introduced by Mallet-Paret and Sell. We study the existence, absence and uniqueness of periodic orbits in the level sets of the discrete Lyapunov functional and describe the global attractor topologically and geometrically.

Ms. Rui Hu

Memorial University

Applied Dynamical Systems Seminar

Friday, April 17, 2009

2:00p.m., HH-3017

Stability and Bifurcation Analysis in a Neural Network Model with Delay and Diffusion

We consider a delayed neural network model with diffusion. By analyzing the distributions of the eigenvalues of the system and applying the center manifold theory and normal form computation, we show that, regarding the connection coefficients as the perturbation parameter, the system, with the different boundary conditions, undergoes some bifurcations including transcritical bifurcation, Hopf bifurcation and Hopf-zero bifurcation. The normal forms are given to determine the stabilities of the bifurcated solutions.

Dr. Marco Merkli

Memorial University

Applied Dynamical Systems Seminar

Thursday, April 9, 2009

1:00p.m., HH-3017

Evolution of Open Quantum Systems (II)

This is the continuation of the first talk.

Pengtao Li

Peking University

Analysis & PDE Seminar

Thursday, April 9, 2009

2:00p.m., HH-3026

Strichartz estimates through Schroedinger's maximal operator, continued

This is a continuation of the talk that was given on April 2, 2009.

Walter de Siqueira Pedra

Institut für Mathematik, Universität Mainz

Colloquium

Monday, April 6, 2009

2:00p.m., HH-3017

The Equilibrium States of Interacting Fermions on the Lattice

We define a non-perturbative renormalization flow for a general class of non-relativistic models of interacting fermions on the lattice at weak coupling. This class includes in particular the Hubbard model. A new feature of our method is the fact that Fermi surfaces are dynamical objects, and thus counter-terms for controlling IR-singularities are not needed. The main application of our method is a proof, in the 2-dimensional case, of the uniqueness of the periodic KMS-state at temperature T and coupling constant λ, whenever |λ log (T)| is small. The last bound corresponds to the prediction of the BCS-theory for the critical temperature for the superconducting phase transition.

Pengtao Li

Peking University

Analysis & PDE seminar

Thursday, April 2, 2009

2:00p.m., HH-3026

Strichartz estimates through Schroedinger's maximal operator

We are going to report a recent result by K. Rogers on the affirmative answer to a question of Carleson regarding the sharp range of s for which e^{it △}f → f a.e. with f in the homogeneous Sobolev space .{H}^s.

Dr. Marco Merkli

Memorial University of Newfoundland

Applied Dynamical Systems Seminar

Friday, April 3, 2009

2:00p.m., HH-3017

Evolution of Open Quantum Systems

This talk is a presentation of recent progress in the mathematical theory of open quantum systems. Open systems consist of "small parts" interacting with "big parts" (environments). They are non-commutative, infinite dimensional dynamical systems evolving according to the Heisenberg (or Liouville) equation of quantum mechanics. We outline a recent theory of quantum resonances, allowing us to describe in detail the reduced (effective) dynamics of the small parts of the system. We consider an application to quantum computing, where the small system is a quantum bit (qubit) register. We explain recent advances in the rigorous analysis of coherence and entanglement of qubits.

Jian Fang

Harbin Institute of Technology

Departmental Colloquium

Friday, March 27, 2009

2:00p.m., HH-3017

Monotone Wavefronts in Reaction-Diffusion Systems

Many mathematical models from combustion physics, chemical kinetics and

spatial ecology are governed by reaction-diffusion systems. One of central

problems for such a system is about traveling waves and evolution dynamics. In this talk, I will first give a brief review on wavefronts and spreading speeds for cooperative and weakly coupled reaction-diffusion systems with monostable and bistable nonlinearities. Then I will report on our recent work for the partially degenerate case (i.e., some but not all diffusion coefficients are zero). Under appropriate assumptions, we establish the existence of a family of monostable wavefronts and a unique (up to translation) bistable wavefront. It turns out that the spreading speed coincides with the minimal wave speed in the monostable case. We also make some remarks on the smoothness and global stability of the obtained bistable wavefront.

Dr. Sergey Sadov

Memorial University of Newfoundland

Analysis and PDE Seminar

Thursday, March 26, 2009

2:00p.m., HH-3026

A Kernel Interpolating Between Hilbert's and Cauchy's and $L^p$ Estimates Along a Curve For the Laplace Transform

This is a continuation of March 19th's talk.

