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We address the problem of applying the Kolmogorov-Sinai method of entropic analysis, expressed in a generalized non-extensive form, to the dynamics of the logistic map at the chaotic threshold, which is known to be characterized by a power…
It is shown that there is a mapping of the replica approach to disordered systems with finite replica index $n$ on the Tsallis non-extensive statistics, if the average thermodynamic entropy differs from the information entropy for the…
How to find unknown distributions is questioned in many pieces of research. There are several ways to figure them out, but the main question is which acts more reasonably than others. In this paper, we focus on the maximum entropy principle…
We propose a new way of defining entropy of a system, which gives a general form which may be nonextensive as Tsallis entropy, but is linearly dependent on component entropies, like Renyi entropy, which is extensive. This entropy has a…
Learning and decision-making in domains with naturally high noise-to-signal ratio, such as Finance or Healthcare, is often challenging, while the stakes are very high. In this paper, we study the problem of learning and acting under a…
We present a data-driven method for solving the linear quadratic regulator problem for systems with multiplicative disturbances, the distribution of which is only known through sample estimates. We adopt a distributionally robust approach…
The possibility of detracting the decoherence due to the acceleration process of the two-qutrit system is investigated, where we examined the behaviour of the relative entropy and the non-local information. For this purpose, the accelerated…
It is impossible to recover a vector from $\mathbb{R}^m$ with less than $m$ linear measurements, even if the measurements are chosen adaptively. Recently, it has been shown that one can recover vectors from $\mathbb{R}^m$ with arbitrary…
Partial diffusion scheme is an effective method for reducing computational load and power consumption in adaptive network implementation. The Information is exchanged among the nodes, usually over noisy links. In this paper, we consider a…
The thermodynamic definition of entropy can be extended to nonequilibrium systems based on its relation to information. To apply this definition in practice requires access to the physical system's microstates, which may be prohibitively…
We focus on a linear chain of $N$ first-neighbor-coupled logistic maps at their edge of chaos in the presence of a common noise. This model, characterised by the coupling strength $\epsilon$ and the noise width $\sigma_{max}$, was recently…
In many problems in data mining and machine learning, data items that need to be clustered or classified are not points in a high-dimensional space, but are distributions (points on a high dimensional simplex). For distributions, natural…
During the past few years, nonextensive statistics has been successfully applied to explain many different kinds of systems. Through these studies some interpretations of the entropic parameter q, which has major role in this statistics, in…
We research adaptive maximum likelihood-type estimation for an ergodic diffusion process where the observation is contaminated by noise. This methodology leads to the asymptotic independence of the estimators for the variance of observation…
Systems driven away from thermal equilibrium constantly deliver entropy to their environment. Determining this entropy production requires detailed information about the system's internal states and dynamics. However, in most practical…
This contribution reviews the parallel dynamics of Q-Ising neural networks for various architectures: extremely diluted asymmetric, layered feedforward, extremely diluted symmetric, and fully connected. Using a probabilistic signal-to-noise…
We introduce a framework for the control of discrete-time switched stochastic systems with uncertain distributions. In particular, we consider stochastic dynamics with additive noise whose distribution lies in an ambiguity set of…
In this work, an adaptive predictive control scheme for linear systems with unknown parameters and bounded additive disturbances is proposed. In contrast to related adaptive control approaches that robustly consider the parametric…
We look at chaotic systems evolving in fractal phase space. The entropy change in time due to the fractal geometry is assimilated to the information growth through the scale refinement. Due to the incompleteness, at any scale, of the…
Following the theory of information measures based on the cumulative distribution function, we propose the fractional generalized cumulative entropy, and its dynamic version. These entropies are particularly suitable to deal with…