Distance between consecutive entries
in permutations

by
David S. Gunderson
University of Manitoba

Joint work with P. Ballister and B. Bollobas, University of Memphis

Abstract:

Given a permutation S on {1, 2,..., n}, define its distance set to be {|S(i+1) – S(i)|: i=1, 2,..., n–1}. For example, when n=5, the permutation (S(1),..., S(5))=(5,1,4,2,3) has distance set {1,2,3,4} with all possible differences, however the permutation (1,2,3,4,5) has distance set {1}. On average, how large is the distance set of a random permutation?

This question was loosely motivated by a famous open problem in graph theory called "the graceful tree conjecture."

Time: Thursday, February 23, 3:00 PM
Location: 130 Solon Campus Center

Lack-of-fit testing of a regression model
with response missing at random

by

Xiaoyu Li
Department of Statistics and Probability
Michigan State University

UMD Faculty Candidate

Abstract: Missing-data problem is a widely discussed topic in many areas while the minimum distance method is a classical method for model checking problems. In this talk we analyze the linear regression model with response missing at random by imputation and minimum distance method. We propose a class of lack-of-fit tests for fitting a linear regression model when response variables are missing at random. These tests are based on a class of minimum integrated square distances between a kernel type estimator of a regression function and the parametric regression function being fitted. These tests are shown to be consistent against a large class of fixed alternatives. The corresponding test statistics are shown to have asymptotic normal distributions under null hypothesis and a class of nonparametric local alternatives. Some simulation results are also presented.

Time: Tuesday, February 28, 4:00PM
Location: 130 Solon Campus Center

Sampling in Population Networks
by
Katie St. Clair
Department of Mathematics, Carleton College
UMD alumnus

Abstract: In classic sampling scenarios (like simple random sampling), the population is made up of independent sampling units – selecting Ann to be in your sample will not affect whether her brother Bob is also selected.  But we could decide to link Ann and Bob by their sibling relationship, so sampling Ann would also lead us to Bob (and vice versa).  If we link the entire population in this manner, then we can view the population as a network with two nodes (units) linked if and only if they are siblings. Sampling designs that follow links within our population are called "ink-tracing" sampling designs. In this talk I will discuss how link-tracing designs are used to sample people (usually to uncover what are deemed “hidden” populations) and to sample the environment (usually to uncover rare, clustered species).  I’ll also discuss how to use link-tracing samples to form unbiased population estimates.

Time: Thursday, March 1, 3:00PM
Location: 120 Solon Campus Center

Autoregressive model selection with simultaneous sparse coefficient estimation
by
Hailin Sang
Indiana University, Bloomington

UMD Faculty Candidate

Abstract: In this talk we study a sparse coefficient estimation procedure for
autoregressive (AR) models based on penalized conditional maximum likelihood. The penalized conditional maximum likelihood estimator (PCMLE) thus developed has the advantage of performing simultaneous coefficient estimation and model selection. Mild conditions are given on the penalty function and the innovation process, under which the PCMLE satisfies a strong consistency and oracle property, respectively. Two penalty functions, least absolute shrinkage and selection operator (LASSO) and smoothly clipped average deviation (SCAD), are considered as examples, and SCAD is shown to have better performances than LASSO. At the end, we provide a simulation study and an application of this method to historical price data of the US Industrial Production Index for consumer goods, and the result is very promising.

Time: Friday, March 2, 3:00 PM
Location: 130 Solon Campus Center

On fully parametric power-divergence minimization
by
Davide Ferrari
University of Modena, Italy

UMD Faculty Candidate

Abstract: In this talk, I discuss robust parameter estimation based on power divergence measures. The parameter estimator is indexed by a single constant q, which balances the trade-off between robustness and efficiency. If q = 1, the procedure is maximum likelihood; if q<1, we obtain a robust estimator. We study the mean squared error under contaminated data and devise a criterion function for optimal selection of q. The estimator shows remarkable robustness and yet gives negligible losses of efficiency compared to maximum likelihood.The method is accurate for multivariate problems in the presence of a relevant fraction of bad data. Various examples of both real and simulated data will be presented to illustrate the procedure.

Time: Tuesday, March 6, 3:00 PM
Location: 130 Solon Campus Center

Response adaptive randomization in the presence
of mismeasurement

by

Xuan Li
University of Manitoba, Canada

UMD Faculty Candidate

Abstract: Response adaptive randomization represents a major advance in clinical trial methodology that helps balance the benefits of the collective and the benefits of the individual and improves efficiency without undermining the validity and integrity of the clinical research. Response adaptive designs use information so far accumulated from the trial to modify the randomization procedure and deliberately bias treatment allocation in order to assign more patients to the potentially better treatment. No attention has been paid to incorporating the problem of errors-in-variables in adaptive clinical trials. In this talk, we examine some important issues and methods of response adaptive design of clinical trials in the presence of mismeasurement.

