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Pari/GP was designed for algebraic number theory. As such it does not have some standard features that other general purpose computer algebra systems have such as Gröbner bases and multivariate polynomial factorization. In this letter I say a few words about the history of Pari/GP, the impact Pari/GP has had on number theory, and some of the unique software design features of Pari/GP. I've also included a short bio from Henri, Bill and Karim.

Generalizing the work of A. Morra and the authors, we give explicit formulas for the Dirichlet series generating function of $D_l$-extensions of odd prime degree $l$ with given quadratic resolvent. Over the course of our proof, we explain connections between our formulas and the Ankeny-Artin-Chowla conjecture, the Ohno-Nakagawa relation for binary cubic forms, and other topics.

International audience

To test if the evaluation of body dissatisfaction by images could be an interesting tool to detect perinatal depression early in pregnancy, questioning patients about their body image instead of their depressive symptoms.A sample of 457 women was recruited in a longitudinal study. Three evaluations were performed at the 4th and 8th months of pregnancy and during post-partum. During these evaluations, sociodemographic data were collected and psychiatric scales were completed, including Edinburgh Postnatal Depression Scale (EPDS), Eating Disorder Examination-Questionnaire (EDE-Q), Pictorial Body Image Scale (PBIS) and Body Shape Questionnaire (BSQ).33% of the women who were unsatisfied with their body image suffered from perinatal depression vs. 11.3% of the women who were not (p 0.0001). The risk of perinatal depression was 4 times higher in women dissatisfied with their body image (p 0.001) if unintended pregnancy and age are taken into account and is 3 times significantly higher in women with higher levels of eating disorders symptoms (p 0.001) if unintended pregnancy and age are taken into account. Our sample was a privileged population, as often in the literature.The administration of a simple scale (PBIS) during an early visit during pregnancy allows detecting perinatal depression. This should prevent the stigmatization of women during pregnancy and reduce the risk of not diagnosing depression during pregnancy and post-partum.

In adults, grip force has reliably been used to investigate motor simulation evoked by linguistic action, suggesting that motor phenomena are linked to semantic action. The parietal and frontal lobes and their connexions are essential neural structures for pragmatic aspects of hand semantic action. In this perspective, the aim of the study was to determine the extent to which two groups of children and adolescents, classically characterized by degree of axonal myelination in fronto-parietal circuits, monitored the occurrence of nouns and manual action verbs presented auditorily while holding a grip force sensor. Differential effects of grip force were seen only in the adolescents when monitoring action verbs. Interestingly, weaker effects of grip force were modulated by noun targets only in the younger children, revealing that the ability to profit from a full semantic representation of verbs is not clearly established in the younger children. Grip force modulation was observed as early as 300 ms post target onset and peaked at the 500–750 ms window of observation for both groups. These group differences are in line with the motor simulation difficulties seen in younger children. The results may also indicate that degree of grip force in response to specific linguistic categories parallels the maturation of the parietal-frontal circuits, including the anterior intra-parietal area which plays a determining role in semantic aspects of hand action.

We investigated the extent to which a complex finger sequence impacts on hand switching costs in a sequential action. Response component latencies (premotor, motor, and movement) were compared in no-switch (same finger performed the action of pressing and reaching) and switch conditions (pressing with one finger and completing the reaching action with the homologous finger from the other hand). Results showed that the switch condition presented longer latency for premotor and movement components. For the motor component, however, switch condition was faster. This expands the previous literature investigating switching costs using simple finger movements in more complex tasks. A mechanical explanation of the interplay between response subcomponents is provided to explain the inversion of response pattern for the motor component.

BACKGROUND The variability in resources for managing critical events among maternity hospitals may impact maternal safety. Our main objective was to assess the risk of postpartum maternal death according to hospitals' organizational characteristics. A secondary objective aimed to assess the specific risk of death due to postpartum hemorrhage (PPH). METHODS This national population-based case-control study included all 2007-2009 postpartum maternal deaths from the national confidential enquiry (n = 147 cases) and a 2010 national representative sample of parturients (n = 14,639 controls). To adjust for referral bias, cases were classified by time when the condition/complication responsible for the death occurred: postpartum maternal deaths due to conditions present before delivery (n = 66) or during or after delivery (n = 81). Characteristics of delivery hospitals included 24/7 on-site availability of an anesthesiologist and an obstetrician, level of perinatal care, number of deliveries annually, and their teaching and profit status. In teaching and other nonprofit hospitals in France, obstetric care is organized on the principle of collective team-based management, while in for-profit hospitals, this organization is based mostly on that of "one woman-one doctor." Logistic regression models were used to estimate adjusted odds ratios (aORs) and 95% confidence intervals (CIs) for postpartum maternal death. RESULTS The risk of maternal death from prepartum conditions was lower for women who gave birth in for-profit compared with teaching hospitals (aOR, 0.3; 95% CI, 0.1-0.8; P = .02) and in hospitals with

