Espace-temps globalement hyperboliques conformément plats

Les espace-temps conformément plats de dimension supérieure ou égal à 3 sont des variétés localement modelées l'espace-temps d'Einstein où il agit la composante connexe de l'identité du groupe des difféomorfismes conformes.Un espace-temps M est globalement hyperbolique s'il admet une hypersurface S de type espace qui est rencontrée une et une seule fois par toute courbe causale de M. L'hypersurface S est alors dite hypersurface de Cauchy de M.L'ensemble des espace-temps globalement hyperboliques conformément plats, identifiés à difféomorphisme conforme près, est naturellement muni d'une relation d'ordre partielle: on dit que N étends M s'il existe un plongement conforme de M dans N tel que l'image de toute hypersurface de Cauchy de M est une hypersurface de Cauchy de N. Les éléments maximaux par rapport à cette relation d'ordre sont appelés espace-temps maximaux.Le premier résultat qu'on a prouvé est l'existence et unicité de l'extension maximale pour un espace-temps conformément plat globalement hyperbolique donné. Ce résultat généralise un théorème de Choquet-Bruhat et Geroch relatif aux espace-temps solutions des équation d'Einstein.L'unicité de l'extension maximale permet de prouver le résultat suivant:Théorème:En dimension supérieur ou égal à 3, l'espace d'Einstein est le seul espace-temps conformément plat maximal simplement connexe admettant une hypersurface de Cauchy compacte.Si l'hypersurface de Cauchy S du revêtement universel d'un espace-temps M est compacte on obtient donc que M est un quotient fini de l'espace d'Einstein. La structure des géodésiques de l'espace d'Einstein et l'unicité de l'extension maximale permettent de prouver :Théorème:Soit M un espace-temps conformément plat maximal de dimension supérieur ou égal à 3, qui contient deux géodésiques lumières distinctes, librement homotopes et ayant les mêmes extrémités. Alors M est un quotient fini de l'espace d'Einstein.Dans le cas où l'hypersurface S' du revêtement universel M' de M est non compacte on montre chaque point p de M' est déterminé par le compact de S 'constitué par l'intersection de son passé causal ou de son futur causal avec l'hypersurface S', suivant que p appartient au passé ou au futur de S'. Onappelle ce compact l'ombre de p sur S'. L'espace-temps M' s'identifie donc à un sous-ensemble des compacts de S'.Ce point de vue permet d'avoir une compréhension plus profonde de la maximalité d'un espace-temps. En fait on a différentes notions de maximalité :un espace-temps pourrait être maximal parmi les espace-temps conformément plats mais avoir un majorant qui n'est pas conformément plat, i.e. il pourrait exister un plongement conforme dans un espace-temps globalement hyperbolique qui ne soit pas conformément plat.Grâce à la notion d'ombre, on prouve que la structure causale induite sur la frontière de Penrose du revêtement universel d'un espace-temps conformément plat permet de caractériser les espace-temps maximaux parmi tous les espace-temps globalement hyperboliques, on obtient:Théorème:Tout espace-temps globalement hyperbolique conformément plat M qui est maximal parmi les espace-temps globalement hyperbolique conformément plats est aussi maximal parmi tous les espace-temps globalement hyperboliques.On conclut avec une discussion détaillée sur la maximalité des espaces-temps globalement hyperboliques maximaux parmi les espace-temps à courbure constante, suivant le signe de la courbure: lorsque la courbure est négative ou nulle, l'espace-temps est maximal aussi parmi tous les espace-temps globalement hyperboliques, mais cela n'est jamais vrai lorsque la courbure est strictement positiveAs a consequence of the Lorentzian version of Liouville s Theorem, everyconformally flat space-time of dimension 3 is a (Ein1,n,O0(2, n + 1))-manifold. The Einstein s space-time Ein1,n is the space Sn . S1 with theconformal class of the metric d2 dt2, where d2 and dt2 are the canonicalRiemannian metrics of Sn and R. The group O0(2, n+1) is the group of theconformal diffeomorphisms of Ein1,n whose action preserve the orientationand the time-orientation of Ein1,n. A space-time M is globally hyperbolicif it contains a spacelike hypersurface which intersects every inextensiblecausal curve of M exactly in one point. As a consequence M is not compact.The hypersurface is called a Cauchy hypersurface of M. Geroch s Theorem([?]) say that if M is globally hyperbolic, then M is homeomorphic to.R. There is a naturally defined partial order on the set of globally hyperbolicspace-times (up to conformal diffeomorphism) : M M0 if does existsa conformal embedding f : M ,! M0 which sends Cauchy hypersurfaces ofM to Cauchy hypersurfaces of M0 (f is called a Cauchy-embedding ). Wecall C-maximal space-times the maximal elements for this partial order onthe set of globally hyperbolic space-times. We can restrict the partial orderto the subset of conformally flat space-times : in this case we call themaximal elements C0-maximal space-times. The first result of the thesis isa generalization of a Theorem proved by Choquet-Bruhat and Geroch in[?] : let M be a globally hyperbolic conformally flat space-time. Then thereis a globally hyperbolic conformally flat C0-maximal space-time N and aCauchy-embedding f : M ,! N. The space-time N is unique up to conformaldiffeomorphisms.The uniqueness of the C0-maximal extension imply that every globally hyperbolicconformally flat simply connected C0-maximal space-time (of dimension3) with a compact Cauchy hypersurface is conformally diffeomorphicto gEin1,n.In the second part of the thesis we study the injectivity of the developingmap of a globally hyperbolic conformally flat space-time M looking at theshape of its the causal boundary.We say that two points p, q are conjugatedin a space-time M if there are two different lightlike geodesics and whichstart at p and meet at q, such that and don t intersect between p and q.The most remarkable result of this part is : let M a globally hyperbolicconformally flat C0-maximal space-time. If fM has two conjugated pointsthen fM ' gEin1,n. In particular M is a finite quotient of gEin1,n.As a consequence of this result we obtain that the developing map of Mrestricted to the chronological past and future of every point is injective.In the last part of the thesis we give an abstract construction of the Cmaximalextension for a given conformally flat globally hyperbolic spacetime.The idea is that a globally hyperbolic space-time is completely determinedby one of his Cauchy hypersurfaces. This result helps to understandhow to relate the different notions of maximality. In particular we provethat every conformally flat globally hyperbolic space-time M which is C0-maximal is also C-maximal.AVIGNON-Bib. numérique (840079901) / SudocSudocFranceF

