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The Breadth First Search (BFS) algorithm is the foundation and building block of many higher graph-based operations such as spanning trees, shortest paths and betweenness centrality. The importance of this algorithm increases each day due…
This work presents a formalism to improve the predictive accuracy of physical models by learning generalizable augmentations from sparse data. Building on recent advances in data-driven turbulence modeling, the present approach, referred to…
Grain boundaries (GBs) are ubiquitous defects in crystalline materials. However, they remain less explored in block copolymer ordered phases. Here, we develop a self-consistent field theory framework to investigate GB structure and…
Algebras of generalized functions offer possibilities beyond the purely distributional approach in modelling singular quantities in non-smooth differential geometry. This article presents an introductory survey of recent developments in…
We describe a random matrix approach that can provide generic and readily soluble mean-field descriptions of the phase diagram for a variety of systems ranging from QCD to high-T_c materials. Instead of working from specific models, phase…
We study the geometry of deep (neural) networks (DNs) with piecewise affine and convex nonlinearities. The layers of such DNs have been shown to be {\em max-affine spline operators} (MASOs) that partition their input space and apply a…
The increasing use of microfluidics in industrial, biomedical, and clinical applications requires a more and more precise control of the microfluidic flows and suspended particles or cells. This leads to higher demands in three-dimensional…
We show that many important convex matrix functions can be represented as the partial infimal projection of the generalized matrix fractional (GMF) and a relatively simple convex function. This representation provides conditions under which…
Physics-based differentiable rendering (PBDR) has become an efficient method in computer vision, graphics, and machine learning for addressing an array of inverse problems. PBDR allows patterns to be generated from perceptions which can be…
The increasing share of renewable energy and distributed electricity generation requires the development of deep learning approaches to address the lack of flexibility inherent in traditional power grid methods. In this context, Graph…
Roughness determines many functional properties of surfaces, such as adhesion, friction, and (thermal and electrical) contact conductance. Recent analytical models and simulations enable quantitative prediction of these properties from…
Generalized symmetries (also known as categorical symmetries) is a newly developing technique for studying quantum field theories. It has given us new insights into the structure of QFT and many new powerful tools that can be applied to the…
A novel power consensus algorithm for DC microgrids is proposed and analyzed. DC microgrids are networks composed of DC sources, loads, and interconnecting lines. They are represented by differential-algebraic equations connected over an…
We propose a method for redistricting, decomposing a geographical area into subareas, called districts, so that the populations of the districts are as close as possible and the districts are compact and contiguous. Each district is the…
In this paper, we develop a novel weighted Laplacian method, which is partially inspired by the theory of graph Laplacian, to study recent popular graph problems, such as multilevel graph partitioning and balanced minimum cut problem, in a…
A connected and nonempty graph A is defined as generalized t-edge distance-balanced, while for each edge f={\alpha}\{beta} the number of edges nearer to {\alpha} than \{beta} are equal to t-times of edges nearer to \{beta} than to {\alpha},…
Converting quad meshes to smooth manifolds, guided subdivision offers a way to combine the good highlight line distributions of recent G-spline constructions with the refinability of subdivision surfaces. Specifically, we present a C2…
We organize a table of regular graphs with minimal diameters and minimal mean path lengths, large bisection widths and high degrees of symmetries, obtained by enumerations on supercomputers. These optimal graphs, many of which are newly…
This short note presents some variant schemes of boundary variation diminishing (BVD) algorithm in one dimension with the results of numerical tests for linear advection equation to facilitate practical use. In spite of being presented in…
Topological data analysis leverages topological features to analyze datasets, with applications in diverse fields like medical sciences and biology. A key tool of this theory is the persistence diagram, which encodes topological information…