A simplified mathematical model for urban microclimate simulation

Techniques for modelling urban microclimates and urban block surfaces temperatures are desired by urban planners and architects for strategic urban designs at the early design stages. This paper introduces a simplified mathematical model for urban simulations (UMsim) including urban surfaces temperatures and microclimates. The nodal network model has been developed by integrating coupled thermal and airflow model. Direct solar radiation, diffuse radiation, reflected radiation, long-wave radiation, heat convection in air and heat transfer in the exterior walls and ground within the complex have been taken into account. The relevant equations have been solved using the finite difference method under the Matlab platform. Comparisons have been conducted between the data produced from the simulation and that from an urban experimental study carried out in a real architectural complex on the campus of Chongqing University, China in July 2005 and January 2006. The results show a satisfactory agreement between the two sets of data. The UMsim can be used to simulate the microclimates, in particular the surface temperatures of urban blocks, therefore it can be used to assess the impact of urban surfaces properties on urban microclimates. The UMsim will be able to produce robust data and images of urban environments for sustainable urban design.

Modelling acidosis and the cell cycle in multicellular tumour spheroids

A partial differential equation model is developed to understand the effect that nutrient and acidosis have on the distribution of proliferating and quiescent cells and dead cell material (necrotic and apopotic) within a multicellular tumour spheroid. The rates of cell quiescence and necrosis depend upon the local nutrient and acid concentrations and quiescent cells are assumed to consume less nutrient and produce less acid than proliferating cells. Analysis of the differences in nutrient consumption and acid production by quiescent and proliferating cells shows low nutrient levels do not necessarily lead to increased acid concentration via anaerobic metabolism. Rather, it is the balance between proliferating and quiescent cells within the tumour which is important; decreased nutrient levels lead to more quiescent cells, which produce less acid than proliferating cells. We examine this effect via a sensitivity analysis which also includes a quantification of the effect that nutrient and acid concentrations have on the rates of cell quiescence and necrosis.

Spectral theory of some non-selfadjoint linear differential operators

We give a characterisation of the spectral properties of linear differential operators with constant coefficients, acting on functions defined on a bounded interval, and determined by general linear boundary conditions. The boundary conditions may be such that the resulting operator is not selfadjoint. We associate the spectral properties of such an operator $S$ with the properties of the solution of a corresponding boundary value problem for the partial differential equation $\partial_t q \pm iSq=0$. Namely, we are able to establish an explicit correspondence between the properties of the family of eigenfunctions of the operator, and in particular whether this family is a basis, and the existence and properties of the unique solution of the associated boundary value problem. When such a unique solution exists, we consider its representation as a complex contour integral that is obtained using a transform method recently proposed by Fokas and one of the authors. The analyticity properties of the integrand in this representation are crucial for studying the spectral theory of the associated operator.

Modeling electrocortical activity through improved local approximations of integral neural field equations

Neural field models of firing rate activity typically take the form of integral equations with space-dependent axonal delays. Under natural assumptions on the synaptic connectivity we show how one can derive an equivalent partial differential equation (PDE) model that properly treats the axonal delay terms of the integral formulation. Our analysis avoids the so-called long-wavelength approximation that has previously been used to formulate PDE models for neural activity in two spatial dimensions. Direct numerical simulations of this PDE model show instabilities of the homogeneous steady state that are in full agreement with a Turing instability analysis of the original integral model. We discuss the benefits of such a local model and its usefulness in modeling electrocortical activity. In particular, we are able to treat “patchy” connections, whereby a homogeneous and isotropic system is modulated in a spatially periodic fashion. In this case the emergence of a “lattice-directed” traveling wave predicted by a linear instability analysis is confirmed by the numerical simulation of an appropriate set of coupled PDEs.

