Patchy populations in stochastic environments: Critical number of patches for persistence

We introduce a model for the dynamics of a patchy population in a stochastic environment and derive a criterion for its persistence. This criterion is based on the geometric mean (GM) through time of the spatial-arithmetic mean of growth rates. For the population to persist, the GM has to be greater than or equal to1. The GM increases with the number of patches (because the sampling error is reduced) and decreases with both the variance and the spatial covariance of growth rates. We derive analytical expressions for the minimum number of patches (and the maximum harvesting rate) required for the persistence of the population. As the magnitude of environmental fluctuations increases, the number of patches required for persistence increases, and the fraction of individuals that can be harvested decreases. The novelty of our approach is that we focus on Malthusian local population dynamics with high dispersal and strong environmental variability from year to year. Unlike previous models of patchy populations that assume an infinite number of patches, we focus specifically on the effect that the number of patches has on population persistence. Our work is therefore directly relevant to patchily distributed organisms that are restricted to a small number of habitat patches.

The number of rational points of a class of Artin-Schreier curves

We determine the number of F-q-rational points of a class of Artin-Schreier curves by using recent results concerning evaluations of some exponential sums. In particular, we determine infinitely many new examples of maximal and minimal plane curves in the context of the Hasse-Weil bound. (C) 2002 Elsevier Science (USA).

Local complexity of Delone sets and crystallinity

This paper characterizes when a Delone set X in R-n is an ideal crystal in terms of restrictions on the number of its local patches of a given size or on the heterogeneity of their distribution. For a Delone set X, let N-X (T) count the number of translation-inequivalent patches of radius T in X and let M-X (T) be the minimum radius such that every closed ball of radius M-X(T) contains the center of a patch of every one of these kinds. We show that for each of these functions there is a gap in the spectrum of possible growth rates between being bounded and having linear growth, and that having sufficiently slow linear growth is equivalent to X being an ideal crystal. Explicitly, for N-X (T), if R is the covering radius of X then either N-X (T) is bounded or N-X (T) greater than or equal to T/2R for all T > 0. The constant 1/2R in this bound is best possible in all dimensions. For M-X(T), either M-X(T) is bounded or M-X(T) greater than or equal to T/3 for all T > 0. Examples show that the constant 1/3 in this bound cannot be replaced by any number exceeding 1/2. We also show that every aperiodic Delone set X has M-X(T) greater than or equal to c(n)T for all T > 0, for a certain constant c(n) which depends on the dimension n of X and is > 1/3 when n > 1.

Single mode Lamb waves in composite laminated plates generated by piezoelectric transducers

The technique of permanently attaching piezoelectric transducers to structural surfaces has demonstrated great potential for quantitative non-destructive evaluation and smart materials design. For thin structural members such as composite laminated plates, it has been well recognized that guided Lamb wave techniques can provide a very sensitive and effective means for large area interrogation. However, since in these applications multiple wave modes are generally generated and the individual modes are usually dispersive, the received signals are very complex and difficult to interpret. An attractive way to deal with this problem has recently been introduced by applying piezoceramic transducer arrays or interdigital transducer (IDT) technologies. In this paper, the acoustic wave field in composite laminated plates excited by piezoceramic transducer arrays or IDT is investigated. Based on dynamic piezoelectricity theory, a discrete layer theory and a multiple integral transform method, an analytical-numerical approach is developed to evaluate the input impedance characteristics of the transducer and the surface velocity response of the plate. The method enables the quantitative evaluation of the influence of the electrical characteristics of the excitation circuit, the geometric and piezoelectric properties of the transducer array, and the mechanical and geometrical features of the laminate. Numerical results are presented to validate the developed method and show the ability of single wave mode selection and isolation. The results show that the interaction between individual elements of the piezoelectric array has a significant influence on the performance of the IDT, and these effects can not be neglected even in the case of low frequency excitation. It is also demonstrated that adding backing materials to the transducer elements can be used to improve the excitability of specific wave modes. (C) 2002 Elsevier Science Ltd. All rights reserved.

