Euler characteristics and elliptic curves

Let E be a modular elliptic curve over ℚ, without complex multiplication; let p be a prime number where E has good ordinary reduction; and let F∞ be the field obtained by adjoining to ℚ all p-power division points on E. Write G∞ for the Galois group of F∞ over ℚ. Assume that the complex L-series of E over ℚ does not vanish at s = 1. If p ⩾ 5, we make a precise conjecture about the value of the G∞-Euler characteristic of the Selmer group of E over F∞. If one makes a standard conjecture about the behavior of this Selmer group as a module over the Iwasawa algebra, we are able to prove our conjecture. The crucial local calculations in the proof depend on recent joint work of the first author with R. Greenberg.

A joint hazard and time scaling model to compare survival curves.

To provide a more general method for comparing survival experience, we propose a model that independently scales both hazard and time dimensions. To test the curve shape similarity of two time-dependent hazards, h1(t) and h2(t), we apply the proposed hazard relationship, h12(tKt)/ h1(t) = Kh, to h1. This relationship doubly scales h1 by the constant hazard and time scale factors, Kh and Kt, producing a transformed hazard, h12, with the same underlying curve shape as h1. We optimize the match of h12 to h2 by adjusting Kh and Kt. The corresponding survival relationship S12(tKt) = [S1(t)]KtKh transforms S1 into a new curve S12 of the same underlying shape that can be matched to the original S2. We apply this model to the curves for regional and local breast cancer contained in the National Cancer Institute's End Results Registry (1950-1973). Scaling the original regional curves, h1 and S1 with Kt = 1.769 and Kh = 0.263 produces transformed curves h12 and S12 that display congruence with the respective local curves, h2 and S2. This similarity of curve shapes suggests the application of the more complete curve shapes for regional disease as templates to predict the long-term survival pattern for local disease. By extension, this similarity raises the possibility of scaling early data for clinical trial curves according to templates of registry or previous trial curves, projecting long-term outcomes and reducing costs. The proposed model includes as special cases the widely used proportional hazards (Kt = 1) and accelerated life (KtKh = 1) models.

Radial and tangential dispersion patterns in the mouse retina are cell-class specific.

The retina is derived from a pseudostratified germinal zone in which the relative position of a progenitor cell is believed to determine the position of the progeny aligned in the radial axis. Such a developmental mechanism would ensure that radial arrays of cells which comprise functional units in the mature central nervous system are also clonally related. The present study has tested this hypothesis by using X chromosome-inactivation transgenic mosaic mice. We report that the retina shows a conspicuous distinction for clonally related neuroblasts of different laminar and functional fates: the rod photoreceptor, Müller, and bipolar cells are aligned in the radial axis, whereas the cone photoreceptor, horizontal, amacrine, and ganglion cells are tangentially displaced with respect to them. These results indicate that the dispersion of cell classes across the retinal surface is differentially constrained. Some classes of retinal neuroblast exhibit a significant tangential, as well as radial, component in their dispersion from the germinal zone, whereas others disperse only in the radial dimension. Consequently, the majority of radial columns within the mature retina must be derived from multiple progenitors. Because the cone photoreceptor, horizontal, amacrine, and ganglion cells establish nonrandom matrices in their cellular distributions within the respective retinal layers, tangential dispersion may be the means by which these matrices are constructed.

Determination of absorption curves, dissolution profiles and establishment of in vitro-in vivo correlation by in silico methods using GastroPlusTM and DDDPlusTM

The use of computer programs to predict drug absorption in humans and to simulate dissolution profiles has become a valuable tool in the pharmaceutical area. The objective of this study was to use in silico methods through software GastroPlusTM and DDDPlusTM to simulate drug absorption curves and dissolution profiles, and to establish in vitro-in vivo correlations (IVIVCs). The work presented herein is divided into five chapters and includes the drugs ketoprofen, pyrimethamine, metronidazole, fluconazole, carvedilol and doxazosin. In Chapter 1, simulated plasma curves for ketoprofen matrix tablets are presented and IVIVC was established. The use of simulated intrinsic dissolution tests for pyrimethamine and metronidazole as a tool for biopharmaceutics classification is detailed in Chapter 2. In Chapter 3, simulation of plasma curves for fluconazole capsules with different dissolution profiles is demonstrated as a tool for biowaiver. IVIVC studies were also conducted for carvedilol immediate-release tablets from dissolution profiles in Chapter 4. Chapter 5 covers the application of simulated dissolution tests for development of doxazosin extended-release formulations. Simulation of plasma curves and IVIVC using the software GastroPlusTM as well as intrinsic dissolution tests and dissolution profiles using the software DDDPlusTM proved to be a tool of wide application in predicting biopharmaceutical characteristics of drugs and formulations, allowing the reduction of time and costs of experimental laboratory work.

