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

Genetic associations between flight speed and growth traits in Nellore cattle

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

Lipid and energy contents in the bodies of queens of Atta sexdens rubropilosa Forel (Hymenoptera, Formicidae): pre-and post-nuptial flight

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Considerations on corrosion and weld repair effects on the fatigue strength of a steel structure critical to the flight-safety

The aim of this study is to analyze the effects of corrosion and successive tungsten inert gas (TIC) welding repairs on the reverse bending fatigue strength of AISI 4130 steel used in components critical to the flight-safety. The tests were performed on hot-rolled steel plate specimens, 1.10 mm and 1.60 mm thick, by means of a SCHENK PWS equipment, with load ratio R = -1, constant amplitude, 30 Hz frequency and room temperature. It was observed that the reverse bending fatigue strength of AISI 4130 steel decreases due to the corrosion and the TIC welding and re-welding processes. (C) 2010 Elsevier Ltd. All rights reserved.

Repair Welding Effects on the Bending Fatigue Strength of AISI 4130 Aeronautical Steel used in a Critical to the Flight-Safety Structure

The aim of this study was to analyze the effect of successive TIG (tungsten inert gas) welding repairs on the reverse bending fatigue strength of AISI 4130 steel, which is widely used in components critical to the flight-safety. In order to simulate the abrupt maneuvers, wind bursts, motor vibration and helixes efforts, which generate cyclic bending loadings at the welded joints of a specific aircraft component called motor cradle, experimental reverse bending fatigue tests were carried out on specimens made from hot-rolled steel plate, 1.10 mm (0.043 in) thick, by mean of a SCHENK PWS equipment, with load ratio R = -1, under constant amplitude, at 30 Hz frequency and room temperature. It was observed that the bending fatigue strength decreases after the TIG (Tungsten Inert Gas) welding process application on AISI 4130 steel, with subsequent decrease due to re-welding sequence as well. Microstructural analyses and microhardness measurements on the base material, heat-affected zone (HAZ) and weld metal, as well as the effects of the weld bead geometry on the obtained results, have complemented this study.

Considerations about the welding repair effects on the structural integrity of an airframe critical to the flight-safety

Structures critical to the flight-safety are commonly submitted to several maintenance repairs at the welded joints in order to prolong the in-service life of aircrafts. The aim of this study is to analyze the effects of Tungsten Inert Gas (TIG) welding repair on the structural integrity of the AISI 4130 aeronautical steel by means of experimental fatigue crack growth tests in base-material, heat-affected zone (HAZ) and weld metal. The tests were performed on hot-rolled steel plate specimens, 0.89 mm thick, with load ratio R = 0.1, constant amplitude, at 10 Hz frequency and room temperature. Increase of the fracture resistance was observed in the weld metal but decreasing in the HAZ after repair. The results were associated to microhardness and microstructural changes with the welding sequence. (C) 2010 Published by Elsevier Ltd.