Tuesday, April 03, 11:00AM-1:00 PM, Conference room

February 25, 2018 by Duan Chen
Categories: Updates
Professor: Daniel Onofrei, Department of Mathematics, University of Houston
Title:Active manipulation of scalar wave fields and applications
Abstract: In this talk we will describe our recent results about the characterization of continuous boundary data (i.e., pressure or normal velocity) on active single sources or arrays for the approximation of different prescribed scalar wave field patterns in given exterior (bounded or unbounded) regions of space. We will present the theoretical ideas behind our results as well as numerical simulations with applications in scattering cancellation, field synthesis and inverse source problems.

 

Wednesday, March 21, 3:25PM, Conference room

February 25, 2018 by Duan Chen
Categories: Updates
Professor: Leonid Koralov, Department of Mathematics, University of Maryland
Title:  Large Time Behavior of Randomly Perturbed Dynamical Systems
 Abstract:  We will discuss several asymptotic problems for randomly perturbed flows

(and related problems for  Markov chains with rare transitions). One class of flows (with regions where a strong flow creates a trapping mechanism) leads to a new class of elliptic and parabolic boundary value problems with
non-standard boundary conditions. The same boundary value problems appear as a limiting object when studying the
asymptotic behavior of diffusion processes with pockets of large diffusivity.
 We will also discuss how large-deviation techniques can be used
to study the asymptotic behavior of solutions to quasi-linear parabolic equations with a small parameter at the
second order term and the long time behavior of the corresponding diffusion processes.

 

Friday, March 16, 11:00AM, Fretwell 315

February 25, 2018 by Duan Chen
Categories: Updates
Professor: Yi Sun, Department of Mathematics, University of South Carolina
Title: Kinetic Monte Carlo Simulations of Multicellular Aggregate Self-Assembly in Biofabrication
 Abstract:  We present a 3D lattice model to study self-assembly of multicellular aggregates by using kinetic Monte Carlo (KMC) simulations. This model is developed to describe and predict the time evolution of postprinting structure formation during tissue or organ maturation in a novel biofabrication technology–bioprinting. Here we simulate the self-assembly and the cell sorting processes within the aggregates of different geometries, which can involve a large number of cells of multiple types.

 

Friday, Jan 19, 11:00AM-12:00Noon, Fretwell 315

January 12, 2018 by Duan Chen
Categories: Updates
Dr. Donald Richards, Department of Statistics, Penn State University
Title:Distance Correlation: A New Tool for Detecting Association and Measuring
Correlation Between Data Sets

Abstract: The difficulties of detecting association, measuring correlation, and establishing cause and effect have fascinated mankind since time immemorial. Democritus, the Greek philosopher, underscored well the importance and the difficulty of proving causality when he wrote, “I would rather discover one cause than gain the kingdom of Persia.’’

To address the difficulties of relating cause and effect, statisticians have developed many inferential techniques. Perhaps the most well-known method stems from Karl Pearson’s coefficient of correlation, introduced in the late 19th century.

I will introduce in this lecture the recently-devised distance correlation coefficient and describe its advantages over the Pearson and other classical measures of correlation. We will review an application of the distance correlation coefficient to data drawn from large astrophysical databases, where it is desired to classify galaxies according to various types. Further, the lecture will analyze data arising in the on-going national discussion of the relationship between state-by-state homicide rates and the stringency of state laws governing firearm ownership.

The lecture will also describe a remarkable singular integral which lies at the core of the theory of the distance correlation coefficient. We will describe generalizations of this singular integral to truncated Maclaurin expansions of the cosine function and to the theory of spherical functions on symmetric cones.

Tuesday, January 9th, 11:00AM-12:00 noon, Conference room

January 07, 2018 by Duan Chen
Categories: Updates
Professor:Jae Woo JEONG, Department of Mathematics, Miami University
Title:Numerical Methods for Biharmonic Equations on non-convex Domains
Abstract: Several methods constructing C1-continuous basis functions have been introduced for the numerical solutions of fourth-order partial differential equations. However, implementing these C1-continuous basis functions for biharmonic equations is complicated or may encounter some difficulties. In the framework of IGA (IsoGeometric Analysis), it is relatively easy to construct highly regular spline basis functions to deal with high order PDEs through a single patch approach. Whenever physical domains are non convex polygons, it is desirable to use IGA for PDEs on non-convex domains with multi-patches. In this case, it is not easy to make patchwise smooth B-spline functions global smooth functions.In this talk, we propose two new approaches constructing C1-continuous basis functions for biharmonic equation on non-convex domain: (i) Firstly, by modifying Bezier polynomials or B-spline functions, we construct hierarchical global C1-continuous basis functions whose imple- mentation is as simple as that of conventional FEM (Finite Element Methods). (ii) Secondly, by taking advantages of proper use of the control point, weights, and NURBS (Non-Uniform Rational B-Spline), we construct one-patch C1-continuous geometric map onto an irregular physical domain and associated C1-continuous basis functions. Hence, we can avoid the difficulties aris- ing multi patch approaches. Both of the proposed methods can be easily extended to construct highly smooth basis functions for the numerical solutions of higher order partial differential equations.

