The gradually truncated Lévy flight: Stochastic process for complex systems

Power-law distributions, i.e. Levy flights have been observed in various economical, biological, and physical systems in high-frequency regime. These distributions can be successfully explained via gradually truncated Levy flight (GTLF). In general, these systems converge to a Gaussian distribution in the low-frequency regime. In the present work, we develop a model for the physical basis for the cut-off length in GTLF and its variation with respect to the time interval between successive observations. We observe that GTLF automatically approach a Gaussian distribution in the low-frequency regime. We applied the present method to analyze time series in some physical and financial systems. The agreement between the experimental results and theoretical curves is excellent. The present method can be applied to analyze time series in a variety of fields, which in turn provide a basis for the development of further microscopic models for the system. © 2000 Elsevier Science B.V. All rights reserved.

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.

Tsallis statistics and gradually truncated Levy flight - distribution of an economical index

Tsallis postulated a generalized form for entropy and give rise to a new statistics now known as Tsallis statistics. In the present work, we compare the Tsallis statistics with the gradually truncated Levy flight, and discuss the distribution of an economical index-the Standard and Poor's 500-using the values of standard deviation as calculated by our model. We find that both statistics give almost the same distribution. Thus we feel that gradual truncation of Levy distribution, after certain critical step size for describing complex systems, is a requirement of generalized thermodynamics or similar. The gradually truncated Levy flight is based on physical considerations and bring a better physical picture of the dynamics of the whole system. Tsallis statistics gives a theoretical support. Both statistics together can be utilized for the development of a more exact portfolio theory or to understand better the complexities in human and financial behaviors. A comparison of both statistics is made. (C) 2002 Published by Elsevier B.V. B.V.

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.

Gradually truncated log-normal in USA publicly traded firm size distribution

We study the statistical distribution of firm size for USA and Brazilian publicly traded firms through the Zipf plot technique. Sale size is used to measure firm size. The Brazilian firm size distribution is given by a log-normal distribution without any adjustable parameter. However, we also need to consider different parameters of log-normal distribution for the largest firms in the distribution, which are mostly foreign firms. The log-normal distribution has to be gradually truncated after a certain critical value for USA firms. Therefore, the original hypothesis of proportional effect proposed by Gibrat is valid with some modification for very large firms. We also consider the possible mechanisms behind this distribution. (c) 2006 Published by Elsevier B.V.

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.

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.

Distribuição de lei de potência gradualmente truncada aplicada na educação: vestibular da Academia da Força Aérea

Pós-graduação em Física - IGCE

A distribuição de lei de potência gradualmente truncada na educação: exame de vestibular da UNESP

Pós-graduação em Física - IGCE

Distribuições estatísticas: citações de publicações científicas e de cientistas

Pós-graduação em Física - IGCE

Observations on the flight paths of the day-flying moth Virbia lamae during periods of mate location: do males have a strategy for contacting the pheromone plume?

1. To maximize the probability of rapid contact with a female’s pheromone plume, the trajectories of male foraging flights might be expected to be directed with respect to wind flow and also to be energetically efficient. 2. Flights directed either upwind, downwind, or crosswind have been proposed as optimal strategies for rapid and/or energetically efficient plume contact. Other possible strategies are random and Lévy walks, which have trajectories and turn frequencies that are not dictated by the direction of wind flow. 3. The planar flight paths of males of the day-active moth Virbia lamae were recorded during the customary time of its sexual activity. 4. We found no directional preference in these foraging flights with respect to the direction of contemporaneous wind flow, but, because crosswind encompasses twice the possible orientations of either upwind or downwind, a random orientation is in effect a de facto crosswind strategy. 5. A crosswind preference should be favoured when the plume extends farther downwind than crosswind, and this strategy is realized by V. lamae males by a random orientation of their trajectories with respect to current wind direction

Probing the oligomeric structure of an enzyme by electrospray ionization time-of-flight mass spectrometry.

