## Johns Hopkins Applied Math and Statistics (AMS)

## Graduate Student Seminar

## Fall 2023

## Talks every Tuesday 1:30-2:30pm, Wyman N425.

Live spreadsheet for talks and abstracts (click for view-only link).

## Schedule

## September

Sep 12 (Lightning Talks)

Barbara Fiedorowicz, slides

Title: Finding the Optimal Number of Current Measurements to Identify Crack in a Material

Abstract: In this talk, I will give an overview of the early stages of this project to find the minimum number of current measurements needed to identify a crack in a material. To discretize our problem, we overlay a graph on our material, restricting the number of possible points through which we can conduct current. The goal is to find the minimum number of measurement pairs (sources and sinks) necessary to identify which edge in the graph has been compromised as a result of the crack in the system. This talk will discuss two approaches: one involving the set cover problem and the other involving a heuristic model. It will also discuss results found from particular kinds of graphs, outlining both adaptive and nonadaptive strategies.

Title: Complexity of Convex Optimization: Different Oracle Settings and Transfers of Bounds

Abstract: I'll give an overview of some recent work with Dr. Basu, in which we investigate information complexity (aka oracle complexity) of convex optimization across different oracle settings and provide some "transfer" results between them. Highlights include that we are able to "lift" lower bounds from the continuous to the mixed-integer case, and also transfer bounds from the exact-information case to the inexact or stoahcastic setting.

Sep 19 (Lightning Talks)

Drew Henrichsen

Title: Rendezvous Search on a Sphere: The Astronaut Problem

Abstract: In a rendezvous search problem, the goal is to find an optimal strategy for two agents in a specified region to use in order to meet in the minimum expected time. The astronaut problem considers two agents on a sphere representing a featureless planet. The agents can see everything within a detection radius r and have a maximum allowed speed of movement. Although the problem is decades old, there are no published results. We consider multiple strategies, providing both theoretical bounds and Monte Carlo simulation estimates. Some of the strategies are iterative, restarting if the agents have not met, so they involve geometric waiting time distributions. Although one might expect the optimal meeting time to vary inversely with the detection area, which is of the order of r^2, upper bounds that vary inversely with r are obtained in both the symmetric and asymmetric settings.

Zan Ahmad

Title: Mathematical Cardiology

Abstract: Many mathematical tools can be useful for studying the cardiovascular system. My work aims to develop and apply tools in computational fluid dynamics, image analysis and statistical learning/operator learning to better understand, diagnose and treat adverse cardiac events. I'll try and cover a broad range of tools and how they have been or can be implemented for this mission, and touch on some things I have and will be working on.

Sep 26 (Lightning Talks)

Tianyi Chen, slides

Title: Organoid Intelligence and Analysis of time series of networks

Abstract: In this presentation, I will delve into the forefront of artificial intelligence: Organoid Intelligence. A brain organoid is a miniature, in vitro resembling of the brain, cultivated from pluripotent stem cells. To understand these organoids, neuroscientists deduce an effective connectivity network for its neurons from periodical recording, resulting in a time series of networks. To analyze the time series of networks, I will introduce the "spectral mirror method," a technique that provides low dimensional Euclidean representations—termed "mirrors"—for the dynamic structure inherent in the time series of networks. This innovative method not only enables the visualization of network evolution but also redefines network inference challenges, such as change-point detection, within a classical framework. In conclusion, I will elaborate on a specific model, allowing us to derive the analytical form of the mirror and perform change-point localization based on this mirror.

Kailee Lin, slides

Title: Functional Graph Theory 101 and Application to Stanley's Chromatic Polynomial Conjecture

Abstract: In this talk we will go over basic ideas in functional graph theory, including what is a funtional graph/tree, what does this new functional approach buy us, and how do polynomials come into the picture? We will then use this understanding to explore a new approach to understanding Stanley's chromatic polynomial conjecture (from 1995) which is says following: Suppose I secretly pick a tree, and generate all the proper colorings of this secret tree. Then for each proper coloring, I make a histogram of how many times each color was used. I leave this set of histograms on my desk, but burn all other evidence. If you are the detective, can you determine what my secret tree was? Stanley says yes.

