Related papers: Symbolic Sequences and Tsallis Entropy
Reliably counting and generating sequences of items remain a significant challenge for neural networks, including Large Language Models (LLMs). Indeed, although this capability is readily handled by rule-based symbolic systems based on…
We introduce a method to estimate the complexity function of symbolic dynamical systems from a finite sequence of symbols. We test such complexity estimator on several symbolic dynamical systems whose complexity functions are known exactly.…
This study addresses the problem of learning a summary causal graph on time series with potentially different sampling rates. To do so, we first propose a new causal temporal mutual information measure for time series. We then show how this…
The Tsallis entropy, which is a generalization of the Boltzmann-Gibbs entropy, plays a central role in nonextensive statistical mechanics of complex systems. A lot of efforts have recently been made on establishing a dynamical foundation…
Searches for statistically significant correlations between arrival directions of ultra-high energy cosmic rays and classes of astrophysical objects are common in astroparticle physics. We present a method to test potential correlation…
This paper studies properties of binary runlength-limited sequences with additional constraints on their Hamming weight and/or their number of runs of identical symbols. An algebraic and a probabilistic (entropic) characterization of the…
We present an exact approach to analyze and quantify the sensitivity of higher moments of probabilistic loops with symbolic parameters, polynomial arithmetic and potentially uncountable state spaces. Our approach integrates methods from…
In this work, a symbolic dynamical formulation based upon discrete iterative mappings derived from the Collatz conjecture is introduced. It is demonstrated that this formulation naturally induces a ternary alphabet useful for characterizing…
The coupled entropy is proven to correct a flaw in the derivation of the Tsallis entropy and thereby solidify the theoretical foundations for analyzing the uncertainty of complex systems. The Tsallis entropy originated from considering…
The Tsallis entropy barrier or the roundness barrier based dynamic stochastic resonance mechanisms are put forward and simulated. The systems with various Tsallis q values exhibit the effects of emergence as a result of the noise-induced…
We investigate the random walk of prices by developing a simple model relating the properties of the signs and absolute values of individual price changes to the diffusion rate (volatility) of prices at longer time scales. We show that this…
We present a simple and general argument showing that a class of dynamical correlations give rise to the so-called Tsallis nonextensive statistics. An example of a system having such a dynamics is given, exhibiting a non-Boltzmann energy…
We provide a rigorous first-principle derivation of the non-additive Tsallis' entropy by employing the Chaitin-Kolmogorov algorithmic information theory. By applying non-local restrictive rules on the string formation (grammar), we show…
A theory of symbolic dynamic systems with long-range correlations based on the consideration of the binary N-step Markov chains developed earlier in Phys. Rev. Lett. 90, 110601 (2003) is generalized to the biased case (non equal numbers of…
A theory of systems with long-range correlations based on the consideration of binary N-step Markov chains is developed. In our model, the conditional probability that the i-th symbol in the chain equals zero (or unity) is a linear function…
We provide an update of the overview of imprints of Tsallis nonextensive statistics seen in a multiparticle production processes. They reveal an ubiquitous presence of power law distributions of different variables characterized by the…
The ultimate purpose of the statistical analysis of ordinal patterns is to characterize the distribution of the features they induce. In particular, knowing the joint distribution of the pair Entropy-Statistical Complexity for a large class…
The spectral symbols are useful tools to analyse the eigenvalue distribution when dealing with high dimensional linear systems. Given a matrix sequence with an asymptotic symbol, the last one depends only on the spectra of the individual…
The property of Tsallis entropy is examined when considering tow systems with different temperatures to be in contact with each other and to reach the thermal equilibrium. It is verified that the total Tsallis entropy of the two systems…
The paper extends the analysis of the entropies of the Poisson distribution with parameter $\lambda$. It demonstrates that the Tsallis and Sharma-Mittal entropies exhibit monotonic behavior with respect to $\lambda$, whereas two generalized…