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We consider here a class of groupoids obtained via an equivalence relation (the subgroupoids of pair groupoids). We generalize to Haar Systems in these groupoids some results related to entropy and pressure which are well known in…
With increasing use of digital control it is natural to view control inputs and outputs as stochastic processes assuming values over finite alphabets rather than in a Euclidean space. As control over networks becomes increasingly common,…
The meromorphic functional calculus developed in Part I overcomes the nondiagonalizability of linear operators that arises often in the temporal evolution of complex systems and is generic to the metadynamics of predicting their behavior.…
We prove asymptotic results for a modification of the cross-entropy estimator originally introduced by Ziv and Merhav in the Markovian setting in 1993. Our results concern a more general class of decoupled measures on shift spaces over a…
In the previous papers (Kui\'{c} et al. in Found Phys 42:319-339, 2012; Kui\'{c} in arXiv:1506.02622, 2015), it was demonstrated that applying the principle of maximum information entropy by maximizing the conditional information entropy,…
We introduce two new classes of measures of information for statistical experiments which generalise and subsume $\phi$-divergences, integral probability metrics, $\mathfrak{N}$-distances (MMD), and $(f,\Gamma)$ divergences between two or…
We show why the amount of information communicated between the past and future--the excess entropy--is not in general the amount of information stored in the present--the statistical complexity. This is a puzzle, and a long-standing one,…
During the last two decades, concentration inequalities have been the subject of exciting developments in various areas, including convex geometry, functional analysis, statistical physics, high-dimensional statistics, pure and applied…
We develop the technique of reduced word manipulation to give a range of results concerning reduced words and permutations more generally. We prove a broad connection between pattern containment and reduced words, which specializes to our…
Assessing the degree of semantic relatedness between words is an important task with a variety of semantic applications, such as ontology learning for the Semantic Web, semantic search or query expansion. To accomplish this in an automated…
Complexity matching characterizes the role of information in interactions between systems and can be traced back to the 1957 Introduction to Cybernetics by Ross Ashby. We argue that complexity can be expressed in terms of crucial events,…
Two approaches to studying the correlation functions of the binary Markov sequences are considered. The first of them is based on the study of probability of occurring different ''words'' in the sequence. The other one uses recurrence…
Distinguishability and predictability are part of complementarity relations which apply to two different kinds of interference experiments, with and without a path-detector, respectively. In [Opt. Comm. 179, 337 (2000)], Englert and Bergou…
The problem of appropriately matching items subject to compatibility constraints arises in a number of important applications. While most of the literature on matching theory focuses on a static setting with a fixed number of items, several…
Information theory allows us to investigate information processing in neural systems in terms of information transfer, storage and modification. Especially the measure of information transfer, transfer entropy, has seen a dramatic surge of…
We consider a protocol for the two-time measurement of entropic observables in quantum open systems driven out of thermal equilibrium by coupling to several heat baths. We concentrate on the Markovian approximation of the time-evolution and…
Motivated by the analysis of accelerometer data, we introduce a specific finite mixture of hidden Markov models with particular characteristics that adapt well to the specific nature of this type of data. Our model allows for the…
While it is an important problem to identify the existence of causal associations between two components of a multivariate time series, a topic addressed in Runge et al. (2012), it is even more important to assess the strength of their…
We extend previously proposed measures of complexity, emergence, and self-organization to continuous distributions using differential entropy. This allows us to calculate the complexity of phenomena for which distributions are known. We…
In this paper, we present some results on information, complexity and entropy as defined below and we discuss their relations with the Kolmogorov-Sinai entropy which is the most important invariant of a dynamical system. These results have…