## October

Oct 3

Thabo Samakhoana

Title: Scalable Projection-Free Optimization Methods via MultiRadial Duality Theory

Abstract: Recent works have developed new projection-free first-order methods based on utilizing radial linesearches and normal vector computations to maintain feasibility. These oracles are often cheaper than orthogonal projection or linear optimization subroutines but have the drawback of requiring a known strictly feasible point to do these linesearches with respect to. In this work, we develop new theory and algorithms which can operate using these cheaper linesearches while only requiring knowledge of points strictly satisfying each constraint separately. Convergence theory for several resulting “multiradial” gradient methods is established.

Oct 10

Mao Hong, slides

Title: A policy gradient method for confounded POMDPs

Abstract: Existing works on policy gradient methods for offline reinforcement learning (RL) have been mostly developed for the fully observable environments with Markovian transition dynamics, which may not be known a priori. In this talk, I will introduce a novel offline policy gradient method for partially observable Markov decision processes (POMDPs), with a main focus on theoretical results of identification, estimation, and policy optimization.

Oct 17

Alan Luner, slides

Title: Performance Estimation and Improved Convergence via Averaging and Extrapolation

Abstract: When we consider theoretical convergence guarantees for an algorithm, we are only concerned with the worst-case function for that algorithm. Given a specified (and fixed-length) algorithm, performance estimation allows us to find this worst-case function through a finite-dimensional and numerically solvable SDP. In this talk, we use peformance estimation to look at the effects of averaging and extrapolation on smooth and non-smooth gradient descent problems. We then show how these numerical results can (hopefully) be generalized to improved convergence rates.

Oct 24

Ao Sun

Title: The Pareto record frontier on the simplex: Dirichlet observations

Abstract: For i.i.d. observations X^(1), X^(2), ... from the d-dimensional simplex S_d := {x = (x_1, ..., x_d): x_j ≥ 0 for all 1 ≤ j ≤ d and x_+ ≤ 1 }, where x_+ := Σ x_j, each having the marginal distribution of the first d coordinates of a Dirichlet(1, 1, ..., 1, a) distribution for a given a > 0, consider the boundary (relative to S_d), or "frontier'', F_n of the closed Pareto record-setting (RS) region RS_n := {x \in S_d: x ⊀ X^(i) for all 1 ≤ i ≤ n} at epoch n, where x ≺ y means that x_j < y_j for 1 ≤ j ≤ d. (When a = 1, the sampling is uniform from S_d.) Let F_n^- := min { x_+: x ∈ F_n } and F_n^+ := max { x_+: x ∈ F_n }. We describe typical and almost sure behavior of F_n^+ and F_n^- as n → ∞. As a rough summary, up to log factors we almost surely have 1 - F^+_n = Θ(n^{-1/a}) while 1 - F^-_n = Θ(n^{-1/(a+d-1)}). Fill and Naiman (Electron. J. Probab., 2020) studied the corresponding problem, where the coordinates of each observation are independent unit-mean Exponential random variables. For the Dirichlet model, the results concerning the asymptotic behavior of 1 - F^-_n, obtained by the proof techniques discussed therein, have been significantly improved by utilizing the theory of “generators” (minima of F_n) along with the first- and second-moment methods. This is based on ongoing joint work with my Ph.D. dissertation advisor, Jim Fill.

