Related papers: Symbolic Sequences and Tsallis Entropy
We show that classical chaining bounds on the suprema of random processes in terms of entropy numbers can be systematically improved when the underlying set is convex: the entropy numbers need not be computed for the entire set, but only…
We study the N-step binary stationary ergodic Markov chain and analyze its differential entropy. Supposing that the correlations are weak we express the conditional probability function of the chain through the pair correlation function and…
Overplotted line charts can obscure trends in temporal data and hinder prediction. We conduct a user study comparing three alternatives-aggregated, trellis, and spiral line charts against standard line charts on tasks involving trend…
In this article we introduce two new perfect simulation algorithms for chains with infinite memory. Both algorithms belong to the coupling of past procedures. The novelty of our approach is that it allows to include unknown states to the…
A sequence $S=s_{1}s_{2}..._{n}$ is \emph{nonrepetitive} if no two adjacent blocks of $S$ are identical. In 1906 Thue proved that there exist arbitrarily long nonrepetitive sequences over 3-element set of symbols. We study a generalization…
Long-range correlations are found in symbolic sequences from human language, music and DNA. Determining the span of correlations in dolphin whistle sequences is crucial for shedding light on their communicative complexity. Dolphin whistles…
Recently, simple dynamical systems such as the 1-d maps on the interval, gained significant attention in the context of statistical physics and complex systems. The decay of correlations in these systems, can be characterized and measured…
We demonstrate that linear combinations of subregion entropies with canceling boundary terms, commonly used to calculate the topological entanglement entropy, may suffer from spurious nontopological contributions even in models with zero…
In this paper we consider the fractional parts of a general sequence, for example the sequence $\alpha \sqrt{n}$ or $\alpha n^2$. We give a general method, which allows one to show that long-range correlations (correlations where the…
Traditional thermodynamic trade-off relations usually apply to quantities that depend linearly on probability distributions. In contrast, many important information-theoretic measures, such as entropies, are nonlinear and therefore…
This paper addresses the question of the fluctuations of the empirical entropy of a chain of infinite order. We assume that the chain takes values on a finite alphabet and loses memory exponentially fast. We consider two possible…
Information entropy is applied to the analysis of time series generated by dynamical systems. Complexity of a temporal or spatio-temporal signal is defined as the difference between the sum of entropies of the local linear regions of the…
A quantum random walk on the integers exhibits pseudo memory effects, in that its probability distribution after N steps is determined by reshuffling the first N distributions that arise in a classical random walk with the same initial…
In this paper we complete the study on the asymptotic behaviour of the entanglement entropy for Kitaev chains with long range pairing. We discover that when the couplings decay with the distance with a critical exponent new properties for…
Symbolic relative entropy, an efficient nonlinear complexity parameter measuring probabilistic divergences of symbolic sequences, is proposed in our nonlinear dynamics analysis of heart rates considering equal states. Equalities are not…
This paper studies the use of the Tsallis Entropy versus the classic Boltzmann-Gibbs-Shannon entropy for classifying image patterns. Given a database of 40 pattern classes, the goal is to determine the class of a given image sample. Our…
The Hofstadter Q-sequence, with its simple definition, has defied all attempts at analyzing its behavior. Defined by a simple nested recurrence and an initial condition, the sequence looks approximately linear, though with a lot of noise.…
Symbolic regression, i.e. predicting a function from the observation of its values, is well-known to be a challenging task. In this paper, we train Transformers to infer the function or recurrence relation underlying sequences of integers…
A causal query will commonly not be identifiable from observed data, in which case no estimator of the query can be contrived without further assumptions or measured variables, regardless of the amount or precision of the measurements of…
In two previous experiments we investigated the neural precursors of subjects' "free" choices for one of two options (pressing one of two buttons, and choosing between adding and subtracting numbers). In these experiments the distribution…