Claude Bardos, Université Denis Diderot, Paris
“Scalings and Stability for the Vlasov Equation”
The Vlasov equation is a transport equation of plasma physics. Moreover it turns out that it is at the cross road of many other sciences that may be explained by the fact that it explicitly takes into account diverse phenomena which influence can be measured in terms of scalings. This is what I will try to describe avoiding going into detailed mathematics which includes basic open problems.
Boaz Nadler, Weizmann Institute,
“Unsupervised Ensemble Regression: Making Accurate Predictions”
Consider a regression problem where there is no labeled data and the only observations are the predictions f_i(x_j) of m experts f_i over many samples x_j. With no knowledge on the accuracy of the experts, is it still possible to accurately estimate the unknown responses y_j? Can one still detect the least or most accurate experts? In this work we propose a framework to study these questions, based on the assumption that the m experts have uncorrelated deviations from the optimal predictor. Assuming the mean of the response is known, we develop methods to detect the best and worst regressors, and derive U-PCR, a novel principal components approach for unsupervised ensemble regression.
We provide theoretical support for U-PCR and illustrate its improved accuracy over the ensemble mean and median on a variety of regression problems.
Yoel Shkolnisky, Tel Aviv University,
“Mathematical Opportunities and Challenges in Electron Microscopy”.
The field of electron microscopy and in particular cryo-electron microscopy is undergoing a transformative change that is revolutionizing structural biology. In particular, recent instrumentation and algorithmic breakthroughs introduce capabilities that until recently were unimaginable.
In a nutshell, electron microscopy is a method to determine the three-dimensional structure of molecules from their two-dimensional images taken by an electron microscope. In this talk, I will introduce cryo-electron microscopy, its mathematical aspects and open challenges.
In the discussion part, I'd like to share my experience with interdisciplinary research, and discuss possible practices for interdisciplinary collaboration and impact.
Eitan Tadmor, University of Maryland
“Graphs and Games in Short-range Interactions”
The large time dynamics of short-range interactions is determined by the connectivity of dynamic graphs. On a larger hydrodynamic scale, the large-crowd dynamics is determined by the enstrophy. On still larger scale of clusters, one is interested in games based on interactions among such clusters. I will provide a brief overview of known results and open problems of short-range interactions in thee settings.
Gershon Wolansky, Technion
“Limit Theorems in Optimal Transport Theory and Application to Optimal Networks”
I will review the fundamental theory of optimal transport (Monge-Kantorovich) from a dynamical point of view, and introduce some new limit theorems. One of the application of these limit theorems is an algorithm for optimal networks (e.g. an irrigation systems) which, unlike all other algorithms for optimal networks, is convex.