Mr. Ahmad Ababneh

Memorial University of Newfoundland

Combinatorics Seminar

Friday, March 20, 2009

2:00p.m., C-3033

Disjoint Starter Sequences

In this talk we are going to discuss starter sequences, which are defined as arranged sequences of all possible differences in an abelian group. For example, 6, 2, 5, 2, 1, 1, 6, 5 is a starter sequence of order 4. Using this design we will introduce a new combinatorial design called disjoint starter sequences, where two starter sequences are disjoint if no difference occurs in the same position in both sequences. Further applications will be introduced, such as the product theorem of disjoint starters and round robin tournaments played on neutral ground.

Ms. Luju Liu

Memorial University of Newfoundland

Applied Dynamical Systems Seminar

Friday, March 20, 2009

1:00p.m., HH-3017

A Tuberculosis Model With Migration

A tuberculosis (TB) model with migration is proposed and investigated. We first introduce the basic reproduction number, and then prove a threshold type result: TB disease dies out and the disease-free equilibrium is globally asymptotically stable if the basic reproduction number is less than one; while TB disease uniformly persists in the population and there is at least one endemic equilibrium if this number is greater than one. In the latter case, we further show that this endemic equilibrium is globally attractive provided that the immigration rates of migrant workers from villages to towns or cities and

infectious migrant workers from towns or cities to villages are small. Numerical simulations also indicate that there is a globally attractive endemic equilibrium if the basic reproduction number is greater than one, and that the spread of TB may be reduced if some effective actions are taken.

Dr. Sergey Sadov

Memorial University of Newfoundland

Analysis and PDE Seminar

Thursday, March 19, 2009

2:00p.m., HH-3026

A Kernel Interpolating Between Hilbert's and Cauchy's and $L^p$ Estimates Along a Curve For the Laplace Transform

Classical Hilbert inequalities assert boundedness of the bilinear forms with

Hankel-type Hilbert's matrix $A(m,n)=1/(m+n)$ and Toeplitz-like Cauchy's matrix $A(m,n)=1/(m-n)$ on the space of square-integrable sequences. We introduce a matrix that interpolates between these two cases, $A(m,n)=1/(ma+nb)$, where $a$ and $b$ are complex numbers with modulus 1 and $mne n$. This family of bilinear forms is uniformly bounded on $l2$.

The discrete inequality has a natural integral analog, which is intimately

related with Plancherel-like formula for the Laplace transform along rays in the complex plane. Estimates for the Laplace and Fourier transform along a sufficiently well-behaved curve in the complex plane follow. Using interpolation, the results are extended to Hausdorff-Young type inequalities for $L^p$ norms.

This is a joint work with A.Merzon (Mexico).

Dr. Nabil Shalaby

Memorial University of Newfoundland

Combinatorics Seminar

Friday, March 13, 2009

2:00p.m., SN-2101

Skolem-Langford Type Sequences

Skolem-Langford type sequences are generalizations of Skolem sequences. A Skolem sequence is a sequence of pairs of numbers from 1 to n, such that the 1s are one position apart, the 2s are 2 positions apart, etc. For example, 3, 5, 2, 3, 2, 4, 5, 1, 1, 4 is a Skolem sequence of order n = 5. This concept which was discovered by Skolem is closely related to important mathematical concepts such as the golden ratio, Steiner triple systems and difference number sets.

We discuss several Skolem-Langford type sequences, their applications and some open problems.

Mr. Yijun Lou

Memorial University of Newfoundland

Applied Dynamical Systems Seminar

Friday, March 13, 2009

1:00p.m., HH-3017

Climate-Based Malaria Transmission Model with Age-structure

In this talk, we present an age-structured model of malaria transmission. We first introduce the basic reproduction ratio for this model and then show that the disease-free periodic state is globally asymptotically stable when this ratio is less than one, and there exists at least one positive periodic state and the disease persists when it is greater than one. We further use these analytic results to study the malaria transmission cases in KwaZulu-Natal Province, South Africa, to determine how well they represent the biological system and, consequently, how useful their predictions are. Some sensitivity analysis of the basic reproduction ratio is performed, and in particular, the potential impact of climate change on seasonal transmission and populations at risk of the disease is analyzed.

