Germinal Cocho

Scale-free foraging by primates emerges from their interaction with a complex environment

Scale-free foraging patterns are widespread among animals. These may be the outcome of an optimal searching strategy to find scarce, randomly distributed resources, but a less explored alternative is that this behaviour may result from the interaction of foraging animals with a particular distribution of resources. We introduce a simple foraging model where individual primates follow mental maps and choose their displacements according to a maximum efficiency criterion, in a spatially disordered environment containing many trees with a heterogeneous size distribution. We show that a particular tree-size frequency distribution induces non-Gaussian movement patterns with multiple spatial scales (Lévy walks). These results are consistent with field observations of tree-size variation and spider monkey (Ateles geoffroyi) foraging patterns. We discuss the consequences that our results may have for the patterns of seed dispersal by foraging primates.

Universality of Rank-Ordering Distributions in the Arts and Sciences

Searching for generic behaviors has been one of the driving forces leading to a deep understanding and classification of diverse phenomena. Usually a starting point is the development of a phenomenology based on observations. Such is the case for power law distributions encountered in a wealth of situations coming from physics, geophysics, biology, lexicography as well as social and financial networks. This finding is however restricted to a range of values outside of which finite size corrections are often invoked. Here we uncover a universal behavior of the way in which elements of a system are distributed according to their rank with respect to a given property, valid for the full range of values, regardless of whether or not a power law has previously been suggested. We propose a two parameter functional form for these rank-ordered distributions that gives excellent fits to an impressive amount of very diverse phenomena, coming from the arts, social and natural sciences. It is a discrete version of a generalized beta distribution, given by f(r) = A(N+1-r)b/ra, where r is the rank, N its maximum value, A the normalization constant and (a, b) two fitting exponents. Prompted by our genetic sequence observations we present a growth probabilistic model incorporating mutation-duplication features that generates data complying with this distribution. The competition between permanence and change appears to be a relevant, though not necessary feature. Additionally, our observations mainly of social phenomena suggest that a multifactorial quality resulting from the convergence of several heterogeneous underlying processes is an important feature. We also explore the significance of the distribution parameters and their classifying potential. The ubiquity of our findings suggests that there must be a fundamental underlying explanation, most probably of a statistical nature, such as an appropriate central limit theorem formulation.

On the behavior of journal impact factor rank-order distribution

An empirical law for the rank-order behavior of journal impact factors is found. Using an extensive data base on impact factors including journals on education, agrosciences, geosciences, mathematics, chemistry, medicine, engineering, physics, biosciences and environmental, computer and material sciences, we have found extremely good fittings outperforming other rank-order models. Based in our results, we propose a two-exponent Lotkaian Informetrics. Some extensions to other areas of knowledge are discussed.

Fitting Ranked Linguistic Data with Two-Parameter Functions

It is well known that many ranked linguistic data can fit well with one-parameter models such as Zipf’s law for ranked word frequencies. However, in cases where discrepancies from the one-parameter model occur (these will come at the two extremes of the rank), it is natural to use one more parameter in the fitting model. In this paper, we compare several two-parameter models, including Beta function, Yule function, Weibull function—all can be framed as a multiple regression in the logarithmic scale—in their fitting performance of several ranked linguistic data, such as letter frequencies, word-spacings, and word frequencies. We observed that Beta function fits the ranked letter frequency the best, Yule function fits the ranked word-spacing distribution the best, and Altmann, Beta, Yule functions all slightly outperform the Zipf’s power-law function in word ranked- frequency distribution.

Tail universalities in rank distributions as an algebraic problem: The beta-like function

Although power laws of the Zipf type have been used by many workers to fit rank distributions in different fields like in economy, geophysics, genetics, soft-matter, networks, etc. these fits usually fail at the tail. Some distributions have been proposed to solve the problem, but unfortunately they do not fit at the same time the body and the tail of the distribution. We show that many different data in rank laws, like in granular materials, codons, author impact in scientific journal, etc. can be very well fitted by the integrand of a beta function (that we call beta-like function). Then we propose that such universality can be due to the fact that systems made from many subsystems or choices, present stretched exponential frequency-rank functions which qualitatively and quantitatively are well fitted with the beta-like function distribution in the limit of many random variables. We give a plausibility argument for this observation by transforming the problem into an algebraic one: finding the rank of successive products of numbers, which is basically a multinomial process. From a physical point of view, the observed behavior at the tail seems to be related with the onset of different mechanisms that are dominant at different scales, providing crossovers and finite size effects.

Discrete systems, cell-cell interactions and color pattern of animals. I. Conflicting dynamics and pattern formation.

The morphogenesis of the color pattern of animals is modeled within the framework of a clonal model. The model takes into account the, sometimes conflicting, cell-cell and cell-background interactions. The color patterns of some reptiles and mammals are found to be consistent with the predictions of the model.

The tails of rank-size distributions due to multiplicative processes: from power laws to stretched exponentials and beta-like functions

Although power laws have been used to fit rank distributions in many different contexts, they usually fail at the tail. Here we show that many different data in rank laws, like in granular materials, codons, author impact in scientific journals, etc are very well fitted by a β-like function ({a, b} distribution). Since this distribution is indeed ubiquitous, it is reasonable to associate it with some kind of general mechanism. In particular, we have found that the macrostates of the product of discrete probability distributions imply stretched exponential-like frequency-rank functions, which qualitatively and quantitatively can be fitted with the {a,b} distribution in the limit of many random variables. We show this by transforming the problem into an algebraic one: finding the rank of successive products of a given set of numbers.

Discrete systems, cell-cell interactions and color pattern of animals. II: Clonal theory and cellular automata

The morphogenesis of the color pattern of animals is modeled with cellular automata. The cell-cell near neighbor interactions are taken into account and impose restrictions on the model. The allowed patterns are observed in reptiles, felines and fishes.

Antigenic homology of HIV-1 GP41 and human platelet glycoprotein GPIIIa (integrin β3)

Fifty-eight of 89 serum samples (65.17%) from HIV-1-infected individuals at various disease stages contain antibodies that react with a platelet peptide located in the cytoplasmic domain of integrin beta3, glycoprotein GPIIIa (aa749-761; sequence DRKEFAKFEEERA). Rabbit polyclonal antibodies raised against the synthetic platelet peptide also react with the structurally homologous HIV-1 gp41-derived peptide (EKNEQELLELDKW(A)) and bind to a Western blot band with molecular weight corresponding to HIV-1 gp41. These findings point to molecular mimicry between HIV-1 and a human membrane protein found in platelets and other cells that could be of pathologic consequence.

Rank Diversity of Languages: Generic Behavior in Computational Linguistics

Statistical studies of languages have focused on the rank-frequency distribution of words. Instead, we introduce here a measure of how word ranks change in time and call this distribution rank diversity. We calculate this diversity for books published in six European languages since 1800, and find that it follows a universal lognormal distribution. Based on the mean and standard deviation associated with the lognormal distribution, we define three different word regimes of languages: “heads” consist of words which almost do not change their rank in time, “bodies” are words of general use, while “tails” are comprised by context-specific words and vary their rank considerably in time. The heads and bodies reflect the size of language cores identified by linguists for basic communication. We propose a Gaussian random walk model which reproduces the rank variation of words in time and thus the diversity. Rank diversity of words can be understood as the result of random variations in rank, where the size of the variation depends on the rank itself. We find that the core size is similar for all languages studied.