Power-law distributions for the citation index of scientific publications and scientists

The number of citations of a scientific publication or of an individual scientist has become an important factor of quality assessment in science. We report a study of the statistical distribution of the citation index of both scientific publications and scientists. We give numerical evidence that Tsallis (power law) statistics explains the entire distribution over eight orders of magnitude (10-4 to 10(4)). Also, we draw Zipf plots in order to analyze the statistical distribution of the citation index of Brazilian and international physicists and chemists. The relatively small group of Brazilian scientists seems more adequate to explain the dynamics of the citation index. In this case, we find that the distribution of the citation index can also be explained by a gradually truncated power law with similar parameters. We finally discuss possible mechanisms behind the citation index of scientists and scientific publications.

Friction losses in valves and fittings for power-law fluids

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Power law distribution in education: Effect of economical, teaching, and study conditions in university entrance examination

We studied the statistical distribution of student's performance, which is measured through their marks, in university entrance examination (Vestibular) of UNESP (Universidade Estadual Paulista) with respect to (i) period of study - day versus night period (ii) teaching conditions - private versus public school (iii) economical conditions - high versus low family income. We observed long ubiquitous power law tails in physical and biological sciences in all cases. The mean value increases with better study conditions followed by better teaching and economical conditions. In humanities, the distribution is close to normal distribution with very small tail. This indicates that these power law tails in science subjects axe due to the nature of the subjects themselves. Further and better study, teaching and economical conditions axe more important for physical and biological sciences in comparison to humanities at this level of study. We explain these statistical distributions through Gradually Truncated Power law distributions. We discuss the possible reason for this peculiar behavior.

The gradually truncated Levy flight for systems with power-law distributions

Power-law distributions have been observed in various economical and physical systems. Levy flights have infinite variance which discourage a physical approach. We introduce a class of stochastic processes, the gradually truncated Levy flight in which large steps of a Levy flight are gradually eliminated. It has finite variance and the system can be analyzed in a closed form. We applied the present method to explain the distribution of a particular economical index. The present method can be applied to describe time series in a variety of fields, i.e. turbulent flow, anomalous diffusion, polymers, etc. (C) 1999 Elsevier B.V. B.V. All rights reserved.

Finns growth dynamics, competition and power-law scaling

We study the growth dynamics of the size of manufacturing firms considering competition and normal distribution of competency. We start with the fact that all components of the system struggle with each other for growth as happened in real competitive business world. The detailed quantitative agreement of the theory with empirical results of firms growth based on a large economic database spanning over 20 years is good with a single set of the parameters for all the curves. Further, the empirical data of the variation of the standard deviation of the growth rate with the size of the firm are in accordance with the present theory rather than a simple power law. (C) 2003 Elsevier B.V. B.V. All rights reserved.

Power-law distribution in a learning process: competition, learning and natural selection

In the present work, we propose a model for the statistical distribution of people versus number of steps acquired by them in a learning process, based on competition, learning and natural selection. We consider that learning ability is normally distributed. We found that the number of people versus step acquired by them in a learning process is given through a power law. As competition, learning and selection is also at the core of all economical and social systems, we consider that power-law scaling is a quantitative description of this process in social systems. This gives an alternative thinking in holistic properties of complex systems. (C) 2004 Elsevier B.V. All rights reserved.

Power law distribution in education: University entrance examination

We studied the statistical distribution of candidate's performance which is measured through their marks in university entrance examination (Vestibular) of UNESP (Universidade Estadual Paulista) for years 1998, 1999, and 2000. All students are divided in three groups: Physical, Biological and Humanities. We paid special attention to the examination of Portuguese language which is common for all and examinations for the particular area. We observed long ubiquitous power law tails in Physical and Biological sciences. This indicate the presence of strong positive feedback in sciences. We are able to explain completely these statistical distributions through Gradually Truncated Power law distributions which we developed recently to explain statistical behavior of financial market. The statistical distribution in case of Portuguese language and humanities is close to normal distribution. We discuss the possible reason for this peculiar behavior.

Taylor's power law for ecological communities: an explanation on nonextensive/nonlinear statistical grounds

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Reti di partecipazione fra società di capitale in Italia: presenza di topologie caratterizzate da distribuzioni power law

Quando la probabilità di misurare un particolare valore di una certa quantità varia inversamente come potenza di tale valore, il quantitativo è detto come seguente una power-law, conosciuta anche come legge di Zipf o distribuzione di Pareto. Obiettivo di questa tesi sarà principalmente quello di verificare se il campione esteso di imprese segue la power-law (e se sì, in che limiti). A tale fine si configureranno i dati in un formato di rete monomodale, della quale si studieranno alcune macro-proprietà di struttura a livllo complessivo e con riferimento alle componenti (i singoli subnet distinti) di maggior dimensione. Successivamente si compiranno alcuni approfondimenti sulla struttura fine di alcuni subnet, essenzialmente rivolti ad evidenziare la potenza di unapproccio network-based, anche al fine di rivelare rilevanti proprietà nascoste del sistema economico soggiacente, sempre, ovviamente, nei limiti della modellizzazione adottata. In sintesi, ciò che questo lavoro intende ottenere è lo sviluppo di un approccio alternativo al trattamento dei big data a componente relazionale intrinseca (in questo caso le partecipazioni di capitale), verso la loro conversione in "big knowledge": da un insieme di dati cognitivamente inaccessibili, attraverso la strutturazione dell'informazione in modalità di rete, giungere ad una conoscenza sufficientemente chiara e giustificata.

