WSU Vancouver Mathematics and Statistics Seminar

WSU Vancouver Mathematics and Statistics Seminar (Fall 2018)

Welcome to the WSU Vancouver Seminar in Mathematics and Statistics! The Seminar meets on Thursdays at 4:15-5:05 PM in VUB 225, unless mentioned otherwise. This is the Undergraduate building (marked "N" in the campus map) where all Math/Stat faculty sit. The seminar is open to the public, and here is 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 students. Contact the organizer Bala Krishnamoorthy if you want to invite a speaker, or to give a talk.

Seminars from previous semesters

Date Speaker Topic Slides
Aug 23 Organizational meeting
Aug 30 Nathaniel Saul, WSU Explainable Machine Learning with Topological Data Analysis

Abstract (click to read)

No longer do machine learning algorithms run in the background of our daily lives. Now, doctors interact directly with models to aid in diagnoses, autonomous cars drive around us with little supervision, and judges incorporate model predictions into sentencing. As the complexity of machine learning models and artificial intelligence escape us, we need new mechanisms for understanding model decision making processes.

We propose a new technique for instance based explanation of predictions using Topological Data Analysis. Our method develops an interactive visualization of the learned model, which can be probed by model users. By providing examples of similar observations that influence a model decisions, this technique requires no expert knowledge of machine learning to interpret. We will introduce machine learning, explanation techniques, and Topological Data Analysis, and present ongoing work of using TDA to provide credence to model predictions.

Sep   6 Naveen Somasunderam, Oregon State U. Equidistribution of sequences on the p-adic unit ball

Abstract (click to read)

Techniques from harmonic analysis play a crucial role in understanding problems in analytic number theory. For example, in 1916 Hermann Weyl initiated the study of the equidistribution of sequences on the additive circle, connecting Fourier analysis to number theoretic dynamics. Such techniques can be extended to other locally compact abelian groups, leading to some interesting number theory. We look at the p-adic unit ball as one such example, and show how Fourier analytic techniques can give us an understanding of the distribution of sequences.

This talk is primarily intended to give a general mathematical audience a flavor and appreciation of this type of mathematics, and only a basic knowledge of analysis will be assumed.

Sep   6 Naveen Somasunderam, Oregon State U. Math Ed Seminar in VMMC 202Q at 3 PM:
The ABC pedagogy for teaching mathematics

Abstract (click to read)

We shall describe an active learning strategy for teaching mathematics based on the pedagogy of Dr. David Pengelley.

After presenting the basic pedagogy and mechanics of implementation, we shall discuss the issues involved, solutions, and state the clear advantages of the method.

This pedagogy also provides a great way for graduate students to develop an effective teaching method for their own classes. The talk is intended to invoke active audience participation, stimulating critique, comments, and sharing of experiences so that it serves as a learning experience for the speaker as well as for other participants.

Sep 13 No seminar
Sep 20 Matthew Broussard, WSU In VECS 125
Exploring Artificial Intelligence through Topological Data Analysis

Abstract (click to read)

In recent years neural networks have proven effective at many tasks, including image recognition. However, a trained neural network is a black box. Using the mapper algorithm along with previously developed visualization techniques, we explored methods of understanding the inner workings of the VGG16 neural network.

This is work I did as part of my summer internship at the Air Force Research Laboratory (AFRL) in 2018 (Summer of TDA).

Sep 27 Dustin Arendt, PNNL PNNL capabilities for interactive and explainable machine learning

Abstract (click to read)

This talk will demonstrate two capabilities for interactive and explainable machine learning. The first capability, CHISSL, addresses machine learning’s “elephant in the room”—that good models require substantial human annotated data, which is difficult or expensive to acquire. CHISSL allows an analyst to flexibly explore and annotate large unlabeled datasets. CHISSL is significantly more responsive than existing machine learning techniques, while still maintaining high accuracy. Our second capability, "Escape Routes", is a new approach to exploring high dimensional data. The technique allows an analyst to see plausible pathways linking together arbitrary data points, which we believe is especially helpful to understand a classification model’s behavior across decision boundaries. Both capabilities are generalizable to a multitude of different data types including text, images, sequences, and time series. For future work, we would like to work with other interested researchers who want to try these new capabilities on their challenging data and applications.

