An information-theoretic approach to statistical dependence: Copula information

We discuss the connection between information and copula theories by showing that a copula can be employed to decompose the information content of a multivariate distribution into marginal and dependence components, with the latter quantified by the mutual information. We define the information excess as a measure of deviation from a maximum-entropy distribution. The idea of marginal invariant dependence measures is also discussed and used to show that empirical linear correlation underestimates the amplitude of the actual correlation in the case of non-Gaussian marginals. The mutual information is shown to provide an upper bound for the asymptotic empirical log-likelihood of a copula. An analytical expression for the information excess of T-copulas is provided, allowing for simple model identification within this family. We illustrate the framework in a financial data set. Copyright (C) EPLA, 2009

An empirical test of the gravity p-median model

A customer is presumed to gravitate to a facility by the distance to it and the attractiveness of it. However regarding the location of the facility, the presumption is that the customer opts for the shortest route to the nearest facility.This paradox was recently solved by the introduction of the gravity p-median model. The model is yet to be implemented and tested empirically. We implemented the model in an empirical problem of locating locksmiths, vehicle inspections, and retail stores ofv ehicle spare-parts, and we compared the solutions with those of the p-median model. We found the gravity p-median model to be of limited use for the problem of locating facilities as it either gives solutions similar to the p-median model, or it gives unstable solutions due to a non-concave objective function.

A Spatial-Temporal Downscaling Approach To Construction Of Rainfall Intensity-Duration-Frequency Relations In The Context Of Climate Change

This paper proposes a spatial-temporal downscaling approach to construction of the intensity-duration-frequency (IDF) relations at a local site in the context of climate change and variability. More specifically, the proposed approach is based on a combination of a spatial downscaling method to link large-scale climate variables given by General Circulation Model (GCM) simulations with daily extreme precipitations at a site and a temporal downscaling procedure to describe the relationships between daily and sub-daily extreme precipitations based on the scaling General Extreme Value (GEV) distribution. The feasibility and accuracy of the suggested method were assessed using rainfall data available at eight stations in Quebec (Canada) for the 1961-2000 period and climate simulations under four different climate change scenarios provided by the Canadian (CGCM3) and UK (HadCM3) GCM models. Results of this application have indicated that it is feasible to link sub-daily extreme rainfalls at a local site with large-scale GCM-based daily climate predictors for the construction of the IDF relations for present (1961-1990) and future (2020s, 2050s, and 2080s) periods at a given site under different climate change scenarios. In addition, it was found that annual maximum rainfalls downscaled from the HadCM3 displayed a smaller change in the future, while those values estimated from the CGCM3 indicated a large increasing trend for future periods. This result has demonstrated the presence of high uncertainty in climate simulations provided by different GCMs. In summary, the proposed spatial-temporal downscaling method provided an essential tool for the estimation of extreme rainfalls that are required for various climate-related impact assessment studies for a given region.

Uncertainties In Future Projections Of Extreme Rainfall: The Role Of Climate Model, Emission Scenario And Randomness

Climate change has resulted in substantial variations in annual extreme rainfall quantiles in different durations and return periods. Predicting the future changes in extreme rainfall quantiles is essential for various water resources design, assessment, and decision making purposes. Current Predictions of future rainfall extremes, however, exhibit large uncertainties. According to extreme value theory, rainfall extremes are rather random variables, with changing distributions around different return periods; therefore there are uncertainties even under current climate conditions. Regarding future condition, our large-scale knowledge is obtained using global climate models, forced with certain emission scenarios. There are widely known deficiencies with climate models, particularly with respect to precipitation projections. There is also recognition of the limitations of emission scenarios in representing the future global change. Apart from these large-scale uncertainties, the downscaling methods also add uncertainty into estimates of future extreme rainfall when they convert the larger-scale projections into local scale. The aim of this research is to address these uncertainties in future projections of extreme rainfall of different durations and return periods. We plugged 3 emission scenarios with 2 global climate models and used LARS-WG, a well-known weather generator, to stochastically downscale daily climate models’ projections for the city of Saskatoon, Canada, by 2100. The downscaled projections were further disaggregated into hourly resolution using our new stochastic and non-parametric rainfall disaggregator. The extreme rainfall quantiles can be consequently identified for different durations (1-hour, 2-hour, 4-hour, 6-hour, 12-hour, 18-hour and 24-hour) and return periods (2-year, 10-year, 25-year, 50-year, 100-year) using Generalized Extreme Value (GEV) distribution. By providing multiple realizations of future rainfall, we attempt to measure the extent of total predictive uncertainty, which is contributed by climate models, emission scenarios, and downscaling/disaggregation procedures. The results show different proportions of these contributors in different durations and return periods.

