Related papers: Power laws of complex systems from Extreme physica…
A general simple theory for the interspecific allometric scaling is developed in the $d+1$-dimensional space ($d$ biological lengths and a physiological time) of metabolic states of organisms. It is assumed that natural selection shaped the…
Metabolism of living organisms is a foundation of life. The metabolic rate (energy production per unit time) increases slower than organisms' mass. When this phenomenon is considered across different species, it is called interspecific…
In many complex systems, large events are believed to follow power-law, scale-free probability distributions, so that the extreme, catastrophic events are unpredictable. Here, we study coupled chaotic oscillators that display extreme…
Power-law distributions are typical macroscopic features occurring in almost all complex systems observable in nature. As a result, researchers in quantitative analyses must often generate random synthetic variates obeying power-law…
Production of energy is a foundation of life. Metabolic rate of organisms (amount of energy produced per unit time) generally increases slower than organisms' mass, which has important implications for life organization. This phenomenon,…
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…
According to the universal entropy bound, the entropy (and hence information capacity) of a complete weakly self-gravitating physical system can be bounded exclusively in terms of its circumscribing radius and total gravitating energy. The…
The ubiquity of power-law relations in empirical data displays physicists' love of simple laws and uncovering common causes among seemingly unrelated phenomena. However, many reported power laws lack statistical support and mechanistic…
We try to establish a unified information theoretic approach to learning and to explore some of its applications. First, we define {\em predictive information} as the mutual information between the past and the future of a time series,…
Three laws of information theory have been proposed. Labeling by introducing nonsymmetry and formatting by introducing symmetry are defined. The function L (L=lnw, w is the number of microstates, or the sum of entropy and information,…
We show that an equilibriumlike additivity property can remarkably lead to power-law distributions observed frequently in a wide class of out-of-equilibrium systems. The additivity property can determine the full scaling form of the…
An ecological flow network is a weighted directed graph in which nodes are species, edges are "who eats whom" relationships and weights are rates of energy or nutrients transfer between species. Allometric scaling is a ubiquitous feature…
Hierarchies can be modeled by a set of exponential functions, from which we can derive a set of power laws indicative of scaling. The solution to a scaling relation equation is always a power law. The scaling laws are followed by many…
Motivated by a recent article on open problems in artificial life, here I postulate three laws which form a mathematical framework to describe artificial life evolutionary dynamics. They are based on a continuous approximation of population…
Well protected human and laboratory animal populations with abundant resources are evolutionary unprecedented. Physical approach, which takes advantage of their extensively quantified mortality, establishes that its dominant fraction yields…
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…
We study a one-dimensional chain of harmonically coupled units in an asymmetric anharmonic soft potential. Due to nonlinear localisation of energy, this system exhibits extreme events in the sense that individual elements of the chain show…
The subjects of the paper are the likelihood method (LM) and the expected Fisher information (FI) considered from the point od view of the construction of the physical models which originate in the statistical description of phenomena. The…
We define {\em predictive information} $I_{\rm pred} (T)$ as the mutual information between the past and the future of a time series. Three qualitatively different behaviors are found in the limit of large observation times $T$: $I_{\rm…
This paper investigates the role of size in biological organisms. More specifically, how the energy demand, expressed by the metabolic rate, changes according to the mass of an organism. Empirical evidence suggests a power-law relation…