Dr. Jim Fill, slides

Title: On the probability of a Pareto record

Abstract: Given a sequence of independent random vectors taking values in R^d and having common continuous distribution F, say that the nth observation sets a (Pareto) record if it is not dominated (in every coordinate) by any preceding observation. Let p(F) ☰ p_{n, d}(F) denote the probability that the nth observation sets a record. There are many interesting questions to address concerning p, but this short talk will focus on showing that for fixed d ≥ 2 and n ≥ 1 the image of the mapping p on the domain of all continuous distributions is precisely the interval [n^{-1}, 1], irrespective of d. Our proof relies largely on consideration of two classes of distributions, one being a subclass of the Dirichlet distributions and the other being a certain class of distributions with positively associated coordinates. This is based on ongoing joint work with my Ph.D. advisee Ao Sun.

Oct 31

Title: Sample Complexity and Learnability of Tunable Parameter Selection for Piecewise Structured Algorithms using Neural Networks

Abstract: We approach the problem of making good decisions in the branch-and-cut framework for mixed integer optimization (e.g., which cut to add, which variable to branch on?) by using a neural network to learn these decisions to obtain small branch-and-cut trees. In other words, the neural network will take as input a mixed-integer optimization instance and output a set of decisions that will result in a small branch-and-cut tree for that instance. We provide rigorous sample complexity bounds and demonstrate the eﬃcacy of our approach with computational experiments for the speciﬁc problem of cut selection (at the root node). The question of learning good instance-dependent decisions for branch-and-cut has been studied extensively in recent literature, both from theoretical and computational perspectives. To the best of our knowledge, our work is the ﬁrst one that provides rigorous sample complexity bounds for a neural network approach to the problem. Moreover, our computational results provide evidence that our particular way of using neural networks for cut selection can make a signiﬁcant impact in reducing branch-and-cut tree sizes.

## November

Nov 7

Zhiyue Zhang

Title: A fast exact inference framework for epidemics with missing data

Abstract: I will go through two novel stochastic epidemic models based on two different types of continuous-time Markov chains (CTMCs). Then, using both models, I will derive a modeling framework for epidemics with missing data, in which we have no access to the exact time of each infection / recovery incidence, or even worse, the recovery reports are completely missing.

Nov 14

Hadden Kim

Title: Parallel evolutional deep neural networks

Abstract: Evolutional deep neural networks (EDNN) were introduced as predictive solvers for nonlinear partial differential equations. Starting from any initial condition projected onto the network state, the EDNN parameters are evolved by solving the governing dynamical equations, and without the need for costly training. Several advancements will be discussed: First, multiple EDNNs are utilized simultaneously to predict the evolution of a vector valued state that is governed by coupled nonlinear partial differential equations. Second, the physical domain is decomposed into sub-regions that are solved by separate EDNNs. Boundary information between networks is exchanged to ensure global accuracy of the solution, using a novel EDNN boundary function (EBF). The resulting partition enables parallel execution and, additionally, enables efficient use of multiple smaller networks without sacrificing accuracy.

Nov 21

Thanksgiving break.

Nov 28

Pedro Izquierdo Lehmann

Title: Maximizing the Sweet Spot for Spatial Sound with Loudspeakers

Abstract: The field of spatial sound addresses the question: how to create a spatial auditory illusion over a region of interest with a set of acoustic sources? In this context, the sweet spot is defined as the region where the spatial auditory illusion is achieved. We study the problem of maximizing the sweet spot when reconstructing a desired sound wave using an array of loudspeakers. We introduce a first principles theoretical framework for spatial sound in which the maximization of the sweet spot is expressed as a non-convex variational problem, and we develop a method that aims to solve the variational problem. Proof-of-concept experiments show that our method outperforms state-of-the-art sound field synthesis methods in terms of their binaural azimuth localization and binaural coloration properties.

## December

Dec 5

Benjamin Weinberg

Title: Monitoring Human Breathing With Motion Sensing Data

Abstract: We discuss signal processing and modeling for inferring breath state based on motions of the torso. Topics include signal filtering, classical linear dynamical system identification, and neural network approaches.

Organizers: Josiah Lim, Ian McPherson.

Food coordinators: My Le, Merrick Ohata.