September 2008
Vector Space Methods for Reaction Networks and Kirchhoff Graphs
Friday, 9/12/2008 11:00 AM-12:00 PM
Stratton Hall, 203
SPEAKER: Joseph D. Fehribach (WPI)
ABSTRACT: Reaction networks are systems of chemical, electrochemical or biological reaction steps together with their constituent species. This talk will focus on the use of basic linear algebra results to determine what (if any) overall reactions can result from a given reaction network. The talk will then discuss the existence and construction of Kirchhoff graphs (reaction route graphs) associated with the reaction networks Kirchhoff graphs satisfy the Kirchhoff laws and allow one to study a reaction network as one might use a circuit diagram to study an electrical network. There will be a number of illustrative examples.
For more information, e-mail ma-chair@wpi.edu.
October 2008
Electrostatically Actuated Bistable and Multistable Micro Structures
Friday, 10/24/2008 11:00 AM-12:00 PM
Stratton Hall, 203
SPEAKER: Slava Krylov (Dept of Solid Mechanics and Material Science, Univ. of Tel Aviv)
ABSTRACT: In this work, results of theoretical and experimental study of initially curved electrostatically actuated microbeams with clamped ends is presented. Due to unique combination of non-monotonous stiffness-deflection dependence typical for mechanically bistable structures and of nonlinear electrostatic force abundant in micro and nano systems the structure exhibits sequential snap-through buckling and electrostatic pull-in instability as well as multiple stable configurations at the same voltage (bistability). Reduced order Galerkin and consistently constructed lumped models were built and verified by numerical analysis and experimentally. The minimal initial elevation required for appearance of the bistability in the electrostatically actuated beam is smaller than in the case of an uniform deflection independent loading; closed form approximation of this elevation was evaluated. The devices were fabricated from silicon on insulator (SOI) wafer using deep reactive ion etching and in-plane responses were characterized by means of optical and Scanning Electron microscopy (SEM). Characterization inside a SEM was found to be a useful experimental approach providing stable operational in-vacuo conditions while higher magnification improves the quality of data processing. Model results obtained for the actual dimensions of the device were in good agreement with the experimental data. Designs incorporating bistable beams have clear functional advantages and may result in improved performance of of switches, capacitive based sensors and MEMS/NEMS based nonvolatile memory devices.
For more information, e-mail ma-chair@wpi.edu.
Domain coarsening and curve shortening by volume-preserving mean curvature flow
Friday, 10/31/2008 11:00 AM-12:00 PM
Stratton Hall, 203
SPEAKER: Shibin Dai (WPI)
ABSTRACT: We will first briefly discribe the microscopic mechanisms and macroscopic models of the domain coarsening phenomena that happen in materials science, phase transitions, etc. Then we will concentrate on the volume-preserving mean curvature flow, which is a model when the interfacial reaction is the dominating mechanism. Geometrically, it describes the decay of the area of surfaces that are interfaces separating the two phases while preserving the volumes of each phase, respectively. Heuristic self-similarity arguments suggest a decay rate of the density of the surface area to be a temporal power law. We consider a simplified 2D case when the interface is a collection of non-intersecting smooth convex plane curves, and prove a lower bound on the shortening rate of the averaged curve length, which exhibits the aforementioned power law. The dependence of the power law coefficient on the curve shapes is also presented.
For more information, e-mail ma-chair@wpi.edu.
November 2008
Transformed Epithelial Cells and Fibroblasts/Myofibroblasts
Friday, 11/7/2008 11:00 AM-12:00 PM
Stratton Hall, 203
SPEAKER: Yangjin Kim (Mathematical Biosciences Institute, Ohio State University)
ABSTRACT: In order to understand the role of fibroblasts/myofibroblasts in the early evolution of breast cancer in vitro we developed a mathematical model as well as conduct experiments. In the experiments tumor cells are placed on one side of a membrane and fibroblasts are placed on the other side. The membrane is semi-permeable, allowing only growth factors such as EGF,TGF-beta, but not cells, to cross over. The mathematical model describes the dynamics of the various concentrations of cells and growth factors by a system of partial differential equations. The prescence of extracellular matrix have an effect on tumor grwoth. We demonstrate a good agreement between the simulation of the model and the experiments.
For more information, e-mail ma-chair@wpi.edu.
Discrete Element Modeling of Powder Processing
Friday, 11/14/2008 11:00 AM-12:00 PM
Stratton Hall, 203
SPEAKER: Didier Bouvard (Institut Polytechnique de Grenoble, France)
ABSTRACT: Modeling of processes involving powder materials needs taking into account the particulate nature of these materials. The Discrete Element Method(DEM) is well suited for such a task. It allows the macroscopic behaviour of an assembly of particles to be calculated from the contact forces generated between particles. Rearrangement between particles, a significant signature of powder materials, is explicitly taken into account. DEM has been developed in the recent years to simulate the processing of metal and ceramic powders. We present diverse examples of application on powder compaction and sintering. We also demonstrate how microstructures numerically generated by DEM can be used to compute macroscopic features of partially sintered body such as conduction properties.
For more information, e-mail ma-chair@wpi.edu.
Recovery of active faults from surface displacement fields
Friday, 11/21/2008 11:00 AM-12:00 PM
Stratton Hall, 203
SPEAKER: Darko Volkov (WPI)
ABSTRACT: The goal of this research project is to process measurements of surface displacements in such a way to use them as data for the inverse problem consisting of locating faults and portraying their geometry. Our research is also aiming at determining whether a measured displacement field on the surface is indicative of the onset of a destabilization phase.
We have already entirely solved a two dimensional problem associated to the strike slip model, which essentially reduces displacement fields to two dimensional scalar fields. Deriving the inversion method involved a rigorous mathematical eigenvalue asymptotic analysis, leading to closed form inversion formulas. Those formulas were then tested for robustness in numerical simulations. As the strike slip model is limited in scope (it captures only one of the textbook examples of faults), we have worked on extending our results to fully three dimensional fault problems. In this much more difficult case, we have already obtained very promising closed form formulas (valid for the dominant part of the asymptotic behavior), and we have tested their use on numerical data.
Nonetheless, a complete mathematical analysis of the eigenvalue problem obtained by studying destabilization is still being investigated.
For more information, e-mail ma-chair@wpi.edu.
December 2008
The Explicit Solution of the Laplace Equation with the Robin(third boundary) Condition
Friday, 12/5/2008 11:00 AM-12:00 PM
Stratton Hall, 203
SPEAKER: Alip Mohammed (York University)
ABSTRACT: The inhomogeneous Robin condition with general coeffcient for the Laplace equation on the unit disc is studied in terms of holomorphic functions using Fourier analysis. It is shown that against usual expectations this problem cannot have unique solution unless the coeffcient of the first order term in the boundary condition is a constant. For the case of general coeffcient, it is actually a problem with essential singularity in the domain, but still well-posed under proper assumptions and the unique solution is given explicitly.
For more information, e-mail ma-chair@wpi.edu.
Problems and Results on the Combinatorial Geometry of Patterns
Friday, 12/12/2008 3:00 PM-3:50 PM
Stratton Hall, 308
SPEAKER: Peter Brass (CUNY)
ABSTRACT: In this talk I will present problems, results, and algorithmic applications of combinatorial geometry on geometric patterns. Classical combinatorial geometry, as developed by Erd\H{o}s, studied geometric extremal problems like the maximum number of point-line incidences, or the maximum number of unit distances, or many similar problems. In the last 15 years, it became apparent that these results are an important building block for the analysis of geometric pattern-matching algorithms in the point pattern model. Many algorithms for these problems work by choosing a small pattern fragment of the pattern we try to find, identifying all occurences of the fragment in the background set, and testing each of these fragments whether it can be extended to the entire pattern. In such an algorithm, the bound on the number of fragments we try to extend becomes the dominant term of the complexity. Thus we study, for different types of fragments, the maximum number of occurences of that pattern fragment in a large point set.
For more information, e-mail ma-chair@wpi.edu.
January 2009
Object Recognition in Computer Vision using Signature Curves
Friday, 1/23/2009 11:00 AM-12:00 PM
Stratton Hall, 203
SPEAKER: Cheri Shakiban (University of St. Thomas and IMA)
ABSTRACT: In this talk I will discuss the differential invariant signature curves arising from the theory of moving frames for two and three dimensional closed curves and will give a formulated and discrete method for finding such a curve. Then I will discuss an analog of Latent Semantic Analysis (LSA) and show how an optimal combination of normalizing transformations is utilized to categorize signature curves. I will then give some examples, including one in sorting leaves in the Euclidean plane and the other in sorting DNA supercoils as space curves.
For more information, e-mail ma-chair@wpi.edu.
February 2009
The method of layer potentials for second and higher order elliptic operators
Thursday, 2/5/2009 11:00 AM-12:00 PM
Fuller Laboratories, 311
SPEAKER: Irina Mitrea (University of Virginia)
ABSTRACT: As is well known, many phenomena in Engineering and Mathematical Physics can be modeled by means of boundary value problems for certain elliptic differential operators L in a domain D.