Inherited and acquired risk factors and their combined effects in pediatric stroke

The aim of this study was to identify hereditary and acquired risk-factors as they are related to the occurrence of stroke in children. We identified 21 children with stroke. A search of the Factor V Leiden mutation, the Factor II G20210A variant, and the thermolabile variant of methylenetetrahydrofolate reductase was performed in patients and in a control group (n = 115).We identified risk factors of acquired and/or hereditary nature for stroke in 19 of 21 children. Eleven children had three or more risk factors, seven had two risk factors, and one child had only one risk factor. We found three carriers (14.3%) of the Factor V Leiden mutation, two carriers (9.5%) of the Factor II G20210A variant, eleven (52.4%) thermolabile variant of methylenetetrahydrofolate reductase heterozygote carriers, and one (4.8%) homozygotes for this variant.Frequencies of the Factor V Leiden mutation and the Factor II variant were higher in patients than in controls, suggesting that these variants are associated with an increased risk of stroke in childhood. Homozygosity for the thermolabile variant of methylenetetrahydrofolate reductase was equally frequent amongst patients and controls.Our study confirms that stroke in children is commonly associated with a combination of multiple risk factors, both genetic and acquired, and that the Factor V Leiden mutation and the Factor II G20210A variant are predisposing factors for this situation

Novel MAG Variant Causes Cerebellar Ataxia with Oculomotor Apraxia: Molecular Basis and Expanded Clinical Phenotype

