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Department of Mathematics & Statistics
Math

Colloquium

Academic Year 2019 - 2020

Speaker:  Dr. Travis Loux (Department of Epidemiology and Biostatistics, Saint Louis University). 

Date:  Friday, Dec 6, 2019  

Time: 2 - 3 pm. 

Location: Science East 2204

Title: Estimating Local Health Outcomes from Internet Non-Probability Samples

Abstract:  

In this presentation, we describe an application of multilevel regression with poststratification (MRP) to estimate metro area and ZIP code level prevalence of various health behaviors and outcomes. Participants living in the St. Louis metropolitan area were recruited through Facebook to take a general health survey. Because respondents do not represent the metro area population on numerous characteristics, we use MRP to adjust for selection bias in our sampling strategy. MRP requires the researcher to model an outcome in a sample data set, then apply that model to population data. The population predicted outcomes are aggregated to the level of interest, weighting by population stratum size. We present raw and MRP-adjusted estimates and compare the results to estimates from the Missouri County-Level Study, population-based study using probability sampling. We find that MRP reduces bias by 20 to 50% depending on modeling choices.

Speaker: Glenn Harris (Northern Illinois University). 

Date:  Friday, Nov 8, 2019. 

Time: 2 - 3 pm. 

Location: Science East 2204

Title: Substantial Efficiency in Multi-Objective Optimization 

Abstract: 

Multi-objective optimization is useful in many areas of study, ranging from economics to electronics. A common choice of solution to the problem of optimizing many objectives in a problem is called a properly efficient solution. Properly efficient solutions are solutions for which the loss of at least one objective is in proportion to objectives that stand to gain by switching to any other feasible solution. A substantially efficient solution is the natural extension of that concept where the loss of all objectives that stand to do worse do so proportionately to all those that stand to gain by switching to any other feasible solution. Substantially efficient solutions can find particular use in market type problems. Some results related to substantial efficiency in linear multi-objective optimization problems will be shared.

Speaker: Dean Gregory Budzban (SIUE). 

Date:  Friday, Oct 18, 2019. 

Time: 3 - 4 pm. 

Location: Science East 3360

Title: Introduction to Algebraic Probability via Markov Chains (Part 2)

Abstract: 

Algebraic probability provides a set of techniques that can be used to analyze non-homogeneous Markov chains.  This talk will discuss examples of how the techniques were used to produce verifiable sufficient conditions, based only on the entries of the transition matrices, for the convergence of a class of non-homogeneous Markov chains.  In addition, using results from the solution of the Road Coloring Problem, a general conjecture for sufficient conditions for all non-homogeneous Markov will be stated.

Speaker: Dean Gregory Budzban (SIUE). 

Date:  Friday, September 20, 2019. 

Time: 3 - 4 pm. 

Location: Science East 3360

Title: Introduction to Algebraic Probability via Markov Chains

Abstract: 

Much of modern mathematics involves the use of algebraic methods to shed light in areas of classical analysis, and probability theory is no exception. Markov chain theory provides an intuitive pathway into the techniques of algebraic probability.  This talk will provide an introduction to algebraic probability and present a conjecture concerning an unsolved problem in temporally non-homogeneous Markov chains.


Academic Year 2018 - 2019

Speaker: Dr. Zhu Wang (University of South Carolina)

Date: Friday, April 5,, 2019.

Time: 2 - 3 pm.

Location: Science East 2204.

Title: Proper Orthogonal Decomposition Reduced Order Modeling of Hamiltonian Systems

Abstract:

The proper orthogonal decomposition reduced-order model (POD-ROM) has been widely used as a computationally efficient surrogate model for large-scale numerical simulations of complex systems. However, when applying to a Hamiltonian system, it will destroy the inherent structure of the system. This would result in the instability of reduced-order simulations. In this talk, we will discuss a new reduced-order modeling approach for Hamiltonian systems, which modifies the Galerkin projection-based POD-ROM so that the appropriate Hamiltonian structure can be preserved. We derive a rigorous a priori error estimate for the structure-preserving ROM and demonstrate its effectiveness in several numerical examples.

Speaker: Dr. Craig Cullen (Illinois State University)

Date: Friday, March 22, 2019

Time: 3 - 4 pm. 

Location: Science East 2204

Title: Exploring Trignometric Relationships: Its a Function 

Abstract: 

We examined conceptual understanding of preservice secondary mathematics teachers as they reasoned about chord length and arc length in a directed-length representation related to the sine function. We characterized the ways in which our participants understood the functional relationship between the geometric objectsby describing various aspects of their concept images, and the progression of the images over time. Concept image components progressed from less useful to moreuseful, eventually aligning with components of a standard definition of function and key features of the sine function.

Speaker: Richard Lumor (Analytics Manager, Panera Bread Company). 

Date: Wednesday, February 20, 2019. 

Time: 2 - 3pm. 

Location: Science East 2204

Having worked in a variety of industries including retail, healthcare, financial and workforce solutions, Richard will be sharing his experience as a statistician/data scientist. He will share his experience by discussing projects he has worked on and reflect on the skills he wished he knew before he left graduate school. What skills would you like to learn so you bring value to any organization after graduation?

