WSU Vancouver Mathematics and Statistics Seminar
 WSU Vancouver Mathematics and Statistics Seminar (Fall 2016) Welcome to the WSU Vancouver Seminar in Mathematics and Statistics! The Seminar meets on Wednesdays at 1:10-2 PM in VMMC 214. This is the building marked "J" in the campus map (and here's some information for visitors). Students could sign up for Math 592 (titled Seminar in Analysis) for 1 credit. Talks will be given by external speakers, as well as by WSUV faculty and graduate students. Contact the organizer Bala Krishnamoorthy if you want to invite a speaker, or to give a talk.
Date Speaker Topic Slides Video
Aug 24 Intro, coordination
Aug 31 Jeffrey S. Ovall, Portland St. U. Theoretical and Computational Excursion with the Laplacian

The Laplace operator (Laplacian), $$u\mapsto \Delta u$$, plays a prominent role in applied mathematics, appearing in important mathematical models such as the heat/diffusion equation, the wave equation, the Schrödinger equation, and some forms of the Navier-Stokes equations. As such, it has been studied extensively. Basic properties, such as the Mean Value Theorem for harmonic functions ($$\Delta u=0$$) on a ball or sphere, and the Maximum and Minimum Principles for super-harmonic ($$\Delta u\geq 0$$) and sub-harmonic ($$\Delta u\leq 0$$) functions on bounded domains, are typically presented early in a first course partial differential equations. In our first excursion, we present a result that deserves to be more well-known, namely that the Laplacian and its powers appear very naturally in a series expansion of the average value of a function on a ball or sphere in terms of its radius. This result makes clear how the Laplacian of a function is a measure of deviation between its average on a ball/sphere and its value at the center, and its proof is reasonably simple.

Our second excursion (the rest of the talk) presents a new numerical method for efficiently and accurately approximating function values and derivatives of a harmonic function with prescribed boundary data in 2D. Using integral equations, the notion of harmonic conjugates, and Cauchy's Integral Formulas, only computations along the boundary are needed. The two key computational tools are the trapezoid rule and the Fast Fourier Transform. A Fourier analysis of the trapezoid rule explains why it is an excellent choice in this context, and numerical experiments illustrate the power of the approach.

slides video
Sep   7 Bala Krishnamoorthy, discussion Giving an effective research talk scribe
Sep 14 Anna Johnston, Raytheon Reed-Solomon, the Chinese Remainder Theorem, and Cryptography

Cryptography and coding theory perform very different functions: cryptography makes a message unreadable without the secret key while coding theory makes the message readable even if errors are introduced. As our information world explodes, data is becoming more and more vulnerable to different attacks which cryptography alone can not protect against, such as ransomware and DDOS attacks. This talk describes how the disparate functionality of coding theory and cryptography can be combined to combat these emerging attacks.

slides
Sep 21 No seminar
Sep 28 Ruth Davidson, U. Illinois Phylogenetic Geometry

A phylogeny is a mathematical model of the common evolutionary history of a group of species or genes. While phylogenies are inferred from various data types, in the era of advanced genome sequencing technology the data used to infer the phylogeny is primarily nucleotide or protein sequence data. Phylogeny-inference problems are most often expressed as optimization problems that are in complexity classes such as NP, so polynomial-time heuristics are developed to approximate solutions to these problems. These heuristics can be evaluated using traditional methods such as upper bounds on running time, average case analysis, and statistical consistency. In this talk, we discuss the alternative approach of evaluating polynomial-time heuristics through the lens of polyhedral geometry, and discuss the growing body of literature connecting algebraic geometry to statistics and phylogenetics. No previous knowledge of phylogenetics will be assumed for this talk.

slides video
Oct   4 Alex Dimitrov, WSU Coupled with Math-Bio seminar, 4:10-5:00 PM, Tuesday, in VECS 105:
A vector inhomogeneous Poisson process with stochastic gain as a model of multiunit neural activity
Oct 12 Bala Krishnamoorthy, WSU Linear Programming in Geometric Measure Theory

We present results on two problems related to shapes in geometric measure theory (GMT) that employ techniques from algebraic topology and linear programming. Currents represent generalized surfaces in GMT, and were introduced to study area minimizing surfaces and other related problems. The flat norm provides a natural distance in the space of currents, and works by decomposing a $$d$$-dimensional current into $$d$$- and (the boundary of) $$(d+1)$$-dimensional pieces. A natural question about currents is the following. If the input is an integral current, i.e., a current with integer multiplicities, can its flat norm decomposition be integral as well? Surprisingly, the answer is not known in general. On the other hand, for the discretization of the flat norm on a finite simplicial complex, the analogous statement is true for d-chains in a (d+1)-complex. We develop an analysis framework that extends the result in the simplicial setting to that for $$d$$-currents in $$(d+1)$$-dimensional space, provided a suitable triangulation result holds. We also prove this result holds in 2D. In the second problem, we consider a notion of average shape defined as the median shape of currents using the flat norm distance. In the corresponding simplicial version of the problem, the median chain of a set of input chains in a finite simplicial complex is computed using linear programming.

slides video
Oct 20 Randy LeVeque, U. Washington The SIAM PNW Section Seminar, 3:00-4:00 PM, Thursday, in VUB 107:
New tools for tsunami warning and probabilistic hazard assessment

As events of the past decade have tragically demonstrated, tsunamis pose a major risk to coastal populations around the world—including the Pacific Northwest where the Cascadia Subduction Zone unleashes Magnitude 9 earthquakes every few hundred years. Numerical modeling is an important tool in better understanding past tsunamis and their geophysical sources, in real-time warning and evacuation, and in assessing hazards and mitigating the risk of future tsunamis. I will discuss a variety of techniques from adaptive mesh refinement to probabilistic hazard analysis that are being used for tsunamis and related geophysical hazards.

N.B.: This is an online seminar. We will attend it as a GoToMeeting in the room and time specified. There will be opportunities to ask questions to the speaker.

Oct 26 Anna Ritz, Reed College Signaling Hypergraphs

Cells that receive external signals from the environment respond with a series of molecular reactions that alter their behavior, e.g., causing them to divide, move, or self-destruct. These reactions constitute networks called "signaling pathways" whose alterations can cause cancer and other diseases. Efforts to manually curate signaling pathways from the literature invite the opportunity for computational methods of investigation. Directed graphs are the most common representation of signaling pathways, making them amenable to a wide array of graph-theoretic algorithms. However, directed graphs often inaccurately represent the underlying biology of signaling reactions. In this talk, I will describe an alternative mathematical representation called a "signaling hypergraph" that overcomes many limitations of graph-based representations. I will present the NP-hard shortest hyperpath problem and a mixed integer linear program to solve it, illustrating its applicability to describe plausible reactions when applied to signaling hypergraphs compared to graph alternatives. Signaling hypergraphs exemplify how careful attention to the underlying biology can drive developments in a largely unexplored field of computer science.

slides video
Nov  2 Leslie New, WSU, discussion Communicating mathematics effectively to outsiders
Nov  9 No seminar
Nov 16 Bala Krishnamoorthy, discussion How to read a Mathematics Paper
Nov 30 Danielle Harris, U. St. Andrews Eavesdropping on the ocean: Passive acoustic monitoring technologies to estimate marine mammal population sizes