Homozygous variants in MAG, encoding myelin-associated glycoprotein (MAG), have been associated with complicated forms of hereditary spastic paraplegia (HSP). MAG is a glycoprotein member of the immunoglobulin superfamily, expressed by myelination cells. In this study, we identified a novel homozygous missense variant in MAG (c.124T>C; p.Cys42Arg) in a Portuguese family with early-onset autosomal recessive cerebellar ataxia with neuropathy and oculomotor apraxia. We used homozygosity mapping and exome sequencing to identify the MAG variant, and cellular studies to confirm its detrimental effect. Our results showed that this variant reduces protein stability and impairs the post-translational processing (N-linked glycosylation) and subcellular localization of MAG, thereby associating a loss of protein function with the phenotype. Therefore, MAG variants should be considered in the diagnosis of hereditary cerebellar ataxia with oculomotor apraxia, in addition to spastic paraplegia.This work was funded by National Funds through FCT—Fundação para a Ciência e a Tecnologia, I.P.,under the project UIDB/04293/2020. It was also funded by FEDER funds through the Programa OperacionalFactores de Competitividade—COMPETE 2020 and by Nacional funds through the FCT [COMPETE:POCI-01-0145-FEDER-007440]. This work was also funded in part by the FCT grant FCT-ANR/BEX-GMG/0008/2013and the Porto Neurosciences and Neurologic Disease Research Initiative at the i3S (Norte-01-0145-FEDER-000008),supported by Norte Portugal Regional Operational Programme (NORTE 2020) under the PORTUGAL 2020Partnership Agreement, also through FEDER. The authors also acknowledge the support of the i3S ScientificPlatform Advanced Light Microscopy, member of the PPBI (PPBI-POCI-01-0145-FEDER-022122) and GenomePT(POCI-01-0145-FEDER-022184). MS was the recipient of a fellowship (SFRH/BPD/116046/2016) from the FCTsupported by POPH/MCTES funding.info:eu-repo/semantics/publishedVersio

Hydrops fetalis associated with erythrocyte pyruvate kinase deficiency

The authors report a case of hydrops fetalis due to severe pyruvate kinase deficiency, the most unusual clinical manifestation of this disease. Conclusion Pyruvate kinase deficiency, as other erythrocyte enzymopathies, must be considered in the diferential diagnosis of non-immune hydrops fetalis. This has important implications for clinical investigations, therapy and genetic counselling

Molecular characterization of Portuguese patients with hereditary cerebellar ataxia

© 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).Hereditary cerebellar ataxia (HCA) comprises a clinical and genetic heterogeneous group of neurodegenerative disorders characterized by incoordination of movement, speech, and unsteady gait. In this study, we performed whole-exome sequencing (WES) in 19 families with HCA and presumed autosomal recessive (AR) inheritance, to identify the causal genes. A phenotypic classification was performed, considering the main clinical syndromes: spastic ataxia, ataxia and neuropathy, ataxia and oculomotor apraxia (AOA), ataxia and dystonia, and ataxia with cognitive impairment. The most frequent causal genes were associated with spastic ataxia (SACS and KIF1C) and with ataxia and neuropathy or AOA (PNKP). We also identified three families with autosomal dominant (AD) forms arising from de novo variants in KIF1A, CACNA1A, or ATP1A3, reinforcing the importance of differential diagnosis (AR vs. AD forms) in families with only one affected member. Moreover, 10 novel causal-variants were identified, and the detrimental effect of two splice-site variants confirmed through functional assays. Finally, by reviewing the molecular mechanisms, we speculated that regulation of cytoskeleton function might be impaired in spastic ataxia, whereas DNA repair is clearly associated with AOA. In conclusion, our study provided a genetic diagnosis for HCA families and proposed common molecular pathways underlying cerebellar neurodegeneration.This work was funded by National Funds through FCT—Fundação para a Ciência e a Tecnologia, I.P., under the project UIDB/04293/2020. It was also supported in part by the FCT grant FCT-ANR/BEX-GMG/0008/2013; the Porto Neurosciences and Neurologic Disease Research Initiative at the i3S (Norte-01-0145-FEDER-000008), supported by Norte Portugal Regional Operational Programme (NORTE 2020) under the PORTUGAL 2020 Partnership Agreement, also through FEDER; and by GenomePT (POCI-01-0145-FEDER-022184). M.S. was the recipient of a fellowship (SFRH/BPD/116046/2016) and acknowledges funding from FCT through program DL 57/2016—Norma Transitória.info:eu-repo/semantics/publishedVersio

Teaching science with experimental work and computer simulations in a primary teacher education course: what challenges to promote epistemic practices?

