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For cell-division processes in a window, Cowan introduced four selection rules and two division rules each of which stands for one cell-division model. One of these is the area-weighted in-cell model. In this model, each cell is selected…
Short term load forecasting has an essential medium for the reliable, economical and efficient operation of the power system. Most of the existing forecasting approaches utilize fixed statistical models with large historical data for…
We present a time-dependent extension of logarithmic perturbation theory for nonrelativistic quantum dynamics governed by the Schr\"odinger equation, in which the logarithm of the wave function is expanded in powers of a coupling constant.…
This paper revisits a recently developed methodology based on the matrix Lambert W function for the stability analysis of linear time invariant, time delay systems. By studying a particular, yet common, second order system, we show that in…
Deep-learning models have enabled performance leaps in analysis of high-dimensional functional MRI (fMRI) data. Yet, many previous methods are suboptimally sensitive for contextual representations across diverse time scales. Here, we…
A stochastic algorithm for simulation of fluctuation-induced kinetics of H$_2$ formation on grain surfaces is suggested as a generalization of the technique developed in our recent studies where this method was developed to describe the…
Multiscale stochastic dynamical systems have been widely adopted to a variety of scientific and engineering problems due to their capability of depicting complex phenomena in many real world applications. This work is devoted to…
A new algorithm named EXPected Similarity Estimation (EXPoSE) was recently proposed to solve the problem of large-scale anomaly detection. It is a non-parametric and distribution free kernel method based on the Hilbert space embedding of…
We prove existence, regularity in H\"older classes and estimates from above and below of the fundamental solution of the stochastic Langevin equation. This degenerate SPDE satisfies the weak H\"ormander condition. We use a Wentzell's…
In a previous paper [1] it was discussed the viability of functional analysis using as a basis a couple of generic functions, and hence vectorial decomposition. Here we complete the paradigm exploiting one of the analysis methodologies…
Observations from dynamical systems often exhibit irregularities, such as censoring, where values are recorded only if they fall within a certain range. Censoring is ubiquitous in practice, due to saturating sensors, limit-of-detection…
We present a dynamical and spectral study of Ostrowski's map based on the use of transfer operators. The Ostroswki dynamical system is obtained as a skew-product of the Gauss map (it has the Gauss map as a base and interval fibers) and…
By investigating the crystalline structure of ground-state orthorhombic SrRuO$_3$, we present a benchmark study of some of the most popular density functional theory (DFT) approaches from the local density approximation (LDA),…
Stochastic filtering refers to estimating the probability distribution of the latent stochastic process conditioned on the observed measurements in time. In this paper, we introduce a new class of convergent filters that represent the…
Transformer's recent integration into style transfer leverages its proficiency in establishing long-range dependencies, albeit at the expense of attenuated local modeling. This paper introduces Strips Window Attention Transformer (S2WAT), a…
We present a linearized shear-transformation-zone (STZ) theory of glassy dynamics in which the internal STZ transition rates are characterized by a broad distribution of activation barriers. For slowly aging or fully aged systems, the main…
Large, non-Gaussian spatial datasets pose a considerable modeling challenge as the dependence structure implied by the model needs to be captured at different scales, while retaining feasible inference. Skew-normal and skew-t distributions…
We develop and analyze stochastic approximation algorithms for solving nested compositional bi-level optimization problems. These problems involve a nested composition of $T$ potentially non-convex smooth functions in the upper-level, and a…
Stochastic Thermodynamics (ST) extends the notions of classical thermodynamics to trajectories taken from a nonequilibrium ensemble. This extension yields a simple approach to fluctuation relations in small systems. Multiple time- and…
A fully discrete implicit scheme is proposed for the Swift-Hohenberg model, combining the third-order backward differentiation formula (BDF3) for the time discretization and the second-order finite difference scheme for the space…