Colloquia - Spring 2013
The following list is updated regularly.
| Speaker: |
Dr. Prashant Athavale (University of Toronto) |
January 24, 2013 |
| Title: |
Multiscale Image Analysis with Applications |
| Abstract: |
Images consist of features of varying scales. Thus, multiscale image processing techniques are extremely valuable, especially for medical images. We will discuss multiscale image processing techniques based on variational methods, specifically (BV, L^2) and (BV, L^1) decompositions. We will discuss the applications to real time denoising, deblurring and image registration.
|
| Speaker: |
Dr. Sarang Sane (University of Kansas) |
March 12, 2013 |
| Title: |
Euler Characteristics, Euler Classes and Projective Modules |
| Abstract: |
Starting with the Euler characteristic in graph theory/combinatorics, we trace a brief history, first viewing it as an Euler class in topology, then as an obstruction to splitting of vector bundles and finally get to the more recent notion of the Euler class in algebra/geometry and its use as an obstruction to the splitting of projective modules.
***Time & Location: 2:30 p.m. - 3:30 p.m., Pearce Hall, Room 135 ***
***Refreshments: 2:00 p.m. - 2:30 p.m., Pearce Hall, Room 216 ***
|
| Speaker: |
Dr. Ben McReynolds (Purdue University) |
March 14, 2013 |
| Title: |
Decision Problems and Representation Theory |
| Abstract: |
In a group, we often seek algorithms for deciding basic questions like whether two elements are equal or conjugate. Residual properties on groups provide nice solutions using homomorphisms to finite groups. Once we know that an algorithm exists, we can ask how efficient it is at solving the problem. Nice families of infinite linear representations can provide algorithms that can be made fairly effective. I will discuss connections with effective algorithms, representation theory, profinite groups, and symmetries in manifolds. This topic is centered around a basic question on whether or not certain special representations for free groups exist. If they do, one obtains amazingly effective algorithms for the conjugacy problem in a free group. If they do not exist, one obtains always unexpected symmetries in certain invariants on locally symmetric manifolds. This is joint work with Sean Lawton.
|
| Speaker: |
Dr. Katherine Heller (North Central College) |
March 21, 2013 |
| Title: |
A Glimpse Into Operator Theory Via Adjoints |
| Abstract: |
We will introduce the field of operator by discussing what an operator is and what types of questions operator theorists seek to answer. Then we will look more in-depth at the particular topic of adjoints of composition operators.
|
| Speaker: |
Dr. Jere Confrey & Dr. Alan Maloney (North Carolina State University) |
March 22, 2013 |
| Title: |
Analyzing the Common Core from a Learning Trajectories Perspective |
| Abstract: |
Dr. Confrey and Dr. Maloney will describe the development of the website www.turnonccmath.net where their research group has unpacked the K-8 common core standards into a set of 18 learning trajectories. They will describe the different categories of student thinking that are addressed in the descriptors and illustrate it with key concepts from one of the learning trajectories at the middle grade level.
|
| Speaker: |
Dr. Sounak Chakraborty (University of Missouri-Columbia) |
March 26, 2013 |
| Title: |
Survival Prediction with Simultaneous Shrinkage and Grouping Priors |
| Abstract: |
In this article, we propose Bayesian penalized regression models for high-dimensional survival data. In
the analysis of gene expression data, it is naturally assumed that genes are grouped according to some underlying
process. Our proposed framework is motivated by the need of grouped shrinkage estimation to take such consideration
into account. Special shrinkage priors are assigned on the regression parameters for the high-dimensional data where the
dimension of the covariate space is much larger than the number of subjects. The priors correspond to the elastic net,
group lasso, and fused lasso penalties which are popularly used to incorporate the grouping effect of the covariates
in the analysis of microarray data. We adopted Bayesian Cox proportional hazards model where the cumulative
baseline hazard function is modeled through a discrete gamma process prior. In the proposed Bayesian approach,
the amount of grouped shrinkage are adaptively controlled by estimating tuning parameters via Markov chain Monte
Carlo (MCMC) sampling method. The proposed methodologies are very useful when we want to incorporate the
cluster structure of gene expression data into the models. We assess the prediction performance of our Bayesian
penalized regression methods using simulations and real life high-dimensional survival data sets.
