Related papers: Information without rolling dice
In this paper, we present some results on information, complexity and entropy as defined below and we discuss their relations with the Kolmogorov-Sinai entropy which is the most important invariant of a dynamical system. These results have…
In this research article, we use the Shannon's formalism to investigate the quantum information entropy of a particle trapped by the Aharonov-Bohm-type effect. For quantum information study, it is necessary to investigate the eigenstates of…
We introduce algorithmic information theory, also known as the theory of Kolmogorov complexity. We explain the main concepts of this quantitative approach to defining `information'. We discuss the extent to which Kolmogorov's and Shannon's…
We investigate the concept of entropy in probabilistic theories more general than quantum mechanics, with particular reference to the notion of information causality recently proposed by Pawlowski et. al. (arXiv:0905.2992). We consider two…
We survey diverse approaches to the notion of information: from Shannon entropy to Kolmogorov complexity. Two of the main applications of Kolmogorov complexity are presented: randomness and classification. The survey is divided in two parts…
We study conditional linear information inequalities, i.e., linear inequalities for Shannon entropy that hold for distributions whose entropies meet some linear constraints. We prove that some conditional information inequalities cannot be…
The information processing capacity of a complex dynamical system is reflected in the partitioning of its state space into disjoint basins of attraction, with state trajectories in each basin flowing towards their corresponding attractor.…
We propose a compression-based version of the empirical entropy of a finite string over a finite alphabet. Whereas previously one considers the naked entropy of (possibly higher order) Markov processes, we consider the sum of the…
In the setting of a Gaussian channel without power constraints, proposed by Poltyrev, the codewords are points in an n-dimensional Euclidean space (an infinite constellation) and the tradeoff between their density and the error probability…
This paper concerns the capacity of the discrete noiseless channel introduced by Shannon. A sufficient condition is given for the capacity to be well-defined. For a general discrete noiseless channel allowing non-integer valued symbol…
This paper studies the Shannon regime for the random displacement of stationary point processes. Let each point of some initial stationary point process in $\R^n$ give rise to one daughter point, the location of which is obtained by adding…
We propose a new framework for reasoning about information in complex systems. Our foundation is based on a variational extension of Shannon's information theory that takes into account the modeling power and computational constraints of…
In this paper, we consider contention resolution algorithms that are augmented with predictions about the network. We begin by studying the natural setup in which the algorithm is provided a distribution defined over the possible network…
We investigate the fundamental limits of reliable communication over multi-view channels, in which the channel output is comprised of a large number of independent noisy views of a transmitted symbol. We consider first the setting of…
The logical basis for information theory is the newly developed logic of partitions that is dual to the usual Boolean logic of subsets. The key concept is a "distinction" of a partition, an ordered pair of elements in distinct blocks of the…
Consider a stochastic nonlinear system controlled over a possibly noisy communication channel. An important problem is to characterize the largest class of channels for which there exist coding and control policies so that the closed-loop…
We review with a tutorial scope the information theory foundations of quantum statistical physics. Only a small proportion of the variables that characterize a system at the microscopic scale can be controlled, for both practical and…
In our previous paper [Phys. Rev. E 95, 062122 (2017)] we considered the optical channel modelled by the nonlinear Schr\"odinger equation with zero dispersion and additive Gaussian noise. We found per-sample channel capacity rof this model.…
Similar to the energy flowing process in traditional heat engines, information could be considered to flow in the communication systems with the form of energy and entropy. Combining the thermodynamic Carnot machine and the classical…
In a recent paper, the authors proposed a general methodology for probabilistic learning on manifolds. The method was used to generate numerical samples that are statistically consistent with an existing dataset construed as a realization…