Statistical modelling of extreme rainfall in Madeira Island

Extreme rainfall events have triggered a significant number of flash floods in Madeira Island along its past and recent history. Madeira is a volcanic island where the spatial rainfall distribution is strongly affected by its rugged topography. In this thesis, annual maximum of daily rainfall data from 25 rain gauge stations located in Madeira Island were modelled by the generalised extreme value distribution. Also, the hypothesis of a Gumbel distribution was tested by two methods and the existence of a linear trend in both distributions parameters was analysed. Estimates for the 50– and 100–year return levels were also obtained. Still in an univariate context, the assumption that a distribution function belongs to the domain of attraction of an extreme value distribution for monthly maximum rainfall data was tested for the rainy season. The available data was then analysed in order to find the most suitable domain of attraction for the sampled distribution. In a different approach, a search for thresholds was also performed for daily rainfall values through a graphical analysis. In a multivariate context, a study was made on the dependence between extreme rainfall values from the considered stations based on Kendall’s τ measure. This study suggests the influence of factors such as altitude, slope orientation, distance between stations and their proximity of the sea on the spatial distribution of extreme rainfall. Groups of three pairwise associated stations were also obtained and an adjustment was made to a family of extreme value copulas involving the Marshall–Olkin family, whose parameters can be written as a function of Kendall’s τ association measures of the obtained pairs.

IMPROVED STATISTICAL QCD MODEL FOR THE QUARK CONTENT of THE NUCLEON

The neutron-to-proton ratio of the structure functions, F(2)(n)/F(2)(p), as well as the corresponding difference F(2)(p)-F(2)(n) are obtained within a statistical quark model for the nucleon, where the quark energy levels are given by a central linear confining potential.

Statistical properties of a dissipative kicked system: Critical exponents and scaling invariance

A new universal empirical function that depends on a single critical exponent (acceleration exponent) is proposed to describe the scaling behavior in a dissipative kicked rotator. The scaling formalism is used to describe two regimes of dissipation: (i) strong dissipation and (ii) weak dissipation. For case (i) the model exhibits a route to chaos known as period doubling and the Feigenbaum constant along the bifurcations is obtained. When weak dissipation is considered the average action as well as its standard deviation are described using scaling arguments with critical exponents. The universal empirical function describes remarkably well a phase transition from limited to unlimited growth of the average action. (C) 2012 Elsevier B.V. All rights reserved.

The STATFLUX code: a statistical method for calculation of flow and set of parameters, based on the Multiple-Compartment Biokinetical Model