Nutrient-limited toxin production and the dynamics of two phytoplankton in culture media: a mathematical model

In this paper we have proposed and analyzed a simple mathematical model consisting of four variables, viz., nutrient concentration, toxin producing phytoplankton (TPP), non-toxic phytoplankton (NTP), and toxin concentration. Limitation in the concentration of the extracellular nutrient has been incorporated as an environmental stress condition for the plankton population, and the liberation of toxic chemicals has been described by a monotonic function of extracellular nutrient. The model is analyzed and simulated to reproduce the experimental findings of Graneli and Johansson [Graneli, E., Johansson, N., 2003. Increase in the production of allelopathic Prymnesium parvum cells grown under N- or P-deficient conditions. Harmful Algae 2, 135–145]. The robustness of the numerical experiments are tested by a formal parameter sensitivity analysis. As the first theoretical model consistent with the experiment of Graneli and Johansson (2003), our results demonstrate that, when nutrient-deficient conditions are favorable for the TPP population to release toxic chemicals, the TPP species control the bloom of other phytoplankton species which are non-toxic. Consistent with the observations made by Graneli and Johansson (2003), our model overcomes the limitation of not incorporating the effect of nutrient-limited toxic production in several other models developed on plankton dynamics.

Evolution PDEs and augmented eigenfunctions. half line.

The solution of an initial-boundary value problem for a linear evolution partial differential equation posed on the half-line can be represented in terms of an integral in the complex (spectral) plane. This representation is obtained by the unified transform introduced by Fokas in the 90's. On the other hand, it is known that many initial-boundary value problems can be solved via a classical transform pair, constructed via the spectral analysis of the associated spatial operator. For example, the Dirichlet problem for the heat equation can be solved by applying the Fourier sine transform pair. However, for many other initial-boundary value problems there is no suitable transform pair in the classical literature. Here we pose and answer two related questions: Given any well-posed initial-boundary value problem, does there exist a (non-classical) transform pair suitable for solving that problem? If so, can this transform pair be constructed via the spectral analysis of a differential operator? The answer to both of these questions is positive and given in terms of augmented eigenfunctions, a novel class of spectral functionals. These are eigenfunctions of a suitable differential operator in a certain generalised sense, they provide an effective spectral representation of the operator, and are associated with a transform pair suitable to solve the given initial-boundary value problem.

SHIMMER (1.0): a novel mathematical model for microbial and biogeochemical dynamics in glacier forefield ecosystems

SHIMMER (Soil biogeocHemIcal Model for Microbial Ecosystem Response) is a new numerical modelling framework designed to simulate microbial dynamics and biogeochemical cycling during initial ecosystem development in glacier forefield soils. However, it is also transferable to other extreme ecosystem types (such as desert soils or the surface of glaciers). The rationale for model development arises from decades of empirical observations in glacier forefields, and enables a quantitative and process focussed approach. Here, we provide a detailed description of SHIMMER, test its performance in two case study forefields: the Damma Glacier (Switzerland) and the Athabasca Glacier (Canada) and analyse sensitivity to identify the most sensitive and unconstrained model parameters. Results show that the accumulation of microbial biomass is highly dependent on variation in microbial growth and death rate constants, Q10 values, the active fraction of microbial biomass and the reactivity of organic matter. The model correctly predicts the rapid accumulation of microbial biomass observed during the initial stages of succession in the forefields of both the case study systems. Primary production is responsible for the initial build-up of labile substrate that subsequently supports heterotrophic growth. However, allochthonous contributions of organic matter, and nitrogen fixation, are important in sustaining this productivity. The development and application of SHIMMER also highlights aspects of these systems that require further empirical research: quantifying nutrient budgets and biogeochemical rates, exploring seasonality and microbial growth and cell death. This will lead to increased understanding of how glacier forefields contribute to global biogeochemical cycling and climate under future ice retreat.

A mathematical model for the dynamics of Banana Xanthomonas Wilt with vertical transmission and inflorescence infection

A mathematical model for Banana Xanthomonas Wilt (BXW) spread by insect is presented. The model incorporates inflorescence infection and vertical transmission from the mother corm to attached suckers, but not tool-based transmission by humans. Expressions for the basic reproduction number R0 are obtained and it is verified that disease persists, at a unique endemic level, when R0 > 1. From sensitivity analysis, inflorescence infection rate and roguing rate were the parameters with most influence on disease persistence and equilibrium level. Vertical transmission parameters had less effect on persistence threshold values. Parameters were approximately estimated from field data. The model indicates that single stem removal is a feasible approach to eradication if spread is mainly via inflorescence infection. This requires continuous surveillance and debudding such that a 50% reduction in inflorescence infection and 2–3 weeks interval of surveillance would eventually lead to full recovery of banana plantations and hence improved production.

