Related papers: Spatio-Temporal Patterns for a Generalized Innovat…
Spatiotemporal data mining plays an important role in air quality monitoring, crowd flow modeling, and climate forecasting. However, the originally collected spatiotemporal data in real-world scenarios is usually incomplete due to sensor…
Fickian yet non-Gaussian diffusion is a ubiquitous phenomenon observed in various biological and soft matter systems. This anomalous dynamics is typically attributed to heterogeneous environments inducing spatiotemporal variations in the…
The solutions of Hamiltonian equations are known to describe the underlying phase space of a mechanical system. In this article, we propose a novel spatio-temporal model using a strategic modification of the Hamiltonian equations,…
Boundary-induced pattern formation from a spatially uniform state is investigated using one-dimensional reaction-diffusion equations. The temporal oscillation is successively transformed into a spatially periodic pattern, triggered by…
Human mobility is a key factor in spatial disease dynamics and related phenomena. In computational models host mobility is typically modelled by diffusion in space or on metapolulation networks. Alternatively, an effective force of…
This work presents a model reduction approach for problems with coherent structures that propagate over time such as convection-dominated flows and wave-type phenomena. Traditional model reduction methods have difficulties with these…
Abridged abstract: Inert interactions between randomly moving entities and spatial disorder play a crucial role in quantifying the diffusive properties of a system. These interactions affect only the movement of the entities, and examples…
We propose a new method for spatio-temporal forecasting on arbitrarily distributed points. Assuming that the observed system follows an unknown partial differential equation, we derive a continuous-time model for the dynamics of the data…
Modelling the transmission dynamics of an infectious disease is a complex task. Not only it is difficult to accurately model the inherent non-stationarity and heterogeneity of transmission, but it is nearly impossible to describe,…
In this paper we concentrate on an alternative modeling strategy for positive data that exhibit spatial or spatio-temporal dependence. Specifically we propose to consider stochastic processes obtained trough a monotone transformation of…
Reaction-diffusion systems have been proposed as a model for pattern formation and morphogenesis. The Fickian diffusion typically employed in these constructions model the Brownian motion of particles. The biological and chemical elements…
We present a novel Neural Embedding Spatio-Temporal (NEST) point process model for spatio-temporal discrete event data and develop an efficient imitation learning (a type of reinforcement learning) based approach for model fitting. Despite…
We address the problem of predicting spatio-temporal processes with temporal patterns that vary across spatial regions, when data is obtained as a stream. That is, when the training dataset is augmented sequentially. Specifically, we…
Learning the dynamics of spatiotemporal events is a fundamental problem. Neural point processes enhance the expressivity of point process models with deep neural networks. However, most existing methods only consider temporal dynamics…
Originating from the pioneering study of Alan Turing, the bifurcation analysis predicting spatial pattern formation from a spatially uniform state for diffusing morphogens or chemical species that interact through nonlinear reactions is a…
Contemporary epidemiological models often involve spatial variation, providing an avenue to investigate the averaged dynamics of individual movements. In this work, we extend a recent model by Vaziry, Kolokolnikov, and Kevrekidis [Royal…
Understanding the pattern formation in communities has been at the center of attention in various fields. Here we introduce a novel model, called an "information-particle model," which is based on the reaction-diffusion model and the…
Understanding how patterns and travelling waves form in chemical and biological reaction-diffusion models is an area which has been widely researched, yet is still experiencing fast development. Surprisingly enough, we still do not have a…
Based on a recent model of paradigm shifts by Bornholdt et al., we studied mean-field opinion dynamics in an infinite population where an infinite number of ideas compete simultaneously with their values publicly known. We found that a…
A thermodynamic approach to rapid phase transformations within a diffuse interface in a binary system is developed. Assuming an extended set of independent thermodynamic variables formed by the union of the classic set of slow variables and…