Derivation of the probability distribution function for the local density of states of a disordered quantum wire via the replica trick and supersymmetry

We consider the statistical properties of the local density of states of a one-dimensional Dirac equation in the presence of various types of disorder with Gaussian white-noise distribution. It is shown how either the replica trick or supersymmetry can be used to calculate exactly all the moments of the local density of states.' Careful attention is paid to how the results change if the local density of states is averaged over atomic length scales. For both the replica trick and supersymmetry the problem is reduced to finding the ground state of a zero-dimensional Hamiltonian which is written solely in terms of a pair of coupled spins which are elements of u(1, 1). This ground state is explicitly found for the particular case of the Dirac equation corresponding to an infinite metallic quantum wire with a single conduction channel. The calculated moments of the local density of states agree with those found previously by Al'tshuler and Prigodin [Sov. Phys. JETP 68 (1989) 198] using a technique based on recursion relations for Feynman diagrams. (C) 2001 Elsevier Science B.V. All rights reserved.

Cavity QED analog of the harmonic-oscillator probability distribution function and quantum collapses

We establish a connection between the simple harmonic oscillator and a two-level atom interacting with resonant, quantized cavity and strong driving fields, which suggests an experiment to measure the harmonic-oscillator's probability distribution function. To achieve this, we calculate the Autler-Townes spectrum by coupling the system to a third level. We find that there are two different regions of the atomic dynamics depending on the ratio of the: Rabi frequency Omega (c) of the cavity field to that of the Rabi frequency Omega of the driving field. For Omega (c)

Levene tests of homogeneity of variance for general block and treatment designs

This article develops a weighted least squares version of Levene's test of homogeneity of variance for a general design, available both for univariate and multivariate situations. When the design is balanced, the univariate and two common multivariate test statistics turn out to be proportional to the corresponding ordinary least squares test statistics obtained from an analysis of variance of the absolute values of the standardized mean-based residuals from the original analysis of the data. The constant of proportionality is simply a design-dependent multiplier (which does not necessarily tend to unity). Explicit results are presented for randomized block and Latin square designs and are illustrated for factorial treatment designs and split-plot experiments. The distribution of the univariate test statistic is close to a standard F-distribution, although it can be slightly underdispersed. For a complex design, the test assesses homogeneity of variance across blocks, treatments, or treatment factors and offers an objective interpretation of residual plot.

On measuring quality of a probabilistic commodity forecast for a system that incorporates seasonal climate forecasts

Regional commodity forecasts are being used increasingly in agricultural industries to enhance their risk management and decision-making processes. These commodity forecasts are probabilistic in nature and are often integrated with a seasonal climate forecast system. The climate forecast system is based on a subset of analogue years drawn from the full climatological distribution. In this study we sought to measure forecast quality for such an integrated system. We investigated the quality of a commodity (i.e. wheat and sugar) forecast based on a subset of analogue years in relation to a standard reference forecast based on the full climatological set. We derived three key dimensions of forecast quality for such probabilistic forecasts: reliability, distribution shift, and change in dispersion. A measure of reliability was required to ensure no bias in the forecast distribution. This was assessed via the slope of the reliability plot, which was derived from examination of probability levels of forecasts and associated frequencies of realizations. The other two dimensions related to changes in features of the forecast distribution relative to the reference distribution. The relationship of 13 published accuracy/skill measures to these dimensions of forecast quality was assessed using principal component analysis in case studies of commodity forecasting using seasonal climate forecasting for the wheat and sugar industries in Australia. There were two orthogonal dimensions of forecast quality: one associated with distribution shift relative to the reference distribution and the other associated with relative distribution dispersion. Although the conventional quality measures aligned with these dimensions, none measured both adequately. We conclude that a multi-dimensional approach to assessment of forecast quality is required and that simple measures of reliability, distribution shift, and change in dispersion provide a means for such assessment. The analysis presented was also relevant to measuring quality of probabilistic seasonal climate forecasting systems. The importance of retaining a focus on the probabilistic nature of the forecast and avoiding simplifying, but erroneous, distortions was discussed in relation to applying this new forecast quality assessment paradigm to seasonal climate forecasts. Copyright (K) 2003 Royal Meteorological Society.