|
| Speaker: |
Professor Ravindra Khattree (Oakland University) |
April 4, 2013 |
| Title: |
Antieigenvalues and Antieigenvectors in Applied Statistics |
| Abstract: |
Antieigenvalues and antieigenvectors have been used in statistical work for several years although they were not characterized by these nomenclatures. However, there has recently been a renewed interest in formalizing this concept and presenting new applications of these. Being closely related to eigenvalues yet, having very different properties than eigenvalues, these quantities are very useful in a variety of statistical problems. Examples include the measures of inefficiency of estimators, measure of association, measure of multicollinearity, estimation of signal to noise ratio and tests for various multivariate problems. The present talk provides a brief survey of statistical work including those indicated above, where these quantities arise naturally. Emphasis will be more on methodology and applications than on theoretical developments.
|
| Speaker: |
Professor Douglas Lapp (Central Michigan University) |
April 23, 2013 |
| Title: |
Using Dynamic Representations to Develop Concepts in Abstract Algebra |
| Abstract: |
This talk examines the use of computer algebra systems that allow dynamic linkage of representations for the teaching of abstract algebra. Some preliminary results from a yearlong study examining students’ development of symbolization will be shared. The talk will focus on the concepts of isomorphism, subgroups, cyclic groups and subgroups, cosets, and Lagrange’s theorem. In the study, students were exposed to cooperative learning experiences that prompted them to make sense of symbolization. The role technology played in the symbolization process will be discussed relative to the Kaput, Blanton, & Moreno (2008) model for the development of symbolic meaning.
|
Colloquia - Fall 2012
| Speaker: |
Dr. Libin Rong (Oakland University) |
September 13, 2012 |
| Title: |
Modeling Hepatitis C Virus Dynamics
|
| Abstract: |
Therapy with interferon plus ribavirin leads to hepatitis C virus (HCV) clearance in less than 50% of treated patients. New treatment using direct-acting antiviral agents (DAAs) has the potential to cure patients unresponsive to the interferon-based therapy. In this talk, I will review mathematical models used to study HCV dynamics under interferon-based therapy and introduce new models for DAAs.
|
| Speaker: |
Dr. Selim Esedoglu (University of Michigan) |
October 11, 2012 |
| Title: |
Threshold Dynamics for the Mean Curvature Motion of Networks
|
| Abstract: |
Threshold dynamics is an algorithm for moving an interface (e.g. a surface in 3D) by mean curvature motion. It was proposed by Merriman, Bence, and Osher in 1992, and also extended to networks of surfaces in the same paper. This dynamics arises as gradient flow for the sum of the areas of the surfaces in the network, and plays a prominent role in materials science applications where it describes the motion of grain boundaries in polycrystals (such as most metals) under heat treatment.
Further extension of the algorithm to gradient flow for a weighted energy where the area of each surface in the network is weighted by possibly different constants (called surface tensions) is of great interest for applications, but has remained elusive. In fact, previous attempts at this turn out to be flawed, mainly due to the difficulty of ensuring that certain natural angle conditions are satisfied along triple curves (where three surfaces meet). We describe how to extend threshold dynamics to this unequal surface tension setting. Joint work with Felix Otto.
|
| Speaker: |
Professor Charles Johnson (The College of William and Mary) |
October 16, 2012 |
| Title: |
The Most Powerful Ideas About Matrices
|
| Abstract: |
This will be a talk accessible to all who have had elementary
linear algebra. By a "powerful idea", we mean one that is easy to
understand and prove, but has very strong implications. We survey
several of our picks of such ideas in the area of matrices. There should
be something for everyone.
|
| Speaker: |
Professor Sidney Graham (Central Michigan University) |
October 18, 2012 |
| Title: |
The Ideal Sieve in Dimension Less Than or Equal to One |
| Abstract: |
During my sabbatical, I worked on three projects--Greaves weighted sieve, Dirichlet polynomials,
and the ideal sieve. In this talk, I will concentrate on the last topic, which is joint work with
Hugh Montgomery.
