Jack superpolynomials: physical and combinatorial definitions

Jack superpolynomials are eigenfunctions of the supersymmetric extension of the quantum trigonometric Calogero-Moser-Sutherland. They are orthogonal with respect to the scalar product, dubbed physical, that is naturally induced by this quantum-mechanical problem. But Jack superpolynomials can also be defined more combinatorially, starting from the multiplicative bases of symmetric superpolynomials, enforcing orthogonality with respect to a one-parameter deformation of the combinatorial scalar product. Both constructions turns out to be equivalent. This provides strong support for the correctness of the various underlying constructions and for the pivotal role of Jack superpolynomials in the theory of symmetric superpolynomials.Comment: 6 pages. To appear in the proceedings of the {\it XIII International Colloquium on Integrable Systems and Quantum Groups}, Czech. J . Phys., June 17-19 2004, Doppler Institute, Czech Technical Universit

Evaluation and normalization of Jack superpolynomials

Two evaluation formulas are derived for the Jack superpolynomials. The evaluation formulas are expressed in terms of products of fillings of skew diagrams. One of these formulas is nothing but the evaluation formula of the Jack polynomials with prescribed symmetry, which thereby receives here a remarkably simple formulation. Among the auxiliary results required to establish the evaluation formulas, the determination of the conditions ensuring the non-vanishing coefficients in a Pieri-type rule for Jack superpolynomials is worth pointing out. An important application of the evaluation formulas is a new derivation of the combinatorial norm of the Jack superpolynomials. We finally mention that the introduction of a simpler version of the dominance ordering on superpartitions is fundamental to establish our results.Comment: 42 pages, 10 figures. v2: minor corrections in Eqs (16) and (17

From Jack to Double Jack Polynomials via the Supersymmetric Bridge

The Calogero-Sutherland model occurs in a large number of physical contexts, either directly or via its eigenfunctions, the Jack polynomials. The supersymmetric counterpart of this model, although much less ubiquitous, has an equally rich structure. In particular, its eigenfunctions, the Jack superpolynomials, appear to share the very same remarkable combinatorial and structural properties as their non-supersymmetric version. These super-functions are parametrized by superpartitions with fixed bosonic and fermionic degrees. Now, a truly amazing feature pops out when the fermionic degree is sufficiently large: the Jack superpolynomials stabilize and factorize. Their stability is with respect to their expansion in terms of an elementary basis where, in the stable sector, the expansion coefficients become independent of the fermionic degree. Their factorization is seen when the fermionic variables are stripped off in a suitable way which results in a product of two ordinary Jack polynomials (somewhat modified by plethystic transformations), dubbed the double Jack polynomials. Here, in addition to spelling out these results, which were first obtained in the context of Macdonal superpolynomials, we provide a heuristic derivation of the Jack superpolynomial case by performing simple manipulations on the supersymmetric eigen-operators, rendering them independent of the number of particles and of the fermionic degree. In addition, we work out the expression of the Hamiltonian which characterizes the double Jacks. This Hamiltonian, which defines a new integrable system, involves not only the expected Calogero-Sutherland pieces but also combinations of the generators of an underlying affine ${\widehat{\mathfrak {sl}}_2}$ algebra

Inhibition of Connexin43 hemichannels impairs spatial short-term memory without affecting spatial working memory

Astrocytes are active players in higher brain function as they can release gliotransmitters, which are essential for synaptic plasticity. Various mechanisms have been proposed for gliotransmission, including vesicular mechanisms as well as non-vesicular ones, for example by passive diffusion via connexin hemichannels (HCs). We here investigated whether interfering with connexin43 (Cx43) HCs influenced hippocampal spatial memory. We made use of the peptide Gap19 that blocks HCs but not gap junction channels and is specific for Cx43. To this end, we microinfused transactivator of transcription linked Gap19 (TAT-Gap19) into the brain ventricle of male NMRI mice and assessed spatial memory in a Y maze. We found that the in vivo blockade of Cx43 HCs did not affect the locomotor activity or spatial working memory in a spontaneous alternation Y maze task. Cx43 blockade did however significantly impair the spatial short-term memory in a delayed spontaneous alternation Y maze task. These results indicate that Cx43 HCs play a role in spatial short-term memory

Fisheye keyboard : whole keyboard displayed on small device

In this article, we propose a soft keyboard with interaction inspired by research on visualisation information. Our goal is to find a compromise between readability and usability on a whole character layout for an Ultra mobile PC. The proposed interactions allow to display all keys on a small screen while making pointing easier for the user by expanding any given key as a function of its distance from the stylus

A Compact Model for the Ballistic Subthreshold Current in Ultra-Thin Independent Double-Gate MOSFETs

International audienceWe present an analytical model for the subthreshold characteristic of ultra-thin Independent Double-Gate (IDG) MOSFET working in the ballistic regime. This model takes into account short-channel effects, quantization effects and source-to-drain tunneling (WKB approximation) in the expression of the subthreshold drain current. Important device parameters, such as off-state current or subthreshold swing, can be easily evaluated through this full analytical approach. The model can be successfully implemented in a TCAD circuit simulator for the simulation of IDG MOSFET based-circuits

Le système KeyGlass

International audienceThis paper presents the KeyGlass system : a text entry system with dynamic addition of characters based on those previously entered. The prediction system that we use to optimize our system is based on the joint use of a lexicographic tree and a system using bigrams. We present in this article the different steps that led us to this prediction system. Finally we study, through two experiments (one theoretical and the other one with users), the usefulness and effectiveness of our system during a task of text copy. The results show a significant reduction in the distance covered by the pointer on the soft keyboard. However, users are slower to enter text