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Mean field games and mean field control problems are frameworks to study Nash equilibria or social optima in games with a continuum of agents. These problems can be used to approximate competitive or cooperative situations with a large finite number of agents, and have found a broad range of applications, from economics to crowd motion, energy production and risk management. The solutions are typically characterized by a forward-backward system of partial differential equations (PDE) or stochastic differential equations (SDE).

GPUs have emerged as a popular choice for deep learning. To deal with ever-growing datasets, it is also common to use multiple GPUs in parallel for distributed deep learning. Although achieving cost-effectiveness in these clusters relies on efficient sharing, modern GPU hardware, deep learning frameworks, and cluster managers are not designed for efficient, fine-grained sharing of GPU resources. In this talk, I will present our recent works on efficient GPU resource management, both within a single GPU and across many GPUs in a cluster for hyperparameter tuning, training, and inference. The common thread across all our works is leveraging the interplay between short-term predictability and long-term unpredictability of deep learning workloads

Navigation is an essential requirement for many applications (commercial, retail, military, scientific, ...etc) and in a variety of environments (in-doors, outdoors, space, underwater, and even underground). In this talk, I will overview some of my group's work in localization and navigation focusing on indoor and satellite positioning. The talk will demonstrate how the structure or constraints of the problem can help achieve very accurate localization (e.g. millimeter level indoors) that is robust to Doppler, multipath, and shadowing. The talk will also touch upon various related applications that the group is pursuing in smart health and smart cities. The talk will end with future directions for localization in extreme environments and in the TeraHertz spectrum where localization, environment sensing, and communication converge.

In modern large-scale inference problems, the dimension of the signal to be estimated is comparable or even larger than the number of available observations. Yet the signal of interest lies in some low-dimensional structure, due to sparsity, low-rankness, finite alphabet, ... etc. Non-smooth regularized convex optimization are powerful tools for the recovery of such structured signals from noisy linear measurements. Research has shifted recently to the performance analysis of these optimization tools and optimal turning of their hyper-parameters in high dimensional settings. One powerful performance analysis framework is the Convex Gaussian Min-max Theorem (CGMT). The CGMT is based on Gaussian process methods and is a strong and tight version of the classical Gordon comparison inequality. In this talk, we review the CGMT and illustrate its application to the error analysis of some convex regularized optimization problems.

This workshop is devoted to numerical simulation of groundwater flow and subsurface contamination transport, as well as related problems. The main topics are mathematical modeling of the processes in porous media and the numerical methods for discretization, solution of the discretized systems and numerical treatment of inverse problems. In particular, fractured porous media and partially saturated aquifers will be concerned.

Mean field games and mean field control problems are frameworks to study Nash equilibria or social optima in games with a continuum of agents. These problems can be used to approximate competitive or cooperative situations with a large finite number of agents, and have found a broad range of applications, from economics to crowd motion, energy production and risk management. The solutions are typically characterized by a forward-backward system of partial differential equations (PDE) or stochastic differential equations (SDE)

In this talk I will present recent advancement in automated reasoning, in particular computer-supported theorem proving, for generating and proving software properties that prevent programmers from introducing errors while making changes in this software. When testing programs manipulating the computer memory, our initial results show our work is able to prove that over 80% of test cases are guaranteed to have the expected behavior.

In this talk, we study a mean field game inspired by crowd motion in which agents evolve in a domain and want to reach its boundary minimizing their travel time. Interactions between agents occur through their dynamic, which depends on the distribution of all agents. First, we provide a Lagrangian formulation for our mean field game and prove existence of equilibria, which are shown to satisfy a MFG system. The main result, which relies on the semi-concavity of the value function of this optimal control problem, states that an L^p initial distribution of agents gives rise to an L^p distribution of agents at each time t>0.

Building intelligent visual systems is essential for the next generation of artificial intelligence systems. It is a fundamental tool for many disciplines and beneficial to various potential applications such as autonomous driving, robotics, surveillance, augmented reality, to name a few. An accurate and efficient intelligent visual system has a deep understanding of the scene, objects, and humans. It can automatically understand the surrounding scenes. In general, 2D images and 3D point clouds are the two most common data representations in our daily life. Designing powerful image understanding and point cloud processing systems are two pillars of visual intelligence, enabling the artificial intelligence systems to understand and interact with the current status of the environment automatically. In this talk, I will first present our efforts in designing modern neural systems for 2D image understanding, including high-accuracy and high-efficiency semantic parsing structures, and unified panoptic parsing architecture. Then, we go one step further to design neural systems for processing complex 3D scenes, including semantic-level and instance-level understanding. Further, we show our latest works for unified 2D-3D reasoning frameworks, which are fully based on self-attention mechanisms. In the end, the challenges, up-to-date progress, and promising future directions for building advanced intelligent visual systems will be discussed.