INDEX OF AN IMPLICIT DIFFERENTIAL EQUATION

In this paper we introduce the concept of the index of an implicit differential equation F(x,y,p) = 0, where F is a smooth function, p = dy/dx, F(p) = 0 and F(pp) = 0 at an isolated singular point. We also apply the results to study the geometry of surfaces in R(5).

Oscillation for a second-order neutral differential equation with impulses

We consider a certain type of second-order neutral delay differential systems and we establish two results concerning the oscillation of solutions after the system undergoes controlled abrupt perturbations (called impulses). As a matter of fact, some particular non-impulsive cases of the system are oscillatory already. Thus, we are interested in finding adequate impulse controls under which our system remains oscillatory. (C) 2009 Elsevier Inc. All rights reserved.

Prevalência de papilomavírus humano (HPV) e chlamydia trachomatis (CT) e sua associação com lesões cervicais em uma amostra de mulheres assintomáticas de Porto Alegre, RS

O câncer cervical acomete anualmente cerca de 470.000 mulheres em todo o mundo e mais de 16.000 mulheres no Brasil. O desenvolvimento do câncer cervical e sua associação ao Papilomavírus Humano (HPV) estão bem documentados, sendo este o fator principal para o desenvolvimento do câncer cervical. A infecção genital por Chlamydia trachomatis é estudada como um co-fator no desenvolvimento de neoplasias intraepiteliais cervicais (NICs) e outras alterações celulares significativas em mulheres com histórico de infecção por HPV. Este estudo tem como objetivo conhecer a prevalência de infecção por HPV e Chlamydia trachomatis em uma amostra de mulheres assintomáticas de uma área geográfica localizada na zona norte de Porto Alegre, bem como verificar as características associadas à presença desta co-infecção e sua relação com lesões cervicais. Trata-se de um estudo transversal cujo desfecho é a positividade ao HPV e à Chlamydia trachomatis em uma amostra de mulheres assintomáticas de Porto Alegre. Um total de 1217 amostras de material do colo do útero foi coletado para realização do exame citopatológico e para a identificação do DNA-HPV e DNA-CT através da técnica da Reação em Cadeia da Polimerase (PCR). Colposcopia e biópsia foram realizadas sempre que a citologia estivesse alterada e/ou a PCR para o HPV-DNA fosse positiva. A prevalência de HPV e Chlamydia trachomatis e sua distribuição por faixa etária são descritas, bem como a sua associação com as variáveis estudadas através das Razões de Chances (RC) estimadas por regressão logística múltipla. Observou-se uma prevalência de HPV-DNA de 28,4% (n=346/1217), de CT-DNA de 12,6% (n=152/1208) e de co-infecção por HPV e CT de 6,5% (n=78/1208). Mulheres não brancas (Razão de Chance (RC) =1,60; Intervalo de Confiança (IC) de 95%:1,10-2,38),assalariadas (RC=1,74; IC95%:1,17-2,60) e com parceiro apresentando história de condiloma genital (RC=2,35; IC95%:1,17-4,72) mostraram-se associadas com a positividade para HPV. A infecção por CT mostrou uma associação positiva com mulheres que iniciaram a vida sexual antes dos vinte anos (RC=1,82; IC95%:1,05-3,15) e assalariadas (RC=1,93; IC95%:1,15-3,25). Quanto à co-infecção por HPV e CT, mulheres com mais de três de parceiros sexuais na vida (RC=2,02; IC 95%:1,12-3,65) apresentaram uma associação positiva com o desfecho. Com relação à citologia, tanto a infecção por HPV quanto a co-infecção apresentaram associação significativa com anormalidades citológicas (p≤0.001). Os resultados mostraram uma elevada prevalência de HPV, de CT e de co-infecção em uma amostra de mulheres assintomáticas reforçando dados relatados na literatura. A associação destas infecções com variáveis sócioeconômicas, de comportamento sexual e com lesões do colo uterino, indicam a importância de medidas para a promoção e prevenção de saúde com este alvo específico dentro da rotina de serviços de atenção primária. Desta forma, acredita-se que estes dados possam ser muito úteis no planejamento de programas, incluindo o controle de Doenças Sexualmente Transmissíveis e a utilização de vacinas para o HPV.

