Related papers: On Stochastic Comparison Between Two Coherent Syst…
In this short note, we try to provide the reader with a brief pedagogical account of some similarities and differences between stochastic and deterministic processes. A short presentation of some basic notions related to the mathematical…
In this letter, we show that coherent structures are related to folds of horseshoes which are present in chaotic systems. We develop techniques that allow us to construct coherent structures by manipulating folds in three prototypical…
This article shows how to specify and construct a discrete, stochastic, continuous-time model specifically for ecological systems. The model is more broad than typical chemical kinetics models in two ways. First, using time-dependent hazard…
In this paper I will review some basic aspects of the mechanism of stochastic resonance. Stochastic resonance was first introduced as a possible mechanism to explain long term climatic variation. Since then, there have been many…
We study a system whose dynamics are governed by predictions of its future states. A general formalism and concrete examples are presented. We find that the dynamical characteristics depend on how to shape the predictions as well as on how…
We show that scaling arguments are very useful to analyze the dynamics of periodically modulated noisy systems. Information about the behavior of the relevant quantities, such as the signal-to-noise ratio, upon variations of the noise…
In the literature, there are various notions of stochasticity which measure how well an algorithmically random set satisfies the law of large numbers. Such notions can be categorized by disorder and adaptability: adaptive strategies may use…
Algorithms of control of differential equations solutions are under investigation in the article. Idealized and real modifications of the algorithms are distinguished. An equation, which can be the base equation for investigation of the…
Extending well-structured transition systems to incorporate a probabilistic scheduling rule, we define a new class of stochastic well-structured transition systems that includes population protocols, chemical reaction networks, and many…
Effect of noise in inducing order on various chaotically evolving systems is reviewed, with special emphasis on systems consisting of coupled chaotic elements. In many situations it is observed that the uncoupled elements when driven by…
We consider the classical response in a chaotic system. In contrast to behavior in integrable or almost integrable systems, the nonlinear classical response in a chaotic system vanishes at long times. The response also reveals certain…
Shared Memory is a mechanism that allows several processes to communicate with each other by accessing -- writing or reading -- a set of variables that they have in common. A Consistency Model defines how each process observes the state of…
This paper proposes a variance-based measure of importance for coherent systems with dependent and heterogeneous components. The particular cases of independent components and homogeneous components are also considered. We model the…
Our topic is performance differences between using random and chaos for particle swarm optimization (PSO). We take random sequences with different probability distributions and compare them to chaotic sequences with different but also with…
Time delays are a common perturbation in systems with many states, such as networked, distributed, or decentralized systems. Current methods analyzing the stability of large systems with time delay typically produce very conservative…
Chain-of-Thought (CoT) and Looped Transformers have been shown to empirically improve performance on reasoning tasks and to theoretically enhance expressivity by recursively increasing the number of computational steps. However, their…
A system is considered, which is subject to external and possibly fatal shocks, with dependence between the fatality of a shock and the system age. Apart from these shocks, the system suffers from competing soft and sudden failures, where…
Items in many datasets can be arranged to a natural order. Such orders are useful since they can provide new knowledge about the data and may ease further data exploration and visualization. Our goal in this paper is to define a…
We investigate the dynamical systems modeling conflict processes between a pair of opponents. We assume that opponents are given on a common space by distributions (probability measures) having the similar or self-similar structure. Our…
In this paper an efficient model based diagnostic process is described for systems whose components possess a causal relation between their inputs and their outputs. In this diagnostic process, firstly, a set of focuses on likely broken…