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Designing frustration and topologically constrained disorder in artificial spin ice We are all familiar with classical states of matter as ordered or disordered; and yet some of the most relevant phenomena in nature, from the nano-machinery of life in DNA, to the behavior of animal or human colonies, to the...

A Localized Reduced-Order Modeling Approach for PDEs with Bifurcating Solutions Reduced-order modeling (ROM) commonly refers to the construction, based on a few solutions (referred to as snapshots) of an expensive discretized partial differential equation (PDE), and the subsequent application of low-dimensional discretizations of partial differential equations (PDEs) that can be...

Improving the accuracy of the trapezoidal rule The trapezoidal rule uses function values at equispaced nodes. It is very accurate for integrals over periodic intervals, but is usually quite inaccurate in non-periodic cases. Commonly used improvements, such as Simpson’s rule and the Newton-Cotes formulas, are not much (if at all)...

Dan Massey, Interdisciplinary Telecom Program, ²ÊÃñ±¦µä Cybersecurity Rule 6: Use Cryptography Correctly This talk explores some of the key mathematical concepts used in cybersecurity. Cryptography is one obvious example where mathematics plays a critical role in cybersecurity. However, this talk is not centered around developing new cryptographic...

Peter F. Craigmile, Department of Statistics, The Ohio State University Enhancing statistical inference for stochastic processes using modern statistical methods (This is joint research with Radu Herbei, Matthew Pratola, Huong Nguyen, and Grant Schneider, at The Ohio State University.) Stochastic processes such as stochastic differential equations (SDEs) and Gaussian processes...

Sparse Grid Discontinuous Galerkin Methods for High-Dimensional Transport Equations In this talk, we present sparse grid discontinuous Galerkin (DG) schemes for solving high-dimensional PDEs. We will discuss the construction of the scheme based on sparse finite element spaces built from multiwavelets, its properties and applications in kinetic transport equations, such...

3D radar wavefield imaging of comet interiors The Rosetta mission to comet 67P/C-G revolutionized comet science, but left major questions on the table. Are cometary nuclei primordial or are they collisionally-evolved as predicted by modern theories of planet formation? The CONSERT radar experiment sounded the interior of the nucleus showing...

How to Gamble or Invest If You Must: A Large Deviations Approach The Kelly Criterion (a.k.a. expected log utility maximization) is a well-known criterion function used to select optimal repeated gambles or long-term portfolio investments. It is often rationalized by its asymptotic properties as the investment horizon grows to infinity...

Birth, Death, and Barcodes: Discretization of Continuous Attributes in Bayesian Network Structure Recovery Bayesian networks are graphical models that can be used to represent complex relationships between a large number of random variables. A Bayesian network consists, in part, of a directed acyclic graph in which nodes represent the variables...

Mathematical modeling of cell division Cells are the basic unit of life. All life on earth depends on cells' ability to duplicate themselves. In order to divide successfully, cells must solve fascinating mathematics and physics problems, which this talk will introduce assuming no biology background. A key step in cell...