Related papers: Nonlocal-in-time dynamics and crossover of diffusi…
We present an approach to handle Dirichlet type nonlocal boundary conditions for nonlocal diffusion models with a finite range of nonlocal interactions. Our approach utilizes a linear extrapolation of prescribed boundary data. A novelty is,…
Marginal structural models are a popular method for estimating causal effects in the presence of time-varying exposures. In spite of their popularity, no scalable non-parametric estimator exist for marginal structural models with…
Nonlocality is important in realistic mathematical models of physical and biological systems when local models fail to capture the essential dynamics and interactions that occur over a range of distances. This review illustrates different…
Inspired by random walk on graphs, diffusion map (DM) is a class of unsupervised machine learning that offers automatic identification of low-dimensional data structure hidden in a high-dimensional dataset. In recent years, among its many…
In this paper, a unified nonlocal rational continuum enrichment technique is presented for improving the dispersive characteristics of some well known classical continuum equations on the basis of atomistic dispersion relations. This type…
We investigate the connections between microscopic chaos, defined on a dynamical level and arising from collisions between molecules, and diffusion, characterized by a mean square displacement proportional to the time. We use a number of…
In this paper, we develop and analyze a stochastic algorithm for solving space-time fractional diffusion models, which are widely used to describe anomalous diffusion dynamics. These models pose substantial numerical challenges due to the…
We develop a transfer operator-based method for the detection of coherent structures and their associated lifespans. Characterising the lifespan of coherent structures allows us to identify dynamically meaningful time windows, which may be…
Diffusion models have shown remarkable performance on many generative tasks. Despite recent success, most diffusion models are restricted in that they only allow linear transformation of the data distribution. In contrast, broader family of…
Systems describing the long-range interaction between individuals have attracted a lot of attention in the last years, in particular in relation with living systems. These systems are quadratic, written under the form of transport equations…
In this paper the generalisation of previous author's formulation of fractional continuum mechanics to the case of anisotropic non-locality is presented. The considerations include the review of competitive formulations available in…
This paper presents a shape-theoretic framework for dynamical analysis of nonlinear dynamical systems which appear frequently in several video-based inference tasks. Traditional approaches to dynamical modeling have included linear and…
This article addresses a modification of local time for stochastic processes, to be referred to as `natural local time'. It is prompted by theoretical developments arising in mathematical treatments of recent experiments and observations of…
Complex systems are embedded in our everyday experience. Stochastic modelling enables us to understand and predict the behaviour of such systems, cementing its utility across the quantitative sciences. Accurate models of highly…
We investigate the ensemble and time averaged mean squared displacements for particle diffusion in a simple model for disordered media by assuming that the local diffusivity is both fluctuating in time and has a deterministic average growth…
Time non-locality, or memory, is a non-equilibrium property shared by all physical systems. Here, we show that memory is sufficient to induce a phase of spatial long-range order (LRO) even if the system's primary dynamical variables are…
Non-Markovian local in time master equations give a relatively simple way to describe the dynamics of open quantum systems with memory effects. Despite their simple form, there are still many misunderstandings related to the physical…
We formalize the concept of the modular energy operator within the Page and Wootters timeless framework. As a result, this operator is elevated to the same status as the more studied modular operators of position and momentum. In analogy…
Non-Markovianity may significantly speed up quantum dynamics when the system interacts strongly with an infinite large reservoir, of which the coupling spectrum should be fine-tuned. The potential benefits are evident in many dynamics…
The Dynamic-Mode Decomposition (DMD) is a well established data-driven method of finding temporally evolving linear-mode decompositions of nonlinear time series. Traditionally, this method presumes that all relevant dimensions are sampled…