Related papers: Causality of singular linear discrete time systems

Causality is a non-obvious concept that is often considered to be related to temporality. In this paper we present a number of past and present approaches to the definition of temporality and causality from philosophical, physical, and…

Causal discovery problems use a set of observations to deduce causality between variables in the real world, typically to answer questions about biological or physical systems. These observations are often recorded at regular time…

Dual structures on causal sets called timelets are introduced, being discrete analogs of global time coordinates. Algebraic and geometrical features of the set of timelets on a causal set are studied. A characterization of timelets in terms…

Can the direction of time and the causal structure of space-time be inferred from operational principles? Causal models and tensor networks offer complementary perspectives: the former encodes cause-effect relations via directed graphs,…

The science of causality explains/determines 'cause-effect' relationship between the entities of a system by providing mathematical tools for the purpose. In spite of all the success and widespread applications of machine-learning (ML)…

We consider a planar dynamical system generated by two stable linear vector fields with distinct fixed points and random switching between them. We characterize singularities of the invariant density in terms of the switching rates and…

The statistics of local measurements of joint quantum systems can sometimes be used to distinguish the spatiotemporal structure in which they were measured. We first prove that every bipartite separable density matrix is temporally…

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 multitime multiple recurrences are common in analysis of algorithms, computational biology, information theory, queueing theory, filters theory, statistical physics etc. The theoretical part about them is little or not known. That is…

We present a sample path dependent measure of causal influence between two time series. The proposed measure is a random variable whose expected sum is the directed information. A realization of the proposed measure may be used to identify…

In the paper we study the subject of positivity of systems with sequential fractional difference. We give formulas for the unique solutions of systems in linear and semi-linear cases. The positivity of systems is considered.

For a class of linear switched systems in continuous time a controllability condition implies that state feedbacks allow to achieve almost sure stabilization with arbitrary exponential decay rates. This is based on the Multiplicative…

The information flow-based quantitative causality analysis has been widely applied in different disciplines because of its origin from first principles, its concise form, and its computational efficiency. So far the algorithm for its…

Many real-world processes are trajectories that may be regarded as continuous-time "functional data". Examples include patients' biomarker concentrations, environmental pollutant levels, and prices of stocks. Corresponding advances in data…

We develop a rigorous theory of external influences on finite discrete dynamical systems, going beyond the perturbation paradigm, in that the external influence need not be a small contribution. Indeed, the covariance condition can be…

We introduce a class of variational principles on measure spaces which are causal in the sense that they generate a relation on pairs of points, giving rise to a distinction between spacelike and timelike separation. General existence…

Multiplicative cascades have been introduced in turbulence to generate random or deterministic fields having intermittent values and long-range power-law correlations. Generally this is done using discrete construction rules leading to…

Dynamical systems are widely used in science and engineering to model systems consisting of several interacting components. Often, they can be given a causal interpretation in the sense that they not only model the evolution of the states…

We address causal reasoning in multivariate time series data generated by stochastic processes. Existing approaches are largely restricted to static settings, ignoring the continuity and emission of variations across time. In contrast, we…

Emergence and causality are two fundamental concepts for understanding complex systems. They are interconnected. On one hand, emergence refers to the phenomenon where macroscopic properties cannot be solely attributed to the cause of…