International audience; We give a number of theoretical and practical methods related to the computation of L-functions, both in the local case (counting points on varieties over finite fields, involving in particular a detailed study of Gauss and Jacobi sums), and in the global case (for instance Dirichlet L-functions, involving in particular the study of inverse Mellin transforms); we also give a number of little-known but very useful numerical methods, usually but not always related to the computation of L-functions.

In this course, we introduce the main notions relative to the classical theory of modular forms. A complete treatise in a similar style can be found in the author’s book joint with Stromberg (Cohen and Stromberg, Modular Forms: A Classical Approach, Graduate Studies in Math. 179, American Math. Soc. (2017) [1]).

International audience; We begin by explaining how to compute Fourier expansions at all cusps of any modular form of integral or half-integral weight thanks to a theorem of Borisov-Gunnells and explicit expansions of Eisenstein series at all cusps. Using this, we then give a number of methods for computing arbitrary Petersson products. All this is available in the current release of the Pari/GP package.

Context and objective We previously found that patients with Cushing’s syndrome (CS) scored lower than controls in several domains of cognitive function and that correction of hypercortisolism is not necessarily correlated with short-term improvement in intellectual performance. Here, we examined the long-term outcome in patients treated for CS by assessing the extent to which the detrimental effects of glucocorticoid (GC) excess on cognition can be reversed three years after corrective surgery. Design A battery of neuropsychological tests, including tests of attention, visuospatial processing, learning and memory, and executive functioning were administered pre-treatment and 12, 24 and 36 months post-treatment. Patients and control subjects We included 18 patients with endogenous CS recruited before surgical treatment and 18 controls matched for age, sex and education. Results CS patients performed worse than controls on tests of attention, executive functioning and nonverbal aspects of memory. Moreover, at 36 months following eucortisolism, executive function performance and, to a lesser extent, attention tasks showed limited change compared to pre-treatment testing. Conclusion Chronic hypercortisolism is accompanied by a deleterious impact on aspects of cognitive function. This negative effect on attention, executive performance and nonverbal memory seen in patients with CS suggests a differential effect of excess GCs upon different brain areas and networks. This influence persists years after the return to normal cortisol secretion levels.

Consolidation of a motor skill is characterized by spontaneous improvement in performance between practice sessions. These offline gains can be eliminated if another skill is introduced soon afterward-a phenomenon called retroactive interference. Interference effects have been found in studies using two similar tasks involving the same motor effectors in a manual mode. The present study aimed to determine the extent to which differences in motor production mode modulate interference in skill learning. Healthy participants were assigned to one of three conditions and trained on a finger opposition sequence (FOS) learning task. All subjects were tested 24 h later on the original FOS learning task. Control subjects who were not exposed to a secondary learning task exhibited the expected offline gains after 24 h. Subjects who immediately learned a secondary task after the FOS training, either in the same manual mode (French Sign Language) or in an oral mode (CVC syllables), did not show any offline gains. Interestingly, the amount of interference was equivalent in the manual and oral learning conditions. The results reveal that interference effects in motor skill learning can occur when different effectors are involved in the primary and secondary tasks. The sequence processing abilities of the basal ganglia appear to play a major role in these interference effects.

We give theoretical and practical information on the Pari/GP modular forms package available since the spring of 2018. Thanks to the use of products of two Eisenstein series, this package is the first which can compute Fourier expansions at any cusps, evaluate modular forms near the real axis, evaluate L-functions of non-eigenforms, and compute general Petersson scalar products., Research in the Mathematical Sciences (RMSS), In press

In previous work, Ohno conjectured, and Nakagawa proved, relations between the counting functions of certain cubic fields. These relations may be viewed as complements to the Scholz reflection principle, and Ohno and Nakagawa deduced them as consequences of `extra functional equations' involving the Shintani zeta functions associated to the prehomogeneous vector space of binary cubic forms. In the present paper we generalize their result by proving a similar identity relating certain degree l fields with Galois groups D_l and F_l respectively, for any odd prime l, and in particular we give another proof of the Ohno-Nakagawa relation without appealing to binary cubic forms., Version 2, 16 pages, to appear in Compositio

