# SIAM Student Chapter Seminar/Spring2017

= Spring 2017

Date Speaker Title

March 17 Polly Yu Zeeman deceleration: motivation, simulation and experiment

March 31 Alisha Zachariah Low Complexity (RADAR) Channel Estimation

April 14 Jim Brunner Robust permanence of polynomial dynamical systems

April 28 Zachary Charles Subspace clustering with missing data

Abstracts (2017 Spring) April 28: Zachary Charles Title: Subspace clustering with missing data

Abstract: In many applications (recommender systems, GPS, medical records) we want to recover a matrix given from an incomplete sampling of its entries. Up to this point, work in this area has focused on the case that the underlying matrix is low rank. Unfortunately, this low-rank assumption is often not true in real-life settings. We instead consider the case when the columns of the matrix come from a union of low rank subspaces. This type of model has already been used to great effect in computer vision and image processing. We will show that by clustering the incomplete data points in to groups according to the subspace they come from, we can often recover the true matrix efficiently. This is ongoing work with Rebecca Willett and Amin Jalali.

Note from the speaker: The talk will hopefully be of interest to anybody who enjoys optimization, machine learning, high-dimensional probability, or convex analysis. However, I will not assume background in any of those areas.

April 14: Jim Brunner Title: Robust permanence of polynomial dynamical systems

Abstract: A permanent" dynamical system is one whose positive solutions stay bounded away from zero and infinity. The permanence property has important applications in biochemistry, cell biology, and ecology. Inspired by reaction network theory, we define a class of polynomial dynamical systems called {\it tropically endotactic}. We show that these polynomial dynamical systems are permanent, irrespective to the values of (possibly time-dependent) parameters in these systems. These results generalize the permanence of 2D reversible and weakly reversible mass-action systems.

Comment on the abstract (from Jim): While this talk sounds like a technical analysis talk, I want to emphasize that the interesting thing for the SIAM student chapter is not so much the result but instead the method of proof. I’ll introduce a thing called a “differential inclusion” and try to convince people that we can analyze ODE systems with polynomial right hand sides by turning our heads and squinting at them in the correct way.

March 31: Alisha Zachariah Title: Low Complexity (RADAR) Channel Estimation

Abstract: Several forms of wireless communication involve estimating the channel through which signals are sent. In this talk we will focus on the RADAR channel. My main motivation in this talk is to present an algebraic channel model that has a sophisticated underlying structure. I will present an existing algorithm that uses this and then develop a low complexity improvement that the structure suggests.

March 17: Polly Yu Title: Zeeman deceleration: motivation, simulation and experiment

Abstract: Granted there will be a lot of 'I don't know's, allow me to introduce the idea of cooling a particle beam by magnetic field. Specifically, I will talk about hydrogen atoms, and how to experimentally implement this cooling. Numerical simulation results will be presented along with pretty pictures. Some experimental data (for the non-decelerated beam) will also be presented; they don't look as pretty, but they remind us that experiments are hard, so patience needed when working with experimentalists.