Related papers: Information Theory for Complex Systems Scientists
The information-theoretic representation of quantum systems, which complements the familiar energy description of the density-functional and wave-function-based theories, is here discussed. According to it, the internal disorder of the…
The concept of Shannon entropy of random variables was generalized to measurable functions in general, and to simple functions with finite values in particular. It is shown that the information measure of a function is related to the time…
Entropy governs molecular self-assembly, phase transitions, and material stability, yet remains challenging to quantify and directly control in molecular systems. Here, we demonstrate that the computable information density (CID), a data…
Information theory is a powerful tool to express principles to drive autonomous systems because it is domain invariant and allows for an intuitive interpretation. This paper studies the use of the predictive information (PI), also called…
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…
Science is a constructed narrative of the natural world based on information gathering and its subsequent analysis. In this essay, we develop a novel approach to the epistemic foundations of the scientific narrative, as based on our…
Today, the vast majority of the world's digital information is represented using the fundamental assumption, introduced by Claude Shannon in 1948, that ``...the semantic aspects of communication are irrelevant to the engineering problem (of…
Extracting higher-order structures from multivariate data has become an area of intensive study in complex systems science, as these multipartite interactions can reveal insights into fundamental features of complex systems like emergent…
The Chapter starts with introductory information about quantitative linguistics notions, like rank--frequency dependence, Zipf's law, frequency spectra, etc. Similarities in distributions of words in texts with level occupation in quantum…
Advances in science are being sought in newly available opportunities to collect massive quantities of data about complex systems. While key advances are being made in detailed mapping of systems, how to relate this data to solving many of…
Society's capacity for algorithmic problem-solving has never been greater. Artificial Intelligence is now applied across more domains than ever, a consequence of powerful abstractions, abundant data, and accessible software. As capabilities…
This paper discusses system consequence, a central idea in the project to lift the theory of information flow to the abstract level of universal logic and the theory of institutions. The theory of information flow is a theory of distributed…
Numerous definitions for complexity have been proposed over the last half century, with little consensus achieved on how to use the term. A definition of complexity is supplied here that is closely related to the Kolmogorov Complexity and…
Beyond the local constraints imposed by grammar, words concatenated in long sequences carrying a complex message show statistical regularities that may reflect their linguistic role in the message. In this paper, we perform a systematic…
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…
Data Science is a multidisciplinary field that plays a crucial role in extracting valuable insights and knowledge from large and intricate datasets. Within the realm of Data Science, two fundamental components are Information Theory (IT)…
Numerical analysts might be expected to pay close attention to a branch of complexity theory called information-based complexity theory (IBCT), which produces an abundance of impressive results about the quest for approximate solutions to…
Information theory has been taken as a prospective tool for quantifying the complexity of complex networks. In this paper, we first study the information entropy or uncertainty of a path using the information theory. Then we apply the path…
The authors discuss information-based complexity theory, which is a model of finite-precision computations with real numbers, and its applications to numerical analysis.
Nature is full of random networks of complex topology describing such apparently disparate systems as biological, economical or informatical ones. Their most characteristic feature is the apparent scale-free character of interconnections…