Related papers: Causality of singular linear discrete time systems

We discuss how to characterize the behavior of a chaotic dynamical system depending on a parameter that varies periodically in time. In particular, we study the predictability time, the correlations and the mean responses, by defining a…

This paper investigates the stability properties of a nonlinear fractional differential equation with two discrete delays and a delay-dependent coefficient. Such equations arise in various biological and control systems where temporal…

Linear structural equation models represent direct causal effects as directed edges and confounding factors as bidirected edges. An open problem is to identify the causal parameters from correlations between the nodes. We investigate…

In order to analyze the effect of chaos or order on the rate of decoherence in a subsystem we aim to distinguish effects of the two types of dynamics from those depending on the choice of the wave packet. To isolate the former we introduce…

We consider the solution of large linear systems of equations that arise when two-dimensional singularly perturbed reaction-diffusion equations are discretized. Standard methods for these problems, such as central finite differences, lead…

Change point detection in time series aims to identify moments when the probability distribution of time series changes. It is widely applied in many areas, such as human activity sensing and medical science. In the context of multivariate…

We discuss the emergence of time dilation as a normal feature expected of any system where a central processor may have to wait one or more clock cycles before concluding a local calculation. We show how the process of causal implication in…

We consider a discrete time dynamic system described by a difference equation with periodic coefficients and with additive stochastic noise. We investigate the possibility of the periodicity for the solution. In particular, we found…

We present sufficient conditions under which a given linear nonautonomous system and its nonlinear perturbation are topologically conjugated. Our conditions are of a very general form and provided that the nonlinear perturbations are…

The possibility of non-causal signal propagation is examined for various theories of dense matter. This investigation requires a discussion of definitions of causality, together with interpretations of spacetime position. Specific examples…

A technique is introduced which allows to generate -- starting from any solvable discrete-time dynamical system involving N time-dependent variables -- new, generally nonlinear, generations of discrete-time dynamical systems, also involving…

This paper describes the dynamics of a quantum two-level system (qubit) under the influence of an environment modeled by an ensemble of random matrices. In distinction to earlier work, we consider here separable couplings and focus on a…

Motivated by a real problem in steel production, we introduce and analyze a general class of singularly perturbed linear hybrid systems with both switches and impulses, in which the slow or fast nature of the variables can be…

In this paper we investigate the power instability properties and give necessary and sufficient conditions for the concepts of uniform power instability, power instability and strong power instability for linear discrete-time system…

The idea that chaos could be a useful tool for analyze nonlinear systems considered in this paper and for the first time the two time scale property of singularly perturbed systems is analyzed on chaotic attractor. The general idea…

Formation of stationary localized states in one-dimensional chain as well as in a Cayley tree due to a linear impurity and a nonlinear impurity is studied. Furthermore, a one-dimensional chain with linear and nonlinear site energies at the…

For linear control systems in discrete time controllability properties are characterized. In particular, a unique control set with nonvoid interior exists and it is bounded in the hyperbolic case. Then a formula for the invariance pressure…

We study a specific type of SCM, called a Dynamic Structural Causal Model (DSCM), whose endogenous variables represent functions of time, which is possibly cyclic and allows for latent confounding. As a motivating use-case, we show that…

A typical problem in causal modeling is the instability of model structure learning, i.e., small changes in finite data can result in completely different optimal models. The present work introduces a novel causal modeling algorithm for…

We consider causal models with two observed variables and one latent variables, each variable being discrete, with the goal of characterizing the possible distributions on outcomes that can result from controlling one of the observed…