When L is a differential operator of second order a variety of tools are available for dealing with such problems including boundary integral methods, variational methods, harmonic measure techniques, and methods based on classical harmonic analysis. The situation when the differential operator has higher order (as is the case for instance with anisotropic plate bending when one deals with fourth order) stands in sharp contrast with this as only fewer options could be successfully implemented. Alberto Calderon, one of the founders of the modern theory of Singular Integral Operators, has advocated in the seventies the use of layer potentials for the treatment of higher order elliptic boundary problems. While the layer potential method has proved to be tremendously successful in the treatment of second order problems, this approach is insufficiently developed to deal with the intricacies of the theory of higher order operators and, in fact, it is largely absent from the literature.
In this talk I will discuss some of my work on the Spectral Radius Conjecture for layer potential operators associated with second order elliptic boundary problems in non-smooth domains and recent progress in developing a multiple layer potential approach for the higher order case.
For more information, e-mail ma-chair@wpi.edu.
What do physics, geometry, and complex analysis have in common?
Thursday, 2/5/2009 4:00 PM-5:00 PM
Stratton Hall, 202
SPEAKER: Irina Mitrea (University of Virginia)
ABSTRACT: While mathematics is being used routinely to solve problems in physics, the converse direction has been very little explored. Have you ever used the physics laws of motion to solve problems in geometry? How about complex numbers?
This talk, intended for a general audience, is aimed at exploring unexpected connections between various branches of mathematics and physics with applications to geometry.
For more information, e-mail ma-chair@wpi.edu.
Fixed-Domain Asymptotic Properties of Tapered Maximum Likelihood Estimators
Thursday, 2/12/2009 11:00 AM-12:00 PM
Salisbury Laboratories, 406
SPEAKER: Juan Du (Michigan State University)
ABSTRACT: When the spatial sample size is extremely large, as in many environmental and ecological studies, operations on the large covariance matrix are a numerical challenge. Covariance tapering is a technique to alleviate the numerical challenges. We investigate how tapering affects asymptotic efficiency of the maximum likelihood estimator (MLE) and establish asymptotic properties, particularly asymptotic distribution of the exact MLE and tapered MLE under the fixed-domain asymptotic framework for Matérn model. We show that under some conditions on the tapering function, the tapered MLE is asymptotically as efficient as the true MLE for the microergodic parameter in the Matérn model. The computational gain and comparable estimation are illustrated by simulation study and an application to the US precipitation data in April 1948.
This is joint work with Professor V. S. Mandrekar (Michigan State University) and Professor Hao Zhang (Purdue University).
For more information, e-mail ma-chair@wpi.edu.
Using Moment Generating Function to Show Central Limit Theorem
Thursday, 2/12/2009 4:00 PM-5:00 PM
Stratton Hall, 202
SPEAKER: Juan Du (Michigan State University)
ABSTRACT: The Central Limit theorem is the foundation for many statistical procedures, because it enables us to approximate the distribution of sums and means of independent random variables by the normal distribution. I will use moment generating function, which is an important tool for the distribution convergence, to show the Central Limit Theorem and present some applications to statistical problems.
This talk is suitable for undergraduate students with a basic statistics background.
For more information, e-mail ma-chair@wpi.edu.
Discrete network approximation for determining asymptotics of effective properties of high contrast concentrated composites
Thursday, 2/19/2009 11:00 AM-12:00 PM
Salisbury Laboratories, 406
SPEAKER: Yuliya Gorb (Texas A&M University)
ABSTRACT: A blow up of effective properties of high contrast composites with particles close to touching is of interest. The goal is to derive and justify asymptotic formulas for effective properties of such composites as a characteristic interparticle distance tends to zero. A derivation and justification is done by constructing a so-called discrete network approximation. The main idea of this approximation is based on a reduction of the original continuum problem described by partial differential equations with rough coefficients to a discrete problem on a graph, called a discrete network. The approach is illustrated by considering a highly packed suspension of rigid particles in a Newtonian fluid (vectorial problem), and a medium of finite conductivity with perfectly conducting particles (scalar problem).
For more information, e-mail ma-chair@wpi.edu.
Composites, effective properties and homogenization theory (introduction)
Thursday, 2/19/2009 4:00 PM-5:00 PM
Salisbury Laboratories, 104
SPEAKER: Yuliya Gorb (Texas A&M University)
ABSTRACT: In this talk we will discuss what composite materials are, how one can define their effective properties, and what mathematical questions may be raised in their study. An illustrative one-dimensional example will be presented to demonstrate an asymptotic homogenization method.
This talk is suitable for undergraduate students.
For more information, e-mail ma-chair@wpi.edu.
On breakup of finite-size films and rivulets
Friday, 2/20/2009 11:00 AM-12:00 PM
Stratton Hall, 203
SPEAKER: Lou Kondic (NJIT)
ABSTRACT: In the first part of the talk I will give an overview of various thin liquid film problems involving instabilities, such as flow down an incline, flows on inhomogeneous surfaces, coalescence of drops, and evaporation-induced instabilities. While the emphasis will be on computations and theory, some experimental results will be presented as well.
The second part of the talk will concentrate on recent research of the mechanism of the breakup process involving finite-size films and rivulets. We will see that the breakup process due to finite size effects can be related to a particular mode of instability of infinite films, so called nucleation type of instability. We will also discuss coupling of various types of instabilities, and the competition between them. This competition may be relevant to problems on micro-and nano-scale fluidics relevant to printing applications. Finally, we will revisit the classical problem of rivulet instability and discuss whether finite size effects may be important in determining the relevant instability mechanism. If time allows, an application to breakup of nanometric metal lines illuminated by laser pulses will be presented. The presentation will include discussion of various computational and asymptotic methods relevant to thin film flows.
For more information, e-mail ma-chair@wpi.edu.
Bayesian Strategies For Some Kernel Regression Models
Monday, 2/23/2009 11:00 AM-12:00 PM
Salisbury Laboratories, 406
SPEAKER: Ernest Fokoue (Kettering University)
ABSTRACT: Kernel methods have recently triggered a wave interest from researchers and practitioners in both the Statistics and Machine Learning communities, largely due to their vast applicability in a wide variety of fields. In this talk, I intend to present a variety of Bayesian strategies used the context of regression models based on kernels. I particularly explore prior specification and Bayesian computation for both finite dimensional and infinite dimensional models, with an emphasis on the traditional linear model and the now very popular relevance vector machine. A major part of this talk is dedicated to the introduction of prior structures that are designed to lead to the consistency of the posterior quantities of interest. I provide ample computational evidence as to the merits of the techniques covered, but I finish by offering some elements of the theoretical properties of some of the priors introduced.
For more information, e-mail ma-chair@wpi.edu.
A Gentle Introduction to the Foundation of Statistical Learning Theory
Monday, 2/23/2009 4:00 PM-5:00 PM
Stratton Hall, 203
SPEAKER: Ernest Fokoue (Kettering University)
ABSTRACT: In this talk, I intend to provide a gentle progression into what I believe to be the most fundamental building blocks of the emerging field of statistical learning theory. I lead the audience to some of the niceties and subtleties of the foundations of statistical learning theory, requiring from them nothing more than a basic understanding of mathematical expectation, conditional density function and the ubiquitous Chebyshev's inequality (and its more powerful extensions), as we explore together the general framework from which statistical function estimation (parametric and nonparametric regression) and pattern recognition originate. Throughout this talk, I strive to keep all complicated technical details to the "absolute" bare minimum.
This talk is suitable for undergraduate students.
For more information, e-mail ma-chair@wpi.edu.
Heteroscedastic Unbalanced Nested Design, Fully Nonparametric ANCOVA, and Applications
Wednesday, 2/25/2009 11:00 AM-12:00 PM
Stratton Hall, 202
SPEAKER: Shu-Min Liao (Pennsylvania State University)
ABSTRACT: This talk consists of three parts. Firstly, in the context of a nonparametric model for the unbalanced heteroscedastic two-fold nested design, we consider the problem of testing for the sub-class effect. We establish, via theoretical derivations and numerical evidence, that, when the number of sub-classes is large, the classical F-test procedure is very sensitive to departures from homoscedasticity, even under normality, regardless of whether the model is balanced or unbalanced. For this reason, new testing procedures are developed to accommodate heteroscedasticity.
Secondly, we propose a new fully nonparametric ANCOVA model. The term fully nonparametric means that it is suitable for all types of ordinal data, and allows for heteroscedasticity and arbitrary form of the covariate effect. Under this model we develop a new test procedure for the (simple) covariate effect.
The development is based on conceptual connection between nested design and ANCOVA, which we uncover. The key idea is that covariates can be thought of as nested factors with many levels. Under suitable smoothing assumptions the test statistic for nested design is extended to ANCOVA. Some new asymptotic tools, based on an application of the projection principle, are introduced to obtain a new class of quadratic forms, whose asymptotical approximation is then utilized to establish the limiting distributions of the proposed test statistic under the null hypotheses and local alternatives.
All proposed methods and their properties are demonstrated on simulated and real data. Finally, innovative applications based on these new findings are briefly outlined.
For more information, e-mail ma-chair@wpi.edu.
