Collisions of particles in locally AdS spacetimes I. Local description and global examples

We investigate 3-dimensional globally hyperbolic AdS manifolds containing "particles", i.e., cone singularities along a graph $\Gamma$. We impose physically relevant conditions on the cone singularities, e.g. positivity of mass (angle less than $2\pi$ on time-like singular segments). We construct examples of such manifolds, describe the cone singularities that can arise and the way they can interact (the local geometry near the vertices of $\Gamma$). We then adapt to this setting some notions like global hyperbolicity which are natural for Lorentz manifolds, and construct some examples of globally hyperbolic AdS manifolds with interacting particles.Comment: This is a rewritten version of the first part of arxiv:0905.1823. That preprint was too long and contained two types of results, so we sliced it in two. This is the first part. Some sections have been completely rewritten so as to be more readable, at the cost of slightly less general statements. Others parts have been notably improved to increase readabilit

Some open questions on anti-de Sitter geometry

We present a list of open questions on various aspects of AdS geometry, that is, the geometry of Lorentz spaces of constant curvature -1. When possible we point out relations with homogeneous spaces and discrete subgroups of Lie groups, to Teichm\"uller theory, as well as analogs in hyperbolic geometry.Comment: Not a research article in the usual sense but rather a list of open questions. 19 page

Collisions of particles in locally AdS spacetimes II Moduli of globally hyperbolic spaces

We investigate 3-dimensional globally hyperbolic AdS manifolds containing "particles", i.e., cone singularities of angles less than $2\pi$ along a time-like graph $\Gamma$. To each such space we associate a graph and a finite family of pairs of hyperbolic surfaces with cone singularities. We show that this data is sufficient to recover the space locally (i.e., in the neighborhood of a fixed metric). This is a partial extension of a result of Mess for non-singular globally hyperbolic AdS manifolds.Comment: 29 pages, 3 figures. v2: 41 pages, improved exposition. To appear, Comm. Math. Phys. arXiv admin note: text overlap with arXiv:0905.182

Fuchsian convex bodies: basics of Brunn--Minkowski theory

The hyperbolic space \H^d can be defined as a pseudo-sphere in the $(d+1)$ Minkowski space-time. In this paper, a Fuchsian group $\Gamma$ is a group of linear isometries of the Minkowski space such that \H^d/\Gamma is a compact manifold. We introduce Fuchsian convex bodies, which are closed convex sets in Minkowski space, globally invariant for the action of a Fuchsian group. A volume can be associated to each Fuchsian convex body, and, if the group is fixed, Minkowski addition behaves well. Then Fuchsian convex bodies can be studied in the same manner as convex bodies of Euclidean space in the classical Brunn--Minkowski theory. For example, support functions can be defined, as functions on a compact hyperbolic manifold instead of the sphere. The main result is the convexity of the associated volume (it is log concave in the classical setting). This implies analogs of Alexandrov--Fenchel and Brunn--Minkowski inequalities. Here the inequalities are reversed

Galactosemia: genotipo y fenotipo de siete pacientes

Rev Neurol. 2004 Jun 16-30;38(12):1132-5. [Galactosemia: the genotype and phenotype of seven patients]. [Article in Spanish] Martins E, Teixeira J, Cardoso ML, Lima MR, Briones-Godino P, Barbot C. SourceUnidad de Metabolismo, Hospital de Niños Maria Pia, Oporto, Portugal. [email protected] Abstract INTRODUCTION: Despite early dietary therapy, many patients with galactosemia show a neurodegenerative disease specially evident in speech impairment and movement disorders. Magnetic resonance imaging of the brain, show cerebral white matter changes with hypomielinization bilateral and symetrical periventricular hypersignal in T2. PATIENTS AND METHODS: We presented clinical and neuroradiological data of seven children (3 to 12 years of age) with classical galactosemia. All had a typical presentation in neonatal period. Two children had normal development (10 and 12 years-old), four presented developmental delay (10, 7, 4 and 3 years-old), and one showed a dystonic cerebral palsy (kernicterus). RESULTS: The brain MRI showed the typical involvement of white matter, in five children, and basal ganglia abnormalities in the kernicterus patient. Three patients are homozygous for Q188R mutation and two are compound heterozygous. CONCLUSION: We found a positive correlation among developmental delay, white matter involvement and Q188R mutation

Iron-refractory iron deficiency anaemia: A clinical entity with recent molecular characterisation and description

