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Arithmétique des droites de Kummer
No full textElliptic curves have been used in numerous cryptographic protocols for the past forty years and their arithmetic has been widely studied. In several applications, it is essential to perform the scalar multiplication on an elliptic curve efficiently. This computation is achieved with Montgomery XZ-coordinates and the Montgomery ladder. This system of coordinates is a particular case of Kummer lines. On the other hand, abelian varieties of higher dimension are more and more popular in cryptography, but their arithmetic has been less studied. The universal system of coordinates in higher dimension is based on theta functions, and gives another example of Kummer lines when used on an elliptic curve. In this thesis, we introduce a framework for Kummer lines which unifies the system of coordinates and the various formulas found in the literature. This global framework enables us to give an algorithmic method to derive formulas for the arithmetic of Kummer lines, using in particular some tools in dimension 2. We also introduce some variants of the ladder to perform the scalar multiplication. This also enables us to classify elliptic curves via simple criteria on their Kummer line. We give applications to isogeny volcanoes and integer factorization via ECM. The ideas developed in this thesis, although focused on the arithmetic of elliptic curves and Kummer lines, try to use at most the general context of abelian varieties and the universal system of coordinates from theta functions, leaving the opportunity to generalize the ideas in higher dimension.Les courbes elliptiques sont utilisées dans de nombreux protocoles cryptographiques depuis quarante ans et leur arithmétique a été largement étudiée. Dans de nombreuses applications, effectuer une multiplication scalaire efficacement sur une courbe elliptique est essentiel. Ce calcul s’effectue avec les coordonnées XZ de Montgomery et le Montgomery ladder. Ce système de coordonnées est un cas particulier de droite de Kummer. D’un autre côté, les variétés abéliennes de dimension supérieure sont de plus en plus populaires en cryptographie, mais leur arithmétique a été moins étudiée. Le système de coordonnées universel en dimension supérieure est basé sur les fonctions thêta, et donne un autre exemple de droite de Kummer lorsque appliqué à une courbe elliptique. Dans cette thèse, nous introduisons un cadre pour les droites de Kummer qui unifie les différents systèmes de coordonnées et les différentes formules déjà connues dans la littérature. Ce point de vue plus général permet de donner une méthode algorithmique pour déterminer des formules pour l’arithmétique des droites de Kummer, notamment en utilisant des outils en dimension 2. Nous introduisons des variantes du ladder pour effectuer la multiplication scalaire. Cela nous permet également de classifier les courbes elliptiques à partir de critères simples sur leur droite de Kummer. Nous donnons des applications aux volcans d’isogénies et à la factorisation d’entiers via ECM. Les idées développées dans cette thèse, bien qu’orientées sur l’arithmétique des courbes elliptiques et des droites de Kummer, essaient d’utiliser au plus le cadre général des variétés abéliennes et du système de coordonnées universel des fonctions thêta, ce qui laisse la place à la généralisation de ces idées en dimension supérieure
Etude d’objets combinatoires en dimension supérieure
No full textThis thesis explores higher-dimensional generalizations of classical combinatorial objects such as permutations, combinatorial maps, and mosaic floorplans. Its comprehensive goal is to develop combinatorial tools to better understand these higher dimensional objects. The first part of this thesis focuses on the combinatorial properties of random tensor models, whose Feynman graphs are (D + 1)-colored graphs that extend the notion of combinatorial maps. This analysis focuses on tensor models with interactions of order six or higher. We begin by studying the 1/N expansion, where N denotes the size of the tensors, of the sextic O(N)3 model, which generalizes in a non-trivial way the sextic U(N)3 model. Some of the interactions considered in this model lead to a graph structure at leading order in the 1/N expansion that differs drastically from previously studied models. We then investigate a second asymptotic expansion known as the double scaling limit. We implement this expansion for the prismatic tensor model, a restricted version of the sextic O(N)3 model in which we consider only the prismatic interaction. Studying this expansion requires analyzing sub-leading order graphs in the 1/N expansion, whose structure is generally unknown. To address this, we use the scheme decomposition, originally introduced by Gurau and Schaeffer Ann. Inst. Henri Poincaré Comb. Phys. Interact. 