Comparative Studies in Statistics: Some Recent Developments
Wednesday, 2/25/2009 4:00 PM-5:00 PM
Stratton Hall, 202
SPEAKER: Shu-Min Liao (Pennsylvania State University)
ABSTRACT: The role of randomization in statistical comparative experiments is well understood as it is simple: If experimental units are not assigned to treatments in a controlled randomized fashion, an unanticipated influential factor can distort the comparison. While randomization does offer protection, the precision of the comparison can be improved by properly accounting, or adjusting, for influential factors. The term covariate will be used for any factor that we want to adjust for in a comparative study.
Two common approaches to adjusting for covariates are the Nested Model and Analysis of Covariance (ANCOVA). Basically, the Nested Model deals with discrete covariates, while ANCOVA deals with continuous covariates. In the classical settings, the two approaches were studied separately under a set of assumptions which are unrealistic in many applications. For example, the ANCOVA approach requires modeling of the (continuous) covariate effect, and both approaches assume homogeneity of variances.
In this talk, we first introduce a new procedure for testing for the presence of covariate effect in a Nested Model (also known as the sub-class effect) without requiring those assumptions. Next, we present a conceptual connection, which we uncovered, between the Nested Model and ANCOVA approaches.
The key idea is very simple: continuous covariates can be thought of as discrete covariates with many distinct values (equivalently, as nested factors with many levels). Under suitable smoothing assumptions, this idea is exploited for extending the new procedure to ANCOVA without requiring modeling of the covariate effect.
The main focus of this talk is the innovative (but simple) ideas behind these new findings. Figures are used to help the audience visualize those ideas, and all proposed methods are demonstrated on both simulated and real data.
This talk is suitable for undergraduate students.
For more information, e-mail ma-chair@wpi.edu.
Hyperelasticity
Thursday, 2/26/2009 4:00 PM-5:00 PM
Salisbury Laboratories, 104
SPEAKER: Marian Bocea (North Dakota State University)
ABSTRACT: Hyperelasticity is one of several nonlinear models that can be used to understand the behavior of many useful materials (for example, rubber). I will introduce some ideas from Continuum Mechanics with a focus on the particular case of hyperelastic materials which are defined in terms of an "elastic energy density", or "stored energy function". It will be shown that because of a basic constitutive requirement the stored energy function cannot be convex. One consequence is that the energy minimization problem in this context cannot be handled using the classical methods of the Calculus of Variations. New ideas and modern analytical tools have been introduced to address this and other related issues.
This talk is suitable for undergraduate students.
For more information, e-mail ma-chair@wpi.edu.
On Some Model Problems Related to Polycrystal Plasticity
Friday, 2/27/2009 11:00 AM-12:00 PM
Stratton Hall, 203
SPEAKER: Marian Bocea (North Dakota State University)
ABSTRACT: I will describe a unifying approach to the derivation and analysis of several models of (first-failure) dielectric breakdown, electrical resistivity, and polycrystal plasticity. All of these may be viewed as limiting cases of various power-law models via De Giorgi's Gamma-convergence; the effective yield set in each case is characterized by means of variational principles associated to supremal functionals acting on fields subject to constant rank differential constraints. I will indicate a number of highly degenerate nonlinear PDEs which play a role in the analysis of these
problems.
For more information, e-mail ma-chair@wpi.edu.
March 2009
Regularization for Stationary Multivariate Time Series
Wednesday, 3/4/2009 11:00 AM-12:00 PM
Stratton Hall, 202
SPEAKER: Xiaodong Lin (University of Cincinnati)
ABSTRACT: The past decade has seen a rapid development of regularization techniques such as ridge regression, LASSO, SCAD, LARS and their extensions. However, these techniques have been developed mainly for circumstances where the observations are independent. In practice, many classes of interesting problems such as financial time series involve dependent data. In this talk, we describe extensions of the results of penalized methods for independent data to stationary multivariate time series. Under mild regularity conditions, our penalized estimators are sparse-consistent and possess well-known oracle properties. We demonstrate the utility of our results by developing a sparse version of the full factor GARCH model, and show the applicability of our theory and methods via real and simulated data. Our methods provide a framework for applications of regularization techniques to other multivariate time series models, spatial and temporal models, dynamic network models and more.
For more information, e-mail ma-chair@wpi.edu.
Privacy Preserving Distributed Statistical Analysis
Wednesday, 3/4/2009 4:00 PM-5:00 PM
Stratton Hall, 202
SPEAKER: Xiaodong Lin (University of Cincinnati)
ABSTRACT: Many organizations, among them government agencies, corporations, employers and medical insurers, assemble and in many cases disseminate highly sensitive information about individuals and establishments. Some do so responsibly, while others are less careful.
Data confidentiality is the field within the statistical and computer sciences that addresses how to make tradeoffs in today's electronic world between the conflicting goals of protecting the privacy of data subjects and making useful information available from the data for policy and research purposes.
This talk will be an accessible introduction to data confidentiality research for distributed data sources, emphasizing the nature and scale of the issues. I will describe methods by which computation can be performed over the distributed data, while preserving individual data privacy. Some interesting current research problems will also be presented.
This talk is suitable for undergraduate students.
For more information, e-mail ma-chair@wpi.edu.
H. J. Gay Lecture "Scaling Limits of Large Systems"
Monday, 3/16/2009 4:00 PM-5:00 PM
Bartlett Center
SPEAKER: Srinivasa Varadhan (Courant Institute of Mathematical Sciences at New York University)
ABSTRACT: We will discuss the longtime behavior of large systems of interacting particles that evolve in time. The number of particles is conserved. When we rescale space, the local density as a
function of space will evolve slowly to its equilibrium value, which is a constant indicating uniform density. With suitable rescaling of time, it will evolve, in the limit, according to some nonlinear PDE. We will examine several examples of this behavior.
For more information, e-mail ma-chair@wpi.edu.
Dimensionality Reduction for Classification with High-Dimensional Data
Thursday, 3/26/2009 11:00 AM-12:00 PM
Higgins Laboratories, 202
SPEAKER: Siva Tian (University of Southern California)
ABSTRACT: High-dimensional classification is becoming an increasingly important problem. We propose a Multivariate Adaptive Stochastic Search (MASS) approach which first reduces the dimension of the data space and then applies a standard classification method to the reduced space. One key advantage of MASS is that it automatically adjusts to either mimic variable selection type methods, such as the Lasso, or variable combination methods, such as PCA, or somewhere between the two approaches. The adaptivity of MASS allows it to perform well in situations where pure variable selection or variable combination methods fail. Another major advantage of our approach is that MASS can accurately project the data into very lowdimensional non-linear, as well as linear, spaces. MASS uses a stochastic search algorithm to select a handful of optimal projection directions from a large number of random directions in each iteration. We provide some theoretical justification for MASS and demonstrate its strengths on an extensive range of simulation studies and real world data sets by comparing it to many classical and modern classification methods.
For more information, e-mail ma-chair@wpi.edu.
Coefficient Shrinkage Methods for Linear Regression
Thursday, 3/26/2009 4:00 PM-5:00 PM
Higgins Laboratories, 202
SPEAKER: Siva Tian (University of Southern California)
ABSTRACT: In regression analysis, prediction accuracy and model interpretation are two important issues, particularly when there are too many variables available. In this talk, I will introduce two different coefficient shrinkage approaches for linear regression:
1. Ridge Regression which estimates the parameters by minimizing the standard least squares criterion plus an additional squared penalty (L2) on the b's.
2. The LASSO which is similar to Ridge Regression except that the penalty on the b's is the absolute value (L1) rather than the square (L2).
Comparisons of these two methods will be conducted on a simulation study.
This talk is suitable for undergraduate students.
For more information, e-mail ma-chair@wpi.edu.
The American Institute of Mathematics
Monday, 3/30/2009 11:00 AM-12:00 PM
Stratton Hall, 308
SPEAKER: Brian Conrey (Executive Director, American Institute of Mathematics)
ABSTRACT: The American Institute of Mathematics was started by John Fry in 1994 with the idea of getting teams of mathematicians to solve important research problems. In this presentation I will talk about some of the things that AIM has been involved with over the past 15 years.
For more information, e-mail ma-chair@wpi.edu.
Levi L. Conant Lecture Series "The Riemann Hypothesis"
Monday, 3/30/2009 4:00 PM-5:00 PM
Higgins Laboratories, 116
SPEAKER: Brian Conrey (Executive Director, The American Institute of Mathematics)
ABSTRACT: The famous Riemann Hypothesis is nearly 150 years old. It was on Hilbert's list of 23 problems in 1900 and now it's on the Clay list of Millennium Prize Problems--there's a million dollar reward for its solution. Many people regard it as the most important unsolved problem in all of mathematics. In this talk we will explain exactly what the Riemann Hypothesis is and give some of the colorful history that has grown up around efforts to solve it.
For more information, e-mail ma-chair@wpi.edu.
