The Fuchsian differential equation of the square lattice Ising model χ(3)\chi(3) susceptibility

Using an expansion method in the variables $x_i$ that appear in the $(n-1)$-dimensional integrals representing the $n$-particle contribution to the Ising square lattice model susceptibility $\chi$, we generate a long series of coefficients for the 3-particle contribution $\chi^{(3)}$, using a $N^4$ polynomial time algorithm. We give the Fuchsian differential equation of order seven for $\chi^{(3)}$ that reproduces all the terms of our long series. An analysis of the properties of this Fuchsian differential equation is performed.Comment: 15 pages, no figures, submitted to J. Phys.

Contribution of Cerebellar Sensorimotor Adaptation to Hippocampal Spatial Memory

Complementing its primary role in motor control, cerebellar learning has also a bottom-up influence on cognitive functions, where high-level representations build up from elementary sensorimotor memories. In this paper we examine the cerebellar contribution to both procedural and declarative components of spatial cognition. To do so, we model a functional interplay between the cerebellum and the hippocampal formation during goal-oriented navigation. We reinterpret and complete existing genetic behavioural observations by means of quantitative accounts that cross-link synaptic plasticity mechanisms, single cell and population coding properties, and behavioural responses. In contrast to earlier hypotheses positing only a purely procedural impact of cerebellar adaptation deficits, our results suggest a cerebellar involvement in high-level aspects of behaviour. In particular, we propose that cerebellar learning mechanisms may influence hippocampal place fields, by contributing to the path integration process. Our simulations predict differences in place-cell discharge properties between normal mice and L7-PKCI mutant mice lacking long-term depression at cerebellar parallel fibre-Purkinje cell synapses. On the behavioural level, these results suggest that, by influencing the accuracy of hippocampal spatial codes, cerebellar deficits may impact the exploration-exploitation balance during spatial navigation

Computing Galois Groups of Completely Reducible Differential Equations

AbstractWe give an algorithm to calculate a presentation of the Picard–Vessiot extension associated to a completely reducible linear differential equation (i.e. an equation whose Galois group is reductive). Using this, we show how to compute the Galois group of such an equation as well as properties of the Galois groups of general equations

Teneur en ribulose-1,5-bisphosphate carboxylase/oxygénase des feuilles de luzerne (Medicago sativa L). Facteurs de variation génétiques et agronomiques

On a déterminé, par des dosages immunochimiques, la teneur en ribulose-1,5-bisphosphate carboxylase/ oxygénase (rubisco) de feuilles situées sur la tige principale de plantes ayant atteint le stade «liseré violet». En partant du haut de la tige, cette teneur augmente jusqu'à la feuille à l'aisselle de laquelle est située la première inflorescence au stade «liseré violet» (rang 0) puis décroît régulièrement jusque vers la base de la tige. La teneur en rubisco de la feuille de rang 0 a été déterminée, aux époques de récolte, sur 11 génotypes. Elle ne semble pas corrélée aux teneurs en matière sèche ou en azote de cette feuille mais varie entre 5 et 15% de la teneur en matière sèche selon le cycle de récolte et le génotype. La teneur en rubisco augmente nettement entre le 1 er et le 2e cycle puis reste sensiblement constante du 2e au 4e pour les types méditerranéens. Dans le cas des types flamands, on observe une teneur maximale marquée au 2e ou au 3e cycle.Ribulose-1,5-bisphosphate carboxylase/oxygenase content of alfalfa (Medicago sativa L) leaves. Effects of genotype and cutting stage. The content of ribulose-1,5-bisphosphate carboxylase/oxygenase (rubisco) has been determined in leaves on the main stem of plants at the late budding stage by an immunochemical method. Starting from the stem top, the content of rubisco increases up to the leaf where the 1st inflorescence at the late budding stage is located (0 level) and then decreases towards the oldest part of the main stem (table I). Rubisco content of the 0 level leaf has been determined at the cutting (late budding) stages in 11 populations of alfalfa (table II, fig 1). Rubisco content varies much more than dry matter or nitrogen, and varies more between cutting stages than between populations (table III). Rubisco content does not seem to be correlated with dry matter or nitrogen content of the 0 level leaf (table IV), but ranges between 5 and 15% of the dry weight, depending on the population and on the cutting stage. The content of rubisco clearly increases from the first to the second cutting stage and remains nearly constant from the second to the fourth cutting stage in mediterranean type populations. With Flemish type populations, a maximum content is noted at the 2nd or 3rd cutting stage (fig 1). There is no simple correlation between these trends and the variations in climatic data (temperature, period of sunshine or radiation energy). Insofar as these results can be extended from a single leaf to the whole crop, they should have general consequences on the structure of plant nitrogen and on the way alfalfa is used for animal feeding, for dehydration or leaf protein extraction

Teneur en ribulose-1,5-bisphosphate carboxylase/oxygénase des feuilles de luzerne (Medicago sativa L). Facteurs de variation génétiques et agronomiques

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