Friday, Jan 12, 11:00AM-12:00Noon, Fretwell 315

January 04, 2018 by Duan Chen
Categories: Updates
Dr. Roman Kazinnik, Data Scientist at Brighthouse Financial
Title:Deep learning and mathematical perspectives: historical developments and modern challenges
Abstract:  Artificial Intelligence (AI) is often viewed as a massive parallel optimization problem, and has gained its popularity presumably due to the recent wide availability of parallel computing power.  On one hand, AI departs from fundamental mathematical conceptions: it doesn’t prescribe any PDE when solving inverse problems, and AI learning algorithms do not care about dense representations in functional space. However, there is a great deal of mathematical principles that are in widely implemented by modern AI. 

In this talk I am going to cover some of these techniques and principles that are deployed by AI, and familiar to the applied mathematicians. I will also show how a lack of rigorous underlying model presents, perhaps, one of the major challenges in deploying modern AI methodologies. I consider building such rigorous underlying modeling principles as one of the most interesting modern challenges applied mathematicians can find in AI.

 

Friday, Dec 1st, 4:00PM-5:00PM, Fretwell 206

November 16, 2017 by Duan Chen
Categories: Updates
Professor: Louis H Kauffman, Department of Mathematics, Statistics, and Computer Science University of Illinois at Chicago
Title:Graphical Invariants of Knots and Links
Abstract:This talk is joint work with Qingying Deng. We generalize the signed Tutte polynomial relationship with the Kauffman bracket model of the Jones polynomial to  a new polynomial defined on signed cyclic graphs (graphs with signed edges and cyclic orders at the vertices) and show how these graphs are codings for checkerboard colorable virtual links. We show how virtualization of classical links corresponds to simple operations on the planar signed cyclic graphs. We relate our new polynomial invariant to both the bracket polynomials for virtual knots and links and to the Bollobas-Riordan polynomial.

 

Friday, October 13, 11:00AM-12:00Noon, Conference room

October 11, 2017 by Duan Chen
Categories: Updates
Professor Yanlai Chen , Dept of Mathematics, University of Massachusetts, Dartmouth
Title:Ultra-efficient Reduced Basis Method and Its Integration with Uncertainty Quantification
Abstract: Models of reduced computational complexity is indispensable in scenarios where a large number of numerical solutions to a parametrized problem are desired in a fast/real-time fashion. Thanks to an offline-online procedure and the recognition that the parameter-induced solution manifolds can be well approximated by finite-dimensional spaces, reduced basis method (RBM) and reduced collocation method (RCM) can improve efficiency by several orders of magnitudes. The accuracy of the RBM solution is maintained through a rigorous a posteriori error estimator whose efficient development is critical and involves fast eigensolvers. After giving a brief introduction of the RBM/RCM, this talk will show our recent work on significantly delaying the curse of dimensionality for uncertainty quantification, and new fast algorithms for speeding up the offline portion of the RBM/RCM by around 6-fold.

 

Wednesday, August 30, 2:00PM-3:00PM, Conference room

August 23, 2017 by Duan Chen
Categories: Updates
Professor Seokchan Kim, Dept of Mathematics, ChangWon National University, Changwon, Korea
Title:FEM to compute Numerical Solution of PDEs with Corner Singularities using SIF
Abstract: We consider the Poisson equation with homogeneous Dirichlet boundary condition defined on non convex polygonal domain with one re-entrant corner. Solution of such equation has singular behavior near that re-entrant corner and can be expressed as a sum of the regular part and the singular part. The coefficient of the singular part is called ‘the Stress Intensity Factor. The talk is to introduce a new method to obtain an accurate numerical solution for the Poisson Equation with corner singularities using the Stress Intensity Factor.

 

Friday, March 31, 11:00AM-12:00Noon, Conference room

March 27, 2017 by Duan Chen
Categories: Updates
Ching-Shan Chou, Department of Mathematics, The Ohio State University
Title:Cell signaling, cell morphogenesis and cell-cell communication
Abstract: Cell-to-cell communication is fundamental to biological processes which require cells to coordinate their functions. In this talk, we will present the first computer simulations of the yeast mating process, which is a model system for investigating proper cell-to-cell communication. Computer simulations revealed important robustness strategies for mating in the presence of noise. These strategies included the polarized secretion of pheromone, the presence of the alpha-factor protease Bar1, and the regulation of sensing sensitivity.