Model selection methods for high-dimensional data and their applications to genome-wide association studies
Tuesday, 3/31/2009 11:00 AM-12:00 PM
Stratton Hall, 203
SPEAKER: Zheyang Wu (Yale University)
ABSTRACT: In the past several years, genome-wide association studies (GWAS) have led to many discoveries of genetic variations affecting complex disease risks. GWAS query up to one million single nucleotide polymorphisms (SNPs) over the whole genome from high-density genotyping platforms. Mining a very large number of SNPs data in GWAS requires model selection in a high-dimensional space. It is crucial to devise an effective strategy to identify truly associated SNPs that exert both individual and interacting effects. In this talk I present a theoretical study for the statistical power of SNP search strategies based on model selections: marginal selection, exhaustive search, forward selection, and stratified search. For a specific genetic model, our results reveal the mechanisms for how different factors, such as effect size, allele frequency, and gene-gene interaction, jointly affect statistical power. We compare the performances of different model selection strategies over a wide space of genetic parameters. Our results, implemented as an R package, can provide researchers fast and accurate consultation on the most effective and efficient means of SNP detection. The novel statistical approach used in the power calculation is based on deriving asymptotical distributions and correlation structures for relevant test statistics. It has general applicability to high-dimensional model selection with random predictors. Besides this main topic, I will briefly introduce a joint marker detection method proposed for practical GWAS. I may also touch upon a statistical decision theory for penalized model selection: the penalty terms that lead model-selection procedure to achieve sharp asymptotic minimaxity over a wide range of sparse parameter spaces.
For more information, e-mail ma-chair@wpi.edu.
Simple regression and gene detection
Tuesday, 3/31/2009 4:00 PM-5:00 PM
Stratton Hall, 308
SPEAKER: Zheyang Wu (Yale University)
ABSTRACT: Simple regression is a statistical model for studying the association between a predictor variable and a response variable, based on observed data vectors. In this talk, we will introduce the concept, the parameter estimation, and the hypothesis test for simple regression. For hypothesis test, we consider two cases: fixed predictor vs. random predictor. We will discuss this statistical methodology with the motivation and the application in hunting genes associated with quantitative genetic traits.
This talk is suitable for undergraduate students.
For more information, e-mail ma-chair@wpi.edu.
April 2009
What Should Mathematicians Do? (How to Make Money with Mathematics)
Thursday, 4/9/2009 4:00 PM-5:00 PM
Higgins Laboratories, 116
SPEAKER: Shane Chalke (Founder, Chalke Incorporated and Finetre Corporation)
ABSTRACT: Too often, great work in mathematics is consumed only by other mathematicians. At the same time, the mathematical foundations of many areas of finance are light years behind current theory. In bridging this divide lies great opportunity. Throughout his career, Shane Chalke has built strong businesses by applying mathematical concepts to complex, and sometimes simple, business problems. He has found that the analysis used in business can be so steeped in tradition and inertia that over time the analysis is faulty. By updating the mathematical foundations of business, and "packaging" this analysis for non-mathematicians (mere mortals), significant economic gains can be achieved. Chalke will speak about his experience in the intersection of mathematics and business, and what mathematicians can do to make an impact on the economic world.
This talk is suitable for students.
For more information, e-mail ma-chair@wpi.edu.
Systems Biology of Cell Signaling
Friday, 4/10/2009 11:00 AM-12:00 PM
Stratton Hall, 203
SPEAKER: Qing Nie (University of California, Irvine)
ABSTRACT: The proper growth, development, and survival of an organism require extensive and accurate communication among the cells of the organism. Hence, cells sense and react to a wide variety of stimuli, which convey information such as nutrients, harmful insults, and the state of neighboring cells. Using a systems biology approach that integrates modeling and experimentation, we study two cell signaling systems: 1) robust sensing and signal transduction during mating of yeast cells, and 2) proliferative control of cell lineages in mammalian olfactory epithelium.
For more information, e-mail ma-chair@wpi.edu.
H. J. Gay Lecture "Are Most Triangles Acute or Obtuse?"
Tuesday, 4/14/2009 4:00 PM-5:00 PM
Salisbury Laboratories, 105
SPEAKER: Gilbert Strang (MIT)
ABSTRACT: This talk has two separate parts, both about shapes. First, we ask how a change from circle to polygon affects the solution to a differential equation inside. Key examples are the eigenvalue problem for Laplace's equation, and Poisson's equation u_xx + u_yy = 1. The area between the circle and polygon becomes a crucial quantity and we ask how this leading term in the error might be removed--to improve the accuracy of the eigenvalues and the solution.
Part 2 is about an innocent question--Is a random triangle acute or obtuse? Everything depends on the meaning of "random." Are the angles random or the sides? Is the distribution uniform or normal? New answers keep coming, and some are surprising.
For more information, e-mail ma-chair@wpi.edu.
Some recent problems on Taylor dispersion
Tuesday, 4/21/2009 11:00 AM-12:00 PM
Stratton Hall, 203
SPEAKER: Burt Tilley (Olin College)
ABSTRACT: G.I. Taylor originally found that the diffusion of a solute in a flowing solvent in a capillary depends on the characteristic velocity of the flow. This dispersion is found not only in mass transport applications, but also in the transfer of heat. We consider two recent problems in where Taylor dispersion plays a significant role in the system behavior.
The first problem centers on experiments with glycerol-water thin films flowing down an inclined plane reveal localized instability that is primarily three dimensional is observed. These transient structures, referred to as dimples, appear initially as nearly isotropic depressions on the interface. A linear stability analysis of a binary mixture model in which barodiffusive effects dominate over the Soret effect reveals unstable modes when the components of the mixture have different bulk densities and surface tensions. This instability occurs when Fickian diffusion and Taylor dispersion effects are small, and is driven by solutalcapillary stresses arising from gradients in concentration of one component across the depth of the film. Qualitative comparison between the experiments and the linear stability results over a wide range of parameters is presented.
The second problem centers on residential geothermal heating systems have been developed over the past few decades as an alternative to fossil-fuel based heating. Through mathematical modeling the relationship between the operating parameters of the heat pump and the piping length of the geothermal system, which is directly correlated to the cost of the system is investigated. A model of a simple configuration of a single pipe surrounded concentrically by grout and then by soil is considered, where the soil region has a constant ambient temperature. The conduction between the two regions is modeled with a classical thermal resistance. Taylor dispersion effects are significant at higher Peclet numbers associated with this system, and Taylor dispersion in the fluid and thermostat frequency dictate the minimum tubing length needed for successful operation in an insulated subsystem. We consider both steady state and transient (cyclic operation) analyses and find that the axial dispersion increases linearly in the cycle rate for large flow rates. We find that the estimated tubing length for complete energy transport is increased when Taylor dispersion is included, but that this effect can be mitigated with an appropriate choice of the borehole radius. We close with some open mathematical problems that are of current interest.
For more information, e-mail ma-chair@wpi.edu.
Using Popular Science in Mathematical Modeling
Tuesday, 4/21/2009 4:00 PM-5:00 PM
Stratton Hall, 308
SPEAKER: Burt Tilley (Olin College)
ABSTRACT: How do you know whether a story in the media is true? How do you evaluate quantitative evidence that is presented? How do you judge the conclusions drawn from this quantitative evidence? What skills does a person need in order to approach these tasks independently and confidently? The ability to mathematically model a problem, formulate a solution, and articulate this solution in the problem's original context effectively answers these questions.
Two models, which were developed from projects from a mathematical modeling course developed at Olin College are presented. The first centers on the efficacy of educational programs to prevent the spread of the AIDS virus. The second considers patient-controlled analgesia: a mode of pain management where the patient administers small amounts of pain medication as needed without the risk of overdose.
This talk is suitable for undergraduate students.
For more information, e-mail ma-chair@wpi.edu.
AMS Sectional Meeting
Saturday, 4/25/2009 - Sunday, 4/26/2009 7:30 AM-6:00 PM
Higgins Laboratories, 102
- Fees are US$40/AMS or CMS members; US$60/nonmembers; US$5/emeritus members, students, or unemployed mathematicians.
Invited addresses will be by Octav Cornea, Universite of Montreal; Fengbo Hang, New York University, Courant Institute of Mathematical Sciences; Umberto Mosco, Worcester Polytechnic Institute; and Kevin Whyte, University of Illinois at Chicago.
See the AMS Website for the most up-to-date lists of Invited Addresses and Special Sessions.
For more information, e-mail meet@ams.org.
May 2009
A model for stochastic volatility. Estimation.
Friday, 5/1/2009 11:00 AM-12:00 PM
Stratton Hall, 203
SPEAKER: Ionut Florescu (Stevens Institute)
ABSTRACT: This talk is composed of two parts. In the first part I will present a stochastic volatility model where the volatility is modeled as a continuous time Markov Chain. A methodology for automatically estimating the nodes and the transition probabilities of this hidden Markov Chain is exposed. In the second part of the talk we will discuss about the procedure after the estimates are found. Specifically, we will construct a multinomial tree which approximates the continuous time price process and with its help we estimate the price of any call or put option. We then use this tree to estimate a value for the CBOE Volatility Index (VIX) and we look at the differences between our estimated value and the value observed on the market. As a side note we discover that toward the end of last year (Aug-Dec 2008) the relationship between VIX and the S&P500 price has been unusually high.
Note: this work is developed in collaboration with Forrest Levin and Hongwei Qu.
For more information, e-mail ma-chair@wpi.edu.
