Related papers: On Complexity and Emergence
The notion of slow entropy, both upper and lower slow entropy, was defined by Katok and Thouvenot as a more refined measure of complexity for dynamical systems, than the classical Kolmogorov-Sinai entropy. For any subexponential rate…
Markov categories are a novel framework to describe and treat problems in probability and information theory. In this work we combine the categorical formalism with the traditional quantitative notions of entropy, mutual information, and…
We propose an operational, quantitative definition of intelligence for arbitrary physical systems. The intelligence density of a system is the ratio of the logarithm of its independent outputs to its total description length. A system…
Entropy measures have become increasingly popular as an evaluation metric for complexity in the analysis of time series data, especially in physiology and medicine. Entropy measures the rate of information gain, or degree of regularity in a…
Information plays an important role in our understanding of the physical world. We hence propose an entropic measure of information for any physical theory that admits systems, states and measurements. In the quantum and classical world,…
Entropy concept was introduced by Clausius 160 years ago, and has been continually enriched, developed and interpreted by the researchers in many different scientific disciplines ever since. Thermodynamics and other scientific disciplines…
The quest for a scientific description of consciousness has given rise to new theoretical and empirical paradigms for the investigation of phenomenological contents as well as clinical disorders of consciousness. An outstanding challenge in…
Here we deconstruct, and then in a reasoned way reconstruct, the concept of "entropy of a system," paying particular attention to where the randomness may be coming from. We start with the core concept of entropy as a COUNT associated with…
Different notions of entropy play a fundamental role in the classical theory of dynamical systems. Unlike many other concepts used to analyze autonomous dynamics, both measure-theoretic and topological entropy can be extended quite…
There are numerous characterizations of Shannon entropy and Tsallis entropy as measures of information obeying certain properties. Using work by Faddeev and Furuichi, we derive a very simple characterization. Instead of focusing on the…
A qualitatively new, much more liberal and efficient organisation of science is proposed and justified, in connection with growing debate about further role and development of fundamental science. Although the key ideas can be explained…
Psychology has had difficulty accounting for the creative, context-sensitive manner in which concepts are used. We believe this stems from the view of concepts as identifiers rather than bridges between mind and world that participate in…
The problem of Shannon entropy estimation in countable infinite alphabets is addressed from the study and use of convergence results of the entropy functional, which is known to be discontinuous with respect to the total variation distance…
The rising complexity of our terrestrial surrounding is an empirical fact. Details of this process evaded description in terms of physics for long time attracting attention and creating myriad of ideas including non-scientific ones. In this…
We trace the history of empirical entropy, touching briefly on its relation to Markov processes, normal numbers, Shannon entropy, the Chomsky hierarchy, Kolmogorov complexity, Ziv-Lempel compression, de Bruijn sequences and stochastic…
In a topological dynamical system the complexity of an orbit is a measure of the amount of information (algorithmic information content) that is necessary to describe the orbit. This indicator is invariant up to topological conjugation. We…
Previously proposed measures of entanglement, such as entanglement of formation and assistance, are shown to be special cases of the relative entropy of entanglement. The difference between these measures for an ensemble of mixed states is…
Complexity theory provides a wealth of complexity classes for analyzing the complexity of decision and counting problems. Despite the practical relevance of enumeration problems, the tools provided by complexity theory for this important…
In their position paper entitled "Towards a new, complexity science of learning and education", Jorg et al. (2007) argue that educational research is in crisis. In their opinion, the transdisciplinary and interdiscursive approach of…
In direct response to requests for a logico-mathematical test of the conjecture, we formally disprove a recently conjectured artificial intelligence trade-off between epistemic certainty and scope in its published universal hyperbolic…