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We present a new multigrid method called neural multigrid which is based on joining multigrid ideas with concepts from neural nets. The main idea is to use the Greenbaum criterion as a cost functional for the neural net. The algorithm is…
The purpose of this paper is to analyze an efficient method for the solution of the nonlinear system resulting from the discretization of the elliptic Monge-Amp\`ere equation by a $C^0$ interior penalty method with Lagrange finite elements.…
Common techniques for the spatial discretisation of PDEs on a macroscale grid include finite difference, finite elements and finite volume methods. Such methods typically impose assumed microscale structures on the subgrid fields, so…
We apply the monotone domain decomposition iterative method to a nonlinear integro-differential equation of Volterra type and prove its convergence. To do this, by adding a term in both sides of the original equation we make a linear…
Depth estimation from monocular images is a challenging problem in computer vision. In this paper, we tackle this problem using a novel network architecture using multi scale feature fusion. Our network uses two different blocks, first…
Discretizing continuous-time linear systems typically requires numerical integration. This document presents a convenient method for discretizing the dynamics, input, and process noise state-space matrices of a continuous-time linear system…
This article is talking about the study constructive method of structural identification systems with chaotic dynamics. It is shown that the reconstructed attractors are a source of information not only about the dynamics but also on the…
Complex networks have been characterised by their specific connectivity patterns (network motifs), but their building blocks can also be identified and described by node-motifs---a combination of local network features. One technique to…
The need to smoothly cover a computational domain of interest generically requires the adoption of several grids. To solve the problem of interest under this grid-structure one must ensure the suitable transfer of information among the…
Edge-weighted graphs play an important role in the theory of Robinsonian matrices and similarity theory, particularly via the concept of level graphs, that is, graphs obtained from an edge-weighted graph by removing all sufficiently light…
We propose a primal-dual backward reflected forward splitting method for solving structured primal-dual monotone inclusion in real Hilbert space. The algorithm allows to use the inexact computations of the Lipschitzian and cocoercive…
After generalizing the concept of clusters to incorporate clusters that are linked to other clusters through some relatively narrow bridges, an approach for detecting patches of separation between these clusters is developed based on an…
In this paper, in addition to the earlier introduced involutive divisions, we consider a new class of divisions induced by admissible monomial orderings. We prove that these divisions are noetherian and constructive. Thereby each of them…
Finite difference based micromagnetic simulations are a powerful tool for the computational investigation of magnetic structures. In this paper, we demonstrate how the discretization of continuous micromagnetic equations introduces a…
A monotone self-mapping of the nonnegative orthant induces a monotone discrete-time dynamical system which evolves on the same orthant. If with respect to this system the origin is attractive then there must exists points whose image under…
A collision-based hybrid method for the discrete ordinates approximation of the multigroup neutron transport equation is developed for two-dimensional time-dependent problems. At each time step, this algorithm splits the neutron transport…
In this work, we propose a new algorithm for finding a zero in the sum of two monotone operators where one is assumed to be single-valued and Lipschitz continuous. This algorithm naturally arises from a non-standard discretization of a…
The graph identification problem consists of discovering the interactions among nodes in a network given their state/feature trajectories. This problem is challenging because the behavior of a node is coupled to all the other nodes by the…
We study the equilibrium phase diagram of binary mixtures of hard spheres as well as of parallel hard cubes. A superior cluster algorithm allows us to establish and to access the demixed phase for both systems and to investigate the subtle…
We undertake a detailed numerical study of the twin phenomena of stochastic and vibrational resonance in a discrete model system in the presence of bichromatic input signal. A two parameter cubic map is used as the model that combines the…