3 (2016) and which adapts in a non trivial way the one introduced by Chapuy, Marcus and Schaeffer for combinatorial maps SIAM Journal on Discrete Mathematics (2009). This allows us to characterize the structure of the leading-order graphs in the double scaling limit and to determine the dominant contribution to the two-point function in this expansion. Additionally, we investigate duality properties between different tensor models whose symmetries are governed by the groups O(N) and Sp(N). We prove that the transformation N ! −N maps the Feynman graph amplitudes of one model to those of the other. This duality holds for the so-called uncolored models, where the tensor symmetry is given by d copies of the groups O(N) or Sp(N), and for the so-called symmetric models where the tensors transform under representations of only one copy of these two groups. In both cases, we prove that this duality holds for models with interactions of arbitrary order. The second part of this thesis focuses on d-floorplans and d-permutations, the higher dimensional analogs of mosaic floorplans and permutations. A floorplan is a partition of a rectangle by other rectangles with no empty rooms. Additionally, a floorplan is said to be mosaic if the segments induced by the partitioning of the bounding rectangle are non crossing. Similarly, a d-dimensional floorplan is a partition of a d-dimensional hyperrectangle with n disjoint interior d-dimensional hyperrectangles and no empty rooms. This partitioning induces borders, which are (d − 1)-hyperrectangles. A d-floorplan is a d-dimensional floorplan for which there are no borders crossing. A d-permutation is a tuple of (d − 1) permutations which can be represented as a d-dimensional point diagram. We first construct a generating tree for d-floorplans. Given a d-floorplan, we can remove its top box and unequivocally fill the resulting empty space in order to obtain a smaller d-floorplan. The structure of the tree is defined by this operation and generalizes the one of mosaic floorplans. However, the associated labels and the rewriting rule appear to be significantly more involved in higher dimensions. This allow us to find the first numbers of the enumeration sequences of d-floorplans, which do not match with any known sequences. Then, we establish a bijection between 2d−1-floorplans and d-permutations characterized by forbidden patterns [...]Dans cette thèse, nous nous intéressons à des généralisations en dimensions supérieure de différents objets combinatoires: les permutations, les cartes et les rectangulations. L’objectif général de celle-ci, est de développer des outils combinatoires permettant de mieux comprendre ces objets de dimension supérieure. Le premier axe de cette thèse est consacré à l’analyse combinatoire des modèles de tenseurs aléatoires. Les graphes de Feynman de ces modèles sont des graphes D + 1−colorés qui généralisent les cartes combinatoires. L’analyse présentée ici se concentre sur les modèles de tenseurs dont les interactions sont d’ordre six ou plus. Nous étudions tout d’abord l’expansion en 1/N, où N est la taille des tenseurs, du modèle sextique O(N)3 qui généralise de manière non-triviale le modèle sextique U(N)3. Certaine interactions présentes dans ce modèle donnent lieu à une structure des graphes dominant drastiquement différente de celles observées dans des modèles précédemment étudiés. Nous étudions ensuite une seconde expansion asymptotique dite double limite d’échelle. Nous implémentons celle-ci pour le modèle de tenseurs prismatique, une version restreinte du modèle O(N)3 sextique où l’on ne considère qu’une seule interaction dite prismatique. L’étude de cette expansion recquiert d’étudier des graphs d’ordre non dominant de l’expansion en 1/N, dont la structure n’est généralement pas connue. Nous utilisons pour cela la décomposition en schéma, initialement introduite par Gurau et Schaeffer Ann. Inst. Henri Poincaré Comb. Phys. Interact. 3 (2016) et qui généralise de manière non triviale celle introduite par Chapuy, Marcus et Schaeffer pour les cartes combinatoires SIAM Journal on Discrete Mathematics (2009). Celle-ci nous permet de caractériser la structure des graphes dominant dans la double limite d’échelle et de déterminer la contribution principale à la fonction à deux points dans cette expansion. Par ailleurs, nous nous intéressons à des propriétés de dualités entre différents modèles de tenseurs, dont les symétries sont déterminées par les groupes O(N) et Sp(N). Nous prouvons que le changement N ! −N, permet d’associer les amplitudes des graphes de Feynman d’un modèle à celle d’un autre. Cette dualité s’applique aussi bien à des modèles dits décolorés, où la symétrie des tenseurs est donnée par d copies des groupes O(N) ou Sp(N), qu’à des modèles dits symétriques où les tenseurs se transforment dans des représentations d’une copie de ces deux groupes. Dans ces deux cas, nous prouvons que cette dualité tient pour des modèles possédant des interactions de n’importe quel ordre. Le second axe de cette thèse porte sur l’étude des d-rectangulations et des d-permutations qui généralisent les rectangulations et les permutations en dimensions supérieures. Une rectangulation est une partition d’un rectangle par des rectangles sans espaces vide tel qu’aucun des segments induits par ce partitionnage ne se croisent. De manière similaire, une rectangulation d-dimensionelle est une partition d’un hypperectangle ddimensionel en n hypperectangles d-dimensionels sans espaces vides. Ce partitionnage induit des bordures, qui sont des hyperrectangles (d − 1)-dimensionels. Une d-rectangulation, est alors une rectangulation ddimensionelle pour laquelle aucune bordures ne se croisent. Une d-permutation est quant à elle un couple de d − 1 permutations pouvant être représentées par un diagramme de points d-dimensionel. Nous construisons tout d’abord un arbre de génération des d-rectangulations. Étant donné une drectangulation, il est possible de supprimer le block maximal et d’obtenir une rectangulation plus petite. La structure de l’arbre de génération est définie par cette opération et généralise l’arbre de génération des rectangulations [...
