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

Lipid-protein interactions in wheat gluten : a renewal

International audienc

Sol–gel-processed hybrid silica-PDMS layers for the optics of high-power laser flux systems

International audienceThe laser-induced damage of optical components of high-power laser systems such as the National Ignition Facility (NIF) (Murray, Proc SPIE 3492:1–10, 1998) and Laser MegaJoule (LMJ) (André, Fusion Eng Des 44:43–49, 1999) can have a significant impact on the operating costs of these laser systems since optimal shaping to carry out ignition is required. Laser-induced damage (LID) of fused silica appears on the exit surface, mostly at 3ω, and tends to grow exponentially with each laser shot. This damage affects the performance of optical components and limits their lifetime. The damage is due to thermal explosions of microdefects or microabsorbers, and these explosions emit a plasma that generates shock waves introducing cracks that increase the damage. This paper, thus proposes the deposit of an elastic layer on the exit surface to mitigate the shock waves and thereby decrease the extent of the damage volume. To this end, we have developed a mendable sol–gel-processed hybrid inorganic–organic layer. The hybrid layer is a nanocomposite made of silica and polydimethylsiloxane (PDMS). Their resultant mechanical properties can be tuned by adjusting the elastomer/silica ratio and catalysis conditions. The synthesis used to create these layers was investigated with an infrared spectrometer. The optical quality of the hybrid layers was checked by UV/visible/NIR spectrophotometry and thickness uniformity were mapped via reflectometry. Young’s modulus, Poison’s ratio, and the hardness have been measured in order to characterize the mechanical properties of these layers. The surface acoustic waves technique was used to determine Young’s modulus and Poison’s ratio of an optical layer obtained by a sol–gel process. The hardness has been measured with a homemade indenter. The results of first measurements of laser damage made with an excimer laser at 351 and 353 nm demonstrated a reduction of the laser-induced damage threshold with the PDMS/silica ratio