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Jon Stallrich, NC State, Sign-Informative Design and Analysis of Supersaturated Designs

Much of the literature on the design and analysis of supersaturated designs (SSDs), in which the number of factors exceeds the number of runs, rests on design principles assuming a least-squares analysis.  More recently, researchers have discovered the potential of analyzing SSDs with penalized regression methods like the LASSO and Dantzig selector estimators.  There exists much theoretical work for these methods…

John Lagergren, SIAM Student Chapter: Graduate Student Tutorial

Mann 404

Machine learning has become widely popular in fields like computer vision, natural language processing, and speech recognition, often performing tasks better than humans. A fundamental building block of many of these algorithms is a neural network known as a multilayer perceptron. In this tutorial we will discuss how to construct these networks and how to train them using back propagation…

130th Math Department Anniversary Celebration

Register now for a weekend anniversary celebration marking 130 years of mathematics education and research here at NC State. The history of mathematics at the university dates to 1889, when math courses were among the first taught as NC State ushered in its inaugural class of students. Harrelson Hall was the former home of the…

Yan Zhuang, Davidson College, Counting permutations by peaks, descents, and cycle type

We present a general formula describing the joint distribution of two permutation statistics—the peak number and the descent number—over any set of permutations whose quasisymmetric generating function is a symmetric function. Our formula involves a certain kind of plethystic substitution on quasisymmetric generating functions. We apply this result to cyclic permutations, involutions, and derangements, and…

JungHwan Park, Georgia Tech, Rational cobordisms and integral homology

We prove that every rational homology cobordism class in the subgroup generated by lens spaces is represented by a unique connected sum of lens spaces whose first homology embeds in any other element in the same class. As an application, we show that the natural map from the Z/pZ homology cobordism group to the rational…

Eric Hallman, NC State, Sharp 2-norm Error Bounds for LSQR and the Conjugate Gradient Method

When running any iterative algorithm it is useful to know when to stop. Here we review LSQR and LSLQ, two iterative methods for solving \min_x \|Ax-b\|_2 based on the Golub-Kahan bidiagonalization process, as well as estimates for the 2-norm error \|x-x_*\|_2, where x_* is the minimum norm solution. We also review the closely related Craig's…

Mikhail Klibanov, UNC Charlotte, Carleman Estimates for Globally Convergent Numerical Methods for Coefficient Inverse Problems

The ill-posedness and nonlinearity are two factors causing the phenomenon of multiple local minima and ravines of conventional least squares cost functionals for Coefficient Inverse Problems. Since any minimization method can stop at any point of a local minimum, then the problem of numerical solution of any Coefficient Inverse Problems becomes inherently unstable and so…

Mohammad Farazmand, NC State, Extreme Events in Chaos

SAS 2102

Chaos refers to seemingly random and unpredictable dynamics of a system that evolves in time. Certain chaotic systems exhibit an additional level of complexity: intermittent extreme events that are noticeably distinct from the usual chaotic dynamics.  These extreme events include ocean rogue waves, extreme weather patterns, and epileptic seizure.  I will discuss several examples of these…

Research Statements and CVs

An afternoon workshop/discussion lead by Ilse Ipsen on preparing your research statements and CVs for the job search.

Ákos Nagy, Duke University, Complex Monopoles

Self-duality equations in gauge theory can be complexified in many inequivalent ways, but there are two obvious options: One can extend Hodge duality in either a complex linear fashion, or in a conjugate linear one. In general, the two cases result in two very different equations. The first case was first studied by Haydys, while…

Shahar Kovalsky, Duke University, Planar surface embeddings and non-convex harmonic maps

Mappings between domains are among the most basic and versatile tools used in the computational analysis and manipulation of shapes. Their applications range from animation in computer graphics to analysis of anatomical variation and anomaly detection in medicine and biology. My talk will start with a brief overview of discrete computational shape mapping, surface parameterization…