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Phone: 218-726-8747 / 218-726-8254
Fax: 218-726-8399
Email: mathstat@d.umn.edu
Undergraduate Studies
Email: math.dus@d.umn.edu
Graduate Studies
Email: math.dgs@d.umn.edu
140 Solon Campus Center (map)
1117 University Drive
Duluth, MN 55812-3000

Home > Seminars and Colloquia

LectureThe Department of Mathematics and Statistics offers a weekly colloquium series on Thursdays. Most colloquia begin between 3:00 and 3:30. Seminars alternate between those aimed at Undergraduate (type U) and Graduate (type G) audiences. Calendar of current events


Type Date Title Speaker
G 5/2/12 A Covariance Regression Model Xiaoyue Niu
Penn State University
G 5/2/12 Statistical Models for Estimating and Predicting HIV/AIDS Epidemics Le Bao
Penn State University
U 5/3/12  Honors Colloquium Justin Sabrowsky,Yue Wang, Yan Zhuang
UMD Undergraduate Students
Department of Mathematics & Statistics
U 4/26/12 Mathematical Contest in Modeling 2012 Moses Koppendrayer, James McKeown, Jesse Schmieg, Can Jin, Zhiren Lu, Jiayi Wang, Jinze Gu, Matthew Hanson, Derek Mayer
UMD Undergraduate Students
Department of Mathematics & Statistics
U 4/19/12 The Dynamics of Newton’s Method Thomas Cameron
UMD undergraduate math major
G 4/12/12 Keeping it real: some challenges in computational algebraic geometry Marshall Hampton
Department of Mathematics & Statistics
U 4/5/12 Tricolorability Game James McKeown
UMD Math/Music major
G 3/29/12 Research Topics Faculty of the UMD Department
of Mathematics and Statistics
U 3/22/12 Hard Problems: The Road to the World's Toughest Math Contest Documentary Film
G 3/20/12 Bayesian inverse prediction modeling of unobservable time to treatment threshold using auxiliary longitudinal data Miranda L. Lynch
Postdoctoral Fellow, Department of Biostatistics, Harvard School of Public Health
G 3/8/12 Response adaptive randomization in the presence of mismeasurement Xuan Li
University of Manitoba, Canada
UMD Faculty Candidate
G 3/6/12 On fully parametric
power-divergence minimization
Davide Ferrari
University of Modena, Italy
G 3/2/12 Autoregressive model selection with simultaneous sparse coefficient estimation Hailin Sang
Indiana University, Bloomington
UMD Faculty Candidate
U 3/1/12 Sampling in Population Networks Katie St. Clair Department of Mathematics, Carleton College
G 2/27/12 Lack-of-fit testing of a regression model with response missing at random Xiaoyu Li
Department of Statistics and Probability
Michigan State University
UMD Faculty Candidate
G 2/23/12 Distance between consecutive entries
in permutations
David S. Gunderson
University of Manitoba
U 2/16/12 The Capture and Analysis of Aerial Photos of Lake Superior Thomas Cameron
UMD undergraduate math major
G 2/9/12 Ideas and Methods in Discrete Optimization Uwe Leck
University of Wisconsin Superior
U 2/2/12 Using Mathematics to Create
Symmetry Patterns
Professor Joseph A. Gallian
UMD Department of Mathematics & Statistics
G 1/26/12 An Ideal Schedule for Major League Baseball Kristin Riesgraf
MS Candidate:  Program in Applied and Computational
G 12/22/11 Expression Patterns of Codon Usage and Homopolymers in the 13-Lined Ground Squirrel Amy Virta
MS Candidate: Program in Applied and Computational
G 12/19/11 An Investigation of Erdos' Method: A Schemefor Generating Carmichael Numbers Trevor Brennan
MS Candidate: Program in Applied and Computational
G 12/15/11 Stoichiometric Modeling of Nutrient and Biomass Flux in the Gulf of Mexico Nathan L. Pollesch
MS Candidate: Program in Applied and Computational
U 12/15/11 Neuroscience and the Mathematical Mind Peter Baumgartner,
UMD Mathematics and Mathematics Education major
G 12/12/11 Gracefule Kayak Paddles Ann Litersky
MS Candidate: Program in Applied and Computational Mathematics
G 12/8/11 On a Combinatorial Identity of J. Borwein Steve Rosenberg
Associate Professor, Department of Mathematics and Computer Science, University of Wisconsin-Superior
U 12/1/11 Undercover Symmetry Frank A. Farris Santa Clara Unversity/Carleton College
G 11/17/11 Hearing Geometry Marshall Hampton, Department of Mathematics & Statistics
U/G 11/10/11 A simple forced oscillator: Implications of KAM theory Jim Walsh, Oberlin College
G 11/3/11 Magic squares and orthogonal arrays Donald L. Kreher, Michigan Technological University
U 10/27/11 Knotted Arcs Eric Rawdon, Mathematics Department, University of St. Thomas
U/G 10/20/11 Goshawk invasions and population cycles Dick Green
Department of Mathematics and Statistics
U TBA Julia Robinson and Hilbert's Tenth Problem DVD
G 10/6/11 Perfect r-domination in the Kronecker products of cycles Pranava K. Jha
Department of Computer Science, St. Cloud State University
U 9/29/11 Breaking Driver's License Codes Joe Gallian
Department of Mathematics & Statistics
G 9/22/11 Tracking the three-dimensional evolution of mechanical percolation in nanocomposite materials Sarah Baxter
Department of Mechanical Engineering
University of South Carolina