The code STATFLUX, implementing a new and simple statistical procedure for the calculation of transfer coefficients in radionuclide transport to animals and plants, is proposed. The method is based on the general multiple-compartment model, which uses a system of linear equations involving geometrical volume considerations. Flow parameters were estimated by employing two different least-squares procedures: Derivative and Gauss-Marquardt methods, with the available experimental data of radionuclide concentrations as the input functions of time. The solution of the inverse problem, which relates a given set of flow parameter with the time evolution of concentration functions, is achieved via a Monte Carlo Simulation procedure.Program summaryTitle of program: STATFLUXCatalogue identifier: ADYS_v1_0Program summary URL: http://cpc.cs.qub.ac.uk/summaries/ADYS_v1_0Program obtainable from: CPC Program Library, Queen's University of Belfast, N. IrelandLicensing provisions: noneComputer for which the program is designed and others on which it has been tested: Micro-computer with Intel Pentium III, 3.0 GHzInstallation: Laboratory of Linear Accelerator, Department of Experimental Physics, University of São Paulo, BrazilOperating system: Windows 2000 and Windows XPProgramming language used: Fortran-77 as implemented in Microsoft Fortran 4.0. NOTE: Microsoft Fortran includes non-standard features which are used in this program. Standard Fortran compilers such as, g77, f77, ifort and NAG95, are not able to compile the code and therefore it has not been possible for the CPC Program Library to test the program.Memory, required to execute with typical data: 8 Mbytes of RAM memory and 100 MB of Hard disk memoryNo. of bits in a word: 16No. of lines in distributed program, including test data, etc.: 6912No. of bytes in distributed Program, including test data, etc.: 229 541Distribution format: tar.gzNature of the physical problem: the investigation of transport mechanisms for radioactive substances, through environmental pathways, is very important for radiological protection of populations. One such pathway, associated with the food chain, is the grass-animal-man sequence. The distribution of trace elements in humans and laboratory animals has been intensively studied over the past 60 years [R.C. Pendlenton, C.W. Mays, R.D. Lloyd, A.L. Brooks, Differential accumulation of iodine-131 from local fallout in people and milk, Health Phys. 9 (1963) 1253-1262]. In addition, investigations on the incidence of cancer in humans, and a possible causal relationship to radioactive fallout, have been undertaken [E.S. Weiss, M.L. Rallison, W.T. London, W.T. Carlyle Thompson, Thyroid nodularity in southwestern Utah school children exposed to fallout radiation, Amer. J. Public Health 61 (1971) 241-249; M.L. Rallison, B.M. Dobyns, F.R. Keating, J.E. Rall, F.H. Tyler, Thyroid diseases in children, Amer. J. Med. 56 (1974) 457-463; J.L. Lyon, M.R. Klauber, J.W. Gardner, K.S. Udall, Childhood leukemia associated with fallout from nuclear testing, N. Engl. J. Med. 300 (1979) 397-402]. From the pathways of entry of radionuclides in the human (or animal) body, ingestion is the most important because it is closely related to life-long alimentary (or dietary) habits. Those radionuclides which are able to enter the living cells by either metabolic or other processes give rise to localized doses which can be very high. The evaluation of these internally localized doses is of paramount importance for the assessment of radiobiological risks and radiological protection. The time behavior of trace concentration in organs is the principal input for prediction of internal doses after acute or chronic exposure. The General Multiple-Compartment Model (GMCM) is the powerful and more accepted method for biokinetical studies, which allows the calculation of concentration of trace elements in organs as a function of time, when the flow parameters of the model are known. However, few biokinetics data exist in the literature, and the determination of flow and transfer parameters by statistical fitting for each system is an open problem.Restriction on the complexity of the problem: This version of the code works with the constant volume approximation, which is valid for many situations where the biological half-live of a trace is lower than the volume rise time. Another restriction is related to the central flux model. The model considered in the code assumes that exist one central compartment (e.g., blood), that connect the flow with all compartments, and the flow between other compartments is not included.Typical running time: Depends on the choice for calculations. Using the Derivative Method the time is very short (a few minutes) for any number of compartments considered. When the Gauss-Marquardt iterative method is used the calculation time can be approximately 5-6 hours when similar to 15 compartments are considered. (C) 2006 Elsevier B.V. All rights reserved.

Statistical quark model for the nucleon structure function

A statistical quark model, with quark energy levels given by a central linear confining potential is used to obtain the light sea-quark asymmetry, d̄/ū, and also for the ratio d/u, inside the nucleon. After adjusting a temperature parameter by the Gottfried sum rule violation, and chemical potentials by the valence up and down quark normalizations, the results are compared with experimental data available. © 2009 American Institute of Physics.

Improved statistical quark model for the nucleon structure function

An improved statistical quark model, with quark energy levels given by a central linear confining potential, is used to obtain the light sea-quark asymmetry, d̄/ū, and also for the corresponding difference d̄-ū, inside the nucleon. In the model, a temperature parameter is adjusted by recent results obtained for the Gottfried sum rule violation, with two chemical potentials adjusted by the valence up and down quark normalizations. The results are compared with available recent experimental data. © 2010 American Institute of Physics.

