Related papers: Universal statistics of selected values
In probability theory, there is a tendency to treat one random variable with a given distribution as being just as good as any other. By and large this is fine because probability is (mostly) concerned with distributional properties of…
Physics is based on probabilities as fundamental entities of a mathematical description. Expectation values of observables are computed according to the classical statistical rule. The overall probability distribution for one world covers…
We consider several one-species population dynamics model with finite and infinite carrying capacity, time dependent growth and effort rates and solve them analytically. We show that defining suitable scaling functions for a given time, one…
One explanation for the impressive recent boom in network theory might be that it provides a promising tool for an understanding of complex systems. Network theory is mainly focusing on discrete large-scale topological structures rather…
Shepard's universal law of generalization is a remarkable hypothesis about how intelligent organisms should perceive similarity. In its broadest form, the universal law states that the level of perceived similarity between a pair of stimuli…
Systems as diverse as genetic networks or the world wide web are best described as networks with complex topology. A common property of many large networks is that the vertex connectivities follow a scale-free power-law distribution. This…
We are living in an uncertain and dynamically changing world, where optimal decision-making under uncertainty is directly linked to the survival of species. However, evolutionary selection pressures that shape value-based decision-making…
We revisit the classical population genetics model of a population evolving under multiplicative selection, mutation and drift. The number of beneficial alleles in a multi-locus system can be considered a trait under exponential selection.…
We investigate the survivor distributions of a spatially extended model of competitive dynamics in different geometries. The model consists of a deterministic dynamical system of individual agents at specified nodes, which might or might…
A unified approach is proposed to describe the statistics of the short time dynamics of multiscale complex systems. The probability density function of the relevant time series (signal) is represented as a statistical superposition of a…
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…
For a given distribution, learning algorithm, and performance metric, the rate of convergence (or data-scaling law) is the asymptotic behavior of the algorithm's test performance as a function of number of train samples. Many learning…
Weak purifying selection, acting on many linked mutations, may play a major role in shaping patterns of molecular evolution in natural populations. Yet efforts to infer these effects from DNA sequence data are limited by our incomplete…
One of the most intriguing questions in evolution is how organisms exhibit suitable phenotypic variation to rapidly adapt in novel selective environments which is crucial for evolvability. Recent work showed that when selective environments…
We reconsider the deterministic haploid mutation-selection equation with two types. This is an ordinary differential equation that describes the type distribution (forward in time) in a population of infinite size. This paper establishes…
If evolution can be connected to the principle of least action, and if it is depicted in evolution space versus time then it corresponds to the direction of ultimate causation. As an organism evolves and follows a path of proximate…
In probability theory and statistics, the IID model represents a single population, and a large, potentially infinite sample from this population. Main theorems, in particular the central limit theorem and laws of large number (LLN) assure…
The prevalence of many urban phenomena changes systematically with population size. We propose a theory that unifies models of economic complexity and cultural evolution to derive urban scaling. The theory accounts for the difference in…
Natural populations often show enhanced genetic drift consistent with a strong skew in their offspring number distribution. The skew arises because the variability of family sizes is either inherently strong or amplified by population…
We study the rescaled probability distribution of the critical depinning force of an elastic system in a random medium. We put in evidence the underlying connection between the critical properties of the depinning transition and the extreme…