The CMSA Interdisciplinary Science Seminar will take place on Thursdays from 9:00 – 10:00am ET. This seminar concentrates on geometric analysis, algorithms, and mathematical biology with an emphasis on genetics. The seminar is dedicated to applications of mathematics and computer science to life science and medicine. We hope the seminar will serve the role of facilitating collaborations between mathematicians, physicists, and computer scientists with domain experts in biology and medicine.
The schedule below will be updated as talks are confirmed.
|3/18/2021||Omri Ben-Eliezer (CMSA)||Title: Adversarially robust streaming algorithms|
Abstract: Streaming algorithms are an important class of algorithms designed for analyzing and summarizing large-scale datasets. In this context, the goal is usually to obtain algorithms whose space complexity (or memory consumption) is as small as possible, making them convenient to use on a single machine.
Traditionally, streaming algorithms have been analyzed in the static setting, where the stream of incoming data is fixed in advance and does not depend on the algorithm’s outputs. This, however, is unrealistic in many situations. In this talk, I will present and discuss adversarially robust streaming algorithms, whose output is correct with high probability even when the stream updates are adaptively chosen as a function of previous outputs. This regime has received surprisingly little attention until recently, and many intriguing problems are still open. I will mention some of the recent results, discussing algorithms that are well-suited for the adversarially robust regime (random sampling), algorithms that are not robust (linear sketching), and efficient techniques to turn algorithms that work in the standard static setting into robust streaming algorithms.
The results demonstrate strong connections between the streaming context and various other areas in computer science, combinatorics and statistics.
Based on joint works with Noga Alon, Yuval Dagan, Rajesh Jayaram, Shay Moran, Moni Naor, David Woodruff, and Eylon Yogev.
|3/25/2021||Cliff Taubes (Department of Mathematics, Harvard University)||Title: Introduction to 4-dimensional differential topology.|
Abstract: Differential topology is the study of smooth manifolds. I hope to tell you where the frontier lies between knowledge and ignorance with regards to smooth 4-dimensional manifolds (which is by far the hardest dimension to understand).
|4/1/2021||Canceled – Frontiers in Applied Mathematics and Computation|
|Enno Keßler||Title: Supergeometry and Super Riemann Surfaces of Genus Zero|
Abstract: Supergeometry is a mathematical theory of geometric spaces with anti-commuting coordinates and functions which is motivated by the concept of supersymmetry from theoretical physics. I will explain the functorial approach to supermanifolds by Molotkov and Sachse. Super Riemann surfaces are an interesting supergeometric generalization of Riemann surfaces. I will present a differential geometric approach to their classification in the case of genus zero and with Neveu-Schwarz punctures.
|4/15/2021||Cheng Yu (Department of Mathematics, University of Florida)||Title: Weak solutions to the isentropic system of gas dynamics |
Abstract: In this talk, I will discuss the global weak solutions to the isentropic system of gas dynamics: existence and non-uniqueness. In the first part, we generalized the renormalized techniques introduced by DiPerna-Lions to build up the global weak solutions to the compressible Navier-Stokes equations with degenerate viscosities. This existence result holds for any $\gamma>1$ in any dimensional spaces for the large initial data. In the second part, we proved that for any initial data belonging to a dense subset of the energy space, there exists infinitely many global weak solutions to the isentropic Euler equations for any $1<\gamma\leq 1+2/n$. Our result is based on a generalization of convex integration techniques by De Lellis-Szekelyhidi and weak vanishing viscosity limit of the Navier-Stokes equations. The first part is based on the joint works with D. Bresch and A. Vasseur, and the second one is based on our recent joint work with R. M Chen and A. Vasseur.
|4/22/2021||Matt Novack (New York University)||Title: Convex Integration and Fluid Turbulence|
Abstract: The Navier-Stokes and Euler equations are the fundamental models for describing viscous and inviscid fluids, respectively. Based on ideas which date back to Kolmogorov and Onsager, solutions to these equations are expected to dissipate energy even in the vanishing viscosity limit, which in turn suggests that such solutions are somewhat rough and thus only weak solutions. At these low regularity levels, however, one may construct wild weak solutions using convex integration methods. These methods originated in the works of Nash and Gromov and were adapted to the context of fluid equations by De Lellis and Szekelyhidi Jr. In this talk, we will survey the history of both phenomenological theories of turbulence and convex integration. Finally, we discuss recent joint work with Tristan Buckmaster, Nader Masmoudi, and Vlad Vicol in which we construct wild solutions to the Euler equations which deviate from Kolmogorov’s predictions.