Electrospray ionization time-of-flight (ESI-TOF) mass spectrometry was used to study the quaternary structure of 4-oxalocrotonate tautomerase (EC 5.3.2; 4OT), and four analogues prepared by total chemical synthesis. Wild-type 4OT is a hexamer of 62 amino acid subunits and contains no cysteine residues. The analogues were: (desPro1)4OT, a truncated construct in which Pro1 was deleted; (Cpc1)4OT in which Pro1 was replaced with cyclopentane carboxylate; a derivative [Met(O)45]4OT in which Met45 was oxidized to the sulfoxide; and an analogue (Nle45)4OT in which Met45 was replaced with norleucine. ESI of (Nle45)4OT, (Cpc1)4OT, and 4OT from solution conditions under which the native enzyme was fully active (5 mM ammonium bicarbonate buffer, pH 7.5) gave the intact hexamer as the major species detected by TOF mass spectrometry. In contrast, analysis of [Met(O)45]4OT and (desPro1)4OT under similar conditions yielded predominantly monomer ions. The ESI-TOF measurements were consistent with structural data obtained from circular dichroism spectroscopy. In the context of kinetic data collected for 4OT and these analogues, ESI-TOF mass spectrometry also provided important evidence for the structural and mechanistic significance of the catalytically important Pro1 residue in 4OT.

Identification Of Corynebacterium Spp. Isolated From Bovine Intramammary Infections By Matrix-assisted Laser Desorption Ionization-time Of Flight Mass Spectrometry.

Corynebacterium species (spp.) are among the most frequently isolated pathogens associated with subclinical mastitis in dairy cows. However, simple, fast, and reliable methods for the identification of species of the genus Corynebacterium are not currently available. This study aimed to evaluate the usefulness of matrix-assisted laser desorption ionization/mass spectrometry (MALDI-TOF MS) for identifying Corynebacterium spp. isolated from the mammary glands of dairy cows. Corynebacterium spp. were isolated from milk samples via microbiological culture (n=180) and were analyzed by MALDI-TOF MS and 16S rRNA gene sequencing. Using MALDI-TOF MS methodology, 161 Corynebacterium spp. isolates (89.4%) were correctly identified at the species level, whereas 12 isolates (6.7%) were identified at the genus level. Most isolates that were identified at the species level with 16 S rRNA gene sequencing were identified as Corynebacterium bovis (n=156; 86.7%) were also identified as C. bovis with MALDI-TOF MS. Five Corynebacterium spp. isolates (2.8%) were not correctly identified at the species level with MALDI-TOF MS and 2 isolates (1.1%) were considered unidentified because despite having MALDI-TOF MS scores >2, only the genus level was correctly identified. Therefore, MALDI-TOF MS could serve as an alternative method for species-level diagnoses of bovine intramammary infections caused by Corynebacterium spp.

A Metabolomic Protocol For Plant Systematics By Matrix-assisted Laser-desorption/ionization Time-of Flight Mass Spectrometry.

Matrix-assisted laser desorption/ionization time-of flight mass spectrometry (MALDI-TOF MS) has been widely used for the identification and classification of microorganisms based on their proteomic fingerprints. However, the use of MALDI-TOF MS in plant research has been very limited. In the present study, a first protocol is proposed for metabolic fingerprinting by MALDI-TOF MS using three different MALDI matrices with subsequent multivariate data analysis by in-house algorithms implemented in the R environment for the taxonomic classification of plants from different genera, families and orders. By merging the data acquired with different matrices, different ionization modes and using careful algorithms and parameter selection, we demonstrate that a close taxonomic classification can be achieved based on plant metabolic fingerprints, with 92% similarity to the taxonomic classifications found in literature. The present work therefore highlights the great potential of applying MALDI-TOF MS for the taxonomic classification of plants and, furthermore, provides a preliminary foundation for future research.

Profile Of Phenolic Compounds Of Brazilian Virgin Olive Oils By Rapid Resolution Liquid Chromatography Coupled To Electrospray Ionisation Time-of-flight Mass Spectrometry (rrlc-esi-tof-ms).

In recent years, agronomical researchers began to cultivate several olive varieties in different regions of Brazil to produce virgin olive oil (VOO). Because there has been no reported data regarding the phenolic profile of the first Brazilian VOO, the aim of this work was to determine phenolic contents of these samples using rapid-resolution liquid chromatography coupled to electrospray ionisation time-of-flight mass spectrometry. 25 VOO samples from Arbequina, Koroneiki, Arbosana, Grappolo, Manzanilla, Coratina, Frantoio and MGS Mariense varieties from three different Brazilian states and two crops were analysed. It was possible to quantify 19 phenolic compounds belonging to different classes. The results indicated that Brazilian VOOs have high total phenolic content because the values were comparable with those from high-quality VOOs produced in other countries. VOOs from Coratina, Arbosana and Grappolo presented the highest total phenolic content. These data will be useful in the development and improvement of Brazilian VOO.