The Montagne Noire (southern France) possesses one of the most complete Cambrian successions in the western peri-Gondwana margin and might provide a good stratigraphic reference for both regional charts and international correlations. However, to date, the lower Cambrian succession of the northern Montagne Noire has been supposed to be devoid of biostratigraphically significant fossils. The complex tectonostratigraphic framework of the area (a range divided into Axial Zone, northern and southern Montagne Noire) exacerbated problems related to regional correlations and palaeogeographic reconstructions. As a result, the chronostratigraphic context of the lower Cambrian of northern Montagne Noire is still uncertain and stratigraphic reports have broadly relied on putative lithostratigraphic correlations with the southern Montagne Noire. The purpose of this study is to characterise, for the first time, the fossil record of carbonate beds and lenses of the northern Montagne Noire occurring at the top of the siliciclastic-dominated Marcory Formation, in order to provide regional bio- and chronostratigraphic constraints on lower Cambrian strata. Moreover, this study is aimed at improving international chronostratigraphic correlation. Carbonate beds and lenses cropping out along the Orque Cliff, in the Melagues thrust slice, were investigated. They yielded a faunal assemblage constituted of molluscs (Igorella cf. ungulata and Igorella moncereti n. sp.), hyoliths (Conotheca brevica), chancelloriids (Archiasterella cf. pentactina and Allonnia sp.) and tommotiids (Lapworthella rete). L. rete is recorded in upper Meishucunian (Cambrian Stage 3) strata of the Yangtze Platform (South China) where it is used as index fossil of the Cambrian Stage 3 Sinosachites flabelliformis–Tannuolina zhangwentangi Assemblage Zone. Therefore, the presence of this tommotiid provides evidence that the studied carbonate beds and lenses are Cambrian Age 3 (Atdabanian according to the Siberian chart). The upper part of the Marcory Formation in the Melagues slice, dated as Cambrian Stage 3, might represent a lateral equivalent of the mixed (carbonate-siliciclastic) Pardailhan Formation defined in the southern Montagne Noire.

The present study offers a brief review of the literature about isolated agraphia (IA) and discusses a new case in the context of contemporary neuropsychological models of reading and spelling. The studies of IA, within the cognitive neuropsychological framework, have dealt with issues related to the universality of cognitive models, the autonomy of orthographic lexicon/phonological mediation of writing/spelling, the multiplicity of patterns of symptoms associated with IA, and the neural bases of IA. CBH, a 59-year-old female, freelance journalist with a history of stroke-induced bilateral parietal lobe lesion displayed symptoms of IA. CBH's performance on experimental tasks related to reading and writing suggests that IA may not be restricted to one or the other syndrome of dysgraphia, access to the orthographic lexicon does not require phonological mediation, hence, it is autonomous, and the left parietal lobe plays a crucial role in spelling.

Resume But L’objectif principal de cette etude etait de comparer les performances de l’imagerie polarimetrique pour le diagnostic des CIN avec celles de la colposcopie classique. Patientes et methodes Nous avons mene une etude prospective monocentrique. Un diagnostic colposcopique lors d’une premiere consultation a ete compare au diagnostic colposcopique guide par polarimetrie lors d’une deuxieme consultation. Une biopsie systematique predeterminee en plus des biopsies dirigees par colposcopie, voire par polarimetrie en cas de nouvelle zone anormale, pour chaque patiente a permis de calculer la sensibilite et la specificite de chaque technique et de les comparer. Resultats Nous avons inclus 141 patientes ayant un FCU anormal. Soixante-neuf pour cent des 67 conisations effectuees ont retrouve une CIN2+. La sensibilite et la specificite de la colposcopie polarimetrique ont ete identiques a celles de la colposcopie classique. Conclusion Nous n’avons pas montre d’amelioration des performances diagnostiques des CIN du col en utilisant l’etude de la polarisation seule. Nous avons observe des reponses interessantes concernant d’autres caracteristiques de la lumiere qui seront etudiees lors d’une prochaine etude.

