Related papers: Geometry of Information Integration
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,…
Partial Information Decomposition (PID) has become one of the most prominent information-theoretic frameworks for describing the structure and quality of information in complex systems. Despite its widespread utility, there exists no unique…
Integrated information theory is a mathematical, quantifiable theory of conscious experience. The linchpin of this theory, the $\phi$ measure, quantifies a system's irreducibility to disjoint parts. Purely as a measure of irreducibility, we…
The partial information decomposition (PID) framework is concerned with decomposing the information that a set of (two or more) random variables (the sources) has about another variable (the target) into three types of information: unique,…
Researchers in many disciplines have previously used a variety of mathematical techniques for analyzing group interactions. Here we use a new metric for this purpose, called 'integrated information' or 'phi.' Phi was originally developed by…
We introduce a new approach to evaluating entangled quantum networks using information geometry. Quantum computing is powerful because of the enhanced correlations from quantum entanglement. For example, larger entangled networks can…
Originally developed as a theory of consciousness, integrated information theory provides a mathematical framework to quantify the causal irreducibility of systems and subsets of units in the system. Specifically, mechanism integrated…
We analyze the geometry of a joint distribution over a set of discrete random variables. We briefly review Shannon's entropy, conditional entropy, mutual information and conditional mutual information. We review the entropic information…
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…
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…
We study how information geometry is described by bulk geometry in the gauge/gravity correspondence. We consider a quantum information metric that measures the distance between the ground states of a CFT and a theory obtained by perturbing…
Information theory is widely accepted as a powerful tool for analyzing complex systems and it has been applied in many disciplines. Recently, some central components of information theory - multivariate information measures - have found…
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'…
In order to analyze and extract different structural properties of distributions, one can introduce different coordinate systems over the manifold of distributions. In Evolutionary Computation, the Walsh bases and the Building Block Bases…
Complex systems are found in most branches of science. It is still argued how to best quantify their complexity and to what end. One prominent measure of complexity (the statistical complexity) has an operational meaning in terms of the…
The concept of autonomy is fundamental for understanding biological organization and the evolutionary transitions of living systems. Understanding how a system constitutes itself as an individual, cohesive, self-organized entity is a…
Information geometry promotes an investigation of the geometric structure of statistical manifolds, providing a series of elucidations in various areas of scientific knowledge. In the physical sciences, especially in quantum theory, this…
We propose a novel measure to assess the presence of meso-scale structures in complex networks. This measure is based on the identification of regular patterns in the adjacency matrix of the network, and on the calculation of the quantity…
In this paper have written the results of the information analysis of structures. The obtained information estimation (IE) are based on an entropy measure of C. Shannon. Obtained IE is univalent both for the non-isomorphic and for the…
The concept of information has emerged as a language in its own right, bridging several disciplines that analyze natural phenomena and man-made systems. Integrated information has been introduced as a metric to quantify the amount of…