Tracking the three-dimensional evolution of mechanical percolation in nanocomposite materials
by

Sarah Baxter
Department of Mechanical Engineering
University of South Carolina

 

Abstract:
One mechanism, expected to play a large role in the sometimes novel, and often enhanced, properties of nanocomposites, is the formation of percolated or connected microstructures. While many novel properties are the direct result of the nano-scaled and closely packed microstructures, significant enhancements of traditional composite mechanical properties may also be due to mechanical percolation effects.

Classic percolation models assess connectivity by defining a percolation threshold, usually a volume fraction, at which the microstructure first appears as connected. This is the dominant mechanism in modeling, for example, composite electrical conductivity or porous media fluid flow. Analysis of the process is relatively binary, unconnected or connected. Mechanical percolation, however, necessarily occurs in tandem with other microstructural mechanisms and is perhaps better described as a continuous process. Thus, while percolation thresholds are still critical to characterization, the mechanical response may not be completely defined by this volume fraction. Mechanical response may depend on a combination of mechanisms enhanced or supported by a percolating microstructure. This is the challenge in modeling the effects of mechanical percolation.

Classic mean-field micromechanics models, with no specific description of microstructural arrangement, cannot capture the variability in effective properties due to a random microstructure or predict the onset of a percolated microstructure. In this work a unit cell micromechanics model was used to calculate the effective composite properties for simulated random microstructures. In this way we are able to track the onset and evolution of mechanical percolation by observing the relevant mechanical effects, which include observations of the range of variable properties, identification of distinct microstructural features associated with minimum and maximum properties, and following the changes in the probability density functions describing the distribution of properties.



Time: Thursday, September 22, 3:00 PM
Location: 130 Solon Campus Center

 


Breaking Driver's License Codes
by

Joe Gallian
Department of Mathematics and Statistics

 

Abstract:
Many states use complicated algorithms or formulas to assign driver's license numbers but keep the method confidential. Just for the fun of it, I attempted to figure out how the states code their license numbers. In this talk I will discuss how I was able to break the original code for Minnesota (Minnesota changed it coding method in the early 2000s) and the current one for Missouri. The talk illustrates an important problem-solving technique used by scientists but is not emphasized in mathematics classes. It also teaches the lesson that sometimes things done just for the sake of curiosity can have applications. The talk is intended for a general audience. No advanced mathematics is needed.



Time: Thursday, September 29, 3:00 PM
Location: 150 Chemistry

 


Perfect r-domination in the Kronecker products of cycles
by

Pranava K. Jha
Department of Computer Science, St. Cloud State University

 

Abstract:
The Kronecker product G x H of graphs G = (V, E) and H = (W, F) defined as follows: V(G x H) = VxW, and E = {{(a, x) , (b, y)}: {a, b} ∈ E and {x, y} ∈ F}. It is variously known as the direct product, tensor product and categorical product.