September 2008
Vector Space Methods for Reaction Networks and Kirchhoff Graphs
Friday, 9/12/2008 11:00 AM-12:00 PM
Stratton Hall, 203
SPEAKER: Joseph D. Fehribach (WPI)
ABSTRACT: Reaction networks are systems of chemical, electrochemical or biological reaction steps together with their constituent species. This talk will focus on the use of basic linear algebra results to determine what (if any) overall reactions can result from a given reaction network. The talk will then discuss the existence and construction of Kirchhoff graphs (reaction route graphs) associated with the reaction networks Kirchhoff graphs satisfy the Kirchhoff laws and allow one to study a reaction network as one might use a circuit diagram to study an electrical network. There will be a number of illustrative examples.
For more information, e-mail ma-chair@wpi.edu.
October 2008
Electrostatically Actuated Bistable and Multistable Micro Structures
Friday, 10/24/2008 11:00 AM-12:00 PM
Stratton Hall, 203
SPEAKER: Slava Krylov (Dept of Solid Mechanics and Material Science, Univ. of Tel Aviv)
ABSTRACT: In this work, results of theoretical and experimental study of initially curved electrostatically actuated microbeams with clamped ends is presented. Due to unique combination of non-monotonous stiffness-deflection dependence typical for mechanically bistable structures and of nonlinear electrostatic force abundant in micro and nano systems the structure exhibits sequential snap-through buckling and electrostatic pull-in instability as well as multiple stable configurations at the same voltage (bistability). Reduced order Galerkin and consistently constructed lumped models were built and verified by numerical analysis and experimentally. The minimal initial elevation required for appearance of the bistability in the electrostatically actuated beam is smaller than in the case of an uniform deflection independent loading; closed form approximation of this elevation was evaluated. The devices were fabricated from silicon on insulator (SOI) wafer using deep reactive ion etching and in-plane responses were characterized by means of optical and Scanning Electron microscopy (SEM). Characterization inside a SEM was found to be a useful experimental approach providing stable operational in-vacuo conditions while higher magnification improves the quality of data processing. Model results obtained for the actual dimensions of the device were in good agreement with the experimental data. Designs incorporating bistable beams have clear functional advantages and may result in improved performance of of switches, capacitive based sensors and MEMS/NEMS based nonvolatile memory devices.
For more information, e-mail ma-chair@wpi.edu.
Domain coarsening and curve shortening by volume-preserving mean curvature flow
Friday, 10/31/2008 11:00 AM-12:00 PM
Stratton Hall, 203
SPEAKER: Shibin Dai (WPI)
ABSTRACT: We will first briefly discribe the microscopic mechanisms and macroscopic models of the domain coarsening phenomena that happen in materials science, phase transitions, etc. Then we will concentrate on the volume-preserving mean curvature flow, which is a model when the interfacial reaction is the dominating mechanism. Geometrically, it describes the decay of the area of surfaces that are interfaces separating the two phases while preserving the volumes of each phase, respectively. Heuristic self-similarity arguments suggest a decay rate of the density of the surface area to be a temporal power law. We consider a simplified 2D case when the interface is a collection of non-intersecting smooth convex plane curves, and prove a lower bound on the shortening rate of the averaged curve length, which exhibits the aforementioned power law. The dependence of the power law coefficient on the curve shapes is also presented.
For more information, e-mail ma-chair@wpi.edu.
November 2008
Transformed Epithelial Cells and Fibroblasts/Myofibroblasts
Friday, 11/7/2008 11:00 AM-12:00 PM
Stratton Hall, 203
SPEAKER: Yangjin Kim (Mathematical Biosciences Institute, Ohio State University)
ABSTRACT: In order to understand the role of fibroblasts/myofibroblasts in the early evolution of breast cancer in vitro we developed a mathematical model as well as conduct experiments. In the experiments tumor cells are placed on one side of a membrane and fibroblasts are placed on the other side. The membrane is semi-permeable, allowing only growth factors such as EGF,TGF-beta, but not cells, to cross over. The mathematical model describes the dynamics of the various concentrations of cells and growth factors by a system of partial differential equations. The prescence of extracellular matrix have an effect on tumor grwoth. We demonstrate a good agreement between the simulation of the model and the experiments.
For more information, e-mail ma-chair@wpi.edu.
Discrete Element Modeling of Powder Processing
Friday, 11/14/2008 11:00 AM-12:00 PM
Stratton Hall, 203
SPEAKER: Didier Bouvard (Institut Polytechnique de Grenoble, France)
ABSTRACT: Modeling of processes involving powder materials needs taking into account the particulate nature of these materials. The Discrete Element Method(DEM) is well suited for such a task. It allows the macroscopic behaviour of an assembly of particles to be calculated from the contact forces generated between particles. Rearrangement between particles, a significant signature of powder materials, is explicitly taken into account. DEM has been developed in the recent years to simulate the processing of metal and ceramic powders. We present diverse examples of application on powder compaction and sintering. We also demonstrate how microstructures numerically generated by DEM can be used to compute macroscopic features of partially sintered body such as conduction properties.
For more information, e-mail ma-chair@wpi.edu.
Recovery of active faults from surface displacement fields
Friday, 11/21/2008 11:00 AM-12:00 PM
Stratton Hall, 203
SPEAKER: Darko Volkov (WPI)
ABSTRACT: The goal of this research project is to process measurements of surface displacements in such a way to use them as data for the inverse problem consisting of locating faults and portraying their geometry. Our research is also aiming at determining whether a measured displacement field on the surface is indicative of the onset of a destabilization phase.
We have already entirely solved a two dimensional problem associated to the strike slip model, which essentially reduces displacement fields to two dimensional scalar fields. Deriving the inversion method involved a rigorous mathematical eigenvalue asymptotic analysis, leading to closed form inversion formulas. Those formulas were then tested for robustness in numerical simulations. As the strike slip model is limited in scope (it captures only one of the textbook examples of faults), we have worked on extending our results to fully three dimensional fault problems. In this much more difficult case, we have already obtained very promising closed form formulas (valid for the dominant part of the asymptotic behavior), and we have tested their use on numerical data.
Nonetheless, a complete mathematical analysis of the eigenvalue problem obtained by studying destabilization is still being investigated.
For more information, e-mail ma-chair@wpi.edu.
December 2008
The Explicit Solution of the Laplace Equation with the Robin(third boundary) Condition
Friday, 12/5/2008 11:00 AM-12:00 PM
Stratton Hall, 203
SPEAKER: Alip Mohammed (York University)
ABSTRACT: The inhomogeneous Robin condition with general coeffcient for the Laplace equation on the unit disc is studied in terms of holomorphic functions using Fourier analysis. It is shown that against usual expectations this problem cannot have unique solution unless the coeffcient of the first order term in the boundary condition is a constant. For the case of general coeffcient, it is actually a problem with essential singularity in the domain, but still well-posed under proper assumptions and the unique solution is given explicitly.
For more information, e-mail ma-chair@wpi.edu.
Problems and Results on the Combinatorial Geometry of Patterns
Friday, 12/12/2008 3:00 PM-3:50 PM
Stratton Hall, 308
SPEAKER: Peter Brass (CUNY)
ABSTRACT: In this talk I will present problems, results, and algorithmic applications of combinatorial geometry on geometric patterns. Classical combinatorial geometry, as developed by Erd\H{o}s, studied geometric extremal problems like the maximum number of point-line incidences, or the maximum number of unit distances, or many similar problems. In the last 15 years, it became apparent that these results are an important building block for the analysis of geometric pattern-matching algorithms in the point pattern model. Many algorithms for these problems work by choosing a small pattern fragment of the pattern we try to find, identifying all occurences of the fragment in the background set, and testing each of these fragments whether it can be extended to the entire pattern. In such an algorithm, the bound on the number of fragments we try to extend becomes the dominant term of the complexity. Thus we study, for different types of fragments, the maximum number of occurences of that pattern fragment in a large point set.
For more information, e-mail ma-chair@wpi.edu.
January 2009
Object Recognition in Computer Vision using Signature Curves
Friday, 1/23/2009 11:00 AM-12:00 PM
Stratton Hall, 203
SPEAKER: Cheri Shakiban (University of St. Thomas and IMA)
ABSTRACT: In this talk I will discuss the differential invariant signature curves arising from the theory of moving frames for two and three dimensional closed curves and will give a formulated and discrete method for finding such a curve. Then I will discuss an analog of Latent Semantic Analysis (LSA) and show how an optimal combination of normalizing transformations is utilized to categorize signature curves. I will then give some examples, including one in sorting leaves in the Euclidean plane and the other in sorting DNA supercoils as space curves.
For more information, e-mail ma-chair@wpi.edu.
February 2009
The method of layer potentials for second and higher order elliptic operators
Thursday, 2/5/2009 11:00 AM-12:00 PM
Fuller Laboratories, 311
SPEAKER: Irina Mitrea (University of Virginia)
ABSTRACT: As is well known, many phenomena in Engineering and Mathematical Physics can be modeled by means of boundary value problems for certain elliptic differential operators L in a domain D.
