Related papers: On the concept of complexity in random dynamical s…
Ranking objects is a simple and natural procedure for organizing data. It is often performed by assigning a quality score to each object according to its relevance to the problem at hand. Ranking is widely used for object selection, when…
Complexity measures are essential to understand complex systems and there are numerous definitions to analyze one-dimensional data. However, extensions of these approaches to two or higher-dimensional data, such as images, are much less…
We consider the task of estimating the entropy of $k$-ary distributions from samples in the streaming model, where space is limited. Our main contribution is an algorithm that requires $O\left(\frac{k \log…
We study dynamical systems forced by a combination of random and deterministic noise and provide criteria, in terms of Lyapunov exponents, for the existence of random attractors with continuous structure in the fibres. For this purpose, we…
This work develops tools to understand how quantum information spreads, scrambles, and is reshaped by measurements in many-body systems. First, I study scrambling and pseudorandomness in the Brownian Sachdev-Ye-Kitaev (SYK) model,…
This paper considers the problem of appearance indication of useful acoustic signal in the signal/noise mixture. Various information characteristics (information entropy, Jensen-Shannon divergence, spectral information divergence and…
Let $K$ denote prefix-free Kolmogorov Complexity, and $K^A$ denote it relative to an oracle $A$. We show that for any $n$, $K^{\emptyset^{(n)}}$ is definable purely in terms of the unrelativized notion $K$. It was already known that…
Complexity measures are introduced, that quantify the change of the natural entropy fluctuations at different length scales in time-series emitted from systems operating far from equilibrium. They identify impending sudden cardiac death…
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…
Conditional differential entropy provides an intuitive measure for relatively ranking time-series complexity by quantifying uncertainty in future observations given past context. However, its direct computation for high-dimensional…
In this article, the dynamics and complexity of a noise induced blood flow system have been investigated. Changes in the dynamics have been recognized by measuring the periodicity over significant parameters. Chaotic as well as non-chaotic…
It is shown that a well-known theory of random stationary processes contain contradictions. Integral representations of correlation functions and random stationary processes are investigated further. The new method of struggle with…
The growing study of time series, especially those related to nonlinear systems, has challenged the methodologies to characterize and classify dynamical structures of a signal. Here we conceive a new diagnostic tool for time series based on…
We study the build up of complexity on the example of 1 kg matter in different forms. We start on the simplest example of ideal gases, and then continue with more complex chemical, biological, life and social and technical structures. We…
The concept of information has emerged as a language in its own right, bridging several disciplines that analyze natural phenomena and man-made systems. Integrated information has been introduced as a metric to quantify the amount of…
Complexity is a multi-faceted phenomenon, involving a variety of features including disorder, nonlinearity, and self-organisation. We use a recently developed rigorous framework for complexity to understand measures of complexity. We…
We introduce a new characteristics of chaoticity of classical and quantum dynamical systems by defining the notion of the dissipation time which enables us to test how the system responds to the noise and in particular to measure the speed…
In present paper we suggest a new universal approach to study complex systems by microscopic, mesoscopic and macroscopic methods. We discuss new possibilities of extracting information on nonstationarity, unsteadiness and non-Markovity of…
In this paper we prove estimates on the behaviour of the Kolmogorov-Sinai entropy relative to a partition for randomly perturbed dynamical systems. Our estimates use the entropy for the unperturbed system and are obtained using the notion…
The stickiness effect is a fundamental feature of quasi-integrable Hamiltonian systems. We propose the use of an entropy-based measure of the recurrence plots (RP), namely, the entropy of the distribution of the recurrence times (estimated…