Simulation of the influence of rate- and state-dependent friction on the macroscopic behavior of complex fault zones with the lattice solid model

In order to understand the earthquake nucleation process, we need to understand the effective frictional behavior of faults with complex geometry and fault gouge zones. One important aspect of this is the interaction between the friction law governing the behavior of the fault on the microscopic level and the resulting macroscopic behavior of the fault zone. Numerical simulations offer a possibility to investigate the behavior of faults on many different scales and thus provide a means to gain insight into fault zone dynamics on scales which are not accessible to laboratory experiments. Numerical experiments have been performed to investigate the influence of the geometric configuration of faults with a rate- and state-dependent friction at the particle contacts on the effective frictional behavior of these faults. The numerical experiments are designed to be similar to laboratory experiments by DIETERICH and KILGORE (1994) in which a slide-hold-slide cycle was performed between two blocks of material and the resulting peak friction was plotted vs. holding time. Simulations with a flat fault without a fault gouge have been performed to verify the implementation. These have shown close agreement with comparable laboratory experiments. The simulations performed with a fault containing fault gouge have demonstrated a strong dependence of the critical slip distance D-c on the roughness of the fault surfaces and are in qualitative agreement with laboratory experiments.

The paternity of the price-quality 'value map'

In the literature on firm strategy and product differentiation, consumer price-quality trade-offs are sometimes represented using consumer 'value maps'. These involve the geometric representation of indifferent price and quality combinations as points along curves that are concave to the 'quality' axis. In this paper, it is shown that the value map for price-quality tradeoffs may be derived from a Hicksian compensated demand curve for product quality. The paper provides the theoretical link between analytical methods employed in the existing literature on firm strategy and competitive advantage with the broader body of economic analysis.

An approach to verifying and debugging simulation models governed by ordinary differential equations: Part 1. Methodology for residual generation

For dynamic simulations to be credible, verification of the computer code must be an integral part of the modelling process. This two-part paper describes a novel approach to verification through program testing and debugging. In Part 1, a methodology is presented for detecting and isolating coding errors using back-to-back testing. Residuals are generated by comparing the output of two independent implementations, in response to identical inputs. The key feature of the methodology is that a specially modified observer is created using one of the implementations, so as to impose an error-dependent structure on these residuals. Each error can be associated with a fixed and known subspace, permitting errors to be isolated to specific equations in the code. It is shown that the geometric properties extend to multiple errors in either one of the two implementations. Copyright (C) 2003 John Wiley Sons, Ltd.

An approach to verifying and debugging simulation models governed by ordinary differential equations: Part 2. Residuals analysis and a case study

In Part 1 of this paper a methodology for back-to-back testing of simulation software was described. Residuals with error-dependent geometric properties were generated. A set of potential coding errors was enumerated, along with a corresponding set of feature matrices, which describe the geometric properties imposed on the residuals by each of the errors. In this part of the paper, an algorithm is developed to isolate the coding errors present by analysing the residuals. A set of errors is isolated when the subspace spanned by their combined feature matrices corresponds to that of the residuals. Individual feature matrices are compared to the residuals and classified as 'definite', 'possible' or 'impossible'. The status of 'possible' errors is resolved using a dynamic subset testing algorithm. To demonstrate and validate the testing methodology presented in Part 1 and the isolation algorithm presented in Part 2, a case study is presented using a model for biological wastewater treatment. Both single and simultaneous errors that are deliberately introduced into the simulation code are correctly detected and isolated. Copyright (C) 2003 John Wiley Sons, Ltd.

Sex- and race-related differences in cross-sectional geometry and bone density of the femoral mid-shaft in older adults

Background : Femoral shaft fracture incidence increases in older adults and is associated with low-energy trauma. Apart from bone density, the distribution and size of bone contributes to its strength. Aim : To examine if bone geometry and density of the femoral mid-shaft in older adults differs by sex and race, we studied 197 White women, 225 Black women, 242 White men, and 148 Black men aged 70-79 years participating in the Health, Aging, and Body Composition study; a prospective cohort study in the USA. A secondary purpose of the study was to examine the association of site-specific muscle and fat to bone geometry and density. Subjects and methods : Subjects were community-dwelling and reported no difficulty walking one-quarter of a mile or climbing stairs. Mid-femoral volumetric bone mineral density (vBMD, mg cm -3 ), total area (TA), cortical area (CA), medullary area (MA), cross-sectional moments of inertia (CSMI: I x , I y , J ), and muscle and fat areas (cm 2 ) were determined by computed tomography (CT; GE CT-9800, 10 mm slice thickness). Results : vBMD was greater in men than women with no difference by race ( p < 0.001). Bone areas and area moments of inertia were also greater in men than women ( p < 0.001), with Black women having higher values than White women for TA and CA. Standardizing geometric parameters for body size differences by dividing by powers of femur length did not negate the sex difference for TA and MA. Significant differences ( p < 0.05) among the four groups also remained for I x and J . Mid-thigh muscle area was an independent contributor to TA in all groups (Std beta = 0.181-0.351, p < 0.05) as well as CA in women (Std beta = 0.246-0.254, p < 0.01) and CSMI in White women (Std beta = 0.175-0.185, p < 0.05). Further, muscle area was a significant contributor to vBMD in Black women. Conclusion : These results indicate that bone geometry and density of the femoral diaphysis differs primarily by sex, rather than race, in older well-functioning adults. In addition, site-specific muscle area appears to have a potential contributory role to bone geometry parameters, especially in women.