When L is a differential operator of second order a variety of tools are available for dealing with such problems including boundary integral methods, variational methods, harmonic measure techniques, and methods based on classical harmonic analysis. The situation when the differential operator has higher order (as is the case for instance with anisotropic plate bending when one deals with fourth order) stands in sharp contrast with this as only fewer options could be successfully implemented. Alberto Calderon, one of the founders of the modern theory of Singular Integral Operators, has advocated in the seventies the use of layer potentials for the treatment of higher order elliptic boundary problems. While the layer potential method has proved to be tremendously successful in the treatment of second order problems, this approach is insufficiently developed to deal with the intricacies of the theory of higher order operators and, in fact, it is largely absent from the literature.
In this talk I will discuss some of my work on the Spectral Radius Conjecture for layer potential operators associated with second order elliptic boundary problems in non-smooth domains and recent progress in developing a multiple layer potential approach for the higher order case.
For more information, e-mail ma-chair@wpi.edu.
What do physics, geometry, and complex analysis have in common?
Thursday, 2/5/2009 4:00 PM-5:00 PM
Stratton Hall, 202
SPEAKER: Irina Mitrea (University of Virginia)
ABSTRACT: While mathematics is being used routinely to solve problems in physics, the converse direction has been very little explored. Have you ever used the physics laws of motion to solve problems in geometry? How about complex numbers?
This talk, intended for a general audience, is aimed at exploring unexpected connections between various branches of mathematics and physics with applications to geometry.
For more information, e-mail ma-chair@wpi.edu.
Fixed-Domain Asymptotic Properties of Tapered Maximum Likelihood Estimators
Thursday, 2/12/2009 11:00 AM-12:00 PM
Salisbury Laboratories, 406
SPEAKER: Juan Du (Michigan State University)
ABSTRACT: When the spatial sample size is extremely large, as in many environmental and ecological studies, operations on the large covariance matrix are a numerical challenge. Covariance tapering is a technique to alleviate the numerical challenges. We investigate how tapering affects asymptotic efficiency of the maximum likelihood estimator (MLE) and establish asymptotic properties, particularly asymptotic distribution of the exact MLE and tapered MLE under the fixed-domain asymptotic framework for Matérn model. We show that under some conditions on the tapering function, the tapered MLE is asymptotically as efficient as the true MLE for the microergodic parameter in the Matérn model. The computational gain and comparable estimation are illustrated by simulation study and an application to the US precipitation data in April 1948.
This is joint work with Professor V. S. Mandrekar (Michigan State University) and Professor Hao Zhang (Purdue University).
For more information, e-mail ma-chair@wpi.edu.
Using Moment Generating Function to Show Central Limit Theorem
Thursday, 2/12/2009 4:00 PM-5:00 PM
Stratton Hall, 202
SPEAKER: Juan Du (Michigan State University)
ABSTRACT: The Central Limit theorem is the foundation for many statistical procedures, because it enables us to approximate the distribution of sums and means of independent random variables by the normal distribution. I will use moment generating function, which is an important tool for the distribution convergence, to show the Central Limit Theorem and present some applications to statistical problems.
This talk is suitable for undergraduate students with a basic statistics background.
For more information, e-mail ma-chair@wpi.edu.
Discrete network approximation for determining asymptotics of effective properties of high contrast concentrated composites
Thursday, 2/19/2009 11:00 AM-12:00 PM
Salisbury Laboratories, 406
SPEAKER: Yuliya Gorb (Texas A&M University)
ABSTRACT: A blow up of effective properties of high contrast composites with particles close to touching is of interest. The goal is to derive and justify asymptotic formulas for effective properties of such composites as a characteristic interparticle distance tends to zero. A derivation and justification is done by constructing a so-called discrete network approximation. The main idea of this approximation is based on a reduction of the original continuum problem described by partial differential equations with rough coefficients to a discrete problem on a graph, called a discrete network. The approach is illustrated by considering a highly packed suspension of rigid particles in a Newtonian fluid (vectorial problem), and a medium of finite conductivity with perfectly conducting particles (scalar problem).
For more information, e-mail ma-chair@wpi.edu.
Composites, effective properties and homogenization theory (introduction)
Thursday, 2/19/2009 4:00 PM-5:00 PM
Salisbury Laboratories, 104
SPEAKER: Yuliya Gorb (Texas A&M University)
ABSTRACT: In this talk we will discuss what composite materials are, how one can define their effective properties, and what mathematical questions may be raised in their study. An illustrative one-dimensional example will be presented to demonstrate an asymptotic homogenization method.
This talk is suitable for undergraduate students.
For more information, e-mail ma-chair@wpi.edu.
On breakup of finite-size films and rivulets
Friday, 2/20/2009 11:00 AM-12:00 PM
Stratton Hall, 203
SPEAKER: Lou Kondic (NJIT)
ABSTRACT: In the first part of the talk I will give an overview of various thin liquid film problems involving instabilities, such as flow down an incline, flows on inhomogeneous surfaces, coalescence of drops, and evaporation-induced instabilities. While the emphasis will be on computations and theory, some experimental results will be presented as well.
The second part of the talk will concentrate on recent research of the mechanism of the breakup process involving finite-size films and rivulets. We will see that the breakup process due to finite size effects can be related to a particular mode of instability of infinite films, so called nucleation type of instability. We will also discuss coupling of various types of instabilities, and the competition between them. This competition may be relevant to problems on micro-and nano-scale fluidics relevant to printing applications. Finally, we will revisit the classical problem of rivulet instability and discuss whether finite size effects may be important in determining the relevant instability mechanism. If time allows, an application to breakup of nanometric metal lines illuminated by laser pulses will be presented. The presentation will include discussion of various computational and asymptotic methods relevant to thin film flows.
For more information, e-mail ma-chair@wpi.edu.
Bayesian Strategies For Some Kernel Regression Models
Monday, 2/23/2009 11:00 AM-12:00 PM
Salisbury Laboratories, 406
SPEAKER: Ernest Fokoue (Kettering University)
ABSTRACT: Kernel methods have recently triggered a wave interest from researchers and practitioners in both the Statistics and Machine Learning communities, largely due to their vast applicability in a wide variety of fields. In this talk, I intend to present a variety of Bayesian strategies used the context of regression models based on kernels. I particularly explore prior specification and Bayesian computation for both finite dimensional and infinite dimensional models, with an emphasis on the traditional linear model and the now very popular relevance vector machine. A major part of this talk is dedicated to the introduction of prior structures that are designed to lead to the consistency of the posterior quantities of interest. I provide ample computational evidence as to the merits of the techniques covered, but I finish by offering some elements of the theoretical properties of some of the priors introduced.
For more information, e-mail ma-chair@wpi.edu.
A Gentle Introduction to the Foundation of Statistical Learning Theory
Monday, 2/23/2009 4:00 PM-5:00 PM
Stratton Hall, 203
SPEAKER: Ernest Fokoue (Kettering University)
ABSTRACT: In this talk, I intend to provide a gentle progression into what I believe to be the most fundamental building blocks of the emerging field of statistical learning theory. I lead the audience to some of the niceties and subtleties of the foundations of statistical learning theory, requiring from them nothing more than a basic understanding of mathematical expectation, conditional density function and the ubiquitous Chebyshev's inequality (and its more powerful extensions), as we explore together the general framework from which statistical function estimation (parametric and nonparametric regression) and pattern recognition originate. Throughout this talk, I strive to keep all complicated technical details to the "absolute" bare minimum.
This talk is suitable for undergraduate students.
For more information, e-mail ma-chair@wpi.edu.
Heteroscedastic Unbalanced Nested Design, Fully Nonparametric ANCOVA, and Applications
Wednesday, 2/25/2009 11:00 AM-12:00 PM
Stratton Hall, 202
SPEAKER: Shu-Min Liao (Pennsylvania State University)
ABSTRACT: This talk consists of three parts. Firstly, in the context of a nonparametric model for the unbalanced heteroscedastic two-fold nested design, we consider the problem of testing for the sub-class effect. We establish, via theoretical derivations and numerical evidence, that, when the number of sub-classes is large, the classical F-test procedure is very sensitive to departures from homoscedasticity, even under normality, regardless of whether the model is balanced or unbalanced. For this reason, new testing procedures are developed to accommodate heteroscedasticity.
Secondly, we propose a new fully nonparametric ANCOVA model. The term fully nonparametric means that it is suitable for all types of ordinal data, and allows for heteroscedasticity and arbitrary form of the covariate effect. Under this model we develop a new test procedure for the (simple) covariate effect.
The development is based on conceptual connection between nested design and ANCOVA, which we uncover. The key idea is that covariates can be thought of as nested factors with many levels. Under suitable smoothing assumptions the test statistic for nested design is extended to ANCOVA. Some new asymptotic tools, based on an application of the projection principle, are introduced to obtain a new class of quadratic forms, whose asymptotical approximation is then utilized to establish the limiting distributions of the proposed test statistic under the null hypotheses and local alternatives.
All proposed methods and their properties are demonstrated on simulated and real data. Finally, innovative applications based on these new findings are briefly outlined.
For more information, e-mail ma-chair@wpi.edu.