Analytical bearing capacity of strip footing in weightless materials with power-law failure criteria

Sokolovskii’s method of characteristics is extended to provide analytical solutions for the ultimate load at the moment of plastic failure under plane-strain conditions of shallow strip foundations on weightless rigid-plastic media with a noncohesive power-law failure envelope. The formulation is made parametrically in terms of the instantaneous friction angle, and the key idea to obtain the bearing capacity is that information can be transmitted from the free surface (where external loads are known) to the contact plane of the foundation. The methodology can consider foundations adjacent to a slope, external surcharges at the free surface, and inclined loads (both on the slope and on the foundation). Sensitivity analyses illustrate the influence on bearing capacity of changes in the different geometrical parameters involved. An application example is presented and design plots are provided, and model predictions are compared with results of bearing capacity tests under low gravity.

Intramolecular vibrational dephasing obeys a power law at intermediate times

Experimental intramolecular vibrational dephasing transients for several large organic molecules are reanalyzed. Fits to the experimental data, as well as full numerical quantum calculations with a factorized potential surface for all active degrees of freedom of fluorene indicate that power law decays, not exponentials, occur at intermediate times. The results support a proposal that power law decays describe vibrational dephasing dynamics in large molecules at intermediate times because of the local nature of energy flow.

A power law for cells

Darwin observed that multiple, lowly organized, rudimentary, or exaggerated structures show increased relative variability. However, the cellular basis for these laws has never been investigated. Some animals, such as the nematode Caenorhabditis elegans, are famous for having organs that possess the same number of cells in all individuals, a property known as eutely. But for most multicellular creatures, the extent of cell number variability is unknown. Here we estimate variability in organ cell number for a variety of animals, plants, slime moulds, and volvocine algae. We find that the mean and variance in cell number obey a power law with an exponent of 2, comparable to Taylor's law in ecological processes. Relative cell number variability, as measured by the coefficient of variation, differs widely across taxa and tissues, but is generally independent of mean cell number among homologous tissues of closely related species. We show that the power law for cell number variability can be explained by stochastic branching process models based on the properties of cell lineages. We also identify taxa in which the precision of developmental control appears to have evolved. We propose that the scale independence of relative cell number variability is maintained by natural selection.

The XMM deep survey in the CDF-S. VI. Obscured AGN selected as infrared power-law galaxies

Context. Accretion onto supermassive black holes is believed to occur mostly in obscured active galactic nuclei (AGN). Such objects are proving rather elusive in surveys of distant galaxies, including those at X-ray energies. Aims. Our main goal is to determine whether the revised IRAC criteria of Donley et al. (2012, ApJ, 748, 142; objects with an infrared (IR) power-law spectral shape), are effective at selecting X-ray type-2 AGN (i.e., absorbed N_H > 10^22 cm^-2). Methods. We present the results from the X-ray spectral analysis of 147 AGN selected by cross-correlating the highest spectral quality ultra-deep XMM-Newton and the Spitzer/IRAC catalogues in the Chandra Deep Field South. Consequently it is biased towards sources with high S/N X-ray spectra. In order to measure the amount of intrinsic absorption in these sources, we adopt a simple X-ray spectral model that includes a power-law modified by intrinsic absorption at the redshift of each source and a possible soft X-ray component. Results. We find 21/147 sources to be heavily absorbed but the uncertainties in their obscuring column densities do not allow us to confirm their Compton-Thick nature without resorting to additional criteria. Although IR power-law galaxies are less numerous in our sample than IR non-power-law galaxies (60 versus 87 respectively), we find that the fraction of absorbed (N_H^intr > 10^22 cm^-2) AGN is significantly higher (at about 3 sigma level) for IR-power-law sources (similar to 2/3) than for those sources that do not meet this IR selection criteria (~1/2). This behaviour is particularly notable at low luminosities, but it appears to be present, although with a marginal significance, at all luminosities. Conclusions. We therefore conclude that the IR power-law method is efficient in finding X-ray-absorbed sources. We would then expect that the long-sought dominant population of absorbed AGN is abundant among IR power-law spectral shape sources not detected in X-rays.

Size frequency distributions of the florid prion protein aggregates in variant Creutzfeldt-Jakob disease follow a power-law function

The objective was to test the hypothesis that the size frequency distributions of the prion protein (PrP) plaques in cases of variant Creutzfeldt-Jakob disease (vCJD) follow a power-law function. The design was a retrospective neuropathological study. The patients were 11 cases of clinically and neuropathologically verified vCJD. Size distributions of the diffuse and florid-type plaques were measured in several areas of the cerebral cortex and hippocampus from each case and a power-law function fitted to each distribution. The size distributions of the florid and diffuse plaques were fitted successfully by a powerlaw function in 100% and 42% of brain areas investigated respectively. Processes of aggregation/disaggregation may be more important than surface diffusion in the pathogenesis of the florid plaques. By contrast, surface diffusion may be a more significant factor in the development of the diffuse plaques. © Springer-Verlag Italia 2006.

Testing for financial crashes using the Log Periodic Power Law model

Many papers claim that a Log Periodic Power Law (LPPL) model fitted to financial market bubbles that precede large market falls or 'crashes', contains parameters that are confined within certain ranges. Further, it is claimed that the underlying model is based on influence percolation and a martingale condition. This paper examines these claims and their validity for capturing large price falls in the Hang Seng stock market index over the period 1970 to 2008. The fitted LPPLs have parameter values within the ranges specified post hoc by Johansen and Sornette (2001) for only seven of these 11 crashes. Interestingly, the LPPL fit could have predicted the substantial fall in the Hang Seng index during the recent global downturn. Overall, the mechanism posited as underlying the LPPL model does not do so, and the data used to support the fit of the LPPL model to bubbles does so only partially. © 2013.