Characterization of a Novel FKS1 Mutation in Candida lusitaniae Shows a Potential Critical Role for MKC1 in Echinocandin Resistance
No full textABSTRACT Caspofungin is an echinocandin antifungal that inhibits glucan synthesis in the fungal cell wall. A Candida parapsil osis bloodstream isolate resistant to echinocandins was recovered from a patient who had undergone allogeneic hematopoietic stem cell transplantation. The FKS1 gene, encoding the target glucan synthase, contained a heterozygous mutation resulting in an I1380T amino acid change, in addition to the naturally occurring P660A polymorphism. When expressed at the equivalent position in the Fks1p protein of C. lusitaniae , P642A and I1359T, alone and in combination, led to 6-, 12-, and ≥256-fold increases in the minimal inhibitory concentration (MIC) of caspofungin, respectively. The caspofungin concentration needed to inhibit 50% of glucan synthase activity was increased 3-, 37-, and 270-fold, respectively. At high drug concentrations, and also in drug-free medium, infrared spectroscopy revealed a decrease in β-glucan content and an increase in chitin in the cell wall of the I1359T Fks1p mutants. Atomic force microscopy showed cell wall damage and cell swelling in both susceptible and resistant strains under caspofungin exposure. Analysis of susceptibility to cell-wall stressors and key factors in cell wall integrity (CWI) and high-osmolarity glycerol (HOG) pathways showed that all strains activated these pathways under caspofungin stress. In the I1359T Fks1p mutants, Mkc1p was constitutively activated even without caspofungin. Deletion of MKC1 restored caspofungin susceptibility, indicating that activation of the CWI pathway is a key molecular determinant of resistance in vitro to caspofungin in these mutants
Communication Notification through User-Level Interrupts for the BXI Network
No full textInternational audienceTo reduce the cost of communications in high-performance computing, it is possible to overlap communications with computations. Some communication protocols, such as rendez-vous, multi-chunk messages, and collectives, may require a completion notification to be processed before they can further progress. With active polling or passive waiting, completions are not processed while the application is busy with computation, and thus communication does not progress. However, with an event-based method like interrupts, it is expected to be much more reactive. Nevertheless, using interrupts usually involves system calls, which are avoided with high-performance networks.The Intel Sapphire Rapids processors introduced user-level interrupts (UINTR), hardware interrupts designed to be used directly in user space, without going through the kernel. However, their current implementation is limited to inter-process communication. They cannot be triggered from a device.In this paper, we propose new mechanisms to extend the scope of user-level interrupts, so as to be able to trigger them from a device and not only from a CPU. We have implemented these mechanisms in the BXI network from Eviden. We have evaluated their performance: we obtain a latency only 2.4 times higher than active polling (v.s. 6 times higher for interrupts with system calls). We have assessed their ability to make communication progress when overlapped with computation; we observe a near-perfect computation/communication overlap
cMFA for multi-omics data integration in microbial community models
No full textInternational audienceUnderstanding microbial community functions is challenging due to complex interactions and assembly mechanisms; however, advances in sequencing have enabled the collection of multi-omics data, including population counts and metabolomic or metatranscriptomic data. Our main objective is to develop a mathematical model capable of integrating time series of multiomics data at a community scale. We introduce the community metabolic flux analysis (cMFA) method, which generalizes metabolic flux analyses, using a list of time series data of experimentally measured production and consumption rates of metabolites and microorganism growth. We aim to infer, for each member of the microbial community, the intracellular distribution of metabolic fluxes. This is a high-dimensional constrained linear regression problem, informed by mass conservation constraints and metatranscriptomic data, encoded in the penalty term. The difficulty here is in accurately inferring latent internal rates from a few observations of exchange fluxes. We evaluated the cMFA method on synthetic data from dynamic models of increasingly complex microbial communities, based on metabolic models of different mutants of Escherichia coli using dynamic flux balance analysis (dFBA). Synthetic metatranscriptomic data were obtained from internal metabolic fluxes in the dynamic model. Different regularization terms were tested, including different levels of sparsity, for the selected penalty weight . To evaluate the robustness of the method, multiple benchmarks were tested. These included assessments of the robustness of the method to data noise, incomplete meta-transcriptomic data, inaccurate prior knowledge of metabolic import rates and expanding the study to a larger microbial community . Currently, we are working with real data ,including data on denitrification and cheese production