Estudo da expansão da Leishmaniose Visceral no estado de São Paulo e de fatores intervenientes

INTRODUÇÃO: Leishmaniose visceral (LV) é uma doença negligenciada que afeta milhões de pessoas no mundo e que constitui um grave problema de saúde pública. OBJETIVOS: Descrever no tempo e no espaço, a dispersão de Lutzomyia longipalpis e a expansão da LV no estado de São Paulo (SP); identificar fatores associados a estes processos. MÉTODOS: Foram realizados estudos descritivos, ecológicos e de análise de sobrevida. Informações sobre o vetor e os casos foram obtidas na Superintendência de Controle de Endemias e no Sistema de Informações de Agravos de Notificação para o período de 1997 a 2014. A área de estudo foi composta pelos 645 municípios de SP. Foram produzidos mapas temáticos e de fluxo e calcularam-se incidência, mortalidade e letalidade por LV em humanos (LVH). Utilizou-se a técnica de análise de sobrevida (Curvas de Kaplan-Meier e Regressão de Cox) para a identificação de fatores associados à dispersão do vetor e expansão da LV. RESULTADOS: A partir da detecção de Lu. longipalpis em Araçatuba em 1997, deram-se a ocorrência do primeiro caso canino (LVC) (1998) e o primeiro caso humano (LVH) autóctones (1999) em SP. Até 2014, foi detectada a presença do vetor em 173 (26,8 por cento ) municípios, LVC em 108 (16,7 por cento ) e LVH em 84 (13 por cento ). A expansão dos três fenômenos ocorreu no sentido noroeste para sudeste e se deram a velocidades constantes. Na região de São José do Rio Preto, a dispersão do vetor deu-se por vizinhança com municípios anteriormente infestados, a expansão da LV relacionou-se com os municípios sede das microrregiões e a doença ocorreu com maior intensidade nas áreas periféricas dos municípios. A presença da Rodovia Marechal Rondon e a divisa com o Mato Grosso do Sul foram fatores associados à ocorrência dos três eventos, assim como a presença da Rodovia Euclides da Cunha para presença do vetor e casos caninos, e, presença de presídios para casos humanos. CONCLUSÕES: A dispersão do vetor e da LV em SP iniciou-se, a partir de 1997, próximo à divisa com o estado do Mato Grosso do Sul, avançou no sentido noroeste para sudeste, na trajetória da rodovia Marechal Rondon, e ocorreu em progressão aritmética, com as sedes das microrregiões de SP tendo papel preponderante neste processo. A ocorrência autóctone de LVC e LVH iniciou-se na sequência da detecção de Lu. longipalpis em Araçatuba e de seu espalhamento por SP e não a partir dos locais onde anteriormente ele já estava presente. O uso da análise de sobrevida permitiu identificar fatores associados à dispersão do vetor e a expansão da LV. Os resultados deste estudo podem ser úteis para aprimorar as atividades de vigilância e controle da LV, no sentido de retardar sua expansão e/ou de mitigar seus efeitos, quando de sua ocorrência.

Migração de solutos em basalto fraturado: quantificação experimental em laboratório e validação matemática