Efeito da restrição hídrica sobre o crescimento de clones de eucalipto

O estabelecimento e o crescimento inicial de espécies florestais no campo são fortemente afetados pela disponibilidade de água no solo e pela época de plantio, por isso, o presente trabalho estuda o impacto do déficit hídrico no crescimento de mudas de dois clones do híbrido Eucalyptus grandis x Eucalyptus urophylla, ambos submetidos a 4 níveis de déficit hídrico, em duas épocas de plantio. O estudo foi realizado na área experimental do Núcleo de Estudos e Difusão de Tecnologia em Florestas, Recursos Hídricos e Agricultura Sustentável (NEDTEC), do Centro de Ciências Agrárias da Universidade Federal do Espírito Santo (CCA-UFES), localizado no município de Jerônimo Monteiro. O trabalho foi realizado em duas épocas distintas, sendo a primeira no período de 09 de fevereiro a 09 de junho de 2009 e a segunda no período de 11 de julho a 07 de novembro de 2009, visando à realização das observações em diferentes condições de regime de radiação, déficit de pressão do vapor do ar, temperatura, umidade relativa do ar e velocidade do vento. O delineamento experimental utilizado foi o inteiramente ao acaso em parcelas subdivididas 2 x 4, alocando-se os 4 níveis de déficits hídricos na parcela principal e as 2 épocas nas subparcelas, com três repetições. Os manejos hídricos aplicados foram: Déficit 0 (D0) sem déficit, Déficit 1(D1) corte da irrigação aos 30 dias de experimentação, permanecendo até o final do experimento, Déficit 2 (D2) corte da irrigação aos 30 dias de experimentação, suspensão da irrigação por 60 dias e posterior retomada da irrigação por mais 30 dias; Déficit 3 (D3) corte da irrigação aos 60 dias de experimentação, prolongando até o final do experimento. Os dados experimentais foram submetidos à análise de variância, e quando significativas, as médias foram comparadas pelo teste de média Tukey a 5% de probabilidade, para cada clone estudado. Com este trabalho, foi possível avaliar o impacto de diferentes déficits hídricos, no crescimento inicial das plantas, em duas épocas do ano e avaliar o incremento no desenvolvimento das plantas durante a aplicação dos tratamentos, com retiradas de amostras médias de cada tratamento a cada 30 dias. As variáveis medidas nos dois experimentos foram altura total da planta, diâmetro ao nível do coleto, número de folhas, área foliar, matéria seca de folhas, matéria seca de haste e ramos, matéria seca de raízes e matéria seca total. Foram avaliadas as variáveis climáticas durante todo o período experimental, nas duas épocas, a fim de determinar a condição do clima em cada época. Para os dois clones estudados, em geral, os déficits hídricos promoveram a redução das variáveis morfológicas estudadas e a época experimental foi o fator que mais influenciou a redução do crescimento das plantas. Sendo que a Época 1 foi a que proporcionou resultados superiores, e a Época 2 foi a que prejudicou mais o desenvolvimento das plantas, reduzindo significativamente todas as variáveis morfológicas em todos os déficits hídricos, inclusive o D0.

Efeito da restrição hídrica sobre o crescimento de clones de eucalipto

O estabelecimento e o crescimento inicial de espécies florestais no campo são fortemente afetados pela disponibilidade de água no solo e pela época de plantio, por isso, o presente trabalho estuda o impacto do déficit hídrico no crescimento de mudas de dois clones do híbrido Eucalyptus grandis x Eucalyptus urophylla, ambos submetidos a 4 níveis de déficit hídrico, em duas épocas de plantio. O estudo foi realizado na área experimental do Núcleo de Estudos e Difusão de Tecnologia em Florestas, Recursos Hídricos e Agricultura Sustentável (NEDTEC), do Centro de Ciências Agrárias da Universidade Federal do Espírito Santo (CCA-UFES), localizado no município de Jerônimo Monteiro. O trabalho foi realizado em duas épocas distintas, sendo a primeira no período de 09 de fevereiro a 09 de junho de 2009 e a segunda no período de 11 de julho a 07 de novembro de 2009, visando à realização das observações em diferentes condições de regime de radiação, déficit de pressão do vapor do ar, temperatura, umidade relativa do ar e velocidade do vento. O delineamento experimental utilizado foi o inteiramente ao acaso em parcelas subdivididas 2 x 4, alocando-se os 4 níveis de déficits hídricos na parcela principal e as 2 épocas nas subparcelas, com três repetições. Os manejos hídricos aplicados foram: Déficit 0 (D0) sem déficit, Déficit 1(D1) corte da irrigação aos 30 dias de experimentação, permanecendo até o final do experimento, Déficit 2 (D2) corte da irrigação aos 30 dias de experimentação, suspensão da irrigação por 60 dias e posterior retomada da irrigação por mais 30 dias; Déficit 3 (D3) corte da irrigação aos 60 dias de experimentação, prolongando até o final do experimento. Os dados experimentais foram submetidos à análise de variância, e quando significativas, as médias foram comparadas pelo teste de média Tukey a 5% de probabilidade, para cada clone estudado. Com este trabalho, foi possível avaliar o impacto de diferentes déficits hídricos, no crescimento inicial das plantas, em duas épocas do ano e avaliar o incremento no desenvolvimento das plantas durante a aplicação dos tratamentos, com retiradas de amostras médias de cada tratamento a cada 30 dias. As variáveis medidas nos dois experimentos foram altura total da planta, diâmetro ao nível do coleto, número de folhas, área foliar, matéria seca de folhas, matéria seca de haste e ramos, matéria seca de raízes e matéria seca total. Foram avaliadas as variáveis climáticas durante todo o período experimental, nas duas épocas, a fim de determinar a condição do clima em cada época. Para os dois clones estudados, em geral, os déficits hídricos promoveram a redução das variáveis morfológicas estudadas e a época experimental foi o fator que mais influenciou a redução do crescimento das plantas. Sendo que a Época 1 foi a que proporcionou resultados superiores, e a Época 2 foi a que prejudicou mais o desenvolvimento das plantas, reduzindo significativamente todas as variáveis morfológicas em todos os déficits hídricos, inclusive o D0.