Comparative Studies in Statistics: Some Recent Developments
Wednesday, 2/25/2009 4:00 PM-5:00 PM
Stratton Hall, 202
SPEAKER: Shu-Min Liao (Pennsylvania State University)
ABSTRACT: The role of randomization in statistical comparative experiments is well understood as it is simple: If experimental units are not assigned to treatments in a controlled randomized fashion, an unanticipated influential factor can distort the comparison. While randomization does offer protection, the precision of the comparison can be improved by properly accounting, or adjusting, for influential factors. The term covariate will be used for any factor that we want to adjust for in a comparative study.
Two common approaches to adjusting for covariates are the Nested Model and Analysis of Covariance (ANCOVA). Basically, the Nested Model deals with discrete covariates, while ANCOVA deals with continuous covariates. In the classical settings, the two approaches were studied separately under a set of assumptions which are unrealistic in many applications. For example, the ANCOVA approach requires modeling of the (continuous) covariate effect, and both approaches assume homogeneity of variances.
In this talk, we first introduce a new procedure for testing for the presence of covariate effect in a Nested Model (also known as the sub-class effect) without requiring those assumptions. Next, we present a conceptual connection, which we uncovered, between the Nested Model and ANCOVA approaches.
The key idea is very simple: continuous covariates can be thought of as discrete covariates with many distinct values (equivalently, as nested factors with many levels). Under suitable smoothing assumptions, this idea is exploited for extending the new procedure to ANCOVA without requiring modeling of the covariate effect.
The main focus of this talk is the innovative (but simple) ideas behind these new findings. Figures are used to help the audience visualize those ideas, and all proposed methods are demonstrated on both simulated and real data.
This talk is suitable for undergraduate students.
For more information, e-mail ma-chair@wpi.edu.
Hyperelasticity
Thursday, 2/26/2009 4:00 PM-5:00 PM
Salisbury Laboratories, 104
SPEAKER: Marian Bocea (North Dakota State University)
ABSTRACT: Hyperelasticity is one of several nonlinear models that can be used to understand the behavior of many useful materials (for example, rubber). I will introduce some ideas from Continuum Mechanics with a focus on the particular case of hyperelastic materials which are defined in terms of an "elastic energy density", or "stored energy function". It will be shown that because of a basic constitutive requirement the stored energy function cannot be convex. One consequence is that the energy minimization problem in this context cannot be handled using the classical methods of the Calculus of Variations. New ideas and modern analytical tools have been introduced to address this and other related issues.
This talk is suitable for undergraduate students.
For more information, e-mail ma-chair@wpi.edu.
On Some Model Problems Related to Polycrystal Plasticity
Friday, 2/27/2009 11:00 AM-12:00 PM
Stratton Hall, 203
SPEAKER: Marian Bocea (North Dakota State University)
ABSTRACT: I will describe a unifying approach to the derivation and analysis of several models of (first-failure) dielectric breakdown, electrical resistivity, and polycrystal plasticity. All of these may be viewed as limiting cases of various power-law models via De Giorgi's Gamma-convergence; the effective yield set in each case is characterized by means of variational principles associated to supremal functionals acting on fields subject to constant rank differential constraints. I will indicate a number of highly degenerate nonlinear PDEs which play a role in the analysis of these
problems.
For more information, e-mail ma-chair@wpi.edu.
March 2009
Regularization for Stationary Multivariate Time Series
Wednesday, 3/4/2009 11:00 AM-12:00 PM
Stratton Hall, 202
SPEAKER: Xiaodong Lin (University of Cincinnati)
ABSTRACT: The past decade has seen a rapid development of regularization techniques such as ridge regression, LASSO, SCAD, LARS and their extensions. However, these techniques have been developed mainly for circumstances where the observations are independent. In practice, many classes of interesting problems such as financial time series involve dependent data. In this talk, we describe extensions of the results of penalized methods for independent data to stationary multivariate time series. Under mild regularity conditions, our penalized estimators are sparse-consistent and possess well-known oracle properties. We demonstrate the utility of our results by developing a sparse version of the full factor GARCH model, and show the applicability of our theory and methods via real and simulated data. Our methods provide a framework for applications of regularization techniques to other multivariate time series models, spatial and temporal models, dynamic network models and more.
For more information, e-mail ma-chair@wpi.edu.
Privacy Preserving Distributed Statistical Analysis
Wednesday, 3/4/2009 4:00 PM-5:00 PM
Stratton Hall, 202
SPEAKER: Xiaodong Lin (University of Cincinnati)
ABSTRACT: Many organizations, among them government agencies, corporations, employers and medical insurers, assemble and in many cases disseminate highly sensitive information about individuals and establishments. Some do so responsibly, while others are less careful.
Data confidentiality is the field within the statistical and computer sciences that addresses how to make tradeoffs in today's electronic world between the conflicting goals of protecting the privacy of data subjects and making useful information available from the data for policy and research purposes.
This talk will be an accessible introduction to data confidentiality research for distributed data sources, emphasizing the nature and scale of the issues. I will describe methods by which computation can be performed over the distributed data, while preserving individual data privacy. Some interesting current research problems will also be presented.
This talk is suitable for undergraduate students.
For more information, e-mail ma-chair@wpi.edu.
H. J. Gay Lecture "Scaling Limits of Large Systems"
Monday, 3/16/2009 4:00 PM-5:00 PM
Bartlett Center
SPEAKER: Srinivasa Varadhan (Courant Institute of Mathematical Sciences at New York University)
ABSTRACT: We will discuss the longtime behavior of large systems of interacting particles that evolve in time. The number of particles is conserved. When we rescale space, the local density as a
function of space will evolve slowly to its equilibrium value, which is a constant indicating uniform density. With suitable rescaling of time, it will evolve, in the limit, according to some nonlinear PDE. We will examine several examples of this behavior.
For more information, e-mail ma-chair@wpi.edu.
Dimensionality Reduction for Classification with High-Dimensional Data
Thursday, 3/26/2009 11:00 AM-12:00 PM
Higgins Laboratories, 202
SPEAKER: Siva Tian (University of Southern California)
ABSTRACT: High-dimensional classification is becoming an increasingly important problem. We propose a Multivariate Adaptive Stochastic Search (MASS) approach which first reduces the dimension of the data space and then applies a standard classification method to the reduced space. One key advantage of MASS is that it automatically adjusts to either mimic variable selection type methods, such as the Lasso, or variable combination methods, such as PCA, or somewhere between the two approaches. The adaptivity of MASS allows it to perform well in situations where pure variable selection or variable combination methods fail. Another major advantage of our approach is that MASS can accurately project the data into very lowdimensional non-linear, as well as linear, spaces. MASS uses a stochastic search algorithm to select a handful of optimal projection directions from a large number of random directions in each iteration. We provide some theoretical justification for MASS and demonstrate its strengths on an extensive range of simulation studies and real world data sets by comparing it to many classical and modern classification methods.
For more information, e-mail ma-chair@wpi.edu.
Coefficient Shrinkage Methods for Linear Regression
Thursday, 3/26/2009 4:00 PM-5:00 PM
Higgins Laboratories, 202
SPEAKER: Siva Tian (University of Southern California)
ABSTRACT: In regression analysis, prediction accuracy and model interpretation are two important issues, particularly when there are too many variables available. In this talk, I will introduce two different coefficient shrinkage approaches for linear regression:
1. Ridge Regression which estimates the parameters by minimizing the standard least squares criterion plus an additional squared penalty (L2) on the b's.
2. The LASSO which is similar to Ridge Regression except that the penalty on the b's is the absolute value (L1) rather than the square (L2).
Comparisons of these two methods will be conducted on a simulation study.
This talk is suitable for undergraduate students.
For more information, e-mail ma-chair@wpi.edu.
The American Institute of Mathematics
Monday, 3/30/2009 11:00 AM-12:00 PM
Stratton Hall, 308
SPEAKER: Brian Conrey (Executive Director, American Institute of Mathematics)
ABSTRACT: The American Institute of Mathematics was started by John Fry in 1994 with the idea of getting teams of mathematicians to solve important research problems. In this presentation I will talk about some of the things that AIM has been involved with over the past 15 years.
For more information, e-mail ma-chair@wpi.edu.
Levi L. Conant Lecture Series "The Riemann Hypothesis"
Monday, 3/30/2009 4:00 PM-5:00 PM
Higgins Laboratories, 116
SPEAKER: Brian Conrey (Executive Director, The American Institute of Mathematics)
ABSTRACT: The famous Riemann Hypothesis is nearly 150 years old. It was on Hilbert's list of 23 problems in 1900 and now it's on the Clay list of Millennium Prize Problems--there's a million dollar reward for its solution. Many people regard it as the most important unsolved problem in all of mathematics. In this talk we will explain exactly what the Riemann Hypothesis is and give some of the colorful history that has grown up around efforts to solve it.
For more information, e-mail ma-chair@wpi.edu.