|4/29/2021||Yijing Wu (Department of Mathematics, University of Maryland, College Park)||Title: An isoperimetric problem with a competing nonlocal singular term|
Abstract: We are interested in the minimization problem of a functional in which the perimeter is competing with a nonlocal singular term comparable to a fractional perimeter, with volume constraint. We prove that minimizers exist and are radially symmetric for small mass, while minimizers cannot be radially symmetric for large mass. For large mass, we prove that the minimizing sequences either split into smaller sets that drift to infinity or develop fingers of a prescribed width. We connect these two alternatives to a related minimization problem for the optimal constant in a classical interpolation inequality.
|5/6/2021||Aaron Fenyes (Institut des Hautes Études Scientifiques)||TBA|
|5/13/2021||Jialin Zhang (Institute of Computing Technology, Chinese Academy of Science)||Title: A Tight Deterministic Algorithm for the Submodular Multiple Knapsack Problem|
Abstract: Submodular function maximization has been a central topic in the theoretical computer science community over the last decade. Plenty of well-performing approximation algorithms have been designed for the maximization of (monotone or non-monotone) submodular functions over a variety of constraints. In this talk, we consider the submodular multiple knapsack problem (SMKP), which is the submodular version of the well-studied multiple knapsack problem (MKP). Roughly speaking, the problem asks to maximize a monotone submodular function over multiple bins (knapsacks). Recently, Fairstein et al. (ESA20) presented a tight (1−1/e−ϵ)-approximation randomized algorithm for SMKP. Their algorithm is based on the continuous greedy technique which inherently involves randomness. However, the deterministic algorithm of this problem has not been understood very well previously. In this paper, we present a tight (1−1/e−ϵ) deterministic algorithm for SMKP. Our algorithm is based on reducing SMKP to an exponential-size submodular maximizaion problem over a special partition matroid which enjoys a tight deterministic algorithm. We develop several techniques to mimic the algorithm, leading to a tight deterministic approximation for SMKP.
|5/20/2021||Shang Su (Department of Cancer Biology, The University of Toledo)||Title: In silico design and evaluation of PROTAC-based protein degrader–Introductory case studies|
Abstract: Proteolysis-targeting chimeras (PROTACs) are heterobifunctional small molecules consisting of two chemical moieties connected by a linker. The simultaneous binding of a PROTAC to both a target protein and an E3 ligase facilitates ubiquitination and degradation of the target protein. Since its proof-of-concept research in 2001, PROTAC has been vigorously developed by both research community and pharma industry, to act against therapeutically significant proteins, such as BRD4, BTK, and STAT3. However, despite the enthusiasm, designing PROTACs is challenging. Till now, no case of de novo rational design of PROTACs has been reported and the successful PROTACs usually came from the functional screen from a limitedly scaled library. As formation of a ternary complex between the protein target, the PROTAC, and the recruited E3 ligase is considered paramount for successful degradation, several computational algorithms (PRosettaC as the example), have been developed to model this ternary complex, which have got partial agreement with the experimental data and in principle inform future rational PROTAC design. Here I will introduce some of these computational methods and share how they model the ternary complexes.
|5/27/2021||Ying Hsang Liu & Moritz Spiller (University of Southern Denmark & Otto von Guericke University Magdeburg)||Title: Predicting Visual Search Task Success from Eye Gaze Data for User-Adaptive Information Visualization Systems |
Abstract: Information visualizations are an efficient means to support the users in understanding large amounts of complex, interconnected data; user comprehension. Previous research suggests that user-adaptive information visualizations positively impact the users’ performance in visualization tasks. This study aims to develop a computational model to predict the users’ success in visual search tasks from eye gaze data and thereby drive such user-adaptive systems. State-of-the-art deep learning models for time series classification have been trained on sequential eye gaze data obtained from 40 study participants’ interaction with a circular and an organizational graph. The results suggest that such models yield higher accuracy than a baseline classifier and previously used models for this purpose. In particular, a Multivariate Long Short Term Memory Fully Convolutional Network (MLSTM-FCN) shows encouraging performance for its use in on-line user-adaptive systems. Given this finding, such a computational model can infer the users’ need for support during interaction with a graph and trigger appropriate interventions in user-adaptive information visualization systems
|6/3/2021||Joaquim I. Goes (Lamont Doherty Earth Observatory at Columbia University)||TBA|
|6/17/2021||Tianqi Wu (CMSA)||TBA|
|6/24/2021||Fang Xie (BIDMC and HMS)||TBA|