We formulate response adaptive designs when the dichotomous response may be misclassified. We consider the optimal allocations under various objectives, investigate the asymptotically best response adaptive randomization procedure, and discuss effects of misclassification on the optimal allocation. We derive an explicit expression for the variance-penalized criterion with misclassified binary responses and propose a new target proportion of treatment allocation under the criterion. A real-life clinical trial and some related simulation results are presented.

Time: Thursday, March 8, 3:00 PM
Location: 130 Solon Campus Center

Bayesian inverse prediction modeling of unobservable time
to treatment threshold using auxiliary longitudinal data

by

Miranda L. Lynch
Postdoctoral Fellow
Department of Biostatistics, Harvard School of Public Health

Abstract: In this presentation, I will describe our development of Bayesian methods for sampling-based inverse prediction. In this work, we make use of a longitudinal data set as the training data. Methods for inverse prediction utilizing correlated data have not been well developed, and we present a methodology that makes express use of the dependency structure in the training data in carrying out the prediction analyses. Using Bayesian methods allows for proper characterization of variability in the predictions, as well as variability arising from using the auxiliary data. I will describe the statistical challenges that arise in such analyses, and an approach to meeting them. We apply the inverse prediction methodology to a problem involving predicting time to reaching a CD4 T-lymphocyte threshold level at which antiretroviral treatment can be initiated in an HIV infected patient.

Time: Tuesday, March 20, 4:00 PM
Location: 130 Solon Campus Center

Hard Problems: The Road to the World's
Toughest Math Contest

Documentary Film

Abstract: Each year more than 100 countries from around the world send a team of their best six high school mathematics students to the International Mathematical Olympiad (IMO). This film tells the stories of the six high school students who represented the United States in the 2006 IMO Competition in Ljubljana, Slovenia. Many of the students featured in the film have participated in UMD's summer undergraduate research program in mathematics. A student who will be at UMD for the summer of  2012 finished second in the 2010 IMO competition.

Time: Thursday, March 22, 3:00 PM
Location: 120 Solon Campus Center

Research Topics

by

Faculty of the UMD Department
of Mathematics and Statistics

Abstract: Members of the UMD Department of Mathematics and Statistics will present some of the many interesting aspects of their research. Get a better understanding of faculty members' research interests and perhaps find a topic that could become the basis for your thesis/project research.

Time: Thursday, March 29, 3:00 PM
Location: 130 Solon Campus Center

 Tricolorability Game

by

James McKeown
UMD Math/Music major

Abstract: In this presentation we discuss a coloring game in which two players take turns coloring the strands of a knot projection using three colors. The winner is the last person able to color a strand. Completed crossings must contain strands all one color, or all different colors. A strand cannot be colored if it breaks this property. Since this is a two-player finite game of perfect information with no ties or draws either the first player can force a win, or the 2nd player can force a win.
We are interested in how such a winning strategy can be found for any knot projection with n crossings. The method is rather brute force.

This talk is based on research I did at an Undergraduate Research Program at the University of Washington in the summer of 2011.

Time: Thursday, April 5, 3:00 PM
Location: 120 Solon Campus Center

 Keeping it real: some challenges in computational algebraic geometry
by
Marshall Hampton
Department of Mathematics & Statistics

Abstract: In pure mathematics, there are many beautiful ideas and theorems in the area of algebraic geometry.  On the other hand, in applied problems we are often only interested in solutions to equations that satisfy certain conditions, such as being real (rather than complex, or even complex-projective).  This talk will survey some of the techniques that can used to find real solutions to systems of polynomial equations, along with some open problems.

Time: Thursday, April 12, 3:00 PM
Location: 130 Solon Campus Center

 The Dynamics of Newton’s Method
by
Thomas Cameron
UMD undergraduate math major
Advisor: Dr. Bruce Peckham

Abstract: Newton's method is often introduced in Calculus as a method to find roots of polynomials. The goal of this project is to investigate the long term behavior of orbits for all initial conditions under Newton's iteration for the family of quartic polynomials: P_a(z)=(z - i)(z + i)( z - a)².

In this project we will see some spectacular pictures and have a deeper understanding of when Newton''s Method works and when it fails. If alpha is real and the starting point for z is real, then all corresponding iterates are real. This results in an easier "real" problem which lives inside the original "complex" problem, and helps us understand some of the mathematics behind the pictures.

Time: Thursday, April 19, 3:00 PM
Location: 120 Solon Campus Center