Model selection methods for high-dimensional data and their applications to genome-wide association studies
Tuesday, 3/31/2009 11:00 AM-12:00 PM
Stratton Hall, 203
SPEAKER: Zheyang Wu (Yale University)
ABSTRACT: In the past several years, genome-wide association studies (GWAS) have led to many discoveries of genetic variations affecting complex disease risks. GWAS query up to one million single nucleotide polymorphisms (SNPs) over the whole genome from high-density genotyping platforms. Mining a very large number of SNPs data in GWAS requires model selection in a high-dimensional space. It is crucial to devise an effective strategy to identify truly associated SNPs that exert both individual and interacting effects. In this talk I present a theoretical study for the statistical power of SNP search strategies based on model selections: marginal selection, exhaustive search, forward selection, and stratified search. For a specific genetic model, our results reveal the mechanisms for how different factors, such as effect size, allele frequency, and gene-gene interaction, jointly affect statistical power. We compare the performances of different model selection strategies over a wide space of genetic parameters. Our results, implemented as an R package, can provide researchers fast and accurate consultation on the most effective and efficient means of SNP detection. The novel statistical approach used in the power calculation is based on deriving asymptotical distributions and correlation structures for relevant test statistics. It has general applicability to high-dimensional model selection with random predictors. Besides this main topic, I will briefly introduce a joint marker detection method proposed for practical GWAS. I may also touch upon a statistical decision theory for penalized model selection: the penalty terms that lead model-selection procedure to achieve sharp asymptotic minimaxity over a wide range of sparse parameter spaces.
For more information, e-mail ma-chair@wpi.edu.
Simple regression and gene detection
Tuesday, 3/31/2009 4:00 PM-5:00 PM
Stratton Hall, 308
SPEAKER: Zheyang Wu (Yale University)
ABSTRACT: Simple regression is a statistical model for studying the association between a predictor variable and a response variable, based on observed data vectors. In this talk, we will introduce the concept, the parameter estimation, and the hypothesis test for simple regression. For hypothesis test, we consider two cases: fixed predictor vs. random predictor. We will discuss this statistical methodology with the motivation and the application in hunting genes associated with quantitative genetic traits.
This talk is suitable for undergraduate students.
For more information, e-mail ma-chair@wpi.edu.
April 2009
What Should Mathematicians Do? (How to Make Money with Mathematics)
Thursday, 4/9/2009 4:00 PM-5:00 PM
Higgins Laboratories, 116
SPEAKER: Shane Chalke (Founder, Chalke Incorporated and Finetre Corporation)
ABSTRACT: Too often, great work in mathematics is consumed only by other mathematicians. At the same time, the mathematical foundations of many areas of finance are light years behind current theory. In bridging this divide lies great opportunity. Throughout his career, Shane Chalke has built strong businesses by applying mathematical concepts to complex, and sometimes simple, business problems. He has found that the analysis used in business can be so steeped in tradition and inertia that over time the analysis is faulty. By updating the mathematical foundations of business, and "packaging" this analysis for non-mathematicians (mere mortals), significant economic gains can be achieved. Chalke will speak about his experience in the intersection of mathematics and business, and what mathematicians can do to make an impact on the economic world.
This talk is suitable for students.
For more information, e-mail ma-chair@wpi.edu.
Systems Biology of Cell Signaling
Friday, 4/10/2009 11:00 AM-12:00 PM
Stratton Hall, 203
SPEAKER: Qing Nie (University of California, Irvine)
ABSTRACT: The proper growth, development, and survival of an organism require extensive and accurate communication among the cells of the organism. Hence, cells sense and react to a wide variety of stimuli, which convey information such as nutrients, harmful insults, and the state of neighboring cells. Using a systems biology approach that integrates modeling and experimentation, we study two cell signaling systems: 1) robust sensing and signal transduction during mating of yeast cells, and 2) proliferative control of cell lineages in mammalian olfactory epithelium.
For more information, e-mail ma-chair@wpi.edu.
H. J. Gay Lecture "Are Most Triangles Acute or Obtuse?"
Tuesday, 4/14/2009 4:00 PM-5:00 PM
Salisbury Laboratories, 105
SPEAKER: Gilbert Strang (MIT)
ABSTRACT: This talk has two separate parts, both about shapes. First, we ask how a change from circle to polygon affects the solution to a differential equation inside. Key examples are the eigenvalue problem for Laplace's equation, and Poisson's equation u_xx + u_yy = 1. The area between the circle and polygon becomes a crucial quantity and we ask how this leading term in the error might be removed--to improve the accuracy of the eigenvalues and the solution.
Part 2 is about an innocent question--Is a random triangle acute or obtuse? Everything depends on the meaning of "random." Are the angles random or the sides? Is the distribution uniform or normal? New answers keep coming, and some are surprising.
For more information, e-mail ma-chair@wpi.edu.
Some recent problems on Taylor dispersion
Tuesday, 4/21/2009 11:00 AM-12:00 PM
Stratton Hall, 203
SPEAKER: Burt Tilley (Olin College)
ABSTRACT: G.I. Taylor originally found that the diffusion of a solute in a flowing solvent in a capillary depends on the characteristic velocity of the flow. This dispersion is found not only in mass transport applications, but also in the transfer of heat. We consider two recent problems in where Taylor dispersion plays a significant role in the system behavior.
The first problem centers on experiments with glycerol-water thin films flowing down an inclined plane reveal localized instability that is primarily three dimensional is observed. These transient structures, referred to as dimples, appear initially as nearly isotropic depressions on the interface. A linear stability analysis of a binary mixture model in which barodiffusive effects dominate over the Soret effect reveals unstable modes when the components of the mixture have different bulk densities and surface tensions. This instability occurs when Fickian diffusion and Taylor dispersion effects are small, and is driven by solutalcapillary stresses arising from gradients in concentration of one component across the depth of the film. Qualitative comparison between the experiments and the linear stability results over a wide range of parameters is presented.
The second problem centers on residential geothermal heating systems have been developed over the past few decades as an alternative to fossil-fuel based heating. Through mathematical modeling the relationship between the operating parameters of the heat pump and the piping length of the geothermal system, which is directly correlated to the cost of the system is investigated. A model of a simple configuration of a single pipe surrounded concentrically by grout and then by soil is considered, where the soil region has a constant ambient temperature. The conduction between the two regions is modeled with a classical thermal resistance. Taylor dispersion effects are significant at higher Peclet numbers associated with this system, and Taylor dispersion in the fluid and thermostat frequency dictate the minimum tubing length needed for successful operation in an insulated subsystem. We consider both steady state and transient (cyclic operation) analyses and find that the axial dispersion increases linearly in the cycle rate for large flow rates. We find that the estimated tubing length for complete energy transport is increased when Taylor dispersion is included, but that this effect can be mitigated with an appropriate choice of the borehole radius. We close with some open mathematical problems that are of current interest.
For more information, e-mail ma-chair@wpi.edu.
Using Popular Science in Mathematical Modeling
Tuesday, 4/21/2009 4:00 PM-5:00 PM
Stratton Hall, 308
SPEAKER: Burt Tilley (Olin College)
ABSTRACT: How do you know whether a story in the media is true? How do you evaluate quantitative evidence that is presented? How do you judge the conclusions drawn from this quantitative evidence? What skills does a person need in order to approach these tasks independently and confidently? The ability to mathematically model a problem, formulate a solution, and articulate this solution in the problem's original context effectively answers these questions.
Two models, which were developed from projects from a mathematical modeling course developed at Olin College are presented. The first centers on the efficacy of educational programs to prevent the spread of the AIDS virus. The second considers patient-controlled analgesia: a mode of pain management where the patient administers small amounts of pain medication as needed without the risk of overdose.
This talk is suitable for undergraduate students.
For more information, e-mail ma-chair@wpi.edu.
AMS Sectional Meeting
Saturday, 4/25/2009 - Sunday, 4/26/2009 7:30 AM-6:00 PM
Higgins Laboratories, 102 - Fees are US$40/AMS or CMS members; US$60/nonmembers; US$5/emeritus members, students, or unemployed mathematicians.
Invited addresses will be by Octav Cornea, Universite of Montreal; Fengbo Hang, New York University, Courant Institute of Mathematical Sciences; Umberto Mosco, Worcester Polytechnic Institute; and Kevin Whyte, University of Illinois at Chicago.
See the AMS Website for the most up-to-date lists of Invited Addresses and Special Sessions.
For more information, e-mail meet@ams.org.
May 2009
A model for stochastic volatility. Estimation.
Friday, 5/1/2009 11:00 AM-12:00 PM
Stratton Hall, 203
SPEAKER: Ionut Florescu (Stevens Institute)
ABSTRACT: This talk is composed of two parts. In the first part I will present a stochastic volatility model where the volatility is modeled as a continuous time Markov Chain. A methodology for automatically estimating the nodes and the transition probabilities of this hidden Markov Chain is exposed. In the second part of the talk we will discuss about the procedure after the estimates are found. Specifically, we will construct a multinomial tree which approximates the continuous time price process and with its help we estimate the price of any call or put option. We then use this tree to estimate a value for the CBOE Volatility Index (VIX) and we look at the differences between our estimated value and the value observed on the market. As a side note we discover that toward the end of last year (Aug-Dec 2008) the relationship between VIX and the S&P500 price has been unusually high.
Note: this work is developed in collaboration with Forrest Levin and Hongwei Qu.
For more information, e-mail ma-chair@wpi.edu.