O comprimento descritivo mínimo na amostragem por transectos lineares

Apresenta·se um breve resumo histórico da evolução da amostragem por transectos lineares e desenvolve·se a sua teoria. Descrevemos a teoria de amostragem por transectos lineares, proposta por Buckland (1992), sendo apresentados os pontos mais relevantes, no que diz respeito à modelação da função de detecção. Apresentamos uma descrição do princípio CDM (Rissanen, 1978) e a sua aplicação à estimação de uma função densidade por um histograma (Kontkanen e Myllymãki, 2006), procedendo à aplicação de um exemplo prático, recorrendo a uma mistura de densidades. Procedemos à sua aplicação ao cálculo do estimador da probabilidade de detecção, no caso dos transectos lineares e desta forma estimar a densidade populacional de animais. Analisamos dois casos práticos, clássicos na amostragem por distâncias, comparando os resultados obtidos. De forma a avaliar a metodologia, simulámos vários conjuntos de observações, tendo como base o exemplo das estacas, recorrendo às funções de detecção semi-normal, taxa de risco, exponencial e uniforme com um cosseno. Os resultados foram obtidos com o programa DISTANCE (Thomas et al., in press) e um algoritmo escrito em linguagem C, cedido pelo Professor Doutor Petri Kontkanen (Departamento de Ciências da Computação, Universidade de Helsínquia). Foram desenvolvidos programas de forma a calcular intervalos de confiança recorrendo à técnica bootstrap (Efron, 1978). São discutidos os resultados finais e apresentadas sugestões de desenvolvimentos futuros. ABSTRACT; We present a brief historical note on the evolution of line transect sampling and its theoretical developments. We describe line transect sampling theory as proposed by Buckland (1992), and present the most relevant issues about modeling the detection function. We present a description of the CDM principle (Rissanen, 1978) and its application to histogram density estimation (Kontkanen and Myllymãki, 2006), with a practical example, using a mixture of densities. We proceed with the application and estimate probability of detection and animal population density in the context of line transect sampling. Two classical examples from the literature are analyzed and compared. ln order to evaluate the proposed methodology, we carry out a simulation study based on a wooden stakes example, and using as detection functions half normal, hazard rate, exponential and uniform with a cosine term. The results were obtained using program DISTANCE (Thomas et al., in press), and an algorithm written in C language, kindly offered by Professor Petri Kontkanen (Department of Computer Science, University of Helsinki). We develop some programs in order to estimate confidence intervals using the bootstrap technique (Efron, 1978). Finally, the results are presented and discussed with suggestions for future developments.

Spatial variability of satured soil hydraulic conductivity in the region of Araguaia River - Brazil.

This study evaluates the spatial variability of saturated hydraulic conductivity in the soil in an area of 51,850 ha at the headwaters of the Araguaia River MT/GO. This area is highly vulnerable because it is a location of recharging through natural water infiltration of the Guarani Aquifer System and an area of intense increases in agriculture since its adoption by growers in the last 30 years. Soil samples were collected at 383 points, geographically located by GPS. The samples were collected from depths of 0 - 20 cm and 60 - 80 cm. Exploratory statistics and box-plot were used in the descriptive analysis and semivariogram were constructed to determine the spatial model. The exploratory analysis showed that the mean hydraulic conductivity in the superficial layer was less than at the level of 60-80 cm; however, the greatest variability evaluated with a coefficient of variation also was from this layer. Data tended towards a normal distribution. These results can be explained by the greater soil compaction in the superficial layer. The semivariogram models, adjusted for the two layers, were exponential and demonstrated moderate and strong dependence, with ranges of 5000 and 3000 utm respectively. It was concluded that soil use is influencing the spatial distribution model of the hydraulic conductivity in the region.

Repression of flagellar genes in exponential phase by CsgD and CpxR, two crucial modulators of Escherichia coli biofilm formation.

Escherichia coli adapts its lifestyle to the variations of environmental growth conditions, swapping between swimming motility or biofilm formation. The stationary-phase sigma factor RpoS is an important regulator of this switch, since it stimulates adhesion and represses flagellar biosynthesis. By measuring the dynamics of gene expression, we show that RpoS inhibits the transcription of the flagellar sigma factor, FliA, in exponential growth phase. RpoS also partially controls the expression of CsgD and CpxR, two transcription factors important for bacterial adhesion. We demonstrate that these two regulators repress the transcription of fliA, flgM, and tar and that this regulation is dependent on the growth medium. CsgD binds to the flgM and fliA promoters around their -10 promoter element, strongly suggesting direct repression. We show that CsgD and CpxR also affect the expression of other known modulators of cell motility. We propose an updated structure of the regulatory network controlling the choice between adhesion and motility.