Os gêneros de Bethylidae (Hymenoptera: Chrysidoidea) de quatro áreas de Mata Atlântica do Espírito Santo

Estudou-se a riqueza e abundância de gêneros de Bethylidae coletados em quatro áreas de mata de encosta da Mata Atlântica do Espírito Santo, com estados de preservação diferentes: Santa Maria de Jetibá (SMJ), Domingos Martins (DM), Pancas (P) e Atílio Vivácqua (AV). Foram coletados 2.840 espécimes alocados em 12 gêneros, sendo Lepidosternopsis Ogloblin e Bakeriella Kieffer citados pela primeira vez para esse estado. A riqueza dos táxons foi obtida através do procedimento Jackknife com auxílio do programa EstimateS. Curvas de acumulação de gêneros foram construídas para avaliar o esforço amostral. Os dados se ajustaram à distribuição geométrica e calculou-se o parâmetro k para comparar as localidades. O perfil genérico não foi equivalente em todas as localidades, e todas foram consideradas perturbadas. SMJ e DM apresentaram riqueza de gêneros maior em comparação com P e AV. As diferenças relatadas neste estudo para as áreas amostradas refletem o grau diferente de preservação das matas. Pseudisobrachium Kieffer e Dissomphalus Ashmead foram os gêneros mais abundantes em SMJ, DM e P e Anisepyris Kieffer em AV. Este estudo reforça o fato de Dissomphalus ser mais abundante em florestas tropicais úmidas e que o perfil genérico encontrado em AV assemelha-se a dados publicados para o cerrado.

Avaliação assistida informatizada : indicadores do potencial cognitivo de crianças com deficiência

A identificação e a avaliação de crianças com desenvolvimento atípico configuram um processo muito importante para subsidiar as estratégias de ensino voltadas para a promoção do potencial de aprendizagem. O interesse em relação ao prognóstico de crianças com deficiência tem impulsionado o desenvolvimento de novas tecnologias e pesquisas relacionadas à avaliação, prevenção e intervenção. Nesse contexto, torna-se relevante verificar com instrumentos adequados indicadores linguísticos, cognitivos e comportamentais, para assim traçar metas a partir daquilo que as crianças podem aprender. Dessa forma, esta pesquisa teve por objetivo verificar se a avaliação assistida informatizada se apresenta como uma modalidade de diagnóstico mais prescritivo do desenvolvimento cognitivo, quando comparada à avaliação psicométrica, na aplicação em crianças com deficiência. Na modalidade assistida há ajuda do examinador para conduzir a criança a um melhor nível de desempenho cognitivo. Participaram 11 crianças que frequentam uma instituição de atendimento clínico, em saúde, para crianças com deficiência, na Grande Vitória. Na avaliação psicométrica foram utilizados a Escala de Maturidade Mental Colúmbia computadorizada – Colúmbiacomp e o Teste de Vocabulário por Imagens Peabody - TVIPcomp. Na avaliação assistida informatizada foram aplicadas três provas voltadas para as habilidades de classificação e raciocínio analógico: Exclusão de Objetos, Exclusão de Figuras Geométricas e Jogo de Analogia de Figuras, no ambiente informatizado SINDAPSI. Protocolos de registro de fatores afetivo-motivacionais e de operações cognitivas foram utilizados durante as tarefas assistidas. Na avaliação do comportamento, o Child Behavior Checklist – CBCL foi respondido pelas mães. Dados documentais e dos instrumentos foram submetidos à análise estatística descritiva para verificar o desempenho das crianças nas duas formas de avaliação informatizada (psicométrica e assistida). Nos testes psicométricos, 64% das crianças alcançaram índice “abaixo da média” no TVIPcomp, e 55% “médio-inferior” no Colúmbiacomp. Em relação ao perfil de desempenho cognitivo, na Prova de Exclusão de Objetos computadorizada 55% das crianças foram avaliadas como “não-mantenedoras”. Na Prova de Exclusão de Figuras Geométricas computadorizada 55% da amostra foi classificada no perfil “alto-escore”, e no Jogo de Analogias de Figuras computadorizado 45% apresentou o perfil “ganhador”. A amostra demonstrou níveis de dificuldade na realização dos testes,tanto na modalidade psicométrica quanto assistida. Contudo, o desempenho nos testes assistidos foi relativamente melhor, evidenciando que o grupo se beneficiou da mediação,implementada na fase de assistência, para melhorar as habilidades cognitivas. Além disso, a apresentação informatizada dos testes apresentou-se como fator motivador para a realização e persistência nas tarefas.

