A Fast Algorithm for Computing the p-Curvature

We design an algorithm for computing the $p$-curvature of a differential system in positive characteristic $p$. For a system of dimension $r$ with coefficients of degree at most $d$, its complexity is \softO (p d r^\omega) operations in the ground field (where $\omega$ denotes the exponent of matrix multiplication), whereas the size of the output is about $p d r^2$. Our algorithm is then quasi-optimal assuming that matrix multiplication is (\emph{i.e.} $\omega = 2$). The main theoretical input we are using is the existence of a well-suited ring of series with divided powers for which an analogue of the Cauchy--Lipschitz Theorem holds.Comment: ISSAC 2015, Jul 2015, Bath, United Kingdo

3D-printed system optimizing dissolution of hyperpolarized gaseous species for micro-sized NMR

International audienceDissolution of hyperpolarized species in liquids of interest for NMR is often hampered by the presence of bubbles that degrade the field homogeneity. Here a device constituted by a bubble pump and a miniaturized NMR cell fitting both inside the narrow bore of an NMR magnet is built by 3D printing. 129Xe NMR experiments performed with hyperpolarized xenon reveal high and homogeneous dissolution of the gas in water

Intergenerational Pathways From Reflective Functioning to Infant Attachment Through Parenting

The aim of this prospective study was to examine temporal pathways from mothers’ reflective functioning (RF) through parenting to infant attachment measured more than 16 months later. Participants were 88 mother–infant dyads from demographically diverse backgrounds and included a group of mothers with histories of childhood maltreatment. RF was assessed using the RF rating of the Adult Attachment Interview before the birth of the baby. Parenting was assessed when the infants were 6 months old using the Maternal Sensitivity scale, as well as when they were 16 months using the Disconnected and Extremely Insensitive Parenting scale. Infant attachment was assessed when the infants were 16 months old using the Strange Situation. As hypothesised, the study findings showed that mothers’ mentalization regarding their own early attachment relationships was associated with later parenting and infant attachment. Negative parenting behaviours explained the link between mothers’ RF about their own attachment relationships and infant attachment disorganization. The findings suggest that mothers’ mentalization about their early attachment relationships has important implications in the transition to becoming parents themselves. Mentalization appears to be particularly important in helping mothers screen and inhibit negative parenting behaviours that would otherwise undermine infant attachment security and organization

Mesopelagic N-2 fixation related to organic matter composition in the Solomon and Bismarck Seas (Southwest Pacific)

Dinitrogen (N-2) fixation was investigated together with organic matter composition in the mesopelagic zone of the Bismarck (Transect 1) and Solomon (Transect 2) Seas (Southwest Pacific). Transparent exopolymer particles (TEP) and the presence of compounds sharing molecular formulae with saturated fatty acids and sugars, as well as dissolved organic matter (DOM) compounds containing nitrogen (N) and phosphorus (P) were higher on Transect 1 than on Transect 2, while oxygen concentrations showed an opposite pattern. N-2 fixation rates (up to similar to 1 nmol N L-1 d(-1)) were higher in Transect 1 than in Transect 2, and correlated positively with TEP, suggesting a dependence of diazotroph activity on organic matter. The scores of the multivariate ordination of DOM molecular formulae and their relative abundance correlated negatively with bacterial abundances and positively with N-2 fixation rates, suggesting an active bacterial exploitation of DOM and its use to sustain diazotrophic activity. Sequences of the nifH gene clustered with Alpha-, Beta-, Gamma- and Deltaproteobacteria, and included representatives from Clusters I, III and IV. A third of the clone library included sequences close to the potentially anaerobic Cluster III, suggesting that N-2 fixation was partially supported by presumably particle-attached diazotrophs. Quantitative polymerase chain reaction (qPCR) primer-probe sets were designed for three phylotypes and showed low abundances, with a phylotype within Cluster III at up to 10(3) nifH gene copies L-1. These results provide new insights into the ecology of non-cyanobacterial diazotrophs and suggest that organic matter sustains their activity in the mesopelagic ocean

On the pp-supports of a holonomic D\mathcal{D}-module

For a smooth variety $Y$ over a perfect field of positive characteristic, the sheaf $D_Y$ of crystalline differential operators on $Y$ (also called the sheaf of $PD$-differential operators) is known to be an Azumaya algebra over $T^*_{Y'},$ the cotangent space of the Frobenius twist $Y'$ of $Y.$ Thus to a sheaf of modules $M$ over $D_Y$ one can assign a closed subvariety of $T^*_{Y'},$ called the $p$-support, namely the support of $M$ seen as a sheaf on $T^*_{Y'}.$ We study here the family of $p$-supports assigned to the reductions modulo primes $p$ of a holonomic $\mathcal{D}$-module. We prove that the Azumaya algebra of differential operators splits on the regular locus of the $p$-support and that the $p$-support is a Lagrangian subvariety of the cotangent space, for $p$ large enough. The latter was conjectured by Kontsevich. Our approach also provides a new proof of the involutivity of the singular support of a holonomic $\mathcal{D}$-module, by reduction modulo $p.$Comment: The article has been rewritten with much improved exposition as well as some additional results, e.g. Corollary 6.3.1. This is the final version, accepted for publication in Inventiones Mathematica

Mothers’ self-focused reflective functioning interacts with childhood experiences of rejection to predict romantic relationship quality and insensitive parenting

Parents exposed to rejection in their childhood could experience bonding disturbances in their current relationships. Reflective functioning (RF), the capacity to understand one’s own and others’ behavior through the lens of underlying mental states (cognitions, emotions), has been identified as a potential protective process. The aim of this longitudinal study was to examine whether RF moderates the effect of parents’ experiences of rejection in childhood on later relationship functioning with partners and infants. Pregnant women with experiences of abuse and neglect were recruited and completed the Adult Attachment Interview, which was coded for RF and experiences of childhood rejection. During two follow‐up assessments, when their infants were 5 and 17 months old, the mothers in our sample who had partners reported on dyadic cohesion with these partners. Further, at 5 months postnatal, mothers completed interaction tasks with their infants, which were later assessed using observational measures (i.e., CARE‐Index). Results of mothers with partners (N = 93) indicated that RF moderated the relationship between dyadic cohesion with partners at 17 months only. Additionally, results with all mothers in the sample (N = 108) indicated that RF moderated the relationship between retrospectively reported experiences of rejection and controlling and unresponsive behaviors with infants. Adequate‐to‐high RF was associated with lower unresponsiveness and higher relationship satisfaction in the context of rejection, while being associated with higher levels of control. These findings have important clinical implications, as RF is amenable to change and can therefore be more prominently implemented within various interventions

The derivation of performance expressions for communication protocols from timed Petri net models

Petri Net models have been extended in a variety of ways and have been used to prove the correctness and evaluate the performance of communication protocols. Several extensions have been proposed to model time. This work uses a form of Timed Petri Nets and presents a technique for symbolically deriving expressions which describe system performance. Unlike past work on performance evaluation of Petri Nets which assumes a priori knowledge of specific time delays, the technique presented here applies to a wide range of time delays so long as the delays satisfy a set of timing constraints. The technique is demonstrated using a simple communication protocol