Related papers: Symbolic Sequences and Tsallis Entropy
A repetition free Longest Common Subsequence (LCS) of two sequences x and y is an LCS of x and y where each symbol may appear at most once. Let R denote the length of a repetition free LCS of two sequences of n symbols each one chosen…
A maximum entropy framework based on Tsallis entropy is proposed to depict long tail behavior of queue lengths in broadband networks. Queue length expression as measured in terms of number of packets involves Hurwitz-zeta function. When the…
The Tsallis entropy is shown to be an additive entropy of degree-q that information scientists have been using for almost forty years. Neither is it a unique solution to the nonadditive functional equation from which random entropies are…
A symbolic method for solving linear recurrences of combinatorial and statistical interest is introduced. This method essentially relies on a representation of polynomial sequences as moments of a symbol that looks as the framework of a…
We investigate symbolic sequences and in particular information carriers as e.g. books and DNA-strings. First the higher order Shannon entropies are calculated, a characteristic root law is detected. Then the algorithmic entropy is…
Entropy estimation of information sources is highly non trivial for symbol sequences with strong long-range correlations. The rabbit sequence, related to the symbolic dynamics of the nonlinear circle map at the critical point as well as the…
We derive the multiplicative duality "q<->1/q" and other typical mathematical structures as the special cases of the (mu,nu,q)-relation behind Tsallis statistics by means of the (mu,nu)-multinomial coefficient. Recently the additive duality…
In the last ten years, the employment of symbolic methods has substantially extended both the theory and the applications of statistics and probability. This survey reviews the development of a symbolic technique arising from classical…
A new numerical characterization of symbolic sequences is proposed. The partition of sequence based on Ke and Tong algorithm is a starting point. Algorithm decomposes original sequence into set of distinct subsequences - a patterns. The set…
The field of information science has greatly developed, and applications in various fields have emerged. In this paper, we evaluated the coding system in the theory of Tsallis entropy for transmission of messages and aimed to formulate the…
Symbolic equations are at the core of scientific discovery. The task of discovering the underlying equation from a set of input-output pairs is called symbolic regression. Traditionally, symbolic regression methods use hand-designed…
We derive the asymptotic distribution of ordinal-pattern frequencies under weak dependence conditions and investigate the long-run covariance matrix not only analytically for moving-average, Gaussian, and the novel generalized coin-tossing…
This article introduces the class of periodic trawl processes, which are continuous-time, infinitely divisible, stationary stochastic processes, that allow for periodicity and flexible forms of their serial correlation, including both…
We propose a straightforward extension of symbolic transfer entropy to enable the investigation of delayed directional relationships between coupled dynamical systems from time series. Analyzing time series from chaotic model systems, we…
Some preliminary evidence suggests the conjecture that the collective behaviour of systems having long-range interactions may be described more effectively by the Tsallis rather than by the Boltzmann/Gibbs/Shannon entropy. To this end, we…
Transfer entropy is used to establish a measure of causal relationships between two variables. Symbolic transfer entropy, as an estimation method for transfer entropy, is widely applied due to its robustness against non-stationarity. This…
The log-periodic equation for the entropy $S = - (k/a) \sum_{i=1}^{N} p_{i} \sin(a \ln p_{i})$, based on the forgotten Sharma-Taneja entropy measure, is studied for the first time with $N$ the total number of system states and $p_{i}$ the…
We study the unitary time evolution of the entropy of entanglement of a one-dimensional system between the degrees of freedom in an interval of length l and its complement, starting from a pure state which is not an eigenstate of the…
The symbolic correlation integral provides a way to measure the complexity of time series and dynamical systems. In the present article we prove limit results for an estimator of this quantity which is based on U-statistics under the…
Neurons modeled by the Rulkov map display a variety of dynamic regimes that include tonic spikes and chaotic bursting. Here we study an ensemble of bursting neurons coupled with the Watts-Strogatz small-world topology. We characterize the…