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Mathematics & Statistics

# Colloquia — Spring 2018

## Thursday, April 26, 2018

Title
Speaker

Time
Place

Small sample GEE estimation of regression parameters for Longitudinal Data
Sudhir Paul
University of Windsor
3:45pm-4:45pm
CMC 204

Abstract

Longitudinal (clustered) response data arise in many bio-statistical applications which, in general, cannot be assumed to be independent. Generalized estimating equation (GEE) is a widely used method to estimate marginal regression parameters for correlated responses. The advantage of the GEE is that the estimates of the regression parameters are asymptotically unbiased even if the correlation structure is misspecified, although their small sample properties are not known. In this paper, two bias adjusted GEE estimators of the regression parameters in longitudinal data are obtained when the number of subjects is small. One is based on a bias correction, and the other is based on a bias reduction. Simulations show that the performances of both the bias-corrected methods are similar in terms of bias, efficiency, coverage probability, average coverage length, impact of misspecification of correlation structure, and impact of cluster size on bias correction. Both these methods show superior properties over the GEE estimates for small samples. Further, analysis of data involving a small number of subjects also shows improvement in bias, MSE, standard error, and length of the confidence interval of the estimates by the two bias adjusted methods over the GEE estimates. For small to moderate sample sizes ($$N ≤ 50$$), either of the bias-corrected methods GEEBc and GEEBr can be used. However, the method GEEBc should be preferred over GEEBr, as the former is computationally easier. For large sample sizes, the GEE method can be used.

## Friday, April 20, 2018

Title
Speaker

Time
Place

TBA
Michael Kosorok
University of North Carolina at Chapel Hill
3:00pm-4:00pm
CMC 130
Chris Tsokos

Abstract

TBA

## Friday, April 13, 2018

Title
Speaker

Time
Place

Multi-crossing Number of Knots: Turning Knots into Flowers
Williams College
3:00pm-4:00pm
CMC 130
Nagle Lecure Series Committee

Abstract

Knots have traditionally been depicted using projections with crossings where two stands cross. But what if we allow three strands to cross at a crossing? Or four strands? Can we find projections of any knot with just one of these multi-crossings? We will discuss these generalizations of traditional invariants to multi-crossing numbers, ubercrossing numbers and petal numbers and their relation to hyperbolic invariants.

## Friday, April 6, 2018

Title
Speaker

Time
Place

TBA
Sayan Mukherjee
Duke University
3:00pm-4:00pm
CMC 130
K. M. Ramachandran

Abstract

TBA

## Friday, March 30, 2018

Title
Speaker

Time
Place

John Mallet-Parret
Brown University
3:00pm-4:00pm
CMC 130
Yuncheng You

Abstract

In this talk we discuss some aspects of delay-differential equations. The historical roots of the subject date from the earliest twentieth century. At that time much of the focus was on linear equations arising in applications in science and engineering, and the methods were often formal and ad hoc. Beginning in the 1960's more attention was paid to nonlinear systems, and a firm theoretical foundation based on infinite-dimensional dynamical systems was established. What has emerged since then is a body of theory with a rich mathematical structure that draws from numerous areas, including dynamical systems, functional analysis, and topology, and which retains close ties with applications. We shall discuss various recent results and ongoing research in delay equations, and we shall also mention some open problems in the field.

## Friday, March 23, 2018

Title
Speaker

Time
Place

Rogue waves in integrable systems
Jianke Yang
University of Vermont
3:00pm-4:00pm
CMC 130
Wen-Xiu Ma

Abstract

Rogue waves are instantaneous large localized waves which arise from a constant background and then retreat back to the same background. They attracted significant interest in recent years due to their relevance to physical phenomena such as freak waves in the ocean and extreme waves in optics. In integrable systems, such waves admit exact analytical expressions and represent a special but important class of solutions. In this talk, we report our work on rogue waves in integrable systems, including the nonlinear Schröedinger equation, the Davey-Stewartson equations, the Ablowitz-Ladik equation and a nonlocal parity-time-symmetric nonlinear Schröedinger equation.

