Educational assessments, specifically standardized and normalized exams, owe most of their foundations to psychological test theory in psychometrics. While the theoretical assumptions of these practices are widespread and relatively uncontroversial i...
In today’s environment of increased uncertainty, firms face new challenges in aligning sustainability orientation (SO) with financial performance (FP). In this non-ergodic world, past trends offer limited insight into the future due to economic...
In this discussion paper we argue that category theory may play a useful role in formulating, and perhaps proving, results in ergodic theory, topogical dynamics and open systems theory (control theory). As examples, we show how to characterize Kolmog...
We propose and discuss two variants of kinetic particle models—cellular automata in 1 + 1 dimensions—that have some appeal due to their simplicity and intriguing properties, which could warrant further research and applications. The first...
The aim of this paper is to examine the role of thermodynamics, and in particular, entropy, for the development of economics within the last 150 years. The use of entropy has not only led to a significant increase in economic knowledge, but also to t...
Closed-form evaluation of key performance indicators (KPIs) of telecommunication networks help perform mathematical analysis under several network configurations. This paper deals with a recent mathematical approach of indefinite quadratic forms to p...
In this paper, we consider general Markov chains with discrete time in an arbitrary measurable (phase) space. Markov chains are given by a classical transition function that generates a pair of conjugate linear Markov operators in a Banach space of m...
Recently, the properties of bouncing oil droplets, also known as “walkers,” have attracted much attention because they are thought to offer a gateway to a better understanding of quantum behavior. They indeed constitute a macroscopic real...
The Thermodynamic Formalism provides a rigorous mathematical framework for studying quantitative and qualitative aspects of dynamical systems. At its core, there is a variational principle that corresponds, in its simplest form, to the Maximum Entrop...
We study Markov operators T, A, and
The recent loophole-free experiments have confirmed the violation of Bell’s inequalities in nature. Yet, in order to insert measured values in Bell’s inequalities, it is unavoidable to make a hypothesis similar to “ergodicity at the hidden variables...
Many natural and engineered dynamical systems, including all living objects, exhibit signatures of what can be called spontaneous dynamical long-range order (DLRO). This order’s omnipresence has long been recognized by the scientific community, as ev...
A new method to describe hyperbolic patterns in two-dimensional flows is proposed. The method is based on the Covariant Lyapunov Vectors (CLVs), which have the properties of being covariant with the dynamics, and thus, being mapped by the tangent lin...
We consider an optimal control problem with the discounted and average payoff. The reward rate (or cost rate) can be unbounded from above and below, and a Markovian switching stochastic differential equation gives the state variable dynamic. Markovia...
Ordinal patterns classifying real vectors according to the order relations between their components are an interesting basic concept for determining the complexity of a measure-preserving dynamical system. In particular, as shown by C. Bandt, G. Kell...
Perturbation bounds are powerful tools for investigating the phenomenon of insensitivity to perturbations, also referred to as stability, for stochastic and deterministic systems. This perspective article presents a focused account of some of the mai...
Polycystic Ovary Syndrome (PCOS) is a widespread hormonal disorder affecting women of reproductive age, often leading to infertility and associated complications. This study presents a comprehensive stochastic mathematical framework to analyze the dy...
Whereas ergodic theories relate to limiting cases of infinite thermal reservoirs and infinitely long times, some ergodicity tendencies may appear also for finite reservoirs and time durations. These tendencies are here explored and found to exist, bu...
Consider a uniquely ergodic
This paper proposes the maximal ratio transmission (MRT) and maximal ratio combining (MRC) protocols for the power beacon (PB) assisted wireless powered sensor networks and analyzes the impact of the imperfect channel state information (CSI) on the p...
We give a concise review of the properties of quantum geometrodynamics in the pilot-wave quantum cosmology, focusing on the issue of its nonlocal character. We also discuss the problem of the origin of quantum probabilities in this theory with a focu...
This paper investigates a stochastic semi-parametric SEIR model characterized by infectivity during the incubation period and influenced by white noise perturbations. First, based on the theory of stochastic persistence, we derive the conditions requ...
Advances in higher-end spectrum utilization has enabled user equipment to dock multiple antenna elements, and hence make use of selectivity via equalization in new generation of mobile networks. The equalization can exploit channel statistics to shap...
Recently, the duality between values (words) and orderings (permutations) has been proposed by the authors as a basis to discuss the relationship between information theoretic measures for finite-alphabet stationary stochastic processes and their...
We review and extend the theory of ideal, homogeneous, incompressible, magnetohydrodynamic (MHD) turbulence. The theory contains a solution to the ‘dynamo problem’, i.e., the problem of determining how a planetary or stellar body produces...
