Applied Mathematics Seminar, Spring 2018

## Mondays 4:00 PM - 5:00 PM, LCB 219

• This seminar can be taken for credit: Students can get 1-3 credits by registering to the Applied Math Seminar class Math 7875 Section 010 for Spring 2018. Students should talk to the seminar organizer before taking it for a credit. Grading is based on attendance and giving a talk by presenting an applied-mathematics paper (not necessarily your own). Student talks will be appropriately labeled to distinguish them from visitor talks. The seminar organizer is available to review your slides, for dry-runs etc.
• Please direct questions or comments about the seminar (or its class) to Yekaterina Epshteyn (epshteyn (at) math.utah.edu)
• Talks are announced through the applied-math mailing list. Please ask the seminar organizer for information about how to subscribe to this list.

Special Joint Statistics/Stochastics and Applied Math Seminar January 12. LCB 219 at 4pm.
Speaker: Daniel Sanz-Alonso, Department of Applied Mathematics, Brown University
Title: New Perspectives on Importance Sampling
Abstract: Importance sampling is a building block of many algorithms in computational statistics, perhaps most notably particle filters. It is the importance sampling step that often limits the accuracy of these algorithms. In this talk I will introduce a new way of understanding importance sampling based on information theory. I will argue that the fundamental problem facing algorithms based on importance sampling can be understood in terms of the distance between certain measures. The results give new understanding on the potential use of importance sampling and particle filters in high (possibly infinite) dimensional spaces.

Special Joint Statistics/Stochastics and Applied Math Seminar January 17. LCB 219 at 4pm.
Speaker: Kevin Moon, Genetics Department and Applied Math Program, Yale University
Title: Nonparametric Estimation of Distributional Functionals in Machine Learning
Abstract: Distributional functionals are integrals of functionals of probability densities and include functionals such as information divergence, mutual information, and entropy. Distributional functionals have many applications in the fields of information theory, statistics, signal processing, and machine learning. Many existing nonparametric distributional functional estimators have either unknown convergence rates or are difficult to implement. In this talk, I present multiple applications of distributional functional estimation, focusing on the problems of dimensionality reduction, extending machine learning tasks to distributional features, and estimating the optimal probability of error (the Bayes error) of a classification problem. I then present a simple, computationally tractable nonparametric estimator of a wide class of distributional functionals that achieves parametric convergence rates under certain smoothness conditions. The asymptotic distribution of the estimator is also derived.

Special Joint Statistics/Stochastics and Applied Math Seminar January 19. LCB 219 at 3pm.
Speaker: Harish Bhat, Department of Mathematics, University of California, Merced
Title: Statistical Estimation and Inference for Stochastic Differential Equations
Abstract: We consider the problem of estimating parameters in stochastic differential equation (SDE) models from discrete-time observations (time series). A key bottleneck is computation of the log likelihood. I will describe a method, density tracking by quadrature (DTQ), to compute densities and likelihoods in low-dimensional systems. DTQ consists of using quadrature to solve, at each time step, the Chapman-Kolmogorov equation associated with a time-discretization of the SDE. After motivating DTQ, I will discuss theoretical and empirical convergence results. These results include convergence in L^1 to both the exact pdf of the Markov chain (with exponential convergence rate), and to the exact pdf of the SDE (with linear convergence rate). I will then propose two methods for nonparametric estimation in the high-dimensional SDE setting. The first is an extension of equation discovery techniques used in the deterministic context, while the second is an expectation maximization approach.

February 5
Speaker: Masashi Mizuno, Department of Mathematics, Nihon University, Japan
Title: Evolution of grain boundaries with lattice orientations and triple junctions effect
Abstract: Grain boundaries and their evolution are strongly related to many properties of materials, like metals and alloys. Mathematically, for planer network case, the motion of the grain boundaries is often described by the geometric curve evolution equations. In these equations, the dynamics of the grain boundaries are assumed to depend only on the shape of the grains. However, grain lattice orientation structure (thus misorientations, which are differences between lattice orientations of neighboring grains), as well as the mobility of the triple junctions of the grains also play an important role on the evolution of the grain boundaries. In this talk, I will introduce a new model of the grain boundary migration that takes into account the dynamics of misorientations, as well as the mobility of the triple junctions. Next, mathematical analysis of the model, in particular, asymptotic behavior of the solution will be presented.

This is a joint work with Yekaterina Epshteyn (The University of Utah) and Chun Liu (Illinois institute of Technology).

February 26
Speaker: Noel Walkington, Department of Mathematics, Carnegie Mellon University
Title: Numerical Approximation of Multiphase Flows in Porous Media
Abstract: This talk will review structural properties of the equations used to model geophysical flows which involve multiple components undergoing phase transitions. Simulations of these problems only model the gross properties of these flows since a precise description of the physical system is neither available nor computationally tractable. In this context mathematics provides an essential foundation to facilitate the integration of phenomenology and physical intuition to develop robust numerical schemes that inherit essential structural and physical properties of the underlying problem.

April 2
Speaker: Graeme Milton, Department of Mathematics, The University of Utah
Title: Exact relations for Green's functions in linear PDE and boundary field equalities: a generalization of conservation laws
Abstract: TBA
Joint work with Daniel Onofrei.

April 9
Speaker: Rodrigo Platte, School of Mathematical and Statistical Sciences, Arizona State University
Title: TBA
Abstract: TBA

April 16
Speaker: Matthew Yancey
Title: TBA
Abstract: TBA

April 23
Speaker: Katayun Barmak, Department of Applied Physics and Applied Mathematics with Materials Science and Engineering, Columbia University
Title: Grain Structure, Grain Boundary Character Distribution and Grain Growth in Thin Metallic Films
Abstract: The types and connectivity of grain boundaries strongly influence materials properties. In the macroscopic description of grain boundaries, a general grain boundary is characterized by five parameters: three parameters to specify the lattice misorientation between the adjoining crystals meeting at the boundary and two parameters to specify the inclination of the boundary plane normal. Grain boundary character distribution (GBCD) gives the relative area of boundaries with a given misorientation and a given boundary normal. Using electron back scatter diffraction in the scanning electron microscope, GBCDs of many materials with grain sizes in the micrometer range have been measured. More recently precession electron diffraction in the transmission electron microscope has allowed these measurements to be extended to nanocrystalline materials. In this talk, GBCD of three nanocrystalline metallic films, aluminum, copper and tungsten (Al, Cu and W), will be compared with their microcrystalline counterparts. Grain structure of the films in the as-deposited and annealed states will be presented and related to crystal structure and bonding. Experimental grain size distributions using image based and crystal orientation mapping based methods in Al and Cu will be compared with the distribution obtained in two-dimensional simulations of grain growth with isotropic boundary energy. The role of structure formation processes during film deposition in the observed difference between experiment and simulation will be noted.

Seminar organizer: Yekaterina Epshteyn (epshteyn (at) math.utah.edu).

155 South 1400 East, Room 233, Salt Lake City, UT 84112-0090, T:+1 801 581 6851, F:+1 801 581 4148