The present talk deals with perfect r-domination in the Kronecker product of k cycles. Under certain conditions on the lengths of the cycles, there exists a vertex partition of the graph into perfect r-dominating sets in each of the following cases: (a) r = 1 and k >2, (b) r> 2 and k = 2, and (c) r> 2 and k = 3. Areas of applications include efficient resource placement and error-correcting codes.



Time: Thursday, October 6, 3:00 PM
Location: 130 Solon Campus Center

 


Julia Robinson and Hilbert's Tenth Problem

(DVD)

 

Abstract:
This one-hour biographical documentary film tells the story of an important American mathematician against a background of mathematical ideas. Julia Robinson, a pioneer among American women in mathematics, rose to prominence in a field where often she was the only woman. Julia Robinson was the first woman elected to the mathematical section of the National Academy of Sciences, and the first woman to become president of the American Mathematical Society.  The film describes Robinson's major contribution to the solution of one of the most important theorems of the Twentieth century and some key events in the history of modern mathematics while conveying the motivations of mathematicians, and exploring the relationship between mathematical research and the development of computers.



Time: TBA
Location: 150 Chemistry


Goshawk invasion and population cycles

by

Dick Green
Department of Mathematics and Statistics

 

Abstract:
The Northern Goshawk is a large, fierce hawk of the north woods. It is seldom seen by birdwatchers outside of the migration period. Migrating hawks are observed at many sites across North America. Duluth is the best hawk watch site for observing migrating goshawks. Numbers fluctuate from several score to several thousand goshawks counted per year. Goshawk numbers show periodic fluctuations, with invasions occurring about every ten years. In this talk I will discuss the bird, hawk counts, goshawk numbers and population fluctuations. Of particular interest is the question of whether population fluctuations are cyclic or not.



Time: Thursday, October 20, 3:00 PM
Location: 150 Chemistry


Knotted Arcs

by

Eric Rawdon
Mathematics Department, University of St. Thomas

 

Abstract:
Recently, some proteins have been classified as being knotted. However, proteins are open (i.e. they have free ends), and knotting, from a mathematical perspective, only is defined for closed curves (i.e. loops). Proteins are special in that the free ends typically lie on the "outside," so many of the protein knot detection techniques work fine for proteins but not so well in more ambiguous situations. How should we define the existence of knotting within open chains (like shoelaces and headphone cords)? We will discuss knotting in open chains and proteins, and search for knots within knots.



Time: Thursday, October 27, 3:00 PM
Location: 150 Chemistry


Magic squares and orthogonal arrays

by

Donald L. Kreher
Michigan Technological University

 

Abstract:
A magic square is an n by n array of integers with the property that the sum of the numbers in each row, each column and the main back diagonals is the same. This sum is the magic sum.

Magic squares have had a long and colorful history. They have attracted the attention of Emperor's Statesman, hobbyists, magicians and yes even mathematicians. In this talk, we show how magic squares are connected with pairs of orthogonal Latin squares. This connection and recursive constructions are then used to show that a magic square exists for all n, except n = 2.

An investigation of the existence of pairs of orthogonal Latin squares is also included



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


A simple forced oscillator: Implications of KAM theory

by

Jim Walsh
Oberlin College

Abstract:
In this talk the dynamics of a simple model of three charged bodies interacting under an inverse square electrostatic force is presented.  I will illustrate the manner in which fractals and chaos arise in the absence of damping when the forcing is periodic. The model easily serves as an alternative to the pendulum, the standard  model of a periodically forced  nonlinear oscillator. While not essential, having completed a multivariable calculus course will prove helpful in following along.



Time: Thursday, November 10, 3:00 PM
Location: 130 Solon Campus Center

 


Hearing Geometry

by

Marshall Hampton
Department of Mathematics & Statistics

Abstract: Why do some instruments produce sounds with a characteristic pitch while others (such as drums) do not? What's the difference between an orchestral xylophone and a marimba? What would a square drum sound like? We will consider these and other questions in the context of "spectral geometry," which relates shapes to differential equations.