Pengtao Li

Peking University and Memorial University

Analysis and PDE Seminar

Thursday, March 12, 2009

2:00 p.m., HH-3026

Generalized Naiver-Stokes equations with data in some local critical Q-spaces.

In this talk we will give a link between Leray mollified solutions to the three-dimensional generalized Naiver-Stokes equations and mild solutions for initial data in the adherence of the test functions for the Q-type norms.

Dr. Danny Dyer

Memorial University of Newfoundland

Combinatorics Seminar

Friday, February 27, 2009

2:00 p.m., SN-2101

Cyclic perfect $T(P_2 cup P_2 cup P_2)$ triple systems

Abstract:

A $T(G)$ triple is formed by taking a graph $G$ and replacing every edge with a $3$-cycle, where all of the new vertices are distinct from all others in $G$. An edge-disjoint decomposition of $3K_n$ into $T(G)$ triples is called a $T(G)$ triple system of order $n$. If we can decompose $K_n$ into copies of a graph $G$, such that we can form a $T(G)$ triple from each graph in the decomposition and produce a partition of the edges of $3K_n$, then the resulting $T(G)$ triple system is called perfect. We show that the spectrum of perfect $T(P_2 cup P_2 cup P_2)$ triple systems for $n$ at least $9$ is $n equiv 1,3!!mod{6}$, and give cyclic constructions for all admissible orders. This is joint work with Josh Manzer.

Dr. Jie Xiao

Memorial University of Newfoundland

Analysis and PDE Seminar

Thursday February 26, 2009

2:00p.m., HH-3026

Faber-Krahn's Inequality for the p-Laplacian Improved and

Geometricalized

Through capacity, volume and Sobolev-type inequality, this talk is devoted to improving and geometricalizing the Faber-Krahn inequality for the principal eigenvalue of the p-Laplacian on a bounded open set with smooth boundary.

**Dr. David A. Pike**Memorial University of Newfoundland

Combinatorics Seminar

Friday, February 20, 2009

2:00p.m., SN-1103

Phylogenetic Networks for Human mtDNA Haplogroup T

Phylogenetic networks are graphs (preferably trees) that show the evolutionary branching and the corresponding historical development of genetic diversity within a population. Using data from an online repository we develop phylogenetic networks for mtDNA haplogroup T, which is one of several known parts within a partition of humanity based upon maternal ancestry. By analysing the structure of the resulting networks for this haplogroup we are able to learn about the order in which genetic mutations occurred within some of its subgroups. We are also able to identify unstable nucleotides and previously unidentified genetic clusters.

Keywords: mitochondrial DNA, phylogenetic networks

**Dr. Chunhua Ou**Memorial University of Newfoundland

Applied Dynamical Systems Seminar

Friday, February 20, 2009

1:00p.m., HH-3017

Asymptotic Analysis Approach to Differential Equations

This talk is intended for our graduate students and interested faculty members. I will mainly talk about asymptotic methods and their applications to differential equations and applied dynamical systems. For second order linear ODEs, I will talk about WKB methods. For nonlinear ODEs, I will present some useful asymptotic methods such as matching asymptotics, boundary layer approaches, and multiple-scale analysis. I will also mention some applications of these methods to analyze dynamics of elliptic and reaction diffusion equations.

Dr. Oznur Yasar Diner

Memorial University of Newfoundland

Combinatorics Seminar

Friday, February 13, 2009

2:00p.m., SN-1103

Forbidden Minor Constructions for 4-Searchable Series-Parallel Graphs

The search number of a graph G is the minimum number of searchers needed to capture an intruder hidden in G. In this context, those graphs that require small number of searchers are of common interest. In particular, we are aiming to obtain the set of minor minimal series-parallel graphs for which four searchers are not sufficient. To this end, we give a set of 17 base graphs and demonstrate a constructive method to obtain many forbidden minors from these graphs. It is known that this set of forbidden minors is finite, however, no general construction method is found to date. This is a joint work with

D. Dyer.

Mr. Jian Fang

Memorial University of Newfoundland

Applied Dynamical Systems Seminar

Friday, Feb. 13, 2009

1:00p.m., HH-3017

"The Existence and Uniqueness of Traveling Waves for

Non-monotone Integral Equations With Applications"

A class of nonlinear integral equations without monotonicity is investigated. It is shown that there is a spreading speed c* for such an integral equation, and that its limiting integral equation admits a unique traveling wave (up to translation) with wave speed greater than or equal to c*, and no traveling wave with wave speed less than c*. These results are also applied to two nonlocal reaction-diffusion population models.