Oct   4 Luminita Vese, UCLA SIAM PNW Seminar, 4 PM
Variational methods in image processing

Abstract (click to read)

Many inverse problems arising in image processing can be solved by variational methods. A functional is minimized, composed of a data fidelity term and a regularizing term. The regularizing term imposes a-priori constraints on the solution and makes the problem well-posed. The unknown is found in the appropriate space of functions that best characterizes the desired properties of the solution. The Euler-Lagrange equation associated with the minimization is obtained and then solved using numerical methods. In this talk I will present several inverse problems arising in imaging applications and their solutions in a variational approach. Examples include image restoration, segmentation, decomposition, and medical applications such as image reconstruction in computer tomography. Theoretical and experimental results will be presented.

We will be joining the seminar from VUB 225.

Oct 11 Benjamin Rapone, WSU Robust Feasibility of Quadratic Systems

Abstract (click to read)

We consider the problem of measuring the margin of robust feasibility of solutions to a system of nonlinear equations. We study the special case of a system of quadratic equations, which shows up in many practical applications such as the power grid and other infrastructure networks. We develop approaches based on topological degree theory to estimate bounds on the robustness margin of such systems. Our methods use tools from convex analysis and optimization theory to cast the problems of checking the conditions for robust feasibility as a nonlinear optimization problem. We conclude with some preliminary modeling results and a discussion about future research directions.

Oct 18 No seminar
Oct 25 Bala Krishnamoorthy, WSU Euler transformation of polyhedral meshes

Abstract (click to read)

Geometric regions are typically represented using polyhedral meshes (including triangulations) in most applications. Efficient coverage of the regions using edges in the mesh is of primary interest in several domains including robotic motion planning and 3D printing. For instance, a robot monitoring or serving the region might want to move "efficiently" along the edges in the mesh so as to cover the entire region without doing any backtracking. In a standard format for 3D printing (termed "sparse infill"), the extruder prints only the edges of the mesh, creating a "skeleton". An ideal print path would start at a point, print every edge exactly once, and return to the start. Such a tour is called an Eulerian tour.

In what is considered the first theorem in graph theory (presented in 1736), Euler described the condition that guarantees when a graph has such a tour - hence the name. But meshes generated using standard approaches are not guaranteed to contain an Eulerian tour of its edges. We present a method to transform any polyhedral mesh into one that is guaranteed to contain an Eulerian tour. We will highlight properties of this transformation using several pictures, including one illustrating its use in 3D printing (as implemented by collaborators in ORNL).

Nov  1 Leslie New, WSU Central place foragers and moving stimuli: A hidden-state model to discriminate the processes affecting movement

Abstract (click to read)

Human activities can influence the movement of organisms, either repelling or attracting individuals depending on whether they interfere with natural behavioral patterns or enhance access to food. To discern the processes affecting such interactions, an appropriate analytical approach must reflect the motivations driving behavioral decisions at multiple scales. In this study, we developed a modelling framework for the analysis of foraging trips by central place foragers. By recognizing the distinction between movement phases at a larger scale and movement steps at a finer scale, our model can identify periods when animals are actively following moving attractors in their landscape. We applied the framework to GPS tracking data of northern fulmars Fulmarus glacialis, paired with contemporaneous fishing boat locations, to quantify the putative scavenging activity of these seabirds on discarded fish and offal. We estimated the rate and scale of interaction between individual birds and fishing boats and the interplay with other aspects of a foraging trip. Our approach can be used to characterize interactions between central place foragers and different anthropogenic or natural stimuli and can be adapted to explore the movement of other species that are subject to multiple dynamic drivers.

Nov  8
Nov 15 No seminar
Nov 29 Emilie Purvine, PNNL In VECS 125
Applications of topology for information fusion

Abstract (click to read)

In the era of "big data" we are often overloaded with information from a variety of sources. Information fusion is important when different data sources provide information about the same phenomena. For example, news articles and social media feeds may both be providing information about current events. In order to discover a consistent world view, or a set of competing world views, we must understand how to aggregate, or "fuse", information from these different sources. In practice much of information fusion is done on an ad hoc basis, when given two or more specific data sources to fuse. For example, fusing two video feeds which have overlapping fields of view may involve coordinate transforms; merging GPS data with textual data may involve natural language processing to find locations in the text data and then projecting both sources onto a map visualization. But how does one do this in general? It turns out that the mathematics of sheaf theory, a domain within algebraic topology, provides a canonical and provably necessary language and methodology for general information fusion. In this talk I will motivate the introduction of sheaf theory through the lens of information fusion examples.

This research was developed with funding from the Defense Advanced Research Projects Agency (DARPA). The views, opinions and/or findings expressed are those of the author and should not be interpreted as representing the official views or policies of the Department of Defense or the U.S. Government. Approved for Public Release, Distribution Unlimited.

Dec   6 Adam Erickson, WSU

Last modified: Wed Oct 31 11:04:18 PDT 2018