For a primitive Dirichlet character $$\chi $$ of conductor $$N$$ set $$\begin{aligned} \Theta (\chi )=\sum _{n\in \mathbb Z } n^\epsilon \chi (n)\,e^{-\pi n^2/N} \end{aligned}$$ (where $$\epsilon =0$$ for $$\chi $$ even, $$\epsilon =1$$ for $$\chi $$ odd), the value of the associated theta series at its point of symmetry under the modular transformation $$\tau \rightarrow -1/\tau $$ . These numbers are related by $$\Theta (\chi )=W(\chi )\Theta (\bar{\chi })$$ to the root number of the $$L$$ -series of $$\chi $$ and hence can be used to calculate the latter quickly if they do not vanish. We describe experiments showing that $$\Theta (\chi )\ne 0$$ for all $$\chi $$ with $$N\le 52{,}100$$ (roughly 500 million primitive characters) except for precisely two characters (up to $$\chi \rightarrow \bar{\chi }$$ ), of conductors $$300$$ and $$600$$ . The proof that $$\Theta (\chi )$$ vanishes in these two cases uses properties of Ramanujan’s modular function of level $$5$$ . We also characterize all $$\chi $$ for which $$W(\chi )$$ is a root of unity and describe some experimental results concerning the algebraic numbers $$\Theta (\chi )/\eta (i)^{1+2\epsilon }$$ when $$N$$ is prime.

Background Rhesus D genotyping with cell-free fetal DNA currently is used throughout the world. Although this technique has spread rapidly, its optimal use is still a matter of debate. This screening test has been introduced mainly for the treatment of RhD-negative pregnant women during the third trimester of pregnancy, thereby avoiding systematic anti-D prophylaxis, yet such a strategy has proved cost-ineffective. Publications reporting on fetal RHD genotyping with cell-free DNA in maternal plasma, specifically during the first trimester of pregnancy, are scarce in the scientific literature. Objective This study sought to assess the performance of noninvasive fetal Rhesus D genotyping in the first trimester of pregnancy with a single-exon real-time polymerase chain reaction assay. Study Design This was a retrospective observational multicenter study. Cell-free fetal DNA was extracted from maternal blood of both nonimmunized and immunized women at 10–14 weeks of gestation. RHD sequence was determined by quantitative polymerase chain reaction, with amplification of exon 10. Results were compared with RhD phenotype data that were obtained by cord blood sampling of neonates. Results In total, 416 serum samples from RhD-negative pregnant women were collected during the first trimester of pregnancy. The test's overall sensitivity and specificity were 100% (95% confidence interval, 96.9–100.0) and 95.2% (95% confidence interval, 90.5–97.6), respectively. The negative and positive predictive values were 99.8% (95% confidence interval, 94.9–100.0) and 97.1% (95% confidence interval, 94.2–98.6), respectively. Fetal RHD status was inconclusive in 9 cases (2.2%). Conclusion Noninvasive fetal RHD determination by single-exon quantitative polymerase chain reaction during the first trimester of pregnancy exhibits high accuracy.

Background  Williams Syndrome (WS) is a neurodevelopmental disorder of genetic origin, characterised by relative proficiency in language in the face of serious impairment in several other domains. Individuals with WS display an unusual sensitivity to noise, known as hyperacusis. Methods  In this study, we examined the extent to which hyperacusis interferes with the perception of speech in children and adults with WS. Participants were required to discriminate words which differed in one consonant of a cluster when these contrasts were embedded in a background of noise. Results  Although the introduction of noise interfered with performance on a consonant cluster discrimination task equally in the WS and control groups, the severity of hyperacusis significantly predicted individual variability in speech perception within the WS group. Conclusions  These results suggest that alterations in sensitivity to input mediate atypical pathways for language development in WS, where hyperacusis exerts an important influence together with other non-auditory factors.

The neuropsychological literature on the processing of emotions in Parkinson's disease (PD) reveals conflicting evidence about the role of the basal ganglia in the recognition of facial emotions. Hence, the present study had two objectives. One was to determine the extent to which the visual processing of emotions and objects differs in PD. The other was to assess the impact of cognitive load on the processing of these types of information. Thirty-one patients with idiopathic PD (IPD) under dopamine replacement therapy (DRT) were compared to 30 control subjects on emotion and object recognition tasks. Recognition of objects was more accurate and faster than recognition of facial expressions of emotion, for both groups of subjects. In a second experiment using an N-back procedure with the same stimuli-a more demanding task with a higher cognitive load-patients with IPD were as accurate as control subjects in detecting the correct sequential presentation of stimuli, but were much slower in their decision responses. This indicates that IPD patients under DRT are not impaired in encoding emotion or object information, but that they have difficulty with the processing demands of the N-back task. Thus, patients with IPD appear to be more sensitive to cognitive load than to type of information, whether facial emotions or objects. In this perspective, one must consider that a deafferented dopaminergic system has problems processing more complex information before one can posit the existence of deficits affecting a specific type of information.