Time: Thursday, November 17, 3:00 PM
Location: 150 Chemistry

 


Undercover Symmetry

by

Frank A. Farris
Santa Clara University/Carleton College

Abstract: Spend some time with the images shown, each a wallpaper pattern with six-fold symmetry.  You can rotate 60 degrees about various points and the pattern is unchanged. You can spin 180 degrees about other points and 120 degrees around still others. A pattern with six-fold symmetry must have these additional three-fold and two-fold symmetries. But in the right-hand image, why do the red bowties seem to have mirror symmetry? Why are they set at such strange angles relative to the orientation of the red hexagons?  These strange features led me to discover new types of symmetry in wallpaper patterns and find strange connections to number theory.


Joe Gallian Joe Gallian


Time: Thursday, December 1, 3:00 PM
Location: 150 Chemistry


On a Combinatorial Identity of J. Borwein

by
Steve Rosenberg
Associate Professor, Department of Mathematics and Computer Science,
University of Wisconsin-Superior

Abstract: Consider a pyramid made out of unit cubes arranged in square horizontal layers, with a ledge of one cube's length around the perimeter of each layer. For any natural number k,we can count the number of ways of choosing k unit cubes from the pyramid such that no two cubes are in the same horizontal layer; we can also count the number of ways of choosing k unit cubes from the pyramid such that no two cubes come from the same vertical slice or two adjacent slices.

In 2010, Jon Borwein and his co-authors made a conjecture equivalent to the statement that these two quantities are always equal.

In this talk, we prove Borwein's conjecture using standard ideas and facts from combinatorics, elementary algebra, and linear algebra.



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


Graceful Kayak Paddles
 by
Ann Litersky
MS Candidate: Program in Applied and Computational Mathematics

Advisor: Dalibor Froncek

Abstract: A kayak paddle is a graph made of two cycles joined by a path.  We can define KP(r,s,l) as two cycles of lengths r and s joined by a path of length l.  If a graph G has m vertices and n edges, then a general vertex labeling of the graph is a one-to-one mapping of the vertex set of G into the set of all non-negative integers.  If we have two vertices, say x and y joined by an edge xy, then we can define the edge length as min{x – y, y – x}, where the subtraction is performed in Z2n+1.  A b- or graceful labeling is a labeling where all the vertex labels must come from {0,1,…,n}, and the set of edge lengths must be equal to {1,…,n}.  If a graph can be labeled using a b-labeling, then it can cyclically decompose K2n+1.  In this thesis we investigate the existence of graceful labelings of kayak paddles.



Time: Thursday, December 12, 10 AM
Location: 130 Solon Campus Center


Neuroscience and the Mathematical Mind
 by
Peter Baumgartner
UMD Mathematics and Mathematics Education major

Abstract: Do we have an innate number sense, or do we develop it as we mature? Is there a part of the brain dedicated to doing mathematics? Can other animals do math? How much math do infants really know? What impact does math-anxiety and performance pressure have on the brain's ability to do math? What happens in the brain when we solve 5 + 2? The emerging field of educational neuroscience can guide us towards answering these questions, as well as direct the way we might teach math in the future. We'll delve into the science behind how the brain does arithmetic and more in this colloquium for a general audience.