## Friday, March 9, 2018

Title
Speaker

Time
Place

Quandle and its applications to knots
Takefumi Nosaka
Tokyo Institute of Technology
Tokyo, Japan
3:00pm-4:00pm
CMC 130
Masahico Saito

Abstract

Quandle is a certain algebraic system, and has applications to knot theory, including “quandle cocycle invariant” which was defined by M. Saito, etc. I show that every cohomology (bilinear) pairing of any knot can be described by a quandle cocycle invariant, and give some relations to classical knot-invariant. In this talk, I begin by introducing quandles, and explain the basic and benefits. Furthermore, I briefly present some of my results, and applications to low-dimensional topology.

## Friday, March 2, 2018

Title
Speaker

Time
Place

Spanning cycles and 2-factors in hypergraphs
Andrzej Czygrinow
Arizona State University
3:00pm-4:00pm
CMC 130
Theo Molla

Abstract

Dirac's theorem states that every graph on n vertices with minimum degree at least $$n/2$$ has a spanning cycle. There are many related results on 2-factors in graphs which generalize this fundamental fact. In this talk we will discuss possible analogs and generalizations of these results to hypergraphs. It turns out that even in the case of 3-uniform hypergraphs there are a few different ways of approaching this problem, as cycles and degrees can be defined in multiple ways.

## Friday, February 16, 2018

Title
Speaker
Time
Place

Computer Networking and Security Studies for Cyber-Physical Infrastructures
Kaiqi Xiong
3:00pm-4:00pm
CMC 130

Abstract

As the International Data Corporation (IDC) predicted, IT spending will reach $5 billion by 2020 —$1.7 billion more than today — driven by the 3rd cyber-physical infrastructures consisting of cloud, mobile, social media, and big data technologies. Computer networking and security plays a very important role in cyber-physical infrastructures. Furthermore, the United Nations predicted in 2016 that an estimated 60% of the world’s population would live in urban areas and one in every three people would settle down in a city by 2030. With a large portion of the population moving into urban areas, people will face various unprecedented challenges interacting with cyber-physical infrastructures. In this talk, I will give an overview of the research in my group and discuss several key computer networking and security challenges we have studied and will continue to address. Then, I will outline a few research topics with potential collaboration in the cyber-physical infrastructures.

## Friday, February 9, 2018

Title
Speaker

Time
Place

What Are Zeta Functions?
Daqing Wan
University of California, Irvine
3:00pm-4:00pm
CMC 130
Xiang-dong Hou

Abstract

Zeta functions are central topics in number theory and arithmetic algebraic geometry. They can be viewed as generating functions for counting “points” (or “solutions”) of polynomial equations, thus contain deep arithmetic and geometric information of the equations. We will explain various zeta functions from this point-of-view, including the Riemann zeta function, the Hasse-Weil zeta function, and zeta functions over finite fields. This introductory talk is accessible to advanced undergraduate students and beginning graduate students.

## Friday, February 2, 2018

Title
Speaker

Time
Place

Topological structure in neural systems
University of Delaware
3:00pm-4:00pm
CMC 130
Nataša Jonoska

Abstract

Twenty-first century neuroscience has been marked by an extraordinary leap in the quantity of data produced by experiments: it is now possible in animal models to record from thousands of individual neural units for days at a stretch, and this growth appears likely to accelerate. However, like much data about biological systems, this data is still expensive to obtain, noisy, and a dramatic sub-sampling of the system being studied. Such confounds make many standard mathematical techniques difficult or impossible to apply. However, one promising recent approach to understanding such complex systems is through techniques adapted from algebraic and combinatorial topology. This language maps surprisingly well onto various qualitative characterizations of neural systems that have been discovered by experimental and theoretical neuroscientists, and provides quantitative tools for understanding and comparing the resulting models. In this talk, we will survey this connection, then focus on a couple of specific examples involving how neural systems represent information.

## Friday, January 26, 2018

Title
Speaker

Time
Place

Dispersive equations with potential
Marius Beceanu
SUNY at Albany
3:00pm-4:00pm
CMC 130
Razvan Teodorescu

Abstract

I'll present some applications of Wiener's Theorem to the study of dispersive equations with scalar potential.

Title
Speaker

Time
Place