Related papers: Learning from Complex Systems: On the Roles of Ent…
Random fields are useful mathematical objects in the characterization of non-deterministic complex systems. A fundamental issue in the evolution of dynamical systems is how intrinsic properties of such structures change in time. In this…
We show how Fisher's information already known particular character as the fundamental information geometric object which plays the role of a metric tensor for a statistical differential manifold, can be derived in a relatively easy manner…
We investigate the effect of different metrizations of probability spaces on the information geometric complexity of entropic motion on curved statistical manifolds. Specifically, we provide a comparative analysis based upon Riemannian…
Shannon information entropy is a natural measure of probability (de)localization and thus (un)predictability in various procedures of data analysis for model systems. We pay particular attention to links between the Shannon entropy and the…
In this paper we introduce a new generalisation of the relative Fisher Information for Markov jump processes on a finite or countable state space, and prove an inequality which connects this object with the relative entropy and a large…
Fisher information and Shannon entropy are fundamental tools for understanding and analyzing dynamical systems from complementary perspectives. They can characterize unknown parameters by quantifying the information contained in variables,…
Many statistical models require an estimation of unknown (co)-variance parameter(s) in a model. The estimation usually obtained by maximizing a log-likelihood which involves log determinant terms. In principle, one requires the…
We have discussed dynamical properties of the Tsallis entropy and the generalized Fisher information in nonextensive systems described by the Langevin model subjected to additive and multiplicative noise. Analytical expressions for the…
Fisher information, lies at the heart of parameter estimation theory, was recently found to have a close relation with multipartite entanglement (Pezz\'{e} and Smerzi, Phys. Rev. Lett. 102, 100401). We use Fisher information to distinguish…
In information theory, Fisher information and Shannon information (entropy) are respectively used to quantify the uncertainty associated with the distribution modeling and the uncertainty in specifying the outcome of given variables. These…
Entanglement is the key quantum resource for improving measurement sensitivity beyond classical limits. However, the production of entanglement in mesoscopic atomic systems has been limited to squeezed states, described by Gaussian…
Fisher information, Shannon information entropy and Statistical Complexity are calculated for the interface of a normal metal and a superconductor, as a function of the temperature for several materials. The order parameter $\Psi({\bf r})$…
Markov random fields area popular model for high-dimensional probability distributions. Over the years, many mathematical, statistical and algorithmic problems on them have been studied. Until recently, the only known algorithms for…
In this chapter, a statistical measure of complexity and the Fisher-Shannon information product are introduced and their properties are discussed. These measures are based on the interplay between the Shannon information, or a function of…
Physical systems behave according to their underlying dynamical equations which, in turn, can be identified from experimental data. Explaining data requires selecting mathematical models that best capture the data regularities. Identifying…
Shannon entropy ($S$), Fisher information ($I$) and a measure equivalent to Fisher-Shannon complexity $(C_{IS})$ of a ro-vibrational state of diatomic molecules (O$_2$, O$_2^+$, NO, NO$^+$) with generalized Kratzer potential is analyzed.…
It is generally accepted that, when moving in groups, animals process information to coordinate their motion. Recent studies have begun to apply rigorous methods based on Information Theory to quantify such distributed computation.…
Statistical inference more often than not involves models which are non-linear in the parameters thus leading to non-Gaussian posteriors. Many computational and analytical tools exist that can deal with non-Gaussian distributions, and…
Structured optical beams possess rich spatial features that are commonly characterized using entropic measures of field complexity. However, such measures do not directly quantify the operational usefulness of optical structure for…
We study the two dimensional system influenced by a non-central potential consisting of a Kratzer potential with a dipole moment, along with a vector potential of the Aharonov-Bohm (AB) effect. We explore various information theoretic…