Sieve methods have been an important tool in analytic number ever since the seminal work of Brun in 1915.
I will first give a brief survey of some of the highlights of sieve methods.
Then I will discuss my work with Montgomery on the ideal sieve.
Briefly stated, the object our project is to contract optimal sieves in certain
simplified situations.
|
| Speaker: |
Dr. Sandy Spitzer (Towson University) &
Dr. Christine Phelps (Central Michigan University) |
November 1, 2012: CANCELLED DUE TO HURRICANE |
| Title: |
Prospective Teachers' Analysis of a Mathematics Lesson: The Effects of an Online Discussion Board |
| Abstract: |
A new vision for teacher education suggests teaching prospective teachers (PTs) to improve their own teaching over time by analyzing mathematics teaching in terms of its effect on student learning. We will present the results of an online intervention aimed at helping PTs learn to analyze student thinking, a necessary skill in learning from teaching over time. The intervention consisted of an online discussion board in which PTs watched a taped lesson, commented on student learning in the lesson, and responded to their classmates’ ideas. Findings suggest that the discussion board intervention helped PTs to look past surface features of the lesson and focus on student mathematical thinking, although significant gaps in their analysis skills remained.
|
| Speaker: |
Dr. Sukanya Basu (Central Michigan University) |
November 8, 2012 |
| Title: |
Periodicity, Chaos and Oscillations in a Class of Planar Monotone Discrete Dynamical Systems with Negative Feedback
|
| Abstract: |
Oscillatory dynamics occur in many real-life applications such as thermostats in mechanical control systems and circadian rhythms in gene regulatory networks. One way to better understand this type of oscillatory dynamics is to study mathematical models involving discrete dynamical systems with negative feedback interconnections. In this talk, I will discuss the oscillatory dynamics of orbits of a class of order-reversing planar monotone maps associated to planar discrete dynamical systems with negative feedback. Among other things, I will give some general yet simple geometrical criteria to determine when orbits of such maps show oscillatory stability in the form of periodicity and when they exhibit oscillatory instability in the form of chaos.
|
| Speaker: |
Dr. Mingan Yang (Central Michigan University) |
November 15, 2012 |
| Title: |
Bayesian (Nonparametric) Statistics and Its Applications |
| Abstract: |
Bayesian statistics is widely used in many fields due to fast development of computation techniques and algorithms. In this talk, I will give a very general introduction and examples of my past, current and future research such as: survival analysis, latent variable model, structural equation modeling, categorical data analysis, longitudinal data analysis and variable selection. In these applications, I focus on enhancing flexibility and efficiency of the Bayesian approaches to tackle practical problems arising from health, medicine, psychology etc.
|
| Speaker: |
Professor Marcus Jobe (Miami University) |
November 20, 2012: CANCELLED |
| Title: |
Elementary Statistical Methods and Measurement Error |
| Abstract: |
How the sources of physical variation interact with a data collection plan determines what can be learned from the resulting dataset, and in particular, how measurement error is reflected in the dataset. The implications of this fact are rarely given much attention in most statistics courses. Even the most elementary statistical methods have their practical effectiveness limited by measurement variation; and understanding how measurement variation interacts with data collection and the methods is helpful in quantifying the nature of measurement error. We illustrate how simple one- and two-sample statistical methods can be effectively used in introducing important concepts of metrology and the implications of those concepts when drawing conclusions from data.
|
|