The objective of this work is to study how teachers’ mediation can promote the development of students’ epistemic practices (EPs), in a classroom environment, using computer simulations (CS) articulated with experimental work (EW). In particular, we want to explore characteristics of teacher mediation using CS articulated with EW as a didactical approach and what EPs occur when students work in the pathway from theory (T) to the observable-world (OW), and vice-versa. We report a multi-case study with two teachers of a primary teacher education course. We use multimodal narratives (a description of what happens in the classroom, using several types of data collected) to analyse the students’ EPs and the teachers’ mediation. This analysis is made using the qualitative analysis software (NVivo 8®). The results point that the differences in the occurrences and pathways found in students’ EPs can be related to the different characteristics of teachers’ mediation. The results also point to the existence of students’ epistemic practices that were differently promoted depending on the use of CS or EW, which means an interesting complementarity between the two teaching approaches. When teachers’ mediation incorporates the use CSs articulated with EW.info:eu-repo/semantics/publishedVersio

Rett syndrome with and without detected MECP2 mutations: an attempt to redefine phenotypes

Background: The diagnosis of Rett syndrome (RTT) is based on a set of clinical criteria, irrespective of mutation status. The aims of this study were (1) to define the clinical differences existing between patients with Rett syndrome with (Group I) and without a MECP2 mutation (Group II), and (2) to characterize the phenotypes associated with the more common MECP2 mutations. Patients and methods: We analyzed 87 patients fulfilling the clinical criteria for RTT. All were observed and videotaped by the same paediatric neurologist. Seven common mutations were considered separately, and associated clinical features analysed. Results: Comparing Group I and II, we found differences concerning psychomotor development prior to onset, acquisition of propositive manipulation and language, and evolving autistic traits. Based on age at observation, we found differences in eye pointing, microcephaly, growth, number of stereotypies, rigidity, ataxia and ataxic-rigid gait, and severity score. Patients with truncating differed from those with missense mutations regarding acquisition of propositive words and independent gait, before the beginning of the disease, and microcephaly, growth, foot length, dystonia, rigidity and severity score, at the time of observation. Patients with the R168X mutation had a more severe phenotype, whereas those with R133C showed a less severe one. Patients with R294X had a hyperactive behaviour, and those with T158M seemed to be particularly ataxic and rigid. Conclusion: A clear regressive period (with loss of prehension and language, deceleration of growth) and the presence of more than three different stereotypies, rigidity and ataxic-rigid gait seemed to be very helpful in differentiating Group I from Group II

Rett syndrome with and without detected MECP2 mutations: An attempt to redefine phenotypes

Abstract Background: The diagnosis of Rett syndrome (RTT) is based on a set of clinical criteria, irrespective of mutation status. The aims of this study were (1) to define the clinical differences existing between patients with Rett syndrome with (Group I) and without a MECP2 mutation (Group II), and (2) to characterize the phenotypes associated with the more common MECP2 mutations. Patients and methods: We analyzed 87 patients fulfilling the clinical criteria for RTT. All were observed and videotaped by the same paediatric neurologist. Seven common mutations were considered separately, and associated clinical features analysed. Results: Comparing Group I and II, we found differences concerning psychomotor development prior to onset, acquisition of propositive manipulation and language, and evolving autistic traits. Based on age at observation, we found differences in eye pointing, microcephaly, growth, number of stereotypies, rigidity, ataxia and ataxic-rigid gait, and severity score. Patients with truncating differed from those with missense mutations regarding acquisition of propositive words and independent gait, before the beginning of the disease, and microcephaly, growth, foot length, dystonia, rigidity and severity score, at the time of observation. Patients with the R168X mutation had a more severe phenotype, whereas those with R133C showed a less severe one. Patients with R294X had a hyperactive behaviour, and those with T158M seemed to be particularly ataxic and rigid. Conclusion: A clear regressive period (with loss of prehension and language, deceleration of growth) and the presence of more than three different stereotypies, rigidity and ataxic-rigid gait seemed to be very helpful in differentiating Group I from Group II

Ataxia com apraxia oculomotora (AOA) como modelo para o estudo das ataxias recessivas.

Doutoramento em Ciências Médica