Related papers: Hidden information and regularities of information…
The introduced entropy functional's (EF) information measure of random process integrates multiple information contributions along the process trajectories, evaluating both the states' and between states' bound information connections. This…
An interactive stochastics, evaluated by an entropy functional (EF) of a random field and informational process' path functional (IPF), allows us modeling the evolutionary information processes and revealing regularities of evolution…
Part 1 has studied the conversion of observed random process with its hidden information to related dynamic process, applying entropy functional measure (EF) of the random process and path functional information measure (IPF) of the dynamic…
Bayesian integral functional measure of entropy-uncertainty (EF) on trajectories of Markov multi-dimensional diffusion process is cutting off by interactive impulses (controls). Each cutoff minimax of EF superimposes and entangles…
The impulses, cutting entropy functional (EF) measure on trajectories Markov diffusion process, integrate information path functional (IPF) composing discrete information Bits extracted from observing random process. Each cut brings memory…
Finding observing path creating its observer is important problem in physics and information science. In observing processes, each observation is act changing the observing process that generates interactive observation. Each interaction is…
Hidden information emerges under impulse interactions with Markov diffusion process modeling interactive random environment. Impulse yes no action cuts Markov correlations revealing Bit of hidden information connected correlated states.…
We study a stochastic control system, described by Ito controllable equation, and evaluate the solutions by an entropy functional (EF), defined by the equation functions of controllable drift and diffusion. Considering a control problem for…
The relationship between Integrated Information Theory (IIT) and the Free-Energy Principle (FEP) remains unresolved, particularly with respect to how integrated information, proposed as the intrinsic substrate of consciousness, behaves…
Shannon's information entropy measures of the uncertainty of an event's outcome. If learning about a system reflects a decrease in uncertainty, then a plausible intuition is that learning should be accompanied by a decrease in the entropy…
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,…
We study how the Shannon entropy of sequences produced by an information source converges to the source's entropy rate. We synthesize several phenomenological approaches to applying information theoretic measures of randomness and memory to…
What is information originating in observation? Until now it has no scientifically conclusive definition. Information is memorized entropy cutting in random observations which processing interactions. Randomness of various interactive…
The aim is formal principles of origin information and information process creating information observer self-creating information in interactive observations. The interactive phenomenon creates Yes-No actions of information Bits in its…
We address the fundamental limits of learning unknown parameters of any stochastic process from time-series data, and discover exact closed-form expressions for how optimal inference scales with observation length. Given a parametrized…
The approach defines information process from probabilistic observation, emerging microprocess,qubit, encoding bits, evolving macroprocess, and extends to Observer information self-organization, cognition, intelligence and understanding…
The field of complex networks studies a wide variety of interacting systems by representing them as networks. To understand their properties and mutual relations, the randomisation of network connections is a commonly used tool. However,…
We extend present Shannon's static statistical information theory to dynamic processes and establish a dynamic statistical information theory. We derive the nonlinear evolution equations of dynamic information density and dynamic…
The paper studies information-theoretic opacity, an information-flow privacy property, in a setting involving two agents: A planning agent who controls a stochastic system and an observer who partially observes the system states. The goal…
Information theory provides a mathematical foundation to measure uncertainty in belief. Belief is represented by a probability distribution that captures our understanding of an outcome's plausibility. Information measures based on…