Related papers: Symbolic Sequences and Tsallis Entropy
We describe in detail two numerical simulation methods valid to study systems whose thermostatistics is described by generalized entropies, such as Tsallis. The methods are useful for applications to non-trivial interacting systems with a…
In many situations, in all branches of physics, one encounters power-like behavior of some variables which are best described by a Tsallis distribution characterized by a nonextensivity parameter $q$ and scale parameter $T$. However, there…
Numerical experiments support the interesting conjecture that statistical methods be applicable not only to fully-chaotic systems, but also at the edge of chaos by using Tsallis' generalizations of the standard exponential and entropy. In…
Identification of causal structures and quantification of direct information flows in complex systems is a challenging yet important task, with practical applications in many fields. Data generated by dynamical processes or large-scale…
We demonstrate that dual entropy expressions of the Tsallis type apply naturally to statistical-mechanical systems that experience an exceptional contraction of their configuration space. The entropic index $\alpha>1$ describes the…
Large Language Models (LLMs) have shown impressive performance in mathematical reasoning tasks when guided by Chain-of-Thought (CoT) prompting. However, they tend to produce highly confident yet incorrect outputs, which poses significant…
This paper addresses the problem of dynamic asset allocation under uncertainty, which can be formulated as a linear quadratic (LQ) control problem with multiplicative noise. To handle exploration exploitation trade offs and induce sparse…
Quasi-power law ensembles are discussed from the perspective of nonextensive Tsallis distributions characterized by a nonextensive parameter $q$. A number of possible sources of such distributions are presented in more detail. It is further…
The paper makes the observation that all orders of information entropy are equal in signals composed of repeating units of distinct symbols where the units can be classified as a member of a symmetry group. This leads to an improved metric…
A large class of technically non-chaotic systems, involving scatterings of light particles by flat surfaces with sharp boundaries, is nonetheless characterized by complex random looking motion in phase space. For these systems one may…
In this paper, we discuss the possibility of unexplored behaviours for the entanglement entropy in extended quantum systems. Namely, we study the R\'enyi entanglement entropy for the ground state of long-range Kitaev chains with slow…
A new approach is proposed to the quantitative estimation of the complexity of multidimensional discrete sequences in terms of the shapes of their trajectories in the extended space of states. This approach is based on the study of the…
Entropy rate of sequential data-streams naturally quantifies the complexity of the generative process. Thus entropy rate fluctuations could be used as a tool to recognize dynamical perturbations in signal sources, and could potentially be…
Neural reasoning accuracy improves when generating intermediate reasoning steps. However, the source of this improvement is yet unclear. Here, we investigate and factorize the benefit of generating intermediate steps for symbolic reasoning.…
We characterise the evolution of a dynamical system by combining two well-known complex systems' tools, namely, symbolic ordinal analysis and networks. From the ordinal representation of a time-series we construct a network in which every…
The non-extensive statistical mechanics has been applied to describe a variety of complex systems with inherent correlations and feedback loops. Here we present a dynamical model based on previously proposed static model exhibiting in the…
For source sequences of length L symbols we proposed to use a more realistic value to the usual benchmark of number of code letters by source letters. Our idea is based on a quantifier of information fluctuation of a source, F(U), which…
We formulate general rules for a coarse-graining of the dynamics, which we term `symbolic dynamics', of feedback networks with monotone interactions, such as most biological modules. Networks which are more complex than simple cyclic…
We numerically test the method of non-sequential recursive pair substitutions to estimate the entropy of an ergodic source. We compare its performance with other classical methods to estimate the entropy (empirical frequencies, return…
Symbolic dynamics has proven to be an invaluable tool in analyzing the mechanisms that lead to unpredictability and random behavior in nonlinear dynamical systems. Surprisingly, a discrete partition of continuous state space can produce a…