Wireless energy collecting technology can effectively reduce the network time overhead and prolong the wireless sensor network (WSN) lifetime. However, the traditional energy collecting technology cannot achieve the balance between ergodic channel ca...
Novel approaches to estimate information measures using neural networks are well-celebrated in recent years both in the information theory and machine learning communities. These neural-based estimators are shown to converge to the true values when e...
This expository paper advocates an approach to physics in which “typicality” is identified with a suitable form of algorithmic randomness. To this end various theorems from mathematics and physics are reviewed. Their original versions sta...
An axiomatic development of control systems theory can systematize important concepts. The current research article is dedicated to the investigation and comparison of two axiomatic approaches to the analysis of discrete linear time-invariant systems...
This paper is concerned with exponential synchronization for a class of coupled neural networks with hybrid delays and stochastic distributed delayed impulses. First of all, based on the average impulsive interval method, total probability formula an...
This paper is devoted to the foundational problems of dendrogramic holographic theory (DH theory). We used the ontic–epistemic (implicate–explicate order) methodology. The epistemic counterpart is based on the representation of data by dendrograms co...
Many-valued (MV; the many-valued logics considered by Łukasiewicz)-algebras are algebraic systems that generalize Boolean algebras. The MV-algebraic probability theory involves the notions of the state and observable, which abstract the probability m...
In this paper it is shown, that if a possibly inhomogeneous Markov chain with continuous time and finite state space is weakly ergodic and all the entries of its intensity matrix are locally integrable, then, using available results from the perturba...
More than 50 years ago, Rufus Bowen noticed a natural relation between the ergodic theory and the dimension theory of dynamical systems. He proved a formula, known today as the Bowen’s formula, that relates the Hausdorff dimension of a conforma...
Human society always wants a safe environment from pollution and infectious diseases, such as COVID-19, etc. To control COVID-19, we have started the big effort for the discovery of a vaccination of COVID-19. Several biological problems have the aspe...
Several quantum dynamical entropies have been proposed that extend the classical Kolmogorov–Sinai (dynamical) entropy. The same scenario appears in relation to the extension of algorithmic complexity theory to the quantum realm. A theorem of Brudno e...
This paper focuses on the ultimate limit theory of image compression. It proves that for an image source, there exists a coding method with shapes that can achieve the entropy rate under a certain condition where the shape-pixel ratio in the encoder/...
Device-to-device (D2D) communication, as one of the promising candidates for the fifth generation mobile network, can afford effective service of new mobile applications and business models. In this paper, we study the resource management strategies...
Information theory, and the concept of information channel, allows us to calculate the mutual information between the source (input) and the receiver (output), both represented by probability distributions over their possible states. In this paper, w...
Taking impulsive effects into account, an impulsive stochastic predator–prey system with the Beddington–DeAngelis functional response is proposed in this paper. First, the impulsive system is transformed into an equivalent system without...
Boltzmann introduced in the 1870s a logarithmic measure for the connection between the thermodynamical entropy and the probabilities of the microscopic configurations of the system. His celebrated entropic functional for classical systems was then ex...
Since its origin in the thermodynamics of the 19th century, the concept of entropy has also permeated other fields of physics and mathematics, such as Classical and Quantum Statistical Mechanics, Information Theory, Probability Theory, Ergodic Theory...
We investigate chaoticity and complexity of a binary general network automata of finite size with external input which we call a computron. As a generalization of cellular automata, computrons can have non-uniform cell rules, non-regular cell connect...
A proposal for a fundamental theory is described in which classical and quantum physics as a representation of the universe as a gigantic dendrogram are unified. The latter is the explicate order structure corresponding to the purely number-theoretic...
Despite its centennial successes in describing physical systems at thermal equilibrium, Boltzmann–Gibbs (BG) statistical mechanics have exhibited, in the last several decades, several flaws in addressing out-of-equilibrium dynamics of many nonl...
This paper considers coordinated multi-cell multicast precoding for massive multiple-input-multiple-output transmission where only statistical channel state information of all user terminals (UTs) in the coordinated network is known at the base stati...
In this paper, we discuss stochastic differential-algebraic equations (SDAEs) and the asymptotic stability assessment for such systems via Lyapunov exponents (LEs). We focus on index-1 SDAEs and their reformulation as ordinary stochastic differential...
Entropy is re-examined as a quantification of ignorance in the predictability of a one dimensional continuous phenomenon. Although traditional estimators for entropy have been widely utilized in this context, we show that both the thermodynamic and S...
Let
Quantum circuits have been widely used as a platform to simulate generic quantum many-body systems. In particular, random quantum circuits provide a means to probe universal features of many-body quantum chaos and ergodicity. Some such features have...
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