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Related papers: Information geometric methods for complexity

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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…

Mathematical Physics · Physics 2010-11-29 C. Cafaro , A. Giffin , S. A. Ali , D. -H. Kim

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…

Mathematical Physics · Physics 2015-06-04 S. A. Ali , C. Cafaro , A. Giffin , D. -H. Kim

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…

Mathematical Physics · Physics 2019-07-24 Steven Gassner , Carlo Cafaro

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…

Data Analysis, Statistics and Probability · Physics 2018-08-22 Sean Alan Ali , Carlo Cafaro , Steven Gassner , Adom Giffin

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…

Data Analysis, Statistics and Probability · Physics 2014-03-18 Carlo Cafaro

A central issue of the science of complex systems is the quantitative characterization of complexity. In the present work we address this issue by resorting to information geometry. Actually we propose a constructive way to associate to a -…

Mathematical Physics · Physics 2017-12-19 Roberto Franzosi , Domenico Felice , Stefano Mancini , Marco Pettini

We discuss the fundamental theoretical framework together with numerous results obtained by the authors and colleagues over an extended period of investigation on the Information Geometric Approach to Chaos (IGAC).

Chaotic Dynamics · Physics 2021-09-01 Carlo Cafaro , Sean A. Ali

Information geometry provides a tool to systematically investigate parameter sensitivity of the state of a system. If a physical system is described by a linear combination of eigenstates of a complex (that is, non-Hermitian) Hamiltonian,…

Quantum Physics · Physics 2013-08-26 Dorje C. Brody , Eva-Maria Graefe

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…

Mathematical Physics · Physics 2017-10-11 Sean Alan Ali , Carlo Cafaro

The introduction of a metric onto the space of parameters in models in Statistical Mechanics and beyond gives an alternative perspective on their phase structure. In such a geometrization, the scalar curvature, R, plays a central role. A…

Statistical Mechanics · Physics 2009-11-10 W. Janke , D. A. Johnston , R. Kenna

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…

Mathematical Physics · Physics 2015-06-17 Domenico Felice , Stefano Mancini , Marco Pettini

In this work we: (1) review likelihood-based inference for parameter estimation and the construction of confidence regions; and, (2) explore the use of techniques from information geometry, including geodesic curves and Riemann scalar…

Methodology · Statistics 2022-04-01 Jesse A Sharp , Alexander P Browning , Kevin Burrage , Matthew J Simpson

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…

Mathematical Physics · Physics 2008-10-28 C. Cafaro , S. A. Ali

Information geometry is a study of statistical manifolds, that is, spaces of probability distributions from a geometric perspective. Its classical information-theoretic applications relate to statistical concepts such as Fisher information,…

Information Theory · Computer Science 2023-10-09 Kumar Vijay Mishra , M. Ashok Kumar , Ting-Kam Leonard Wong

Information geometry is used to quantify the amount of information integration within multiple terminals of a causal dynamical system. Integrated information quantifies how much information is lost when a system is split into parts and…

Information Theory · Computer Science 2017-09-08 Shun-ichi Amari , Naotsugu Tsuchiya , Masafumi Oizumi

Using the generalized entropies which depend on two parameters we propose a set of quantitative characteristics derived from the Information Geometry based on these entropies. Our aim, at this stage, is modest, as we are first constructing…

Mathematical Physics · Physics 2018-02-14 Demetris P. K. Ghikas , Fotios Oikonomou

I review recent works showing that information geometry is a useful framework to characterize quantum coherence and entanglement. Quantum systems exhibit peculiar properties which cannot be justified by classical physics, e.g. quantum…

Quantum Physics · Physics 2018-10-08 Davide Girolami

We propose a unified theoretical framework for quantifying spatio-temporal interactions in a stochastic dynamical system based on information geometry. In the proposed framework, the degree of interactions is quantified by the divergence…

Neurons and Cognition · Quantitative Biology 2016-12-08 Masafumi Oizumi , Naotsugu Tsuchiya , Shun-ichi Amari

Artificial neural networks (ANNs) are powerful tools capable of approximating any arbitrary mathematical function, but their interpretability remains limited, rendering them as black box models. To address this issue, numerous methods have…

Machine Learning · Computer Science 2024-06-11 Abhiram Anand Thiruthummal , Eun-jin Kim , Sergiy Shelyag

The rise of quantum information science has opened up a new venue for applications of the geometric phase (GP), as well as triggered new insights into its physical, mathematical, and conceptual nature. Here, we review this development by…

Quantum Physics · Physics 2015-10-08 Erik Sjöqvist
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