Intravoxel incoherent motion diffusion-weighted imaging in the liver: comparison of mono-, bi- and tri-exponential modelling at 3.0-T.

PURPOSE: To determine whether a mono-, bi- or tri-exponential model best fits the intravoxel incoherent motion (IVIM) diffusion-weighted imaging (DWI) signal of normal livers. MATERIALS AND METHODS: The pilot and validation studies were conducted in 38 and 36 patients with normal livers, respectively. The DWI sequence was performed using single-shot echoplanar imaging with 11 (pilot study) and 16 (validation study) b values. In each study, data from all patients were used to model the IVIM signal of normal liver. Diffusion coefficients (Di ± standard deviations) and their fractions (fi ± standard deviations) were determined from each model. The models were compared using the extra sum-of-squares test and information criteria. RESULTS: The tri-exponential model provided a better fit than both the bi- and mono-exponential models. The tri-exponential IVIM model determined three diffusion compartments: a slow (D1 = 1.35 ± 0.03 × 10(-3) mm(2)/s; f1 = 72.7 ± 0.9 %), a fast (D2 = 26.50 ± 2.49 × 10(-3) mm(2)/s; f2 = 13.7 ± 0.6 %) and a very fast (D3 = 404.00 ± 43.7 × 10(-3) mm(2)/s; f3 = 13.5 ± 0.8 %) diffusion compartment [results from the validation study]. The very fast compartment contributed to the IVIM signal only for b values ≤15 s/mm(2) CONCLUSION: The tri-exponential model provided the best fit for IVIM signal decay in the liver over the 0-800 s/mm(2) range. In IVIM analysis of normal liver, a third very fast (pseudo)diffusion component might be relevant. KEY POINTS: ? For normal liver, tri-exponential IVIM model might be superior to bi-exponential ? A very fast compartment (D = 404.00 ± 43.7 × 10 (-3)  mm (2) /s; f = 13.5 ± 0.8 %) is determined from the tri-exponential model ? The compartment contributes to the IVIM signal only for b ≤ 15 s/mm (2.)

Temporal variability of soil CO2 emission after conventional and reduced tillage described by an exponential decay in time model

To study Assessing the impact of tillage practices on soil carbon losses dependents it is necessary to describe the temporal variability of soil CO2 emission after tillage. It has been argued that large amounts of CO2 emitted after tillage may serve as an indicator for longer-term changes in soil carbon stocks. Here we present a two-step function model based on soil temperature and soil moisture including an exponential decay in time component that is efficient in fitting intermediate-term emission after disk plow followed by a leveling harrow (conventional), and chisel plow coupled with a roller for clod breaking (reduced) tillage. Emission after reduced tillage was described using a non-linear estimator with determination coefficient (R²) as high as 0.98. Results indicate that when emission after tillage is addressed it is important to consider an exponential decay in time in order to predict the impact of tillage in short-term emissions.

Certain problems concerning polynomials and transcendental entire functions of exponential type

Soit $\displaystyle P(z):=\sum_{\nu=0}^na_\nu z^{\nu}$ un polynôme de degré $n$ et $\displaystyle M:=\sup_{|z|=1}|P(z)|.$ Sans aucne restriction suplémentaire, on sait que $|P'(z)|\leq Mn$ pour $|z|\leq 1$ (inégalité de Bernstein). Si nous supposons maintenant que les zéros du polynôme $P$ sont à l'extérieur du cercle $|z|=k,$ quelle amélioration peut-on apporter à l'inégalité de Bernstein? Il est déjà connu [{\bf \ref{Mal1}}] que dans le cas où $k\geq 1$ on a $$(*) \qquad |P'(z)|\leq \frac{n}{1+k}M \qquad (|z|\leq 1),$$ qu'en est-il pour le cas où $k < 1$? Quelle est l'inégalité analogue à $(*)$ pour une fonction entière de type exponentiel $\tau ?$ D'autre part, si on suppose que $P$ a tous ses zéros dans $|z|\geq k \, \, (k\geq 1),$ quelle est l'estimation de $|P'(z)|$ sur le cercle unité, en terme des quatre premiers termes de son développement en série entière autour de l'origine. Cette thèse constitue une contribution à la théorie analytique des polynômes à la lumière de ces questions.

