Related papers: Statistical Laws in Complex Systems
In this paper we quantify the statistical properties and dynamics of the frequency of hashtag use on Twitter. Hashtags are special words used in social media to attract attention and to organize content. Looking at the collection of all…
General characterization of physical measurements is discussed within the framework of a classical information theory. Uncertainty relation for simultaneous measurements of two physical observables is defined in this framework for…
The Gutenberg-Richter law is a fundamental empirical law in seismology describing earthquake frequency-magnitude distributions, with one of its key parameters, the so-called b-value, quantifying the relative frequency of small versus large…
Allometric scaling can reflect underlying mechanisms, dynamics and structures in complex systems; examples include typical scaling laws in biology, ecology and urban development. In this work, we study allometric scaling in scientific…
Zipf's law is a paradigm describing the importance of different elements in communication systems, especially in linguistics. Despite the complexity of the hierarchical structure of language, music has in some sense an even more complex…
Zipf's law, which states that the probability of an observation is inversely proportional to its rank, has been observed in many domains. While there are models that explain Zipf's law in each of them, those explanations are typically…
A plethora of natural, artificial and social systems exist which do not belong to the Boltzmann-Gibbs (BG) statistical-mechanical world, based on the standard additive entropy $S_{BG}$ and its associated exponential BG factor. Frequent…
We review the observations and the basic laws describing the essential aspects of collective motion -- being one of the most common and spectacular manifestation of coordinated behavior. Our aim is to provide a balanced discussion of the…
Data analysis is a powerful tool in all experimental sciences. Statistical methods, such as sampling theory, computer technologies necessary for handling large amounts of data, skill in analysing information contained in different types of…
More than one billion data sampled with different frequencies from several financial instruments were investigated with the aim of testing whether they involve power law. As a result, a known power law with the power exponent around -4 was…
The central philosophy of statistical mechanics (stat-mech) and random-matrix theory of complex systems is that while individual instances are essentially intractable to simulate, the statistical properties of random ensembles obey simple…
The molecular biology revolution of the last seventy five years has transformed our view of living systems. Scientific explanations of biological phenomena are now synonymous with the identification of the genes, proteins, and signaling…
We review the present status of our research and understanding regarding the dynamics and the statistical properties of earthquakes, mainly from a statistical physical viewpoint. Emphasis is put both on the physics of friction and fracture,…
In recent years there has been a surge of interest in the statistics of record-breaking events in stochastic processes. Along with that, many new and interesting applications of the theory of records were discovered and explored. The record…
Even though people in our contemporary, technological society are depending on communication, our understanding of the underlying laws of human communicational behavior continues to be poorly understood. Here we investigate the…
The article introduces corrections to Zipf's and Heaps' laws based on systematic models of the proportion of hapaxes, i.e., words that occur once. The derivation rests on two assumptions: The first one is the standard urn model which…
Many of the numbers appearing in the laws of physics, such as the strength of electromagnetism or the masses of elementary particles, must lie in precise ranges for stars, planets, and chemistry to exist. Why the universe has these values…
Over the last decades, in disciplines as diverse as economics, geography, and complex systems, a perspective has arisen proposing that many properties of cities are quantitatively predictable due to agglomeration or scaling effects. Using…
Complex systems are characterized by specific time-dependent interactions among their many constituents. As a consequence they often manifest rich, non-trivial and unexpected behavior. Examples arise both in the physical and non-physical…
Power law distributions of macroscopic observables are ubiquitous in both the natural and social sciences. They are indicative of correlated, cooperative phenomena between groups of interacting agents at the microscopic level. In this paper…