Dr. Hermann Brunner

Memorial University

Colloquium

Monday, February 9, 2009

2:00pm, HH-3017

"The Numerical Analysis of Volterra Integro-differential Equations"

We discuss recent progress and current work on the numerical analysis and computational solution of Volterra-type integro-differential equations, including equations with delay arguments. Initial-value problems for such equations arise, in standard or "non-standard" versions, in the mathematical modelling of a broad range of biological and physical phenomena in which memory effects play an important role. The talk will focus on numerical schemes based on collocation methods or on discontinuous Galerkin methods. It will also point out a number of open problems in the numerical analysis of these functional differential equations.

Dr. Zhangmin Zhang

Candidate for Tenure-Track Position in Statistics

Carleton University

Friday, February 6

2:00 p.m., HH-3017

"Some Inequalities for Entropies and Characteristic Functions"

Various entropies are introduced from general physical as well as mathematical considerations. A fundamental issue concerning these entropies is their continuity property: How do they change when the underlying distribution varies? By means of a probabilistic coupling technique, an upper bound on the variation of the Tsallis entropy in terms of the Kolmogorov distance is set. The result provides a quantitative characterization of the uniform continuity of the Tsallis

entropy. The parallel result for Shannon entropy is its consequence. The Characteristic function not only encodes all information about the probability distribution function, but also synthesizes it in a most convenient way for many purposes such as spectral analysis. The behavior of characteristic function is the focus of many studies. In particular, it is a fundamental object in probability theory and when the characteristic function is interpreted as the survival amplitude of a quantum state it is relevant to decaying rate of a quantum state.

With respect to distributions having differentiable density and lattice distributions respectively, several inequalities for characteristic functions involving Fisher information are established. An application in estimating the survival probability of a quantum state is illustrated.

Dr. Yuri Bahturin

Memorial University

Wednesday, February 4, 2009

Algebra Seminar

1:00-2:00pm, HH-3017

"Actions of Maximal Growth (joint work with Alexander Olshanskii, Vanderbilt University)"

We study acts and modules of maximal growth over finitely generated free monoids and free associative algebras as well as free groups and free group algebras. The maximality of the growth implies some other specific properties of these acts and modules that makes them close to the free ones; at the same time, we show that being a strong "infiniteness" condition, the maximality of the growth can still be combined with various finiteness conditions, which would normally make finitely generated acts finite and finitely generated modules finite-dimensional.

Dr. Qihao Xie

Candidate for Tenure-Track Position in Statistics

Bombardier Aerospace

Colloquium

Friday, January 30, 2009

2:00 p.m., HH-3017

"Exact inference for a simple exponential step-stress model under type-

I hybrid censoring scheme"

In reliability and life-testing experiments, the researcher is often interested in the effects of extreme or varying stress factors such as temperature, voltage and load on the lifetimes of experimental units. Step-stress test, which is a special class of accelerated life-tests, allows

the experimenter to increase the stress levels at fixed times during the experiment in order to obtain information on the parameters of the life distributions more quickly than under normal operating conditions. In this paper, we consider the simple step-stress model under the exponential distribution when the available data are Type-I hybrid censored. We derive the maximum likelihood estimators (MLEs) of the parameters assuming a cumulative exposure model with lifetimes being exponentially distributed. The exact distributions of the MLEs of parameters are obtained through the use of conditional moment generating functions. We also derive confidence intervals for the parameters using these exact

distributions, asymptotic distributions of the MLEs and the parametric bootstrap methods, and assess their performance through a Monte Carlo simulation study. Finally, we present two examples to illustrate all the methods of inference discussed here.

Dr. Ye Sun

Candidate for Tenure-Track Position in Statistics

University of Toronto

Colloquium

Friday, January 23, 2009

2:00 p.m., HH-3017

"Accurate Likelihood Inference"

Observed likelihood and the tangent of ancillary statistic at the

observed data can be used to achieve a locally defined canonical

parameter so that the new defined model mimics the exponential

models. As a result, very accurate confidence intervals and p-values

can be obtained for very general scalar parameters.

I will demonstrate the high accuracy of the third order likelihood

inference over the other approximated inference for various

well-known statistical models, which are quite commonly used in

elementary statistical books. It shows that the results in the elementary

books can be very misleading.