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Geometric graphs are a special kind of graph with geometric features, which are vital to model many scientific problems. Unlike generic graphs, geometric graphs often exhibit physical symmetries of translations, rotations, and reflections,…
This book collects the lectures about graph theory and its applications which were given to students of mathematical departments of Moscow State University and Peking University. Graph theory is a very wide field with a lot of applications…
The properties of electrons in matter are of fundamental importance. They give rise to virtually all molecular and material properties and determine the physics at play in objects ranging from semiconductor devices to the interior of giant…
We present a detailed description of the generalized geometric cluster algorithm for the efficient simulation of continuum fluids. The connection with well-known cluster algorithms for lattice spin models is discussed, and an explicit full…
Active matter physics and swarm robotics have provided powerful tools for the study and control of ensembles driven by internal sources. At the macroscale, controlling swarms typically utilizes significant memory, processing power, and…
Similarities between models of fragmenting nuclei and disordered systems in condensed matter suggest corresponding methods. Several theoretical models of fragmentation investigated in this fashion show marked differences, indicating…
Multiscale and multiphysics applications are now commonplace, and many researchers focus on combining existing models to construct combined multiscale models. Here we present a concise review of multiscale applications and their source…
We solve Poisson's equation using new multigrid algorithms that converge rapidly. The novel feature of the 2D and 3D algorithms are the use of extra diagonal grids in the multigrid hierarchy for a much richer and effective communication…
We review recent progress and a number of future directions for applications of effective field theory methods to condensed matter systems broadly defined. Our emphasis is on areas that have allowed a fertile exchange of ideas between high…
In many high-impact applications, it is important to ensure the quality of output of a machine learning algorithm as well as its reliability in comparison with the complexity of the algorithm used. In this paper, we have initiated a…
One of the hot topics in machine learning is the field of GNN. The complexity of graph data has imposed significant challenges on existing machine learning algorithms. Recently, many studies on extending deep learning approaches for graph…
Gravitational lensing allows us to probe the structure of matter on a broad range of astronomical scales, and as light from a distant source traverses an intervening galaxy, compact matter such as planets, stars, and black holes act as…
Innovative solutions and developments are being inspected to tackle rising electrical power demand to be supplied by clean forms of energy. The integration of renewable energy generations, varying nature loads, importance of active role of…
Matrices are very popular and widely used in mathematics and other fields of science. Every mathematician has known the properties of finite-sized matrices since the time of study. In this paper, we consider the basic theory of infnite…
Graphs naturally appear in several real-world contexts including social networks, the web network, and telecommunication networks. While the analysis and the understanding of graph structures have been a central area of study in algorithm…
In this paper we provide an overview of a new framework for robot perception, real-world modelling, and navigation that uses a stochastic tesselated representation of spatial information called the Occupancy Grid. The Occupancy Grid is a…
Smart grids (SGs) enable integration of diverse power sources including renewable energy resources. They can contribute to the reduction of harmful gas emission, and support two-way information flow to enhance energy efficiency, along with…
Hyperdimensional (HD) computing is a set of neurally inspired methods for obtaining high-dimensional, low-precision, distributed representations of data. These representations can be combined with simple, neurally plausible algorithms to…
Energy and pollution are urging problems of the 21th century. By gradually changing the actual power grid system, smart grid may evolve into different systems by means of size, elements and strategies, but its fundamental requirements and…
The simulation of the physical movement of multi-body systems at an atomistic level, with forces calculated from a quantum mechanical description of the electrons, motivates a graph partitioning problem studied in this article. Several…