Time: Thursday, December 15, 3:00 PM
Location: 150 Chemistry


Stoichiometric Modeling of Nutrient and Biomass Flux in the Gulf of Mexico

by
Nathan L. Pollesch
MS Candidate: Program in Applied and Computational

Advisor: Harlan Stech

Abstract: The purpose of this thesis is to explore the connections between agricultural runoff influx, oil influx, and oxygen levels in a near-coastal marine environment. The creation of oxygen deficient conditions is investigated through the use of a stoichiometric modeling approach that utilizes a system of ordinary differential equations.  Agricultural runoff is modeled as a source of a limiting nutrient for algae. Oil influx is modeled as a carbon source for bacterial consumption.  The investigation is motivated by the Gulf of Mexico-ecosystem in the wake of the Deepwater Horizon oil rig incident of 2010, which contributed large amounts of oil (carbon) to the Gulf system.  The model consists of an algal class with flexible stoichiometry that utilizes the nutrient for growth and a bacterial class with fixed stoichiometry that assimilates the carbon. A consumer class with fixed stoichiometry that is dependent upon the oxygen present in the system is modeled and is used to indicate oxygen deficient conditions.  Equilibrium, time series, and stability analysis of this five-dimensional system are presented. Through the analyses presented and simulations, it is found that this model reproduces the behavior of the biological processes associated with nutrient enrichment and the creation hypoxic areas, or ‘dead zones’.



Time: Thursday, December 15, 3:00 PM
Location: 130 Solon Campus Center


An Investigation of Erdös' Mdoethod: A Schemefor Generating Carmichael Numbers

by
Trevor Brennan
MS Candidate: Program in Applied and Computational

Advisor: John Greene

Abstract: In 1956 Paul Erdös’ outlined a method for calculating a large number of Carmichael numbers. Fermat’s little theorem states; if p is a prime then for any integer a, ap = a (mod p). A Carmichael number is a composite number, as defined by Korselt’s criterion, which will also satisfy Fermat’s little theorem for an infinite number of bases. For example, the smallest Carmichael number is 561 = 3*11*17 and a561 = a (mod 561) for any positive integer a.  In this project we have explored Erdös’ method in the effort to understand how well it works in producing a large number of Carmichael numbers. In addition, we established some underlying constructions and behaviors of the method.



Time: Monday, December 19, 3:00 PM
Location: 130 Solon Campus Center


Stoichiometric Modeling of Nutrient and Biomass Flux in the Gulf of Mexico

by
Amy Virta
MS Candidate: Program in Applied and Computational

Advisor: Marshall Hampton

Abstract: The 13-lined ground squirrel is particularly interesting to study because of the extremes their bodies go through during hibernation.  Their bodies do amazing physical feats, such as dropping their core temperature to around 0°C, that would be fatal to humans.   It is these physical feats that make the study of their DNA interesting.  This project used data from Dr. Andrews’ biology lab and biostatistical methods to analyze squirrel DNA sequences.  The hope is to find genetic explanations in the codon usage or avoidance of homopolymers that might help shed light on the genes expressed during hibernation.



Time: Thursday, December 22, 3:00 PM
Location: 130 Solon Campus Center

 


An Ideal Schedule for Major League Baseball

by
Kristin Riesgraf
MS Candidate: Program in Applied and Computational

Advisor: Dalibor Froncek

Abstract: Intense competition exists not only on Major League's baseball diamonds but also behind the scenes.  Scheduling for the MLB season is an outsourced job.  Contenders receive the format and the restrictions for the next year's schedule and submit a proposal.  The contract is awarded to the group whose schedule is closest to ideal.  In this project, I wrote my own schedule for the 2012 MLB regular season using concepts of Graph Theory.  The schedule that I created is ideal in a world where no time, travel, or financial constraints exist.



Time: Thursday, January 26, 3:00 PM
Location: 130 Solon Campus Center

 


Using Mathematics to Create
Symmetry Patterns

by
Professor Joseph A. Gallian
UMD Department of Mathematics & Statistics



Abstract: We use video animations to illustrate how mathematics can be used to create computer generated symmetry patterns.  Discrete math, exponential functions, logarithms and modular arithmetic are used to transform basic images into symmetry patterns. These methods were used to create the image for the 2003 Mathematics Awareness Month poster. The talk is intended for a general audience.



Time: Thursday, February 2, 3:00 PM
Location: 120 Solon Campus Center

 


Ideas and Methods in Discrete Optimization
Symmetry Patterns

by
Uwe Leck
University of Wisconsin Superior



Abstract: We survey some of the main ideas used to solve discrete optimization problems and give examples illustrating them. This includes exact methods like complete enumeration, exchange methods, greedy algorithms, partial enumeration as well as non-exact heuristics and approximation algorithms.



