相关论文: Quantifying The Complexity Of Geodesic Paths On Cu…
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…
We compute the asymptotic temporal behavior of the dynamical complexity associated with the maximum probability trajectories on Gaussian statistical manifolds in presence of correlations between the variables labeling the macrostates of the…
Information geometric techniques and inductive inference methods hold great promise for solving computational problems of interest in classical and quantum physics, especially with regard to complexity characterization of dynamical systems…
We study the information geometry and the entropic dynamics of a 3D Gaussian statistical model. We then compare our analysis to that of a 2D Gaussian statistical model obtained from the higher-dimensional model via introduction of an…
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…
A new information-geometric approach to chaotic dynamics on curved statistical manifolds based on Entropic Dynamics (ED) is proposed. It is shown that the hyperbolicity of a non-maximally symmetric 6N-dimensional statistical manifold M_{s}…
We present an analytical computation of the asymptotic temporal behavior of the information geometric complexity (IGC) of finite-dimensional Gaussian statistical manifolds in the presence of microcorrelations (correlations between…
A novel information-geometric approach to chaotic dynamics on curved statistical manifolds based on Entropic Dynamics (ED) is suggested. Furthermore, an information-geometric analogue of the Zurek-Paz quantum chaos criterion is proposed. It…
Two entropic dynamical models are considered. The geometric structure of the statistical manifolds underlying these models is studied. It is found that in both cases, the resulting metric manifolds are negatively curved. Moreover, the…
Motivated by the presence of deep connections among dynamical equations, experimental data, physical systems, and statistical modeling, we report on a series of findings uncovered by the Authors and collaborators during the last decade…
Information geometry and inductive inference methods can be used to model dynamical systems in terms of their probabilistic description on curved statistical manifolds. In this article, we present a formal conceptual reexamination of the…
Research on the use of information geometry (IG) in modern physics has witnessed significant advances recently. In this review article, we report on the utilization of IG methods to define measures of complexity in both classical and,…
The geodesic complexity of a Riemannian manifold is a numerical isometry invariant that is determined by the structure of its cut loci. In this article we study decompositions of cut loci over whose components the tangent cut loci fiber in…
We consider a Gaussian statistical model whose parameter space is given by the variances of random variables. Underlying this model we identify networks by interpreting random variables as sitting on vertices and their correlations as…
It is known that mixed quantum states are highly entropic states of imperfect knowledge (i.e., incomplete information) about a quantum system, while pure quantum states are states of perfect knowledge (i.e., complete information) with…
A novel information-geometrodynamical approach to chaotic dynamics (IGAC) on curved statistical manifolds based on Entropic Dynamics (ED) is presented and a new definition of information geometrodynamical entropy (IGE) as a measure of…
Complex models in physics, biology, economics, and engineering are often sloppy, meaning that the model parameters are not well determined by the model predictions for collective behavior. Many parameter combinations can vary over decades…
It is known that statistical model selection as well as identification of dynamical equations from available data are both very challenging tasks. Physical systems behave according to their underlying dynamical equations which, in turn, can…
We formulate the Riemannian calculus of the probability set embedded with $L^2$-Wasserstein metric. This is an initial work of transport information geometry. Our investigation starts with the probability simplex (probability manifold)…
The manifold of empirical mean values of statistical data ad infinitum has a geometric shape that depends on the probability measure that governs the generating model. Large deviation theory produces entropy functions that depend on both…