In this lecture I will present broader spectrum of complex, multicomponent flows. For example, the models of compressible mixtures describe multicomponent fluids that are mixed on the molecular level. They are different from the models of the multi-phase flows from the first lecture, because there is no division of volume occupied by different species. The existence of global in time weak solutions, and global in time strong solutions for such systems will be explained, and some open problems related to singular limits and weak-strong uniqueness of solutions will be mentioned. At the end of the lecture I will also present another model of two-phase flow describing the motion of compressible and incompressible medium with an interphase given by a condition on the density. I will explain how to prove the existence of solutions and give some applications in modelling of crowd evacuation.

In essence, science is about discovering regularities in Nature. It turns out that such regularities (laws) are written in the language of mathematics. In many cases, such laws are formulated and refined from fundamental “first principles.” Yet, in phenomenological areas such as biology, we have an abundance of data but lack “first principles.” Machine learning and deep learning, in particular, are remarkably successful in classification and prediction tasks. However, such systems, when trained on data, do not, as a rule, provide compact mathematical laws or fundamental first principles. Here we ask how we can identify interpretable compact mathematical laws from complex data-sets when we don’t have access to first principles. I will give an overview of this problem and provide some vignettes of our ongoing work in attacking this problem.

I will start recalling the definitions and basic properties of viscosity solutions to fully nonlinear degenerate elliptic equations, in particular the comparison principles. The main goal of the course is discussing two properties of subsolutions: the Strong Maximum Principle (SMP), i.e., if a subsolution in an open connected set attains an interior maximum then it is constant, and the Liouville property, i.e., if a subsolution in the whole space is bounded form above then it is constant. They are standard results for classical solutions of linear elliptic PDEs, and many extensions are known, especially for divergence form equations. My goal is explaining how the viscosity methods allow to turn around the difficulties of non-smooth solutions, fully nonlinear equations, and their possible degeneracies.

Emergence of nontrivial patterns via collective actions of many individual entities is an ever-present phenomenon in physics, biology and social sciences. It has numerous applications in engineering, for instance, in swarm robotics. I shall demonstrate how tools from mathematical modeling and analysis help us gain understanding of fundamental principles and mechanisms of emergence. I will present my recent results in consensus formation and flocking models, focusing on the effects of noise and delay on their dynamics. Moreover, I will introduce continuum modeling framework for biological network formation, where emergence takes place through the interaction of structure and medium. The models are formulated in terms of ordinary, stochastic and partial differential equations. I shall explain how mathematical analysis of the respective models contributes to the understanding of how individual rules generate and influence the patterns observed on the global scale. A particular example from biology is development of leaf venation as a result of auxin-PIN interaction in the plant tissue. Here our model supported the hypothesis that a-priori polarization of auxin transport does not play a decisive role in leaf venation.

Implantable and wearable technologies are rapidly emerging and showing great promise in various medical therapeutics and diagnostics. These advances from health monitoring to therapeutic applications reorganize many aspects of daily life. Since the invention of the first implantable cardiac pacemaker for patients with arrhythmia in 1958, many implantable medical devices (IMDs) such as implantable cardioverter defibrillators (ICDs) and implantable deep brain stimulators (iDBSs) have been developed and have treated millions of patients. These IMDs eventually need wireless powering and communication for 1) eliminating transcutaneous power/data interconnects that elevate the risk of infection and 2) removing bulky batteries to avoid the risk of repeated surgical intervention. They also need small form factors and soft materials to mitigate tissue fibrosis due to foreign body responses. In this talk, I will introduce a new wireless neural interfacing tool within a cubic millimeter that can potentially record large scale neuronal ensembles over large brain area. The discussion will be focused on its building pieces across a wide range of science and engineering disciplines toward translating those into a complete clinically viable IMD. Also, I will present my recent research on RF-to-ultrasound power relay for powering deep mm-scale implants across air/tissue or tissue/skull media, and an all-soft and wireless pressure sensor tags that aim to address the issues of surgical complexity, tethering effect, and foreign body response. Finally, I will conclude the talk by presenting my future research plans toward clinically viable wireless medical diagnostics and therapeutics.