Time: Thursday, February 9, 3:00 PM
Location: 130 Solon Campus Center

 


The Capture and Analysis of Aerial Photos of Lake Superior

by
Thomas Cameron
UMD undergraduate math major
Advisor: Dr. Jay Austin


Abstract: Although satellite imagery is the optimal method for capturing aerial photos of Lake Superior, photos can only be taken once a day and cloud cover ruins any photo opportunities. The bluffs in Duluth provide an opportunity to employ a more versatile method for capturing aerial photos of Lake Superior. In a proof of method, the process for capturing and analyzing aerial photos of Lake Superior using a single digital camera will be described. The experimental process used to find the numerical values of the parameters necessary to establish projection equations between world measurements and image geometry  and an algorithm that map points of interest from a digital photograph to a map of Lake Superior will be explained.



Time: Thursday, February 16, 3:00 PM
Location: 120 Solon Campus Center

 


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: Pa(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


 Mathematical Contest in Modeling 2012


Moses Koppendrayer, James McKeown, Jesse Schmieg,
Can Jin, Zhiren Lu, Jiayi Wang
Jinze Gu, Matthew Hanson, Derek Mayer

UMD Undergraduate Students
Department of Mathematics & Statistics



Abstract: Each February, a nationwide Mathematical Contest in Modeling (MCM) is held. Contestants have 96 hours to select from one of two problems and submit a solution. This year, three teams represented UMD. All three teams independently developed mathematical models to schedule an optimal mix of multiple day camping trips through a river canyon area.

The teams will discuss the contest problem, their proposed solutions, and their overall experience with the competition.

 


Time: Thursday, April 26, 3:00 PM
Location: 120 Solon Campus Center


 A Covariance Regression Model

Xiaoyue Niu
Penn State University

Abstract: Multivariate analysis often involves statistical models for the covariance matrix of random variables. Estimating the covariance matrix enables us to study the associations among random variables and provides standard error estimates to construct confidence regions. Most of the existing multivariate methods are for homogenous normal populations. However, multivariate data usually contain non-normal measurements of diverse types, including continuous, ordinal, and non-ordered categorical. In this talk, we discuss methods of estimating the covariance matrix in the presence of diverse types of data, with the main deviation from the normal situation being that the population is heterogeneous due to some explanatory variables x.

We propose a covariance regression model for the heterogeneous population, and describe the covariance matrix of continuous variables as a function of other variables, such as categorical variables. The model we propose is a parsimonious model which can be considered as a natural analogy to linear regression for the mean. We present a geometric interpretation of the model and both the maximum likelihood and the Bayesian method for the parameter estimation. We demonstrate the application of the model using a very simple example with two response variables, one continuous and one binary explanatory variables. We also apply the covariance regression model to a large health dataset with four continuous response variables and four categorical variables. We discuss in detail several practical issues when fitting the covariance regression model, such as model selection, interpreting the coefficients, presenting the fitted results, and model misspecification.

This is a joint work with Peter Hoff.


Time: Wednesda, May 2, 3:00 PM
Location: 130 Solon Campus Center


 Statistical Models for Estimating and Predicting
HIV/AIDS Epidemics

Le Bao
Penn State University

 

Abstract: HIV affects both mortality and fertility and, consequently, it has important effects on population growth and the sex and age composition of a population. A fuller understanding of the biological and behavioral determinants of HIV transmission would give us the ability to design effective interventions that target specific mechanisms, situations, and people. However, many countries lack sufficient health information systems to measure the number of individuals living with HIV/AIDS, the rate of new infections, and the need for intervention and treatment. The talk will introduce some statistical methods for estimation and short-term extrapolation of HIV/AIDS trends from limited surveillance data.


Time: Wednesda, May 2, 3:45 PM
Location: 130 Solon Campus Center


 Honors Colloquium

Graduating with Honors from the Department of Mathematics and Statistics requires that students perform a research project with a department faculty member. This year’s honors projects will be presented by

Justin Sabrowsky: The Social Cost of Unemployment
Yue Wang: Cache-Fault Probability and its Approximation
Yan Zhuang: Expected Hitting Times for Taboo Random Walks


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


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