Aplicação da matemática em investimentos financeiros : caderneta de poupança e títulos públicos

Iniciando com um breve estudo de porcentagem e algumas de suas aplicações, o desenvolvimento deste trabalho consiste de uma revisão dos fundamentos da matemática financeira e suas aplicações em dois tipos de investimentos financeiros denominados caderneta de poupança e títulos públicos. Além do clássico estudo de juros simples e compostos, associando-os a progressões aritméticas e geométricas, respectivamente, aborda-se sobre os vários tipos de taxas (proporcionais e equivalentes, nominais e efetivas, variáveis e acumuladas) incluindo a conceituação de taxa por dia útil. Fundamentado nos assuntos mencionados, o trabalho encerra-se com uma aplicação da matemática financeira associada a investimentos na caderneta de poupança e nos diversos títulos públicos negociados no Tesouro Direto.

Automated traffic route identification through the shared nearest neighbour algorithm

Many organisations need to extract useful information from huge amounts of movement data. One example is found in maritime transportation, where the automated identification of a diverse range of traffic routes is a key management issue for improving the maintenance of ports and ocean routes, and accelerating ship traffic. This paper addresses, in a first stage, the research challenge of developing an approach for the automated identification of traffic routes based on clustering motion vectors rather than reconstructed trajectories. The immediate benefit of the proposed approach is to avoid the reconstruction of trajectories in terms of their geometric shape of the path, their position in space, their life span, and changes of speed, direction and other attributes over time. For clustering the moving objects, an adapted version of the Shared Nearest Neighbour algorithm is used. The motion vectors, with a position and a direction, are analysed in order to identify clusters of vectors that are moving towards the same direction. These clusters represent traffic routes and the preliminary results have shown to be promising for the automated identification of traffic routes with different shapes and densities, as well as for handling noise data.

Estimating Local Part Thickness in Midplane Meshes for Finite Element Analysis

Within the development of motor vehicles, crash safety (e.g. occupant protection, pedestrian protection, low speed damageability), is one of the most important attributes. In order to be able to fulfill the increased requirements in the framework of shorter cycle times and rising pressure to reduce costs, car manufacturers keep intensifying the use of virtual development tools such as those in the domain of Computer Aided Engineering (CAE). For crash simulations, the explicit finite element method (FEM) is applied. The accuracy of the simulation process is highly dependent on the accuracy of the simulation model, including the midplane mesh. One of the roughest approximations typically made is the actual part thickness which, in reality, can vary locally. However, almost always a constant thickness value is defined throughout the entire part due to complexity reasons. On the other hand, for precise fracture analysis within FEM, the correct thickness consideration is one key enabler. Thus, availability of per element thickness information, which does not exist explicitly in the FEM model, can significantly contribute to an improved crash simulation quality, especially regarding fracture prediction. Even though the thickness is not explicitly available from the FEM model, it can be inferred from the original CAD geometric model through geometric calculations. This paper proposes and compares two thickness estimation algorithms based on ray tracing and nearest neighbour 3D range searches. A systematic quantitative analysis of the accuracy of both algorithms is presented, as well as a thorough identification of particular geometric arrangements under which their accuracy can be compared. These results enable the identification of each technique’s weaknesses and hint towards a new, integrated, approach to the problem that linearly combines the estimates produced by each algorithm.

Morphology and stability of aggregates of an Oxisol according to tillage system and gypsum application

Morphological characterization and aggregate stability is an important factor in evaluating management systems. The aim of this paper is to evaluate the stability and morphology of the aggregates of a dystrophic Oxisol managed with no-tillage and conventional tillage with and without the residual action of gypsum. The experimental design was randomized blocks arranged in split-split plot, where the treatments were two soil management systems (plots) with 0 and 2000 kg ha-1 of gypsum (subplots) and five depths (0-0.05, 0.05-0.10, 0.10-0.15, 0.15-0.20 and 0.20-0.30 m) as the subsubplots, with four replications. The aggregate morphology was determined through images and later evaluated by the Quantporo software. Stability was determined by the wet method. The results showed that the no-tillage system, with or without gypsum residual effect, provided the aggregates with the largest geometric diameters. The combination of no-tillage system and the gypsum residual effect provided rougher aggregates.