Related papers: Microlocal analysis and evolution equations
Local Fourier analysis is a useful tool for predicting and analyzing the performance of many efficient algorithms for the solution of discretized PDEs, such as multigrid and domain decomposition methods. The crucial aspect of local Fourier…
In this paper I describe a cellular automaton model of a multi-species ecosystem, suitable for the study of emergent properties of macroevolution. Unlike majority of ecological models, the number of coexisting species is not fixed. Starting…
This paper discusses capabilities that are essential to models applied in policy analysis settings and the limitations of direct applications of off-the-shelf machine learning methodologies to such settings. Traditional econometric…
The growth of evolutionary computing (EC) methods in the exploration of complex potential energy landscapes of atomic and molecular clusters, as well as crystals over the last decade or so is reviewed. The trend of growth indicates that…
Neural integral equations are deep learning models based on the theory of integral equations, where the model consists of an integral operator and the corresponding equation (of the second kind) which is learned through an optimization…
These notes are based on a series of lectures given first at the University of Warwick in spring 2008 and then at the Courant Institute, Imperial College London, and EPFL. It is an attempt to give a reasonably self-contained presentation of…
Based on the methods developed in [Kashiwara-Rouquier], we consider microlocalization of the rational Cherednik algebra of type $\Z/l\Z$. Our goal is to construct the irreducible modules and standard modules of the rational Cherednik…
These are lecture notes for five sessions in the AMSI Winter School on 'Computational Modelling of Heterogeneous Media' held at QUT in July 2019 [https://ws.amsi.org.au/]. Aim: Discuss a mix of new mathematical approaches for multiscale…
These are lecture notes for lectures at the Park City Math Institute, summer 2007. We cover aspects of the dimer model on planar, periodic bipartite graphs, including local statistics, limit shapes and fluctuations.
Transport-dominated partial differential equation models have been used extensively over the past two decades to describe various collective migration phenomena in cell biology and ecology. To understand the behaviour of these models (and…
Recently, it has been proven that evolutionary algorithms produce good results for a wide range of combinatorial optimization problems. Some of the considered problems are tackled by evolutionary algorithms that use a representation which…
In this paper we consider traces at initial times for functions with mixed time-space smoothness. Such results are often needed in the theory of evolution equations. Our result extends and unifies many previous results. Our main improvement…
Semilinear stochastic evolution equations with multiplicative Poisson noise and monotone nonlinear drift are considered. We do not impose coercivity conditions on coefficients. A novel method of proof for establishing existence and…
This paper is based on talks delivered in summer 2008 at the Conference on Motives, QFT and Pseudodifferential Operators in Boston, and at the Trimester programme Geometry and Physics, Hausdorff Institute for Mathematics in Bonn The paper…
There is an abundance of empirical evidence in the numerical relativity literature that the form in which the Einstein evolution equations are written plays a significant role in the lifetime of numerical simulations. This paper attempts to…
Known as two cornerstones of problem solving by search, exploitation and exploration are extensively discussed for implementation and application of evolutionary algorithms (EAs). However, only a few researches focus on evaluation and…
In this note we develop a framework which allows to prove an abstract existence result for non-linear evolution equations involving so-called non-induced operators, i.e., operators which are not prescribed by a time-dependent family of…
Motivation: Cryo-Electron Tomography (cryo-ET) visualizes structure and spatial organization of macromolecules and their interactions with other subcellular components inside single cells in the close-to-native state at sub-molecular…
Multi-modal optimization involves identifying multiple global and local optima of a function, offering valuable insights into diverse optimal solutions within the search space. Evolutionary algorithms (EAs) excel at finding multiple…
In this paper convolution type integral equations in the conservative case are studied. The conservative case of convolution type of equations relates to the case of non normal type of equations and is that of the corresponding symbols…