Small-scale cut and fold patterns imposed on sheet material enable its morphing into three-dimensional shapes. This manufacturing paradigm has received much attention in recent years and poses challenges in both fabrication and computation. It is intimately connected with the interpretation of patterned sheets as mechanical metamaterials, typically of negative Poisson ratio. We discuss a fundamental geometric question, namely the targeted programming of a shape morph from a flat sheet to a curved surface, or even between any two shapes. The solution draws on differential geometry, discrete differential geometry, geometry processing and geometric optimization.

I will start recalling the definitions and basic properties of viscosity solutions to fully nonlinear degenerate elliptic equations, in particular the comparison principles. The main goal of the course is discussing two properties of subsolutions: the Strong Maximum Principle (SMP), i.e., if a subsolution in an open connected set attains an interior maximum then it is constant, and the Liouville property, i.e., if a subsolution in the whole space is bounded form above then it is constant. They are standard results for classical solutions of linear elliptic PDEs, and many extensions are known, especially for divergence form equations. My goal is explaining how the viscosity methods allow to turn around the difficulties of non-smooth solutions, fully nonlinear equations, and their possible degeneracies.

The objective of this work is to develop a near-infrared laser device capable of emitting orbital angular momentum (OAM) light. The prototyped device must be suitable for compact, energy-saving optical communication applications. Integrated OAM lasers would revolutionize high capacity data transmission over any telecommunication network environment as OAM light can be guided and transmitted through kilometers of optical fibers as well as propagated in free space and underwater.

In this talk, I will present the recent developments in the topic of the existence of solutions to the two-fluid systems. The compensated compactness technique of P.-L. Lions and E. Feireisl for single-component fluids has certain limitations, distinctly in the context of multi-component flow models. A particular example of such a model is the two-fluids Stokes system with a single velocity field and two densities, and with an algebraic pressure law closure. The first result that I will present is the existence of weak solutions for such a system, using the compactness criterion introduced recently by D. Bresch and P.-E. Jabin. I will also outline an innovative construction of solutions relying on the G. Crippa and C. DeLellis stability estimates for the transport equation. In the last part of my talk, I will relate to a couple of more recent results: the existence of solutions to the one-dimensional system, non-uniqueness of solutions to the inviscid system, and I will comment on issues around weak-strong uniqueness.

I will start recalling the definitions and basic properties of viscosity solutions to fully nonlinear degenerate elliptic equations, in particular the comparison principles. The main goal of the course is discussing two properties of subsolutions: the Strong Maximum Principle (SMP), i.e., if a subsolution in an open connected set attains an interior maximum then it is constant, and the Liouville property, i.e., if a subsolution in the whole space is bounded form above then it is constant. They are standard results for classical solutions of linear elliptic PDEs, and many extensions are known, especially for divergence form equations. My goal is explaining how the viscosity methods allow to turn around the difficulties of non-smooth solutions, fully nonlinear equations, and their possible degeneracies.

We present a novel large-scale dataset and accompanying machine learning models aimed at providing a detailed understanding of the interplay between visual content, its emotional effect, and explanations for the latter in language. In contrast to most existing annotation datasets in computer vision, we focus on the affective experience triggered by visual artworks and ask the annotators to indicate the dominant emotion they feel for a given image and, crucially, to also provide a grounded verbal explanation for their emotion choice.

The need for big data that the internet of things (IoT) has created in recent years has turned the focus on integrating the human body in the quest to understand it better, and in turn use such information for detection and prevention of harmful conditions. Applications in which continuous and uninterrupted operation is required, or where the use of external power sources may be challenging demands the use of self-powered autonomous systems. Organic photovoltaic devices are flexible, lightweight, and soft, capable of interacting with the human body and its mechanical demands. Their processability from solutions permits their adaptation to versatile fabrication techniques such as spin coating, roll-to-roll coating and inkjet printing, with benefits including low material usage and freedom of design. In this talk, I will present how organic photovoltaics can be utilized in printed electronics as energy harvesting devices and go through the historical progress of organic/hybrid photovoltaics as well as the main activities that are ongoing in my research lab ‘Omegalab’.

Abstract

We establish a new oscillation estimate for solutions of nonlinear partial differential e

In this course I will discuss the basics of the classical theory of free boundary problems. We will focus on two problems; the Alt-Caffarelli and obstacle problem. In the first part of the course we will discuss the regularity of the solutions, and in the remainder the full and partial regularity of the free boundary

In this talk, I will introduce our recent efforts on developing novel computational models in the field of biological imaging. I will start with the examples in electron tomography, for which I will introduce a robust and efficient scheme for fiducial marker tracking, and then describe a novel constrained reconstruction model towards higher resolution sub-tomogram averaging. I will then show our work on developing deep learning methods for super-resolution fluorescence microscopy.