The aim of this talk is to investigate the following non local p-Laplacian problem with data a bounded Radon measure.

This dissertation consists of four major contributions to subasymptotic modeling of multivariate and spatial extremes. The dissertation proposes a multivariate skew-elliptical link model for correlated highly-imbalanced (extreme) binary responses, and shows that the regression coefficients have a closed-form unified skew-elliptical posterior with an elliptical prior.

Applied Complexity aims to understand the physical origin of these behaviors and transform them into sustainable technologies that tackle global problems of global interest. These range from energy harvesting to clean water production, the design of smart materials, biomedical applications, information security, artificial intelligence, and global warming. In this talk, I will summarize my group's recent research, discussing present results and future challenges of Applied complexity both as a science and engineering.

Models for flows on networks arise in the study of traffic and pedestrian crowds. These models encode congestion effects, the behavior and preferences of agents, such as aversion to crowds and their attempts to minimize travel time. We will present the Wardrop equilibrium model on networks with flow-dependent costs and its connection with stationary mean-field game.

Skoltech Applied AI center’s mission is to create AI models and frameworks for solving the problems of sustainable development of industry and economy. In my presentation, I will overview the current center's activities, applied and fundamental problem statements, and corresponding recent results.

This talk will provide a brief overview of LoCMOS systems, the technologies used to construct them, and their application to novel applications in biosensing, medical diagnostics, and neuroscience. The integration of integrated circuits into LoCMOS devices poses a number of distinct and vexing challenges, increasing complexity while reducing the need for external instrumentation.

In this work, we proved statistical inference for the common Z-estimator based on adaptively sampled data. Adaptive sampling methods, such as reinforcement learning (RL) and bandit algorithms, are increasingly used for the real-time personalization of interventions in digital applications like mobile health and education. As a result, there is a need to be able to use the resulting adaptively collected user data to address a variety of inferential questions, including questions about time-varying causal effects.

Reinforcement Learning provides an attractive suite of online learning methods for personalizing interventions in Digital Behavioral Health. However, after a reinforcement learning algorithm has been run in a clinical study, how do we assess whether personalization occurred? We might find users for whom it appears that the algorithm has indeed learned in which contexts the user is more responsive to a particular intervention. But could this have happened completely by chance? We discuss some first approaches to addressing these questions.

In the Seminar, we exploit what is the heart of the technique to show gradient estimates allowing the function 𝑓 to belong to very general function spaces. Our technique is very flexible and allows us to show the existence, uniqueness, and well-posedness of the Dirichlet problem in several classes.

In this talk, we show that, besides their optimal O(N) algorithmic complexity, hierarchical matrix operations also benefit from parallel scalability on distributed machines with extremely large core counts. In particular, we describe high-performance, distributed-memory, GPU-accelerated algorithms for matrix-vector multiplication and other operations on hierarchical matrices in the H^2 format.

This talk discusses the non-conforming approximation of Biot's consolidation model. In the first part of the talk, we discuss posteriori error estimators for locking-free mixed finite element approximation of Biot’s consolidation model. In the second part of the talk, we discuss a novel locking-free stochastic Galerkin mixed finite element method for the Biot consolidation model with uncertain Young’s modulus and hydraulic conductivity field.

We present a new constrained K-way data clustering algorithm based on Normalized Cut by Shi and Malik. A novelty in our algorithm lies in selecting constraints automatically from the data by using a multiscale coarsening algorithm.

Eigenvalue problems arising from partial differential equations are used to model several applications in science and engineering, ranging from vibrations of structures, industrial microwaves, photonic crystals, and waveguides, to particle accelerators.

In the big data era, it is necessary to rely on distributed computing. For distributed optimization and learning tasks, in particular in the modern paradigm of federated learning, specific challenges arise, such as decentralized data storage. Communication between the parallel machines and the orchestrating distant server is necessary but slow. To address this main bottleneck, a natural strategy is to compress the communicated vectors. I will present EF-BV, a new algorithm which converges linearly to an exact solution, with a large class of deterministic or random, biased or unbiased compressors.

Advances in Si-based millimeter-wave circuit design, Si-based phased arrays, and low-cost antenna integration techniques have enabled the development of scalable phased arrays supporting 10s to 100s of elements.

