Related papers: A note on the causality of singular linear discret…

As toy models for space-time on the Planck scale, we consider examples of fermion systems in discrete space-time which are composed of one or two particles defined on two up to nine space-time points. We study the self-organization of the…

We consider linear time invariant systems with exogenous stochastic disturbances, and in feedback with structured stochastic uncertainties. This setting encompasses linear systems with both additive and multiplicative noise. Our concern is…

Two nested classes of discrete-time linear time-invariant systems, which differ by the set of periodic signals that they leave invariant, are studied. The first class preserves the property of periodic monotonicity (period-wise…

There are numerous indications that a discrete substratum underlies continuum spacetime. Any fundamentally discrete approach to quantum gravity must provide some prescription for how continuum properties emerge from the underlying…

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…

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…

We investigate the property for an input-output system to map unimodal inputs to unimodal outputs. As a first step, we analyse this property for linear time-invariant (LTI) systems, static nonlinearities, and interconnections of those. In…

We investigate the effect of a nondegenerate quadratic nonlinear dimeric impurity on the formation of stationary localized states in one dimensional systems. We also consider the formation of stationary localized states in a fully nonlinear…

For given non-consistent initial conditions, we study the stability of a class of generalised linear systems of difference equations with constant coefficients and taking into account that the leading coefficient can be a singular matrix.…

The ideas of spacetime discreteness and causality are important in several of the popular approaches to quantum gravity. But if discreteness is accepted as an initial assumption, conflict with Lorentz invariance can be a consequence. The…

Causal inference in a nonlinear system of multivariate timeseries is instrumental in disentangling the intricate web of relationships among variables, enabling us to make more accurate predictions and gain deeper insights into real-world…

This work addresses the exact characterization of the covariance dynamics related to linear discrete-time systems subject to both additive and parametric stochastic uncertainties that are potentially unbounded. Using this characterization,…

The light-rays and wave fronts in a flat class of Godel-type metric are examined to reveal the causality violating features of the space-time. Non-causal features demonstrated by the development of unusual wave front singularities are shown…

We study a control system resembling a singularly perturbed system whose variables are decomposed into groups that change their values with rates of different orders of magnitude. We establish that the slow trajectories of this system are…

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…

The phase transitions and critical properties of two types of inhomogeneous systems are reviewed. In one case, the local critical behaviour results from the particular shape of the system. Here scale-invariant forms like wedges or cones are…

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…

This paper deals with stability of discrete-time switched linear systems whose all subsystems are unstable. We present sufficient conditions on the subsystems matrices such that a switched system is globally exponentially stable under a set…

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 experimental and theoretical challenges posed by the study of dynamically inhomogeneous systems are outlined in the context of cuprates and other oxides. Considering the pitfalls in the single-component approach to the analysis of…