The Interpretation of Verbal Probability Expressions Used in the IAS/IFRS: the auditors Rrgistered with the portuguese securities market commission

One of the main arguments in favour of the adoption and convergence with the international accounting standards published by the IASB (i.e. IAS/IFRS) is that these will allow comparability of financial reporting across countries. However, because these standards use verbal probability expressions (v.g. “probable”) when establishing the recognition and disclosure criteria for accounting elements, they require professional accountants to interpret and classify the probability of an outcome or event taking into account those terms and expressions and to best decide in terms of financial reporting. This paper reports part of a research we carried out on the interpretation of “in context” verbal probability expressions used in the IAS/IFRS by the auditors registered with the Portuguese Securities Market Commission, the Comissão do Mercado de Valores Mobiliários (CMVM). Our results provide support for the hypothesis that culture affects the CMVM registered auditors’ interpretation of verbal probability expressions through its influence on the accounting value (or attitude) of conservatism. Our results also suggest that there are significant differences in their interpretation of the term “probable”, which is consistent with literature in general. Since “probable” is the most frequent verbal probability expression used in the IAS/IFRS, this may have a negative impact on financial statements comparability.

Increase of the delivered energy probability in DES using a fuzzy probabilistic modeling

The paper proposes a methodology to increase the probability of delivering power to any load point by identifying new investments in distribution energy systems. The proposed methodology is based on statistical failure and repair data of distribution components and it uses a fuzzy-probabilistic modeling for the components outage parameters. The fuzzy membership functions of the outage parameters of each component are based on statistical records. A mixed integer nonlinear programming optimization model is developed in order to identify the adequate investments in distribution energy system components which allow increasing the probability of delivering power to any customer in the distribution system at the minimum possible cost for the system operator. To illustrate the application of the proposed methodology, the paper includes a case study that considers a 180 bus distribution network.

Arrow Plot: a new graphical tool for selecting up and down regulated genes and genes differentially expressed on samples subgroups

Background: A common task in analyzing microarray data is to determine which genes are differentially expressed across two (or more) kind of tissue samples or samples submitted under experimental conditions. Several statistical methods have been proposed to accomplish this goal, generally based on measures of distance between classes. It is well known that biological samples are heterogeneous because of factors such as molecular subtypes or genetic background that are often unknown to the experimenter. For instance, in experiments which involve molecular classification of tumors it is important to identify significant subtypes of cancer. Bimodal or multimodal distributions often reflect the presence of subsamples mixtures. Consequently, there can be genes differentially expressed on sample subgroups which are missed if usual statistical approaches are used. In this paper we propose a new graphical tool which not only identifies genes with up and down regulations, but also genes with differential expression in different subclasses, that are usually missed if current statistical methods are used. This tool is based on two measures of distance between samples, namely the overlapping coefficient (OVL) between two densities and the area under the receiver operating characteristic (ROC) curve. The methodology proposed here was implemented in the open-source R software. Results: This method was applied to a publicly available dataset, as well as to a simulated dataset. We compared our results with the ones obtained using some of the standard methods for detecting differentially expressed genes, namely Welch t-statistic, fold change (FC), rank products (RP), average difference (AD), weighted average difference (WAD), moderated t-statistic (modT), intensity-based moderated t-statistic (ibmT), significance analysis of microarrays (samT) and area under the ROC curve (AUC). On both datasets all differentially expressed genes with bimodal or multimodal distributions were not selected by all standard selection procedures. We also compared our results with (i) area between ROC curve and rising area (ABCR) and (ii) the test for not proper ROC curves (TNRC). We found our methodology more comprehensive, because it detects both bimodal and multimodal distributions and different variances can be considered on both samples. Another advantage of our method is that we can analyze graphically the behavior of different kinds of differentially expressed genes. Conclusion: Our results indicate that the arrow plot represents a new flexible and useful tool for the analysis of gene expression profiles from microarrays.