Speaker: Dr. Shrey Sanadhya (The University of Iowa)

Date and Time: Friday Oct 26, 2018 at 2pm 

Location: SE 3252

Title:  On cocycles of Automorphism groups of a Standard Borel Space.   

Abstract: 

Cocycles play an important role in classification of groups of automorphisms of a measure space w.r.t Orbit Equivalence. This theory was developed in papers by Dye, Connes, Feldman, Krieger, Ornstein, Weiss among others. The notion of weak equivalence applied to pairs of automorphism group and its cocycle, refines orbit equivalence. It was studied in works of Bezuglyi, Golodets, Sinelʹshchikov and Hamachi. 

Our goal is to use the notion of weak equivalence in case of Borel Dynamics to refine the existing classification of Orbit Equivalance. I will report a progress in this direction.

Speaker: Dr. Trong Wu (Department of Computer Science, SIUE). 

Date: Friday, Oct. 5, 2018.  

Time: 2 - 3pm. 

Location: Science East 0214

Title: Foundations of Interval Computation

Abstract: 

This talk reports a study of numerical computation problems from a theoretical viewpoint. It shows that computer systems are not capable of computing of real numbers correctly due to the differences between the algebraic structures of real numbers and model numbers. These two classes of numbers are not isomorphic. From this study, we have learned that there are no machine errors or computation errors. If fact, one can view it is a human mistake by putting real valued problem onto a model number platform for computation. This paper proposes use of the concept of computer model numbers to approximate rough numbers for computation. Moreover, we revise an arbitrary initial compact interval to a shortest initial closed-open model interval for ordinary interval computation. This way, we can assure that the final resulting interval will be the shortest interval and that the computation will result in the greatest precision.

Speaker: Dr. Anthony Bosman (Department of Mathematics, Andrews University)


Date: Friday, Sept. 28, 2018. 

Time: 2 - 3 pm

Location: Science East 3252 

Title: I Think Knot: An Introduction to Knots and Surfaces 

Abstract: 

A mathematical knot is an embedding of a circle in 3-dimensional space. Is it ever possible for two knots, when joined, to cancel each other out? This simple question will take us on an interactive tour through knot theory where we'll see how knots are related to surfaces and how important topological invariants — such as the Euler characteristic and genus of a surface — can be powerful tools for studying the structure of knots. We'll also ask how introducing a 4th dimension changes the game and raises new questions that we're still nowhere close to answering today.

Academic Year 2017 - 2018

Speaker: Dr. Bradley Currey (Saint Louis University)

Date: Wednesday, Apr 25, 2018

Time: 2 pm

Location: VC 2007

Title: Reality Check: Explicit Computations in Abstract Harmonic Analysis.

Abstract: 

After a brief introduction to the central idea of abstract harmonic analysis, we describe several contexts in which abstract non-Euclidean Fourier transforms can be rendered concrete and computable. We then present relatively recent results showing how these computations lead to explicit frames in Euclidean space. 

Speaker: Jun Liu (Department of Math & Stats, SIUE)

Date: Friday, Apr 6, 2018

Time: 2pm

Location: PH3303

Title: An Adaptive Factorization Method for Inverse Scattering Problems

Abstract: 

Inverse scattering problems are of great importance in many fields of science and engineering, such as radar and sonar, medical imaging, and non-destructive testing.  In this talk, I will introduce a novel adaptive algorithm, which generates nonuniform sampling points that automatically concentrate near the boundary of an unknown scatterer, to dramatically speed up Kirsch's famous factorization method for inverse acoustic scattering problems. Built upon the well-known adaptive Simpson quadrature method, our proposed adaptive algorithm approximates the integration of an indicator function over a search domainand yields reliable and accurate reconstructions significantly faster than the standard factorization method. Numerical experiments are performed to validate the effectiveness of our proposed algorithm.

Speaker: Erica Metheney of Texas A&M University (and an SIUE alumna)

Title: Generating Graphic Sequences Using Heavy-tailed Distributions with Infinite Mean

Date: Wednesday, 14 March, 2018

Time: 2:00pm

Location: Peck Hall 1402

Abstract: 

Efficient generation of degree sequences requires a procedure that yields sequences that have a high probability of being graphic and follow the desired distribution. Degree distributions with infinite mean present the problem that the probability of generating a graphic sequence by simply sampling from the desired distribution can be quite low. Current procedures that increase the probability of graphicality in the infinite mean case do not retain the heavy-tail in the desired distribution. We present a rejection sampling based procedure that increases the graphicality probability without incurring the distributional losses of current procedures. We also provide simulation results to show the effectiveness of the procedure in application.

