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In an effort to develop the foundations for a non-stochastic theory of information, the notion of $\delta$-mutual information between uncertain variables is introduced as a generalization of Nair's non-stochastic information functional.…

Information Theory · Computer Science 2020-11-26 Anshuka Rangi , Massimo Franceschetti

In this paper, we initiate a first information-theoretic study on multilevel NAND flash memory channels with intercell interference. More specifically, for a multilevel NAND flash memory channel under mild assumptions, we first prove that…

Information Theory · Computer Science 2016-11-15 Yonglong Li , Aleksandar Kavcic , Guangyue Han

We show that the way in which the Shannon entropy of sequences produced by an information source converges to the source's entropy rate can be used to monitor how an intelligent agent builds and effectively uses a predictive model of its…

Adaptation and Self-Organizing Systems · Physics 2007-05-23 James P. Crutchfield , David P. Feldman

The body morphology plays an important role in the way information is perceived and processed by an agent. We address an information theory (IT) account on how the precision of sensors, the accuracy of motors, their placement, the body…

Robotics · Computer Science 2024-08-26 Alexandre Pitti , Kohei Nakajima , Yasuo Kuniyoshi

This paper investigates the problem of securing exponentially fast consensus (exponential consensus for short) for identical agents with finite-dimensional linear system dynamics over dynamic network topology. Our aim is to find the weakest…

Systems and Control · Electrical Eng. & Systems 2023-03-02 Qichao Ma , Jiahu Qin , Brian D. O. Anderson , Long Wang

We revisit the quantum reverse Shannon theorem, a central result in quantum information theory that characterizes the resources needed to simulate quantum channels when entanglement is freely available. We derive a universal additive upper…

Quantum Physics · Physics 2025-10-09 Gilad Gour

The Lyapunov exponent characterizes an exponential growth rate of the difference of nearby orbits. A positive Lyapunov exponent is a manifestation of chaos. Here, we propose the Lyapunov pair, which is based on the generalized Lyapunov…

Chaotic Dynamics · Physics 2015-06-23 Takuma Akimoto , Masaki Nakagawa , Soya Shinkai , Yoji Aizawa

We explicitly compute the maximal Lyapunov exponent for a switched system on $\mathrm{SL}_2(\mathbb R)$. This computation is reduced to the characterization of optimal trajectories for an optimal control problem on the Lie group.

Optimization and Control · Mathematics 2023-12-19 Andrei A. Agrachev , Michele Motta

In this paper we use a path-integral approach to represent the Lyapunov exponents of both deterministic and stochastic dynamical systems. In both cases the relevant correlation functions are obtained from a (one-dimensional) supersymmetric…

Chaotic Dynamics · Physics 2007-05-23 E. Gozzi , M. Reuter

Consider communication over a channel whose probabilistic model is completely unknown vector-wise and is not assumed to be stationary. Communication over such channels is challenging because knowing the past does not indicate anything about…

Information Theory · Computer Science 2013-03-21 Yuval Lomnitz , Meir Feder

As an application of generalised statistical mechanics, it is studied a possible route toward a consistent generalised information theory in terms of a family of non-extensive, non-parametric entropies $H^\pm_D(P)$. Unlike other proposals…

Information Theory · Computer Science 2021-03-23 Jesús Fuentes , Octavio Obregón

Using a combination of analytical and numerical techniques, we show that chaos in globally-coupled identical dynamical systems, be they dissipative or Hamiltonian, is both extensive and sub-extensive: their spectrum of Lyapunov exponents is…

We focus on chaotic dynamical systems and analyze their time series with the use of autoencoders, i.e., configurations of neural networks that map identical output to input. This analysis results in the determination of the latent space…

Neural and Evolutionary Computing · Computer Science 2024-06-19 N. Almazova , G. D. Barmparis , G. P. Tsironis

Realistic modeling of brain involves large number of neurons. The important question is how this size affects transmission efficiency? Here, these issue is studied in terms of Shannon's Theory. Mutual Information between input and output…

Neurons and Cognition · Quantitative Biology 2023-07-26 Bartosz Paprocki , Agnieszka Pregowska , Janusz Szczepanski

We use recent advances in the machine learning area known as 'reservoir computing' to formulate a method for model-free estimation from data of the Lyapunov exponents of a chaotic process. The technique uses a limited time series of…

Chaotic Dynamics · Physics 2018-01-17 Jaideep Pathak , Zhixin Lu , Brian R. Hunt , Michelle Girvan , Edward Ott

Coding theorems in quantum Shannon theory express the ultimate rates at which a sender can transmit information over a noisy quantum channel. More often than not, the known formulas expressing these transmission rates are intractable,…

Quantum Physics · Physics 2010-06-15 Kamil Bradler , Patrick Hayden , Dave Touchette , Mark M. Wilde

Reverse Shannon theorems concern the use of noiseless channels to simulate noisy ones. This is dual to the usual noisy channel coding problem, where a noisy (classical or quantum) channel is used to simulate a noiseless one. The Quantum…

Quantum Physics · Physics 2025-04-10 Zahra Baghali Khanian , Debbie Leung

We study a network whose rich spatiotemporal dynamics have recently been shown to enable dynamics-based computation, including logic gates, short-term memory, and simple encryption. The network's time dynamics can be exactly solved through…

Shannon's analysis of the fundamental capacity limits for memoryless communication channels has been refined over time. In this paper, the maximum volume $M_\avg^*(n,\epsilon)$ of length-$n$ codes subject to an average decoding error…

Information Theory · Computer Science 2016-12-28 Pierre Moulin

Many complex phenomena, from weather systems to heartbeat rhythm patterns, are effectively modeled as low-dimensional dynamical systems. Such systems may behave chaotically under certain conditions, and so the ability to detect chaos based…

Machine Learning · Computer Science 2021-06-17 Hagai Rappeport , Irit Levin Reisman , Naftali Tishby , Nathalie Q. Balaban