Aplicação da RUSLE a uma pequena bacia hidrográfica da Amazônia

A Amazônia vem sofrendo severas mudanças provocadas por atividades antrópicas, dentre as quais se destaca a transformação de áreas de floresta em áreas de uso agropecuário, resultando na intensificação dos processos erosivos. A erosão, com destaque ao arraste de partículas pelo escoamento superficial, causa redução da fertilidade do solo, prejudicando a produtividade agrícola, além de impactar a qualidade e quantidade dos recursos hídricos superficiais, fato agravado pelo forte regime pluviométrico e solos naturalmente pobres da região. Nesse contexto, o conhecimento dos processos erosivos, através da utilização de modelos matemáticos para predição da perda de solo, auxilia na determinação de práticas de manejo para o uso sustentável dos recursos naturais. A presente pesquisa buscou avaliar a aplicabilidade do modelo empírico RUSLE (Revised Universal Soil Loss Equation) na região, o qual considera a interação entre a energia da chuva, as características de solo e relevo, assim como os usos e manejos praticados. A pesquisa aplicou a RUSLE no trecho superior da bacia do igarapé da Prata, com uma área aproximada de 37 km^², que fica localizada no município de Capitão Poço/PA, aproximadamente 160 km da capital Belém, na Meso Região Nordeste Paraense. A metodologia empregada constou da construção de uma base de dados georreferenciada, formada a partir de fontes públicas, que passaram por adequações para inserção no ambiente SIG, que quando combinados permitiram a geração de um mapa de perda de solo da área de estudo. A pequena bacia do igarapé da Prata apresentou valores da perda de solo que variaram entre 0,004 e 72,48 t/ha.ano, com uma média de 5,12 e desvio padrão de 6,97, onde aproximadamente 12% de sua área total apresentam riscos ambientais devido aos processos erosivos. E o percentual restante, para não sofrer riscos, depende de boas práticas conservacionistas.

Statistical properties for a dissipative model of relativistic particles in a wave packet: A parameter space investigation

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Characterization of Soil Surface Roughness Effects on Runoff and Soil Erosion Rates under Simulated Rainfall

This study aims at identifying the influence of soil surface roughness from small to large aggregates (random roughness) on runoff and soil loss and to investigate the interaction with soil surface seal formation. Bulk samples of a silty clay loam soil were sieved to four aggregate-size classes of 3 to 12, 12 to 20, 20 to 45, 45 to 100 mm, and packed in soil trays set at a 5% slope. Rainfall simulations using an oscillating nozzle simulator were conducted for 90 min at an average rainfall intensity of 50.2 mm h(-1). Soil surface roughness was measured using an instantaneous profile laser scanner and surface sealing was studied by macroscopic analysis of epoxy impregnated soil samples. The rainfall simulations revealed longer times to initiate runoff with increasing soil surface roughness. For random roughness levels up to 6 mm, a decrease in final runoff rate with increasing roughness was observed. This can be attributed to a decreased breakdown of the larger roughness elements on rougher surfaces, thus keeping infiltration rate high. For a random roughness larger than 6 mm, a greater final runoff rate was observed. This was caused by the creation of a thick depositional seal in the concentrated flow areas, thus lowering the infiltration rates. Analysis of impregnated soil sample blocks confirmed the formation of a structural surface seal on smooth surfaces, whereas thick depositional seals were visible in the depressional areas of rougher surfaces. Therefore, from our observations it can be learned that soil surface roughness as formed by the presence of different aggregate sizes reduces runoff but that its effect diminishes due to aggregate breakdown and the formation of thick depositional seals in the case of rough soil surfaces. Sediment concentration increased with increasing soil surface roughness, due to runoff concentration in flow paths. Nevertheless, final soil loss rates were comparable for all soil roughness categories, indicating that random roughness is only important in influencing runoff rates and the time to initiate runoff, but not in influencing sediment export through soil loss rates.

On the statistical and transport properties of a non-dissipative Fermi-Ulam model

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

Spatial distribution of runoff depth from a watershed located in a cuesta relief area of São Paulo State, Brazil

This study was undertaken in a 1566 ha drainage basin situated in an area with cuesta relief in the state of São Paulo, Brazil. The objectives were: 1) to map the maximum potential soil water retention capacity, and 2) to simulate the depth of surface runoff in each geographical position of the area based on a typical rainfall event. The database required for the development of this research was generated in the environment of the geographical information system ArcInfo v.10.1. Undeformed soil samples were collected at 69 points. The ordinary kriging method was used in the interpolation of the values of soil density and maximum potential soil water retention capacity. The spherical model allowed for better adjustment of the semivariograms corresponding to the two soil attributes for the depth of 0 to 20 cm, while the Gaussian model enabled a better fit of the spatial behavior of the two variables for the depth of 20 to 40 cm. The simulation of the spatial distribution revealed a gradual increase in the depth of surface runoff for the rainfall event taken as example (25 mm) from the reverse to the peripheral depression of the cuesta (from west to east). There is a positive aspect observed in the gradient, since the sites of highest declivity, especially those at the front of the cuesta, are closer to the western boundary of the watershed where the lowest depths of runoff occur. This behavior, in conjunction with certain values of erodibility and depending on the land use and cover, can help mitigate the soil erosion processes in these areas.