Related papers: Microlocal analysis and evolution equations
Eigenvalue analysis is a well-established tool for stability analysis of dynamical systems. However, there are situations where eigenvalues miss some important features of physical models. For example, in models of incompressible fluid…
Let $\mathcal{M}$ be a holonomic algebraic $\mathcal{D}$-module on the affine line. Its exponential factors are Puiseux germs describing the growth of holomorphic solutions to $\mathcal{M}$ at irregular points. The stationary phase formula…
This article proposes a framework for the study of periodic maps $T$ from a (typically finite) set $X$ to itself when the set $X$ is equipped with one or more real- or complex-valued functions. The main idea, inspired by the time-evolution…
Deep learning has emerged as a technique of choice for rapid feature extraction across imaging disciplines, allowing rapid conversion of the data streams to spatial or spatiotemporal arrays of features of interest. However, applications of…
We develop mathematical framework and computational tools for calculating frequency responses of linear time-invariant PDEs in which an independent spatial variable belongs to a compact interval. In conventional studies this computation is…
In this paper, the issue of adapting probabilities for Evolutionary Algorithm (EA) search operators is revisited. A framework is devised for distinguishing between measurements of performance and the interpretation of those measurements for…
We consider stochastic equations for the class of formal mappings. Existence and uniqueness of solution, as well as evolution property are proved.
This note provides a detailed algorithm to the application of local (perturbation) analysis of differential equations which is normally taught at graduate math courses. Exercise books often present more abstract and simplified versions of…
We study several approaches for constructing a minimal model of Universe evolution by matching different stages of scale factor laws. We discuss the continuity in the transitions among the stages and the time variables involved. We develop…
We present a new method to solve in a semianalytical way the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi evolution equations at NLO order in the x-space. The method allows to construct an evolution operator expressed in form of a rapidly…
1. Theoretical models pertaining to feedbacks between ecological and evolutionary processes are prevalent in multiple biological fields. An integrative overview is currently lacking, due to little crosstalk between the fields and the use of…
The article explores an encoding and structural information processing approach using sparse bit vectors and fixed-length linear vectors. The following are presented: a discrete method of speculative stochastic dimensionality reduction of…
Equations governing physico-chemical processes are usually known at microscopic spatial scales, yet one suspects that there exist equations, e.g. in the form of Partial Differential Equations (PDEs), that can explain the system evolution at…
Multi-agent geographical models integrate very large numbers of spatial interactions. In order to validate those models large amount of computing is necessary for their simulation and calibration. Here a new data processing chain including…
We prove existence, uniqueness and several qualitative properties for evolution equations that combine local and nonlocal diffusion operators acting in different subdomains and coupled in such a way that the resulting evolution equation is…
Recently Rubinfeld et al. (ICS 2011, pp. 223--238) proposed a new model of sublinear algorithms called \emph{local computation algorithms}. In this model, a computation problem $F$ may have more than one legal solution and each of them…
The implementation of deep learning algorithms has brought new perspectives to plankton ecology. Emerging as an alternative approach to established methods, deep learning offers objective schemes to investigate plankton organisms in diverse…
We study the continuity in weighted Fourier Lebesgue spaces for a class of pseudodifferential operators, whose symbol has finite Fourier Lebesgue regularity with respect to $x$ and satisfies a quasi-homogeneous decay of derivatives with…
Local polynomial regression of order one or higher often performs poorly in areas with sparse data. In contrast, local constant regression tends to be more robust in these regions, although it is generally the least accurate approach,…
Some evolution equations with rough time-dependent potential are studied in the case of one-dimensional torus. We show that the solution has higher regularity for the generic values of the coupling constant. The asymptotics for large time…