Related papers: Strong laws for recurrence quantification analysis
Complex risk is a critical factor for both intelligent systems and risk management. In this paper, we consider a special class of risk statistics, named complex risk statistics. Our result provides a new approach for addressing complex…
Article presents general formulation of entanglement measures problem in terms of correlation function. Description of entanglement in probabilistic framework allow us to introduce new quantity which describes quantum and classical…
We relate the computational complexity of finite strings to universal representations of their underlying symmetries. First, Boolean functions are classified using the universal covering topologies of the circuits which enumerate them. A…
I discuss classical and quantum recurrence theorems in a unified manner, treating both as generalisations of the fact that a system with a finite state space only has so many places to go. Along the way I prove versions of the recurrence…
Complex systems are found in most branches of science. It is still argued how to best quantify their complexity and to what end. One prominent measure of complexity (the statistical complexity) has an operational meaning in terms of the…
We shed new light on entanglement measures in multipartite quantum systems by taking a computational-complexity approach toward quantifying quantum entanglement with two familiar notions--approximability and distinguishability. Built upon…
The coupling complexity index is an information measure introduced within the framework of ordinal symbolic dynamics. This index is used to characterize the complexity of the relationship between dynamical system components. In this work,…
Quantitative linguistics has provided us with a number of empirical laws that characterise the evolution of languages and competition amongst them. In terms of language usage, one of the most influential results is Zipf's law of word…
The basic notions related to coherence phenomena are formulated. Two types of coherence are described, state coherence and transition coherence. Useful characteristics for quantifying coherence are defined, such as coherence functions,…
Let X be a subshift satisfy non-uniform structure. In this paper, we give quantitative estimate of the recurrence sets. These results can be applied to a large class of symbolic systems, including beta-shifts, S-gap shifts and their…
Uncertainty relations are old, yet potentially rewarding to explore. By introducing a quantity called the uncertainty matrix, we provide a link between purity and observable incompatibility, and derive several stronger uncertainty relations…
We study an asymptotic behavior of the return probability for the critical random matrix ensemble in the regime of strong multifractality. The return probability is expected to show critical scaling in the limit of large time or large…
Quantum theory is formulated as the uniquely consistent way to manipulate probability amplitudes. The crucial ingredient is a consistency constraint: if the amplitude of a quantum process can be computed in two different ways, the two…
This paper deals with strong invariance principles (known also as strong approximation theorems) for sums of the form $\sum_{n=1}^{[Nt]}F\big(X(n),X(2n),...,X(kn), X(q_{k+1}(n)),X(q_{k+2}(n)),..., X(q_\ell(n))\big)$
We formulate conditions for convergence of Laws of Large Numbers and show its links with of the parts of mathematical analysis such as summation theory, convergence of orthogonal series. We present also applications of the Law of Large…
An example shows that weak decoherence is more restrictive than the minimal logical decoherence structure that allows probabilities to be used consistently for quantum histories. The probabilities in the sum rules that define minimal…
Observables of out-of-equilibrium quantum many-body systems display complex temporal behavior that encodes the underlying physical mechanisms but typically resists straightforward interpretations. We introduce recurrence analysis - a…
A new version of a Strong Law of Large Numbers is proposed in this note for pairwise independent random variables. The main goal is to relax the assumption on a finite expectation for each term.
Despite the superior performance of Large Reasoning Models (LRMs), their reasoning behaviors are often counterintuitive, leading to suboptimal reasoning capabilities. To theoretically formalize the desired reasoning behaviors, this paper…
Previous derivations of the sum and product rules of probability theory relied on the algebraic properties of Boolean logic. Here they are derived within a more general framework based on lattice theory. The result is a new foundation of…