Approximation by harmonic polynomials in star-shaped domains and exponential convergence of Trefftz hp-dGFEM

We study the approximation of harmonic functions by means of harmonic polynomials in two-dimensional, bounded, star-shaped domains. Assuming that the functions possess analytic extensions to a delta-neighbourhood of the domain, we prove exponential convergence of the approximation error with respect to the degree of the approximating harmonic polynomial. All the constants appearing in the bounds are explicit and depend only on the shape-regularity of the domain and on delta. We apply the obtained estimates to show exponential convergence with rate O(exp(−b square root N)), N being the number of degrees of freedom and b>0, of a hp-dGFEM discretisation of the Laplace equation based on piecewise harmonic polynomials. This result is an improvement over the classical rate O(exp(−b cubic root N )), and is due to the use of harmonic polynomial spaces, as opposed to complete polynomial spaces.

The complementary exponential geometric distribution: Model, properties, and a comparison with its counterpart

In this paper, we proposed a new two-parameter lifetime distribution with increasing failure rate, the complementary exponential geometric distribution, which is complementary to the exponential geometric model proposed by Adamidis and Loukas (1998). The new distribution arises on a latent complementary risks scenario, in which the lifetime associated with a particular risk is not observable; rather, we observe only the maximum lifetime value among all risks. The properties of the proposed distribution are discussed, including a formal proof of its probability density function and explicit algebraic formulas for its reliability and failure rate functions, moments, including the mean and variance, variation coefficient, and modal value. The parameter estimation is based on the usual maximum likelihood approach. We report the results of a misspecification simulation study performed in order to assess the extent of misspecification errors when testing the exponential geometric distribution against our complementary one in the presence of different sample size and censoring percentage. The methodology is illustrated on four real datasets; we also make a comparison between both modeling approaches. (C) 2011 Elsevier B.V. All rights reserved.

Temporal variability of soil CO2 emission after conventional and reduced tillage described by an exponential decay in time model

A quantificação do impacto das práticas de preparo sobre as perdas de carbono do solo é dependente da habilidade de se descrever a variabilidade temporal da emissão de CO2 do solo após preparo. Tem sido sugerido que as grandes quantidades de CO2 emitido após o preparo do solo podem servir como um indicador das modificações nos estoques de carbono do solo em longo termo. Neste trabalho é apresentado um modelo de duas partes baseado na temperatura e na umidade do solo e que inclui um termo exponencial decrescente do tempo que é eficiente no ajuste das emissões intermediárias após preparo: arado de disco seguido de uma passagem com a grade niveladora (convencional) e escarificador de arrasto seguido da passagem com rolo destorroador (reduzido). As emissões após o preparo do solo são descritas utilizando-se estimativa não linear com um coeficiente de determinação (R²) tão alto quanto 0.98 após preparo reduzido. Os resultados indicam que nas previsões da emissão de CO2 após o preparo do solo é importante considerar um termo exponencial decrescente no tempo após preparo.

Describing fatigue crack growth and load ratio effects in Al 2524 T3 alloy with an enhanced exponential model

The fatigue crack behavior in metals and alloys under constant amplitude test conditions is usually described by relationships between the crack growth rate da/dN and the stress intensity factor range Delta K. In the present work, an enhanced two-parameter exponential equation of fatigue crack growth was introduced in order to describe sub-critical crack propagation behavior of Al 2524-T3 alloy, commonly used in aircraft engineering applications. It was demonstrated that besides adequately correlating the load ratio effects, the exponential model also accounts for the slight deviations from linearity shown by the experimental curves. A comparison with Elber, Kujawski and "Unified Approach" models allowed for verifying the better performance, when confronted to the other tested models, presented by the exponential model. (C) 2012 Elsevier Ltd. All rights reserved.

Stretched-exponential behavior and random walks on diluted hypercubic lattices

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

Escape and transport for an open bouncer: Stretched exponential decays

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Uniform exponential dichotomy and continuity of attractors for singularly perturbed damped wave equations

For eta >= 0, we consider a family of damped wave equations u(u) + eta Lambda 1/2u(t) + au(t) + Lambda u = f(u), t > 0, x is an element of Omega subset of R-N, where -Lambda denotes the Laplacian with zero Dirichlet boundary condition in L-2(Omega). For a dissipative nonlinearity f satisfying a suitable growth restrictions these equations define on the phase space H-0(1)(Omega) x L-2(Omega) semigroups {T-eta(t) : t >= 0} which have global attractors A(eta) eta >= 0. We show that the family {A(eta)}(eta >= 0), behaves upper and lower semi-continuously as the parameter eta tends to 0(+).