Centromeric DNA amplification triggered by viral proteins activates nuclear cGAS
No full textInternational audienc
<i>MYH7</i> -related myopathies: clinical, myopathological and genotypic spectrum in a multicentre French cohort
No full textCorrespondence to Professor Edoardo Malfatti; [email protected] audienceBackground Myosin heavy chain 7 ( MYH7 )-related myopathies ( MYH7 -RMs) are a group of muscle disorders linked to pathogenic variants in the MYH7 gene, encoding the slow/beta-cardiac myosin heavy chain, which is highly expressed in skeletal muscle and heart. The phenotype is heterogeneous including distal, predominantly axial or scapuloperoneal myopathies with variable cardiac involvement. Methods We retrospectively analysed the clinical, muscle MRI, genetic and myopathological features of 57 MYH7 patients. Patients received a thorough neurological (n=57, 100%), cardiac (n=51, 89%) and respiratory (n=45, 79%) assessment. Muscle imaging findings and muscle biopsies were reappraised in 19 (33%) and 27 (47%) patients, respectively. Results We identified three phenotypes with varying degrees of overlap: distal myopathy (70%), scapuloperoneal (23%) and axial with peculiar cervical spine rigidity called the ‘sphinx’ phenotype (7%). 14% of patients had either dilated cardiomyopathy, hypertrophic cardiomyopathy or left ventricular non-compaction cardiomyopathy. 31% of patients had prominent respiratory involvement, including all patients with the ‘sphinx’ phenotype. Muscle MRI showed involvement of tibialis anterior, followed by quadriceps, and erector spinae in patients with axial phenotype. Cores represented the most common myopathological lesion. We report 26 pathogenic variants of MYH7 gene, 9 of which are novel. Conclusions MYH7 -RMs have a large phenotypic spectrum, including distal, scapuloperoneal or axial weakness, and variable cardiac and respiratory involvement. Tibialis anterior is constantly and precociously affected both clinically and on muscle imaging. Cores represent the most common myopathological lesion. Our detailed description of MYH7 -RMs should improve their recognition and management
Obtaining V2(PO4)3 by sodium extraction from single-phase Na<sub><i>x</i></sub>V<sub>2</sub>(PO<sub>4</sub>)<sub>3</sub> (1 < x < 3) positive electrode materials
No full textLa version soumise (de l'article) déposée porte un titre différentInternational audienceWe report on single-phase NaxV2(PO4)3 compositions (1.5 ≤ x ≤ 2.5) of the Na super ionic conductor type, obtained from a straightforward synthesis route. Typically, chemically prepared c-Na2V2(PO4)3, obtained by annealing an equimolar mixture of Na3V2(PO4)3 and NaV2(PO4)3, exhibits a specific sodium-ion distribution (occupancy of the Na(1) site of only 0.66(4)), whereas that of the electrochemically obtained e-Na2V2(PO4)3 (from Na3V2(PO4)3) is close to 1. Unlike conventional Na3V2(PO4)3, when used as positive electrode materials in Na-ion batteries, the NaxV2(PO4)3 compositions lead to unusual single-phase Na+ extraction/insertion mechanisms with continuous voltage changes upon Na+ extraction/insertion. We demonstrate that the average equilibrium operating voltage observed upon Na+ deintercalation from single-phase Na2V2(PO4)3 is increased up to an average value of ~3.70 V versus Na+/Na (thanks to the activation of the V4+/V5+ redox couple) compared to 3.37 V versus Na+/Na in conventional Na3V2(PO4)3, thus leading to an increase in the theoretical energy density from 396.3 Wh kg–1 to 458.1 Wh kg–1. Electrochemical and chemical Na+ deintercalation from c-Na2V2(PO4)3 enables complete Na-ion extraction, increasing energy density
Structure analysis (XRD and Neutrons) and hydrogen storage properties of Hf1-Ti NbVZr BCC high entropy alloys
No full textInternational audienceThe hydrogen storage properties of Hf 1-x Ti x NbVZr high entropy alloys (HEAs) synthesized by arc melting have been investigated. The first hydrogenation of the alloys was performed at room temperature under 20 bars of hydrogen pressure. Results show an increase in gravimetric hydrogen content with Ti substitutions. Upon hydrogenation, the multiphase alloys (x = 0 and x = 0.25) exhibit a combination of faces-centred-cubic (FCC) hydride and C15 Laves phases, while single-phase alloys (x = 0.5, 0.75, and 1) display FCC structures. The crystal structure evolution during dehydrogenation of HfNbVZr (x = 0) and TiNbVZr (x = 1) HEAs was examined using in-situ neutron diffraction. The analysis demonstrates temperature-dependent desorption behaviour, with HfNbVZr displaying lower desorption temperatures compared to TiNbVZr. Additionally, in-situ neutron diffraction experiments during deuterium desorption indicate a two-step phase transition from FCC dihydride to BCT monohydride, followed by a transition to BCC.</div