A avaliação do risco a contaminação e a escolha de técnicas de remediação de poluentes em aquíferos fraturados depende da quantificação dos fenômenos envolvidos no transporte de solutos. A geometria da fratura, usualmente caracterizada pela abertura, é o principal parâmetro que indiretamente controla o transporte nos aquíferos fraturados. A simplificação mais comum desse problema é assumir que as fraturas são um par de placas planas e paralelas, isto é, com uma abertura constante. No entanto, por causa do limitado número de trabalhos experimentais, não está esclarecida a adequabilidade do uso de uma abertura constante para simular o transporte conservativo em fraturas do Aquífero Serra Geral (ASG), Brasil. O objetivo deste trabalho é avaliar a influência da abertura de uma fratura natural do Aquífero Serra Geral sob o transporte conservativo de solutos. Uma amostra natural de basalto fraturado foi usada em um experimento hidráulico e de transporte de um traçador conservativo (escala de laboratório). O campo de abertura foi medido usando a técnica avançada, de alta resolução e tridimensional, chamada microtomografia computadorizada de raios-X. A concentração de traçador medida foi utilizada para validar uma solução analítica unidimensional da Equação de Advecção-dispersão (ADE). O desemprenho do ajuste da ADE às curvas de passagem experimentais foi avaliado para quatro diferentes tipos de aberturas constantes. Os resultados mostraram que o escoamento de água e o transporte de contaminantes pode ocorrer através de fraturas micrométricas, ocasionando, eventualmente, a contaminação do ASG. A abertura de balanço de massa é a única que pode ser chamada propriamente de \"abertura equivalente\". O uso de aberturas constantes na ADE não permitiu representar completamente o formato das curvas de passagem porque o campo de velocidade não é uniforme e intrinsicamente bidimensional. Portanto, na simulação do transporte deve-se incorporar a heterogeneidade da abertura da fratura.

Pion-kaon scattering amplitude constrained with forward dispersion relations up to 1.6 GeV

In this work we provide simple and precise parametrizations of the existing πK scattering data from threshold up to 1.6 GeV, which are constrained to satisfy forward dispersion relations as well as three additional threshold sum rules. We also provide phenomenological values of the threshold parameters and of the resonance poles that appear in elastic scattering.

Pitfalls in the Evaluation of the Thermodynamic Consistency of Experimental VLE Data Sets

The thermodynamic consistency of almost 90 VLE data series, including isothermal and isobaric conditions for systems of both total and partial miscibility in the liquid phase, has been examined by means of the area and point-to-point tests. In addition, the Gibbs energy of mixing function calculated from these experimental data has been inspected, with some rather surprising results: certain data sets exhibiting high dispersion or leading to Gibbs energy of mixing curves inconsistent with the total or partial miscibility of the liquid phase, surprisingly, pass the tests. Several possible inconsistencies in the tests themselves or in their application are discussed. Related to this is a very interesting and ambitious initiative that arose within the NIST organization: the development of an algorithm to assess the quality of experimental VLE data. The present paper questions the applicability of two of the five tests that are combined in the algorithm. It further shows that the deviation of the experimental VLE data from the correlation obtained by a given model, the basis of some point-to-point tests, should not be used to evaluate the quality of these data.

Graphical User Interface (GUI) for the representation of GM surfaces (using the NRTL model) and curves, including tie-lines and Hessian matrix

A single and very easy to use Graphical User Interface (GUI- MATLAB) based on the topological information contained in the Gibbs energy of mixing function has been developed as a friendly tool to check the coherence of NRTL parameters obtained in a correlation data procedure. Thus, the analysis of the GM/RT surface, the GM/RT for the binaries and the GM/RT in planes containing the tie lines should be necessary to validate the obtained parameters for the different models for correlating phase equlibrium data.

Labour Supply Curves for EU Member and Candidate States: An applied general equilibrium analysis. Factor Markets Working Paper No. 26, June 2012

This paper introduces a more sophisticated modelling of the labour market functioning of the European member and candidate states through the introduction of labour supply curves in an applied general equilibrium model. A labour supply curve offers a middle way in labour supply modelling, sitting between the two commonly adopted extremes of spare capacity and full employment. The first part of the paper outlines the theoretical foundation of the labour supply curve. Real world data is then used to derive labour supply curves for each member state, along with Croatia and Turkey. Finally, the impact of the newly specified labour markets on the results of an illustrative scenario involving reform of the common agricultural policy is explored. The results of computable general equilibrium analysis with the labour supply curve confirm the theoretical expectation that modelling the labour supply through an upwards-sloping curve produces results that lie between the extremes of spare capacity of the labour factor and fully employed labour. This specification captures a greater degree of heterogeneity in the labour markets of the member and candidate states, allowing for a more nuanced modelling of the effects of policy reform, including welfare effects.