Related papers: A new approach to mutual information. II
We introduce a new information-geometric structure associated with the dynamics on discrete objects such as graphs and hypergraphs. The presented setup consists of two dually flat structures built on the vertex and edge spaces,…
Estimation of mutual information between (multidimensional) real-valued variables is used in analysis of complex systems, biological systems, and recently also quantum systems. This estimation is a hard problem, and universally good…
We consider the problem of recovering the community structure in the stochastic block model with two communities. We aim to describe the mutual information between the observed network and the actual community structure in the sparse…
A possible approximate route to obtain the equation of state of the monodisperse hard-sphere system in the metastable fluid region from the knowledge of the equation of state of a hard-sphere mixture at high densities is discussed. The…
The study of inter-human communication requires a more complex framework than Shannon's (1948) mathematical theory of communication because "information" is defined in the latter case as meaningless uncertainty. Assuming that meaning cannot…
We develop numerical and analytical approaches to calculate mutual information between complete paths of two molecular components embedded into a larger reaction network. In particular, we focus on a continuous-time Markov chain formalism,…
In this paper we describe a theory of a cumulative distribution function on a space with an order from a probability measure defined in this space. This distribution function plays a similar role to that played in the classical case.…
We identify a counter-example to the consensus result given in [J. Semonsen et al. Opinion dynamics in the presence of increasing agreement pressure. \textit{IEEE Trans. Cyber.}, 49(4): 1270-1278, 2018]. We resolve the counter-example by…
We consider dynamic versions of the mutual information of lifetime distributions, with focus on past lifetimes, residual lifetimes and mixed lifetimes evaluated at different instants. This allows to study multicomponent systems, by…
This paper presents a new recursive information consensus filter for decentralized dynamic-state estimation. No structure is assumed about the topology of the network and local estimators are assumed to have access only to local…
Mutual information between two random variables is a well-studied notion, whose understanding is fairly complete. Mutual information between one random variable and a pair of other random variables, however, is a far more involved notion.…
For several styles of fidelity constraints -- guaranteed distortion, conditional excess distortion, excess distortion -- we show mutual information upper bounds on the minimum expected description length needed to represent a random…
Mutual information is a well-known tool to measure the mutual dependence between variables. In this paper, a Bayesian nonparametric estimation of mutual information is established by means of the Dirichlet process and the $k$-nearest…
In information theory, the link between continuous information and discrete information is established through well-known sampling theorems. Sampling theory explains, for example, how frequency-filtered music signals are reconstructible…
Recently, the permutation-information theoretic approach has been used in a broad range of research fields. In particular, in the study of highdimensional dynamical systems, it has been shown that this approach can be effective in…
The amount of information exchanged per unit of time between two nodes in a dynamical network or between two data sets is a powerful concept for analysing complex systems. This quantity, known as the mutual information rate (MIR), is…
We propose a channel modeling using jump-diffusion processes, and study the differential properties of entropy and mutual information. By utilizing the Kramers-Moyal and Kolmogorov-Feller equations, we express the mutual information between…
Previously proposed measures of entanglement, such as entanglement of formation and assistance, are shown to be special cases of the relative entropy of entanglement. The difference between these measures for an ensemble of mixed states is…
In this paper, we study some quantum properties of a superposition of displaced squeezed two-mode vacuum and single-photon states, such as the second-order correlation function, the Cauchy-Schwartz inequality, quadrature squeezing,…
Conceptually, partial information decomposition (PID) is concerned with separating the information contributions several sources hold about a certain target by decomposing the corresponding joint mutual information into contributions such…