Related papers: Discrete spacetime and its applications
Modeling the orbital dynamics of objects in galactic disks is crucial to understanding the stability and evolution of disk galaxies. While studies of galactic orbits are largely dominated by $N$-body simulations, perturbative analytical…
The discrete symmetries of the Dirac field on the de Sitter manifold are studied taking into account that this has two portions that can play the role of physical space-times, namely the expanding and a collapsing universes. The proper…
Pinning and depinning of wave fronts are ubiquitous features of spatially discrete systems describing a host of phenomena in physics, biology, etc. A large class of discrete systems is described by overdamped chains of nonlinear oscillators…
The possibility of operating in remote environments using teleoperation systems has been considered widely in the control literature. This paper presents a review on the discrete-time teleoperation systems, including issues such as…
Much is known about asymptotic expansions for asymptotically normal distributions if these distributions are either absolutely continuous or pure lattice distributions. In this paper we begin an investigation of the discrete but non-lattice…
Inspired by the discrete evolution implied by the recent work on loop quantum cosmology, we obtain a discrete time description of usual quantum mechanics viewing it as a constrained system. This description, obtained without any…
A dynamical system with discrete time is studied by means of algebraic geometry. The system admits a reduction that is interpreted as a classical field theory in 2+1-dimensional wholly discrete space-time. The integrals of motion of a…
We present a simple discrete model for the non-linear spatial interaction of different kinds of ``subpopulations'' composed of identical moving entities like particles, bacteria, individuals, etc. The model allows to mimic a variety of…
We analyze the asymptotic behavior of discrete-time, Markovian quantum systems with respect to a subspace of interest. Global asymptotic stability of subspaces is relevant to quantum information processing, in particular for initializing…
The paper studies the asymptotic behaviour of weighted functionals of long-range dependent data over increasing observation windows. Various important statistics, including sample means, high order moments, occupation measures can be given…
We study general models of random fields associated with non-local equations in time and space. We discuss the properties of the corresponding angular power spectrum and find asymptotic results in terms of random time changes.
Deep neural network models have become ubiquitous in recent years, and have been applied to nearly all areas of science, engineering, and industry. These models are particularly useful for data that have strong dependencies in space (e.g.,…
When intelligent spacecraft or space robots perform tasks in a complex environment, the controllable variables are usually not directly available and have to be inferred from high-dimensional observable variables, such as outputs of neural…
Dynamical systems theory is especially well-suited for determining the possible asymptotic states (at both early and late times) of cosmological models, particularly when the governing equations are a finite system of autonomous ordinary…
Sliding mode control of a launch vehicle during its atmospheric flight phase is studied in the presence of unmatched disturbances. Linear time-varying dynamics of the aerospace vehicle is converted into a systematic formula and then dynamic…
Positive systems play an important role in systems and control theory and have found many applications in multi-agent systems, neural networks, systems biology, and more. Positive systems map the nonnegative orthant to itself (and also the…
In this work, resolutions will be given for commonly stated problems associated with a model that assumes that space and time are discretized (i.e., atomized). This model is in contrast to the continuous space-time model that is used in all…
Diffusion models have been widely used in time series and spatio-temporal data, enhancing generative, inferential, and downstream capabilities. These models are applied across diverse fields such as healthcare, recommendation, climate,…
In this article we describe applications of Discrete Differential Forms in computational GR. In particular we consider the initial value problem in vacuum space-times that are spherically symmetric. The motivation to investigate this method…
We derive rigorous results describing the asymptotic dynamics of a discrete time model of spiking neurons introduced in \cite{BMS}. Using symbolic dynamic techniques we show how the dynamics of membrane potential has a one to one…