Arrow plot and CA maps on microarray preprocessing methods

Microarray allow to monitoring simultaneously thousands of genes, where the abundance of the transcripts under a same experimental condition at the same time can be quantified. Among various available array technologies, double channel cDNA microarray experiments have arisen in numerous technical protocols associated to genomic studies, which is the focus of this work. Microarray experiments involve many steps and each one can affect the quality of raw data. Background correction and normalization are preprocessing techniques to clean and correct the raw data when undesirable fluctuations arise from technical factors. Several recent studies showed that there is no preprocessing strategy that outperforms others in all circumstances and thus it seems difficult to provide general recommendations. In this work, it is proposed to use exploratory techniques to visualize the effects of preprocessing methods on statistical analysis of cancer two-channel microarray data sets, where the cancer types (classes) are known. For selecting differential expressed genes the arrow plot was used and the graph of profiles resultant from the correspondence analysis for visualizing the results. It was used 6 background methods and 6 normalization methods, performing 36 pre-processing methods and it was analyzed in a published cDNA microarray database (Liver) available at http://genome-www5.stanford.edu/ which microarrays were already classified by cancer type. All statistical analyses were performed using the R statistical software.

Probability distribution functions

This technical report describes the PDFs which have been implemented to model the behaviours of certain parameters of the Repeater-Based Hybrid Wired/Wireless PROFIBUS Network Simulator (RHW2PNetSim) and Bridge-Based Hybrid Wired/Wireless PROFIBUS Network Simulator (BHW2PNetSim).

Fractional derivatives: probability interpretation and frequency response of rational approximations

The theory of fractional calculus (FC) is a useful mathematical tool in many applied sciences. Nevertheless, only in the last decades researchers were motivated for the adoption of the FC concepts. There are several reasons for this state of affairs, namely the co-existence of different definitions and interpretations, and the necessity of approximation methods for the real time calculation of fractional derivatives (FDs). In a first part, this paper introduces a probabilistic interpretation of the fractional derivative based on the Grünwald-Letnikov definition. In a second part, the calculation of fractional derivatives through Padé fraction approximations is analyzed. It is observed that the probabilistic interpretation and the frequency response of fraction approximations of FDs reveal a clear correlation between both concepts.

Probability and statistics: selected problems

Probability and Statistics—Selected Problems is a unique book for senior undergraduate and graduate students to fast review basic materials in Probability and Statistics. Descriptive statistics are presented first, and probability is reviewed secondly. Discrete and continuous distributions are presented. Sample and estimation with hypothesis testing are presented in the last two chapters. The solutions for proposed excises are listed for readers to references.

Conditional probability applied to the definition of limestone geochemical facies: A new Methodological Approach

A new method, based on linear correlation and phase diagrams was successfully developed for processes like the sedimentary process, where the deposition phase can have different time duration - represented by repeated values in a series - and where the erosion can play an important rule deleting values of a series. The sampling process itself can be the cause of repeated values - large strata twice sampled - or deleted values: tiny strata fitted between two consecutive samples. What we developed was a mathematical procedure which, based upon the depth chemical composition evolution, allows the establishment of frontiers as well as the periodicity of different sedimentary environments. The basic tool isn't more than a linear correlation analysis which allow us to detect the existence of eventual evolution rules, connected with cyclical phenomena within time series (considering the space assimilated to time), with the final objective of prevision. A very interesting discovery was the phenomenon of repeated sliding windows that represent quasi-cycles of a series of quasi-periods. An accurate forecast can be obtained if we are inside a quasi-cycle (it is possible to predict the other elements of the cycle with the probability related with the number of repeated and deleted points). We deal with an innovator methodology, reason why it's efficiency is being tested in some case studies, with remarkable results that shows it's efficacy. Keywords: sedimentary environments, sequence stratigraphy, data analysis, time-series, conditional probability.

Symbolic dynamics and big bang bifurcation in Weibull-Gompertz-Fréchet's growth models

In this paper, motivated by the interest and relevance of the study of tumor growth models, a central point of our investigation is the study of the chaotic dynamics and the bifurcation structure of Weibull-Gompertz-Fréchet's functions: a class of continuousdefined one-dimensional maps. Using symbolic dynamics techniques and iteration theory, we established that depending on the properties of this class of functions in a neighborhood of a bifurcation point PBB, in a two-dimensional parameter space, there exists an order regarding how the infinite number of periodic orbits are born: the Sharkovsky ordering. Consequently, the corresponding symbolic sequences follow the usual unimodal kneading sequences in the topological ordered tree. We verified that under some sufficient conditions, Weibull-Gompertz-Fréchet's functions have a particular bifurcation structure: a big bang bifurcation point PBB. This fractal bifurcations structure is of the so-called "box-within-a-box" type, associated to a boxe ω1, where an infinite number of bifurcation curves issues from. This analysis is done making use of fold and flip bifurcation curves and symbolic dynamics techniques. The present paper is an original contribution in the framework of the big bang bifurcation analysis for continuous maps.