Speaker: Dr. Brittany Froese Hamfeldt (New Jersey Institute of Technology)  

Title: Generalised finite difference methods for fully nonlinear elliptic equations 

Date: Friday, March 2, 2018

Time: 2 pm

Location: PH3303

Abstract:

The relatively recent introduction of viscosity solutions and the Barles-Souganidis convergence framework have allowed for considerable progress in the numerical solution of fully nonlinear elliptic equations. Convergent, wide-stencil finite difference methods now exist for a variety of problems. However, these schemes are defined only on uniform Cartesian meshes over a rectangular domain. We describe a framework for constructing convergent meshfree finite difference approximations for a class of nonlinear elliptic operators. These approximations are defined on unstructured point clouds, which allows for computation on non-uniform meshes and complicated geometries. Because the schemes are monotone, they fit within the Barles-Souganidis convergence framework and can serve as a foundation for higher-order filtered methods. We present computational results for several examples including problems posed on random point clouds, computation of weak and even non-continuous solutions, automatic mesh adaptation, and Monge-Ampere equations arising in optimal transportation.

Speaker: Dr. Jim Parish, SIUE

When: Friday, 23 February, 2018,  2:00 pm

Where: Peck Hall 2412

Title: A Short History of Non-Euclidean Geometry

Abstract: 

The first person to stumble on it refused to take it seriously.

The first person to take it seriously refused to discuss it in public.

The first person to discuss it publicly wrote in a language few mathematicians understood.

The first person to discuss it in a well-known language got curb-stomped by the greatest mathematician of the age.

Here at SIUE, we teach it once a year.

This is the story of non-Euclidean geometry.

Speaker: Dr. Jireh Loreaux, SIUE

When: Friday Dec 1, 3:30 pm - 4:30 pm

Where: PH 0405

Title: Diagonalization of matrices and the Pythagorean Theorem

Abstract: 

There is a natural interpretation of the Pythagorean Theorem in terms of elementary linear algebra. While this interpretation is straightforward, it leads to a much more general statement in operator theory with surprising consequences. In this talk, we explore the relationship between these statements and the diagonalization of matrices by means of a unitary matrix which is a small perturbation of the identity. As part of this presentation I will present a problem which is suitable for an undergraduate research project.

Speaker: Dr. Gabe Spalding of Illinois Wesleyan University

When: Friday, October 20th from 4:00 - 5:00 pm, happy hour to follow

Where: PH 1302

Professor Spalding received his Ph.D. in Applied Physics from the Harvard School of Engineering and Applied Sciences. His research tries to be serious, but is routinely rephrased in terms of playful sci-fi references, from creating a functional sonic screwdriver to Star Trek-style holodecks (computer-generated holograms that are not merely ethereal images; they have corporeal substance) and acoustic tractor beams (research awarded a 2014 Platypus Award from Mental Floss magazine and named a “Top 10 Breakthrough" of the year by Physics World magazine). His 2016 work on Faster-Than-Light Imaging experimentally demonstrated creation and annihilation of spot pair images (where one moves forward in time and the other backwards). If that's not spooky enough for you, check out his work on "Ghost Imaging" using quantum mechanically entangled photon pairs, where the photons incident upon the detecting camera have never interacted with the object imaged. He works, as an activist, to develop and support lab instruction.

Speaker: Dr. Jim Gill of Saint Louis University

When: Friday, September 22, 4:00-5:00pm, happy hour to follow

Where: EB 0165

Title: Finite Dimensional Random Objects

Abstract: We discuss research by several investigators into random objects made of infinitely many smaller pieces and their geometry.  It turns out that many of them have a planar geometry due to a strange property of finite dimensional metric spaces.

Academic Year 2016 - 2017

Speaker: Dr. James Parish

When: Friday, Apr 21, 2017, 3:00-4:00pm, happy hour to follow

Where: Vadalabene Center Room 2306

Title: Simple Closed Geodesics on Rectangular Prisms

Abstract: 

The study of geodesics – locally shortest paths – has been a significant topic in geometry for a very long time. On smooth surfaces, it is a complicated matter of analysis, involving the solution of a pair of nonlinear differential equations. In the last few decades, the study of geodesics on polyhedra has attracted considerable attention. Here, geodesics are easy to construct; they are composed of line segments crossing the faces of the polyhedron, with passage from one face to the next occurring in a predictable fashion. Attention has focused on the identification of closed geodesics, which return to their initial point and direction; the techniques have an algebraic and combinatorial flavor. In this talk, I will discuss geodesics on rectangular prisms – boxes, so long, so wide, and so high – and provide a complete description of simple (i.e., non-self-intersecting) closed geodesics on these polyhedra.

Speaker: Dr. Andrew Neath

When: Wednesday, Mar 29, 2017, 6:00-7:00pm, happy hour to follow

Where: Vadalabene Center Room 2007

Title: Statistical Modeling for Replication Studies

Abstract: 

There is growing concern over the number of scientific findings accepted as truth which then realize failure when the study is replicated. Traditional statistical inference is designed as a look back to how data originates. Perhaps we need to take a better look in anticipation of what data we will we see next. This talk will provide examples of some interesting aspects of statistical problems in analyzing replication studies, and some thoughts on how the information from a single study fits together with what we learn from replication attempts.

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