A anemia por défice de ferro é um importante problema de saúde a nível mundial. Até há poucos anos atrás, considerava--se este défice como sendo de natureza exclusivamente adquirida e os erros de metabolismo eram atribuídos unicamente a patologia de sobrecarga. A descoberta da molécula de hepcidina e a descrição e caracterização molecular da anemia ferropriva refratária ao ferro veio contrariar essa anterior convicção. Os autores apresentam os casos clínicos de duas doentes, primas em segundo grau, com diagnóstico de anemia ferropriva refratária ao ferro, com o objetivo de alertar para esta etiologia, aquando do diagnóstico de uma anemia ferropriva de etiologia desconhecida e refratária a terapêutica com ferro oral e endovenos

Atypical haemolytic-uraemic syndrome caused by factor H mutation: case report and new management strategies in children

Atypical haemolytic uraemic syndrome is causedby alternative complement pathway dysregulation. It has recently been recognised that most cases are due to genetic factors and a growing list of mutations has been described. Atypical haemolytic uraemic syndrome is associated with a dismal prognosis, a relapsing course, high acute mortality and frequent progression to end-stage renal disease. We describe a five-year-old boy admitted with a first recurrence of atypical haemolytic uraemic syndrome. The primary onset of the disease was at 15 months of age, following which there was complete recovery of haematological and renal parameters. His family history was significant in that his mother had died at the age of only 23 years of a stroke with associated thrombotic microangiopathy, suggesting a familial form of the disease. Sequencing of the gene encoding complement factor H revealed a heterozygous SCR20 mutation (3644G>T, Arg1215Leu), confirming the diagnosis. The patient was successfully treated with fresh frozen plasma infusions that induced disease remission. We also review currently evolving concepts about atypical haemolytic uraemic syndrome caused by factor H mutation, its diagnosis, the role of genetic testing and management strategies in children

Towards a sanitation safety plan in the city of braga

A gestão integrada das infra-estruturas urbanas de água e saneamento constitui um desafio das cidades ambientalmente sustentáveis. Alguns avanços no controlo de qualidade dos sistemas de abastecimento de água para consumo humano, baseado em avaliação e gestão de riscos para a saúde pública, têm sido conseguidos através da implementação de planos de segurança da água. Com base nesta metodologia propõem-se, neste trabalho, contributos para a implementação de planos de segurança de saneamento, cobrindo-se, desta forma, todo o ciclo urbano da água com princípios de gestão de riscos. Com esta abordagem, estrutura-se um plano de segurança de saneamento onde são identificados eventos perigosos, avaliados e priorizados riscos para a saúde pública e para o ambiente, assim como se estabelecem medidas de controlo ao longo de todo o sistema de saneamento, percorrendo todas as etapas que o constituem: recolha, tratamento, lançamento no ambiente e reutilização segura de águas residuais. Estes conceitos foram aplicados ao sistema de saneamento da área central da cidade de Braga, para o qual se criou expressamente uma ferramenta informática de suporte, focada nos módulos principais da estrutura de um plano de segurança de saneamento.The integrated management of urban water and sanitation infrastructure is a challenge for environmentally sustainable cities. Positive developments in quality control in drinking water supply systems, based on risk assessment and risk management for public health, have been achieved through the implementation of water safety plans. Based on this methodology, the present work gives contributions for sanitation safety plans implementation. In this way, the urban water cycle is covered with risk management principles. With this approach, a sanitation safety plan is structured in which hazardous events to public health and environment are identified. Also risk assessment, risk prioritization and control measures are established throughout the sanitation system, covering all its steps: collection, treatment, disposal in receiving waters and safe reuse of treated wastewater. These concepts have been applied to the sanitation system of the central area of the city of Braga, for which a support software tool was expressly created, focusing in the core structural modules of a sanitation safety plan

Cation selectivity of the presequence translocase channel Tim23 is crucial for efficient protein import.

Virtually all mitochondrial matrix proteins and a considerable number of inner membrane proteins carry a positively charged, N-terminal presequence and are imported by the TIM23 complex (presequence translocase) located in the inner mitochondrial membrane. The voltage-regulated Tim23 channel constitutes the actual protein-import pore wide enough to allow the passage of polypeptides with a secondary structure. In this study, we identify amino acids important for the cation selectivity of Tim23. Structure based mutants show that selectivity is provided by highly conserved, pore-lining amino acids. Mutations of these amino acid residues lead to reduced selectivity properties, reduced protein import capacity and they render the Tim23 channel insensitive to substrates. We thus show that the cation selectivity of the Tim23 channel is a key feature for substrate recognition and efficient protein import