相关论文: Power laws of complex systems from Extreme physica…

We prove a new extremal inequality, motivated by the vector Gaussian broadcast channel and the distributed source coding with a single quadratic distortion constraint problems. As a corollary, this inequality yields a generalization of the…

Taylor's power law is one of the mostly widely known empirical patterns in ecology discovered in the 20th century. It states that the variance of species population density scales as a power-law function of the mean population density.…

The Price equation shows the unity between the fundamental expressions of change in biology, in information and entropy descriptions of populations, and in aspects of thermodynamics. The Price equation partitions the change in the average…

While most useful information theoretic inequalities can be deduced from the basic properties of entropy or mutual information, up to now Shannon's entropy power inequality (EPI) is an exception: Existing information theoretic proofs of the…

We define a one-parameter family of entropies, each assigning a real number to any probability measure on a compact metric space (or, more generally, a compact Hausdorff space with a notion of similarity between points). These entropies…

The unprecedented prowess of measurement techniques provides a detailed, multi-scale look into the depths of living systems. Understanding these avalanches of high-dimensional data -- by distilling underlying principles and mechanisms --…

G. Edelman, O. Sporns, and G. Tononi introduced in theoretical biology the neural complexity of a family of random variables. This functional is a special case of intricacy, i.e., an average of the mutual information of subsystems whose…

Allometric scaling is one of the most pervasive laws in biology. Its origin, however, is still a matter of dispute. Recent studies have established that maximum metabolic rate scales with an exponent larger than that found for basal…

Zipf's power-law distribution is a generic empirical statistical regularity found in many complex systems. However, rather than universality with a single power-law exponent (equal to 1 for Zipf's law), there are many reported deviations…

Complex systems universally exhibit emergence, where macroscopic dynamics arise from local interactions, but a predictive law governing this process has been absent. We establish and verify such a law. We define a system's causal power at a…

Many natural phenomena can be described by power-laws. A closer look at various experimental data reveals more or less significant deviations from a 1/f spectrum. We exemplify such cases with phenomena offered by molecular biology, cell…

There is little doubt in scientific circles that--counting from the origin of life towards today--evolution has led to an increase in the amount of information stored within the genomes of the biosphere. This trend of increasing information…

Several populational networks present complex topologies when implemented in evolutionary algorithms. A common feature of these topologies is the emergence of a power law. Power law behavior with different scaling factors can also be…

Biological approximations, which are universal for diverse species, are well known. With no other experimental data, their invariance to transformations from one species to another yields exact conservation (with respect to biological…

We investigate an extremal dynamics model of evolution with a variable number of units. Due to addition and removal of the units, the topology of the network evolves and the network splits into several clusters. The activity is mostly…

Extreme-order statistics is applied to the branches of an observer in a many-worlds framework. A unitary evolution operator for a step of time is constructed, generating pseudostochastic behaviour with a power-law distribution when applied…

Constraints on changes in expression levels across all cell components imposed by the steady growth of cells have recently been discussed both experimentally and theoretically. By assuming a small environmental perturbation and considering…

Many physical systems share the property of scale invariance. Most of them show ordinary power-law scaling, where quantities can be expressed as a leading power law times a scaling function which depends on scaling-invariant ratios of the…

Maximizing the speed and precision of communication while minimizing power dissipation is a fundamental engineering design goal. Also, biological systems achieve remarkable speed, precision and power efficiency using poorly understood…

We extend a previously theory for the interspecific allometric scaling developed in a $d+1$-dimensional space of metabolic states. The time, which is characteristic of all biological processes, is included as an extra dimension to $d$…