08:30-09:00 Gathering & Coffee
09:00-09:15 Opening notes
09:15-09:45 Ron Levie, Technion , Israel
Szemerédi Regularity Lemma in Graph Machine Learning
In recent years, graph neural networks (GNNs) have led to groundbreaking achievements in the applied sciences and industry. These achievements pose exciting theoretical challenges: can the success of GNNs be grounded in solid mathematical frameworks?
A GNN is a function that takes graphs (with node features) and returns vectors in a Euclidean space. Since the input space of a GNN is non-Euclidean, i.e., graphs can be of any size and topology, it is more challenging to analyze GNNs than standard neural networks. In this talk, I will demonstrate how one classical result in graph theory, the Szemerédi Regularity Lemma, leads to many theoretical results for GNNs, including generalization bounds, universal approximation theorems, and expressivity analysis, as well as to novel GNN designs that scale very well for large graphs.
09:45-10:15 Eli Konen, Sheba Medical Center and Tel Aviv University
AI in Medical Imaging: pixel analysis is just the tip of the iceberg
10:15-10:45 Coffee break
10:45-11:15 Semyon Tsynkov, NC State University, USA
Transionospheric radar autofocus
Autofocus is a familiar word and a technology that most of us are exposed to in our everyday life. It refers to the capacity of an imaging instrument, such as the camera on one’s mobile phone, to produce sharp, i.e., focused images without user’s intervention. In the talk, we will discuss the challenges and recent progress in the design of autofocus algorithms for spaceborne synthetic aperture radars. The latter are a class of more sophisticated imaging instruments operating on different physical principles — coherent vs. incoherent imaging.
11:15-11:30 Abarbanel Prize Ceremony
11:30-12:00 Prize lecture: Alex Bronstein, Technion
From RealSense to real science — A journey of a curious character
In this wide-audience talk, I will describe my personal journey from my first steps in computational imaging and vision to the more recent infatuation with problems in structural biology and physics.
12:00-13:30 Lunch
13:30-14:00 Students’ lighting talk
14:00-14:30 Edriss S. Titi , Texas A&M University, USA and Weizmann Institute, Israel
Rigorous Analysis and Numerical Implementation of Nudging Data Assimilation Algorithms
In this talk, we will introduce downscaling data assimilation algorithms for weather and climate prediction based on discrete coarse spatial scale measurements of the state variables (or only part of them, depending on the underlying model). The algorithm is based on linear nudging of the coarse spatial scales in the algorithm’s solution toward the coarse spatial scales corresponding to the observed measurements of the unknown reference solution. The algorithm’s solution can be initialized arbitrary and is shown to converge at an exponential rate toward the exact unknown reference solution. This indicates that the dynamics of the algorithm is globally stable (not chaotic) unlike the dynamics of the model that governs the unknown reference solution. Capitalizing on this fact, we will also demonstrate uniform in time error estimates of the numerical discretization of these algorithms, which makes them reliable upon implementation computationally. Furthermore, we will also present a recent improvement of this algorithm by employing nonlinear nudging, which yields super exponential convergence rate toward the unknown exact reference solution. Notably, this algorithm applies to all dissipative systems, however, we will show by examples that it does not work for non-disspative systems.
14:30-15:00 Reuven Cohen, Bar Ilan University, Israel
Constructing cost-effective infrastructure networks
We consider the problem of designing Infrastructure networks that are reliable and low-cost. We present different measures for the reliability of such networks (e.g. power networks, communication networks, etc.), and methods for finding optimal underlying graph structures for various ranges of edge failure probabilities, p. In particular, for low values of p, and a small number of redundant edges, we show that the optimal structure is an underlying skeleton of a 3-regular high girth graph, with the edges replaced by equal length chains of degree 2 vertices. We also present methods for improving existing infrastructure networks with limited resources.
(joint work with Rotem Brand, Baruch Barzel and Simi Haber).
15:00-15:30 Coffee break
15:30-16:00 Michal Feldman, Tel Aviv University, Israel
Ambiguous Contracts
In this work we explore the deliberate infusion of ambiguity into the design of contracts. We show that when the agent is ambiguity-averse and chooses an action that maximizes their max-min utility, then the principal can strictly gain from using an ambiguous contract. We provide insights into the structure of optimal contracts, and establish that optimal ambiguous contracts are composed of simple contracts. We also provide a characterization of ambiguity-proof classes of contracts. Finally, we show that when the agent considers mixed strategies, then there is no advantage in using an ambiguous contract.
Joint work with Paul Duetting, Daniel Peretz and Larry Samuelson.
16:00-16:30 Nir Sharon, Tel Aviv University, Israel
Approximation over nonlinear spaces
In recent years, there have been exciting developments in methods for approximating functions with domains and codomains in nonlinear spaces. This discussion will cover curves over Wasserstein spaces, fields of manifold values, and various geometric approximations, along with a review of recent advances in these areas.
16:30-17:00 Haggai Katriel, Ort Braude, Israel
Optimizing antibiotic treatment: some mathematical results
Antibiotic agents are an indispensable tool for combatting infections. but using them prudently is essential in order to avoid the dangers of relapse, toxicity, and emergence of resistance.
We study the question of designing a dosing plan for an antibiotic treatment which is optimal, in the sense that it will lead to eradication of an infection, while using a minimal amount of antibiotic. We employ simple, and widely used, mathematical models of pharmacokinetics and pharmacodynamics, in order to obtain explicit solutions to this optimization problem. Some implications of these results, and questions for further investigation, will be discussed.