Many IoT devices are expected to be limited in capability and run with minimal power sources/limited batteries. To extend their lifetime, and autonomy, and reduce the cost of deployment, we introduce the concepts of sensor-less and energy-free sensing, where we sense the environment without using any external sensors while consuming minimal or no energy.

This dissertation discusses approaches to building large-scale and efficient graph machine learning models for learning structured representation with applications to engineering and sciences. This work would present how to make Graph Neural Networks (GNNs) go deep by introducing architectural designs and how to automatically search GNN architectures by novel neural architecture search algorithms.

Freeform structures play a prominent role in contemporary architecture. In order to stay within reasonable cost limits, computational shape design has to incorporate aspects of structural analysis and fabrication constraints. The talk discusses solutions to important problems in this area. They concern the design of polyhedral surfaces with nearly rectangular faces, polyhedral surfaces in static equilibrium, the smoothest visual appearance of polyhedral surfaces and the closely related problem of finding material-minimizing forms and structures. From a methodology perspective, there is an interplay of geometry, mechanics and optimization. Classical subjects such as isotropic geometry, a simple Cayley-Klein geometry, play a role as well as most recent developments in discrete differential geometry. We also show how practical requirements have led to new results and open problems in geometry.

Dynamic programming is an efficient technique to solve optimization problems. It is based on decomposing the initial problem into simpler ones and solving these sub-problems beginning from the simplest ones. A conventional dynamic programming algorithm returns an optimal object from a given set of objects.

Random fields are popular models in statistics and machine learning for spatially dependent data on Euclidian domains. However, in many applications, data is observed on non-Euclidian domains such as street networks. In this case, it is much more difficult to construct valid random field models. In this talk, we discuss some recent approaches to modeling data in this setting, and in particular define a new class of Gaussian processes on compact metric graphs.

With the continuous reduction of chip feature size, the continuation of Moore's Law becomes increasingly difficult and heterogeneous integration has become one of the important orientations of electronic technology.

An efficient method is proposed for the numerical solution of the Stokes equations in a domain with a moving bubble and two techniques for the treatment of the boundary conditions are adopted and then compared. The treatment of diffusion of surfactants (anions and cations) in presence of an oscillating bubble is an interesting interdisciplinary problem, with applications to chemistry and biology.

In this talk, I will first give an elementary introduction to basic deep learning models and training algorithms from a scientific computing viewpoint. Using image classification as an example, I will try to give mathematical explanations of why and how some popular deep learning models such as convolutional neural network (CNN) work. Most of the talk will be assessable to an audience who have basic knowledge of calculus and matrix. Toward the end of the talk, I will touch upon some advanced topics to demonstrate the potential of new mathematical insights for helping understand and improve the efficiency of deep learning technologies.

In this thesis, we focus on the design and development of 4D printed sensors. Carbon nanotubes (CNTs) are used as the active sensing medium as they have proven to be ideal for application in sensors due to their high electric conductivity, stability, and mechanical flexibility. The effect of a heat-shrinkable substrate on the electronic and structural properties of CNTs is analyzed in depth, followed by the application in temperature, humidity, and pressure sensors. The results show that the 4D effect results in a more porous yet more conductive film due to an increase in the charge carrier concentration, enabling an improved sensitivity of the devices and allowing us to tune the selectivity based on the shrinking percentage. The developed device was fabricated using a rapid, cost-effective technique that is independent of advanced fabrication facilities to expand its applications to low-resource settings and environments.

This talk will focus on challenges and opportunities in designing middleware for HPC, AI (Deep/Machine Learning), and Data Science. We will start with the challenges in designing runtime environments for MPI+X programming models by considering support for multi-core systems, high-performance networks (InfiniBand and RoCE), GPUs, and emerging BlueField-2 DPUs. Features and sample performance numbers of using the MVAPICH2 libraries will be presented. For the Deep/Machine Learning domain, we will focus on MPI-driven solutions to extract performance and scalability for popular Deep Learning frameworks (TensorFlow and PyTorch), large out-of-core models, and Bluefield-2 DPUs.