Related papers: The Description of Information in 4-Dimensional Ps…
We pedagogically present the information theory as originally established, explaining its essential ideas and paying attention to the expression employed to measure the amount of information. Also we discussed relationships between…
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…
To fully characterize the information that two `source' variables carry about a third `target' variable, one must decompose the total information into redundant, unique and synergistic components, i.e. obtain a partial information…
Non-Hermitian systems with parity-time ($\mathcal{PT}$) symmetry give rise to exceptional points (EPs) with exceptional properties that arise due to the coalescence of eigenvectors. Such systems have been extensively explored in the…
Dynamical system state estimation and parameter calibration problems are ubiquitous across science and engineering. Bayesian approaches to the problem are the gold standard as they allow for the quantification of uncertainties and enable…
In usual quantum theory, the information available about a quantum system is defined in terms of the density matrix describing it on a spacelike surface. This definition must be generalized for extensions of quantum theory which do not have…
Understanding a complex system entails capturing the non-trivial collective phenomena that arise from interactions between its different parts. Information theory is a flexible and robust framework to study such behaviours, with several…
This paper presents Integrated Information Theory (IIT) 4.0. IIT aims to account for the properties of experience in physical (operational) terms. It identifies the essential properties of experience (axioms), infers the necessary and…
We propose a new way of investigating phase transitions in the context of information theory. We use an information-entropic measure of spatial complexity known as configurational entropy (CE) to quantify both the storage and exchange of…
We attempt to describe geometry in terms of informational quantities for the universe considered as a finite ensemble of correlated quantum particles. As the main dynamical principle, we use the conservation of the sum of all kinds of…
Mediated by today's visual displays, information space allows users to discover, access and interact with a wide range of digital and physical information. The information presented in this space may be digital, physical or a blend of both,…
We generalize the Point information gain (PIG) and derived quantities, i.e. Point information entropy (PIE) and Point information entropy density (PIED), for the case of R\'enyi entropy and simulate the behavior of PIG for typical…
The Partial Information Decomposition (PID) [arXiv:1004.2515] provides a theoretical framework to characterize and quantify the structure of multivariate information sharing. A new method (Idep) has recently been proposed for computing a…
Information theoretic quantities play an important role in various settings in machine learning, including causality testing, structure inference in graphical models, time-series problems, feature selection as well as in providing privacy…
Exploiting the theory of state space models, we derive the exact expressions of the information transfer, as well as redundant and synergistic transfer, for coupled Gaussian processes observed at multiple temporal scales. All of the terms,…
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,…
Across the scientific literature, information measurement in the nervous system is posed as a problem of information processing internal to the brain by constructs such as neuronal populations, sensory surprise, or cognitive models.…
Most information dynamics and statistical causal analysis frameworks rely on the common intuition that causal interactions are intrinsically pairwise -- every 'cause' variable has an associated 'effect' variable, so that a 'causal arrow'…
Information theory is an outstanding framework to measure uncertainty, dependence and relevance in data and systems. It has several desirable properties for real world applications: it naturally deals with multivariate data, it can handle…
The characterisation of information processing is an important task in complex systems science. Information dynamics is a quantitative methodology for modelling the intrinsic information processing conducted by a process represented as a…