Related papers: A new approach to mutual information. II
We present estimators for entropy and other functions of a discrete probability distribution when the data is a finite sample drawn from that probability distribution. In particular, for the case when the probability distribution is a joint…
We propose the concept of mutual information for particle pair (MIPP) in curved spacetime, and show that MIPP has potential to be a proper chaos indicator. We tested this method in the Schwarzschild and Kerr spacetime and compared it with…
This paper presents a novel technique for state space reduction of probabilistic specifications, based on a newly developed notion of confluence for probabilistic automata. We prove that this reduction preserves branching probabilistic…
We introduce the concept of {\em information compressibility}, $K_I$, which measures the relative change of number of available microstates of an open system in response to an energy variation. We then prove that at the time in which the…
Orbital entropies, pair entropies, and mutual information have become popular tools for analysis of strongly correlated wave functions. They can quantitatively measure how strongly an orbital participates in the electron correlation and…
Pufferfish privacy (PP) is a generalization of differential privacy (DP), that offers flexibility in specifying sensitive information and integrates domain knowledge into the privacy definition. Inspired by the illuminating formulation of…
Lieb and Ruskai's strong subadditivity theorem, which shows that the conditional mutual information must be nonnegative, is fundamental in quantum theory. It has numerous applications, such as in quantum error correction. When the mutual…
We address the excess entropy, which is a measure of complexity for stationary time series, from the ordinal point of view. We show that the permutation excess entropy is equal to the mutual information between two adjacent semi-infinite…
Motivated by thermodynamic considerations, we analyse the variation of the quantum mutual information on a unitary orbit of a bipartite system's state, with and without global constraints such as energy conservation. We solve the full…
The mutual information characterizes correlations between spatially separated regions of a system. Yet, in experiments we often measure dynamical correlations, which involve probing operators that are also separated in time. Here, we…
Hybrid particle-field methods are computationally efficient approaches for modelling soft matter systems. So far applications of these methodologies have been limited to constant volume conditions. Here, we reformulate particle-field…
Application of stable localized dissipative solitons as basic carriers of information promises the significant progress in the development of new optical communication networks. The success development of such systems requires getting the…
This paper presents a novel approach to machine learning algorithm design based on information theory, specifically mutual information (MI). We propose a framework for learning and representing functional relationships in data using…
In recent years the shperical wave expansion method has been widely applied to the theory and calculation of electromagnetic fields. But the inner product exist in reference[1] is defined on the Banach space[2]. Through redefining the inner…
The mutual information method has demonstrated to be very useful for deriving the potential order parameter of a system. Although the method suggests some constraints which help to define this quantity, there is still some freedom in the…
This Thesis explores how tools from Statistical Physics and Information Theory can help us describe and understand complex systems. In the first part, we study the interplay between internal interactions, environmental changes, and…
Effective bounds on the union probability are well known to be beneficial in the analysis of stochastic problems in many areas, including probability theory, information theory, statistical communications, computing and operations research.…
In a recent, modified double-pinhole diffraction experiment the existence of an interference pattern was established indirectly along with a near-perfect imaging of the double pinhole. Our theoretical analysis shows that the experiment…
By combining a bound on the absolute value of the difference of mutual information between two joint probablity distributions with a fixed variational distance, and a bound on the probability of a maximal deviation in variational distance…
The analogues of Arimoto's definition of conditional R\'enyi entropy and R\'enyi mutual information are explored for abstract alphabets. These quantities, although dependent on the reference measure, have some useful properties similar to…