相关论文: Generalized Singular Spectrum Time Series Analysis

We study the third order in time linear dissipative wave equation known as the Standard Linear Viscoelastic Model, that appears also as the linearization of the so-called Moore-Gibson-Thompson equation in Nonlinear Acoustics. We complete…

Machine learning for differential equations paves the way for computationally efficient alternatives to numerical solvers, with potentially broad impacts in science and engineering. Though current algorithms typically require simulated…

In this paper, we introduce the \textbf{G}eneralized \textbf{L}inear \textbf{S}pectral \textbf{S}tatistics (GLSS) of a high-dimensional sample covariance matrix $\bm{S}_n$, denoted as $\operatorname{tr}f(\bm{S}_n)\bm{B}_n$, which…

In this note, analysis of time delay systems using Lambert W function approach is reassessed. A common canonical form of time delay systems is defined. We extended the recent results of [6] for second order into nth order system. The…

A common problem in astronomy is the determination of the time shift between two otherwise identical time series of measured flux from a variable source, in short the determination of a time lag. Two examples of where this problem occurs…

Differential equations where the graph of some derivative of a function is composed of a finite number of similarity transformations of the graph of the function itself are defined. We call these self-similar differential equations (SSDEs)…

Sample average approximation (SAA) is a technique for obtaining approximate solutions to stochastic programs that uses the average from a random sample to approximate the expected value that is being optimized. Since the outcome from…

We describe a method of analytic evolution of distribution amplitudes (DA) that have singularities, such as non-zero values at the end-points of the support region, jumps at some points inside the support region and cusps. We illustrate the…

We prove a short general theorem which immediately implies some classical results of Hasse, Guillera and Sondow, Paolo Amore, and also Alzer and Richards. At the end we obtain a new representation for the Euler constant gamma. The theorem…

A class of one-dimensional Fokker-Plank equations having a common stationary solution, which is a power function of the state of the process, was found. We prove that these equations also have generalized self-similar solutions which…

Simulated Annealing (SA) is a widely used stochastic optimization algorithm, yet much of its theoretical understanding is limited to asymptotic convergence guarantees or general spectral bounds. In this paper, we develop a finite-time…

Test-time adaption (TTA) has witnessed important progress in recent years, the prevailing methods typically first encode the image and the text and design strategies to model the association between them. Meanwhile, the image encoder is…

Generalized Linear Models (GLMs) and Single Index Models (SIMs) provide powerful generalizations of linear regression, where the target variable is assumed to be a (possibly unknown) 1-dimensional function of a linear predictor. In general,…

Static alias analysis of different type of programming languages has been drawing researcher attention. However most of the results of existing techniques for alias analysis are not precise enough compared to needs of modern compilers.…

This article is devoted to the detection of parameters in anomalous diffusion from a single passive measurement. More precisely, we consider the simultaneous identification of coefficients as well as a time-dependent source term appearing…

The tensorial principal component analysis is a generalization of ordinary principal component analysis, focusing on data which are suitably described by tensors rather than matrices. This paper aims at giving the nonperturbative…

This paper develops an explicit spectral representation for solutions of a one-dimensional linear wave equation with a constant time delay. The model is considered on a bounded interval with non-homogeneous Dirichlet boundary data and a…

Formulas for the solutions of initial value problems for ordinary differential equations with singular $\delta^{(n)}$-like driving terms are derived in the framework of an algebra of generalized functions (of Colombeau type) over a field of…

The study of correlated time-series is ubiquitous in statistical analysis, and the matrix decomposition of the cross-correlations between time series is a universal tool to extract the principal patterns of behavior in a wide range of…

Time-domain wave scattering in an unbounded two-dimensional acoustic medium by sound-hard scatterers is considered. Two canonical geometries, namely a split-ring resonator (SRR) and an array of cylinders, are used to highlight the theory,…