Related papers: Statistical Laws in Complex Systems
The occurrence of workplace accidents is described within the context of self-organized criticality, a theory from statistical physics that governs a wide range of phenomena across physics, biology, geosciences, economics, and the social…
Ordered chains (such as chains of amino acids) are ubiquitous in biological cells, and these chains perform specific functions contingent on the sequence of their components. Using the existence and general properties of such sequences as a…
Power laws and distributions with heavy tails are common features of many experimentally studied complex systems, like the distribution of the sizes of earthquakes and solar flares, or the duration of neuronal avalanches in the brain.…
Behavior of condensed matter systems deviating from the standard equilibrium conditions is discussed. Statistical properties of coupled dynamic-stochastic systems are studied within a combination of the maximum information principle and the…
The evolution of a gas can be described by different models depending on the observation scale. A natural question, raised by Hilbert in his sixth problem, is whether these models provide consistent predictions. In particular, for rarefied…
A recently proposed unified scaling law for interoccurrence times of earthquakes [P. Bak et al., Phys. Rev. Lett. {\bf 88}, 178501 (2002)] is analyzed, both theoretically and with data from Southern California. We decompose the…
The gap in statistics between multi-variate and time-series analysis can be bridged by using entropy statistics and recent developments in multi-dimensional scaling. For explaining the evolution of the sciences as non-linear dynamics, the…
A plethora of natural and socio-economic phenomena share a striking statistical regularity, that is the magnitude of elements decreases with a power law as a function of their position in a ranking of magnitude. Such regularity is known as…
There are many natural, physical, and biological systems that exhibit multiple time scales. For example, the dynamics of a population of ticks can be described in continuous time during their individual life cycle yet discrete time is used…
Taylor's law describes the fluctuation characteristics underlying a system in which the variance of an event within a time span grows by a power law with respect to the mean. Although Taylor's law has been applied in many natural and social…
We consider nonequilibrium systems with complex dynamics in stationary states with large fluctuations of intensive quantities (e.g. the temperature, chemical potential, or energy dissipation) on long time scales. Depending on the…
The theory of large deviations is concerned with the exponential decay of probabilities of large fluctuations in random systems. These probabilities are important in many fields of study, including statistics, finance, and engineering, as…
Deep neural networks exhibit empirical neural scaling laws, with error decreasing as a power law with increasing model or data size, across a wide variety of architectures, tasks, and datasets. This universality suggests that scaling laws…
We investigate the role of a statistical complexity measure to assign equilibration in isolated quantum systems. While unitary dynamics preserve global purity, expectation values of observables often exhibit equilibration-like behavior,…
As the amount of linked data published on the web grows, attempts are being made to describe and measure it. However even basic statistics about a graph, such as its size, are difficult to express in a uniform and predictable way. In order…
Complexity science offers a wide range of measures for quantifying unpredictability, structure, and information. Yet, a systematic conceptual organization of these measures is still missing. We present a unified framework that locates…
Linguistic laws constitute one of the quantitative cornerstones of modern cognitive sciences and have been routinely investigated in written corpora, or in the equivalent transcription of oral corpora. This means that inferences of…
Spatial statistics is an area of study devoted to the statistical analysis of data that have a spatial label associated with them. Geographers often refer to the "location information" associated with the "attribute information," whose…
Any collection can be ranked. Sports and games are common examples of ranked systems: players and teams are constantly ranked using different methods. The statistical properties of rankings have been studied for almost a century in a…
We report the complete statistical treatment of a system of particles interacting via Newtonian forces in continuous boundary-driven flow, far from equilibrium. By numerically time-stepping the force-balance equations of a model fluid we…