Detecção de Chlamydia trachomatis em amostras cervicais por reação em cadeia da polimerase

Chlamydia trachomatis é o agente causal de uma das infecções sexualmente transmissíveis (IST) mais prevalentes da atualidade. Os maiores problemas no controle desta IST estão no caráter assintomático da infecção e no seu difícil diagnóstico laboratorial. Com o advento dos testes moleculares, grandes avanços ocorreram na área do diagnóstico laboratorial da infecção clamidial. O presente trabalho teve por objetivo desenvolver um método de detecção de C. trachomatis por PCR a partir de amostras cérvico-vaginais. A seqüência alvo escolhida para amplificação consiste de um segmento da ORF 4 do plasmídio críptico de ocorrência natural nesta bactéria. Noventa e duas amostras cérvico-vaginais foram submetidas ao protocolo de PCR in house proposto. Os produtos de PCR foram detectados por visualização direta após eletroforese em gel de agarose com brometo de etídio e por exposição radiográfica após hibridização com sonda homóloga. As amostras foram testadas paralelamente pelo método de captura híbrida para detecção de C. trachomatis. O kit COBAS Amplicor (Roche) foi utilizado para resolver resultados discrepantes. A seqüência do fragmento de 201pb foi confirmada por clivagem enzimática e por seqüenciamento. O teste de especificidade dos primers confirmou especificidade dos mesmos frente ao DNA de diferentes agentes patogênicos e da flora normal feminina. Do total de amostras analisadas, 50 foram positivas por captura híbrida, 51 foram positivas por PCR in house e 67 positivaram após hibridização.O teste de McNemar indicou haver concordância entre os métodos analisados dois a dois (P<0,001). Verificou-se concordância moderada nos comparativos entre captura híbrida e PCR (valor de Kappa: 0,45; DP 0,093), captura híbrida e hibridização (valor de kappa: 0,389; DP 0,091) e, PCR e hibridização (valor de Kappa: 0,634: DP 0,077). O método de PCR in house proposto para a detecção de C. trachomatis é uma técnica rápida e de baixo custo para o diagnóstico, controle e monitoramento dos casos da infecção. Estudos complementares, no entanto, são necessários para implementação deste teste em laboratórios da rede pública.

Prevalência da infecção por papilomavírus humano, herpes simplex tipo 1 e 2 e Chlamydia trachomatis em um segmento da população feminina da grande Natal/RN

Sexually transmitted diseases (STDs) are among the largest public health problems, especially in developing countries. The acquisition of these infections during early sexual activity is common and many infections have a benign course. However, in some pathogens remain in the state of latency can be reactivated and cause productive infection that may progress to severe forms. In addition, some of them are transmitted vertically resulting in congenital infection, causing immediate damage or long-term child. The classic risk factors for sexually transmitted agents are: early onset of sexual and reproductive health, multiple sexual partners throughout life, use of oral contraceptives and co-infections with different pathogens. We present the results of a cross-sectional study aimed to estimate the prevalence of genital infection by human papillomavirus (HPV), Herpes simplex virus (HSV) and Chlamydia trachomatis (CT) in a segment of the female population of the metropolitan area Christmas, among those who enrolled voluntarily sought, Basic Health Units for the examination of cancer screening cervix in the period 2008 to 2010. All participants, a total of 261 women answered a standard questionnaire by which identified the socio-demographic characteristics, classical risk factors for STDs, reproductive and sexual activity and smoking. Of each patient were obtained two samples, one for the completion of the Pap test for detection of cellular changes and the other processed for DNA extraction and analyzed by PCR (polymerase chain reaction) to detect the three pathogens studied. The population of the study was composed of sexually active women aged between 13 and 79 years, mean 38.7 years, most of them being married, low education levels and low incomes. The majority (87%) had normal results on cytology and only 2.7% had low-grade cytological abnormalities. Prevalence rates were 37.9% for HPV, 4.6% for CT and 26% for HSV. HPV prevalence was higher in women under 25, unmarried and in those who had multiple sexual partners. Women with simultaneous infection by HSV-1 and 2 had higher prevalence of HPV infection. The prevalence of HSV infection showed no association whatsoever with the risk factors analyzed and HSV-1 was the predominant type among the cases of genital HSV infection. The overall prevalence of C. Trachomatis was relatively low, thus providing greater value in younger women aged less than or equal to 20 years