Mechanical effects on the skeleton: Are there clinical implications?

The basic morphology of the skeleton is determined genetically, but its final mass and architecture are modulated by adaptive mechanisms sensitive to mechanical factors. When subjected to loading, the ability of bones to resist fracture depends on their mass, material properties, geometry and tissue quality. The contribution of altered bone geometry to fracture risk is unappreciated by clinical assessment using absorptiometry because it fails to distinguish geometry and density. For example, for the same bone area and density, small increases in the diaphyseal radius effect a disproportionate influence on torsional strength of bone. Mechanical factors are clinically relevant because of their ability to influence growth, modeling and remodeling activities that can maximize, or maintain, the determinants of fracture resistance. Mechanical loads, greater than those habitually encountered by the skeleton, effect adaptations in cortical and cancellous bone, reduce the rate of bone turnover, and activate new bone formation on cortical and trabecular surfaces. In doing so, they increase bone strength by beneficial adaptations in the geometric dimensions and material properties of the tissue. There is no direct evidence to demonstrate anti-fracture efficacy for mechanical loading, but the geometric alterations engendered undoubtedly increase the structural properties of bone as an organ, increasing the resistance to fracture. Like all interventions, issues of safety also arise. Physical activities involving high strain rates, heavy lifting or impact loading may be detrimental to the joints, leading to osteoarthritis; may stimulate fatigue damage leading with some to stress fractures; or may interact pharmaceutical interventions to increase the rate of microdamage within cortical or trabecular bone.

A semi-analytical solution for vibration of rectangular plates with abrupt thickness variation

A semi-analytical analysis of free vibration of plates with cross-sectional discontinuities due to abrupt changes in thickness is presented. A basic square element divided into suitable subdomains dependent upon the positions of these abrupt changes is used as the basic building element, Admissible functions that satisfy the essential or geometric boundary conditions are used to define the transverse deflection of each subdomain. Continuities in the displacement, slope, moment and higher derivatives between adjacent subdomains are enforced at the interconnecting edges. The resulting global energy functional from the proper assembly of the coupled strain and kinetic energy contributions of each subdomain is then minimized via the Ritz procedure to extract the frequencies and mode shapes. Contour plots of a range of new mode shapes are presented for the enhancement of understanding the dynamic behavior of this class of plates, (C) 2001 Elsevier Science Ltd, All rights reserved.

An inverse design method for elliptical MRI magnets

An inverse, current density mapping (CDM) method has been developed for the design of elliptical cross-section MRI magnets. The method provides a rapid prototyping system for unusual magnet designs, as it generates a 3D current density in response to a set of target field and geometric constraints. The emphasis of this work is on the investigation of new elliptical coil structures for clinical MRI magnets. The effect of the elliptical aspect ratio on magnet performance is investigated. Viable designs are generated for symmetric, asymmetric and open architecture elliptical magnets using the new method. Clinically relevant attributes such as reduced stray field and large homogeneous regions relative to total magnet length are included in the design process and investigated in detail. The preliminary magnet designs have several novel features.

Determining when the absolute state complexity of a Hermitian code achieves its DLP bound

Let g be the genus of the Hermitian function field H/F(q)2 and let C-L(D,mQ(infinity)) be a typical Hermitian code of length n. In [Des. Codes Cryptogr., to appear], we determined the dimension/length profile (DLP) lower bound on the state complexity of C-L(D,mQ(infinity)). Here we determine when this lower bound is tight and when it is not. For m less than or equal to n-2/2 or m greater than or equal to n-2/2 + 2g, the DLP lower bounds reach Wolf's upper bound on state complexity and thus are trivially tight. We begin by showing that for about half of the remaining values of m the DLP bounds cannot be tight. In these cases, we give a lower bound on the absolute state complexity of C-L(D,mQ(infinity)), which improves the DLP lower bound. Next we give a good coordinate order for C-L(D,mQ(infinity)). With this good order, the state complexity of C-L(D,mQ(infinity)) achieves its DLP bound (whenever this is possible). This coordinate order also provides an upper bound on the absolute state complexity of C-L(D,mQ(infinity)) (for those values of m for which the DLP bounds cannot be tight). Our bounds on absolute state complexity do not meet for some of these values of m, and this leaves open the question whether our coordinate order is best possible in these cases. A straightforward application of these results is that if C-L(D,mQ(infinity)) is self-dual, then its state complexity (with respect to the lexicographic coordinate order) achieves its DLP bound of n /2 - q(2)/4, and, in particular, so does its absolute state complexity.

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.

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.