Related papers: Power laws of complex systems from Extreme physica…
The entropy power inequality (EPI) provides lower bounds on the differential entropy of the sum of two independent real-valued random variables in terms of the individual entropies. Versions of the EPI for discrete random variables have…
Heavy-tailed or power-law distributions are becoming increasingly common in biological literature. A wide range of biological data has been fitted to distributions with heavy tails. Many of these studies use simple fitting methods to find…
When two independent analog signals, X and Y are added together giving Z=X+Y, the entropy of Z, H(Z), is not a simple function of the entropies H(X) and H(Y), but rather depends on the details of X and Y's distributions. Nevertheless, the…
We study an extremal projection principle for families of operators ordered by domination, induced by fixed bounded linear mappings acting on a source with an additive baseline. Stability is defined through domination of second--order…
The primordial confrontation underlying the existence of our universe can be conceived as the battle between entropy and complexity. The law of ever-increasing entropy (Boltzmann H-theorem) evokes an irreversible, one-directional evolution…
This paper proposes a unifying variational approach for proving and extending some fundamental information theoretic inequalities. Fundamental information theory results such as maximization of differential entropy, minimization of Fisher…
Since the time of Darwin, scientists have struggled to reconcile the evolution of biological forms in a universe determined by fixed laws. These laws underpin the origin of life, evolution, human culture and technology, as set by the…
Power law distributions have been repeatedly observed in a wide variety of socioeconomic, biological and technological areas. In many of the observations, e.g., city populations and sizes of living organisms, the objects of interest evolve…
Weakly almost i.i.d. quantum sources are sequences of multipartite states whose fixed-size marginals converge, on average, to tensor powers of a reference state, while allowing arbitrary global correlations and entanglement. We establish…
Axion-like particles (ALPs) are a well-motivated dark matter candidate that solve some of the problems in the clustering of large scale structure in cosmology. ALPs are often described by a simplified quadratic potential to specify the…
This paper deals with parameter estimation from extreme measurements. While being a special case of parameter estimation from partial data, in scenarios where only one sample from a given set of K measurements can be extracted, choosing…
Many biological systems perform close to their physical limits, but promoting this optimality to a general principle seems to require implausibly fine tuning of parameters. Using examples from a wide range of systems, we show that this…
In this article, as a new mathematical approach to origin of the basic laws of nature, using a new algebra-axiomatic matrix formalism based on the ring theory and Clifford algebras , "it is shown that certain mathematical forms of…
Many social, technological and biological interactions involve network relationships whose outcome intimately depends on the structure of the network and on the strengths of the connections. Yet, although much information is now available…
In this paper we consider the axiomatic characterization of information and certainty measures in a unified way. We present the general axiomatic system which captures the common properties of a large number of the measures previously…
All matter is made up of fermions -- one of the fundamental type of particles in nature. Fermions follow the Pauli exclusion principle, stating that two or more identical fermions cannot occupy the same quantum state. Antisymmetry of the…
Using data from gene expression databases on various organisms and tissues, including yeast, nematodes, human normal and cancer tissues, and embryonic stem cells, we found that the abundances of expressed genes exhibit a power-law…
In the present work, via computational simulation we study the statistical distribution of people versus number of steps acquired by them in a learning process, considering Darwin classical theory of evolution, i.e. competition, learning…
Power laws arise in a variety of phenomena ranging from matter undergoing phase transition to the distribution of word frequencies in the English language. Usually, their presence is only apparent when data is abundant, and accurately…
The MaxEnt solutions are shown to display a variety of behaviors (beyond the traditional and customary exponential one) if adequate dynamical information is inserted into the concomitant entropic-variational principle. In particular, we…