Related papers: A note on the causality of singular linear discret…
The general aim of this paper is to supply a method to decide whether a discrete system decoheres or not, and under what conditions decoherence occurs, with no need of appealing to computer simulations to obtain the time evolution of the…
If a state is passive for uniformly accelerated observers in n-dimensional anti-de Sitter space-time (i.e. cannot be used by them to operate a perpetuum mobile), they will (a) register a universal value of the Unruh temperature, (b)…
In the present paper we consider controllability and observability of second order linear time invariant systems in matrix form. Without reducing into first order systems we show how the classical conditions for first order linear systems…
Inferring nonlinear and asymmetric causal relationships between multivariate longitudinal data is a challenging task with wide-ranging application areas including clinical medicine, mathematical biology, economics and environmental…
The causality properties of linear time-varing systems under constant time lags are investigated based on the definition and use of the definitions of appropriate Hankel and Toeplitz causal and anticausal operators.
Detecting and localizing change points in sequential data is of interest in many areas of application. Various notions of change points have been proposed, such as changes in mean, variance, or the linear regression coefficient. In this…
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…
We demonstrate the phenomenon of stochastic resonance (SR) for discrete-time dynamical systems. We investigate various systems that are not necessarily bistable, but do have two well defined states, switching between which is aided by…
Linear structural causal models (SCMs) -- in which each observed variable is generated by a subset of the other observed variables as well as a subset of the exogenous sources -- are pervasive in causal inference and casual discovery.…
We investigate discrete-time conewise linear systems (CLS) for which all the solutions exhibit a finite number of switches. By switches, we mean transitions of a solution from one cone to another. Our interest in this class of CLS comes…
Causal discovery, i.e., inferring underlying causal relationships from observational data, is highly challenging for AI systems. In a time series modeling context, traditional causal discovery methods mainly consider constrained scenarios…
In distributed systems where strong consistency is costly when not impossible, causal consistency provides a valuable abstraction to represent program executions as partial orders. In addition to the sequential program order of each…
It is shown that for quantum ensembles consisting of equal particles, the collective micro-causality does not contradict the quantum theory. The amplitudes of the states of such an ensemble can be divided into small portions, for each of…
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…
This paper introduces a linear state-space model with time-varying dynamics. The time dependency is obtained by forming the state dynamics matrix as a time-varying linear combination of a set of matrices. The time dependency of the weights…
The proposed theory of causally structured discrete fields studies integer values on directed edges of a self-similar graph with a propagation rule, which we define as a set of valid combinations of integer values and edge directions around…
Exogenous heterogeneity, for example, in the form of instrumental variables can help us learn a system's underlying causal structure and predict the outcome of unseen intervention experiments. In this paper, we consider linear models in…
This paper presents a new systematic framework for nonlinear singularly perturbed systems in which state-dependent perturbation functions are used instead of constant perturbation coefficients. Under this framework, general results are…
We study the singularity probability of n*n random matrices with i.i.d. entries from highly biased discrete distributions. We obtain sharp non-asymptotic bounds for this probability and derive estimates on the least singular values. Our…
In this paper we provide a notion of causality for the violation of general Linear Temporal Logic (LTL) properties. The current work is a natural extension of the previously proposed approach handling causality in the context of…