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Low-rank matrix decompositions for ab initio nuclear structure

The extension of ab initio quantum many-body theory to higher accuracy and larger systems is intrinsically limited by the handling of large data objects in form of wave-function expansions and/or many-body operators. In this work we present matrix factorization techniques as a systematically improvable and robust tool to significantly reduce the computational cost in many-body applications at the price of introducing a moderate decomposition error. We demonstrate the power of this approach for the nuclear two-body systems, for many-body perturbation theory calculations of symmetric nuclear matter, and for non-perturbative in-medium similarity renormalization group simulations of finite nuclei. Establishing low-rank expansions of chiral nuclear interactions offers possibilities to reformulate many-body methods in ways that take advantage of tensor factorization strategies

Least-square approach for singular value decompositions of scattering problems

It was recently observed that chiral two-body interactions can be efficientlyrepresented using matrix factorization techniques such as the singular valuedecomposition. However, the exploitation of these low-rank structures in a few-or many-body framework is nontrivial and requires reformulations thatexplicitly utilize the decomposition format. In this work, we present a generalleast-square approach that is applicable to different few- and many-bodyframeworks and allows for an efficient reduction to a low number of singularvalues in the least-square iteration. We verify the feasibility of theleast-square approach by solving the Lippmann-Schwinger equation in factorizedform. The resulting low-rank approximations of the $T$ matrix are found tofully capture scattering observables. Potential applications of theleast-square approach to other frameworks with the goal of employing tensorfactorization techniques are discussed.<br

Low-Rank Decompositions of Three-Nucleon Forces via Randomized Projections

Ab initio calculations for nuclei and nuclear matter are limited by the computational requirements of processing large data objects. In this work, we develop low-rank singular value decompositions for chiral three-nucleon interactions, which dominate these limitations. In order to handle the large dimensions in representing three-body operators, we use randomized decomposition techniques. We study in detail the sensitivity of different three-nucleon topologies to low-rank matrix factorizations. The developed low-rank three-nucleon interactions are benchmarked in Faddeev calculations of the triton and ab initio calculations of medium-mass nuclei. Exploiting low-rank properties of nuclear interactions will be particularly important for the extension of ab initio studies to heavier and deformed systems, where storage requirements will exceed the computational capacities of the most advanced high-performance-computing facilities.Comment: 7 pages, 4 figure

Les enclos du haut Moyen Âge de Vauvert à Château-Gontier (Mayenne)

Le site de Vauvert, repéré d’avion par G.Leroux en 1992, se compose de fossés pour la plupart profondément creusés dans les schistes précambriens. Ils limitent plusieurs parcelles carrées ou rectangulaires. La plus ancienne, établie à la fin du viesiècle ou au siècle suivant constitue sans doute le noyau initial du site. Plusieurs parcelles vont venir progressivement entourer cet enclos primitif dont nous n’avons pu fouiller qu’une petite partie, le reste ayant été détruit juste avant l’évaluation de J.-C.Meuret en 1999. Les structures d’habitat découvertes sont rares et souvent mal conservées. Elles se résument à un four domestique, une fosse complexe, quelques trous de poteau, des fosses-tranchées énigmatiques et une sépulture établie dans le fond d’un fossé. La partie explorée de ce site, qui appartient à la périphérie d’un habitat beaucoup plus vaste, n’est plus occupée après la période carolingienne.The Vauvert site, identified from the air by G. Leroux in 1992, consists of ditches most deeply cut in precambrian schists, which delimit several square rectangular plots. The earliest, established by the end of Vth century AD or during the following one, is probably the initial nucleus of the site. Several others progressively surround this basic enclosure; we could only excavate a small part, the rest having been destroyed just before evaluation by J.-C. Meuret in 1999. The domestic structures are few and often ill-preserved: a domestic hearth, a complex pit, some postholes, some engmatic ditches and a grave placed in the bottom of a ditch. The explored part of the site, which belongs to the periphery of a much larger settlement, is no longer occupied after the Carolingian period

Prenatal diagnosis and outcome of fetuses with isolated agenesis of septum pellucidum: cohort study and meta-analysis

Objective: To evaluate the postnatal outcome of children with a prenatal diagnosis of apparently isolated agenesis of the septum pellucidum (ASP). Methods: A retrospective cohort study of cases of prenatally diagnosed ASP followed in two tertiary centers and a meta-analysis combining data from the cohort study with data from published studies identified in a systematic review were carried out. Only cases with apparently isolated ASP on antenatal ultrasound and/or magnetic resonance imaging and with available postnatal follow-up data were considered eligible for inclusion. The following outcomes were analyzed: incidence of chromosomal anomalies, agreement between antenatal and postnatal findings, overall incidence of septo-optic dysplasia (SOD) and incidence of major neurological disability (motor, language, coordination or behavioral disorder or epilepsy) in non-SOD children. The incidence of SOD in infants with apparently normal optic pathways on antenatal imaging was also evaluated. Results: Fifteen cases of isolated ASP, with median postnatal follow-up of 36 months (range, 12-60 months), were selected from the two centers. Six previously published studies met the inclusion criteria for the systematic review and a total of 78 cases were eligible for the analysis, including the 15 cases from our series. Genetic tests were carried out antenatally in 30 fetuses, of which two had an abnormal result (pooled proportion, 9.0% (95% CI, 1.8-20.7%); I2  = 0%). Additional or discordant imaging findings were noted postnatally in 9/70 (pooled proportion, 13.7% (95% CI, 3.5-29.0%); I2  = 63.9%) cases. Of all 78 neonates with available follow-up, SOD was diagnosed postnatally in 14 (pooled proportion, 19.4% (95% CI, 8.6-33.2%); I2  = 51.2%). In 60 cases, the optic pathways were considered to be normal on antenatal imaging, and six of these (pooled proportion, 9.1% (95% CI, 1.1-24.0%); I2  = 62.0%) were diagnosed postnatally with SOD. Of the 46 infants with available neurological follow-up who were not affected by SOD, a major neurological disability was diagnosed in three (pooled proportion, 6.5% (95% CI, 0.5-18.6%); I2  = 40.1%). Conclusions: In the vast majority of cases with a prenatal diagnosis of apparently isolated ASP, the prognosis is favorable. However, an additional anomaly is detected after birth in about 14% of cases and has a negative impact on clinical outcome. Detailed antenatal assessment of the brain and optic pathways is strongly recommended in order to identify the presence of associated anomalies. Antenatal visualization of apparently normal optic pathways does not rule out SOD. © 2021 International Society of Ultrasound in Obstetrics and Gynecology