Crystal energy functions via the charge in types A and C

The Ram-Yip formula for Macdonald polynomials (at t=0) provides a statistic which we call charge. In types A and C it can be defined on tensor products of Kashiwara-Nakashima single column crystals. In this paper we prove that the charge is equal to the (negative of the) energy function on affine crystals. The algorithm for computing charge is much simpler and can be more efficiently computed than the recursive definition of energy in terms of the combinatorial R-matrix.Comment: 25 pages; 1 figur

Scattering Rule in Soliton Cellular Automaton associated with Crystal Base of Uq(D4(3))U_q(D_4^{(3)})

In terms of the crystal base of a quantum affine algebra $U_q(\mathfrak{g})$, we study a soliton cellular automaton (SCA) associated with the exceptional affine Lie algebra $\mathfrak{g}=D_4^{(3)}$. The solitons therein are labeled by the crystals of quantum affine algebra $U_q(A_1^{(1)})$. The scatteing rule is identified with the combinatorial $R$ matrix for $U_q(A_1^{(1)})$-crystals. Remarkably, the phase shifts in our SCA are given by {\em 3-times} of those in the well-known box-ball system.Comment: 25 page

tt-Martin boundary of killed random walks in the quadrant

We compute the $t$-Martin boundary of two-dimensional small steps random walks killed at the boundary of the quarter plane. We further provide explicit expressions for the (generating functions of the) discrete $t$-harmonic functions. Our approach is uniform in $t$, and shows that there are three regimes for the Martin boundary.Comment: 18 pages, 2 figures, to appear in S\'eminaire de Probabilit\'e

Affine crystal structure on rigged configurations of type D_n^(1)

Extending the work arXiv:math/0508107, we introduce the affine crystal action on rigged configurations which is isomorphic to the Kirillov-Reshetikhin crystal B^{r,s} of type D_n^(1) for any r,s. We also introduce a representation of B^{r,s} (r not equal to n-1,n) in terms of tableaux of rectangular shape r x s, which we coin Kirillov-Reshetikhin tableaux (using a non-trivial analogue of the type A column splitting procedure) to construct a bijection between elements of a tensor product of Kirillov-Reshetikhin crystals and rigged configurations.Comment: 26 pages, 3 figures. (v3) corrections in the proof reading. (v2) 26 pages; examples added; introduction revised; final version. (v1) 24 page

Sliding Presentation of the Jeux de Taquin for Classical Lie Groups

International audienceThe simple $GL(n,\mathbb {C})$-modules are described by using semistandard Young tableaux. Any semistandard skew tableau can be transformed into a well defined semistandard tableau by a combinatorial operation, the Schützenberger jeu de taquin. Associated to the classical Lie groups $SP(2n,\mathbb {C})$, $SO(2n+1,\mathbb {C})$, there are other notions of semistandard Young tableaux and jeux de taquin. In this paper, we study these various jeux de taquin, proving that each of them has a simple and explicit formulation as a step-by-step sliding. Any of these jeux de taquin is the restriction of the orthogonal one, associated to $SO(2n+1,\mathbb {C})$

Pharmacological and toxicological effects of Paronychia argentea in experimental calcium oxalate nephrolithiasis in rats

1 - ArticleAim of the study: Renal protection and antiurolithiasic effects of two extracts of Paronychia argentea (PA), a traditional Algerian plant commonly known as Algerian tea, were evaluated. This study was carried out to determine whether the aqueous extract (APA) or the butanolic extract (BPA) of aerial parts could prevent or reduce calculi aggregation in experimental calcium oxalate (Ox) nephrolithiasis in Wistar rats. Materials and methods: The two extracts (APA and BPA) were administrated orally and daily, during 28 days to nephrolithiasic treated rats at the dose of 250, 500 mg/kg b.w. and 10, 20 mg/kg b.w. respectively. Body weight, renal index, liver index, serum level of creatinine, uric acid, urea, K(+), Ca(2+), Mg(2+), Na(+) and transaminase (alanine aminotransferase, ALT; aspartate aminotransferase, AST), phosphatase alkaline activity (PAL) were evaluated following the 28 days treatment in rats. In addition histopathological changes in kidney and liver were stained in hematoxylin eosin (HE). Results: The effect of the extracts could be advantageous in preventing urinary stone retention by reducing renal necrosis and thus inhibit crystal retention. In contradiction with APA, the two doses of BPA attenuated elevation in the serum creatinine (p<0.01) and blood urea levels (p<0.01) (nephroprotective effect). However, the increase in ALT (27%) and PAL (31-51%) serum levels and in the relative liver weights (p<0.01) in the groups treated with doses of APA may indicate that this extract has not a hepatoprotective effect against oxalate toxicity. Conclusions: The presented data indicate that administration of the butanolic extract of aerial parts to rats with NaOx induced lithiasis, and reduced and prevented the growth of urinary stones in experimental calcium oxalate nephrolithiasis in Wistar rats. (C) 2010 Elsevier Ireland Ltd. All rights reserved

Electrospray tandem mass spectrometry of alendronate analogues: fingerprints for characterization of new potential prodrugs

1 - Article1-Hydroxymethylene-1,1-bisphosphonic acids (HMBPs) are important drugs for the treatment of a variety of bone diseases. Since these compounds have no chromophore, their detection is challenging and mass spectrometry (MS) appears to be an appropriate sensitive tool. Our work deals with the analysis by electrospray ionization tandem mass spectrometry (ESI-MSn) of the well-known nitrogen-containing HMBP alendronate and of three analogues, considered as potential prodrugs. These four molecules share a common structure with different protecting groups on the phosphonic acid and on the amine functions. We describe the dissociation mechanisms of nitrogen-containing HMBPs in positive ion mode and we compare, in negative ion mode, our results with literature data. In both modes, the dissociations are essentially losses of ROH, and of phosphorus-containing species (HPO2, ROP(OH)(2) and ROPO(OH)(2)), where R = H, C6H5, or CH3OC6H5. These fingerprints will be of great value for differentiating alendronate from its potential prodrugs in complex biological mixtures. Copyright (c) 2008 John Wiley & Sons, Ltd

Urine collection methods used for non-toilet-trained children in pediatric emergency departments in France A medical practice analysis

International audienceIntroduction - Since April 2015, the French Society of Pediatrics has encouraged suprapubic aspiration (SA) and urethral catheterization (UC) for urine collection in non-toilet-trained children suspected of having urinary tract infections (UTIs) and has tried to reduce the use of urine bag (UB). Objective - To analyze the medical practices concerning urine collection methods used for non-toilet-trained children in pediatric emergency departments in France. Methods - We conducted a descriptive medical practice study in October 2017. All members of the French Society of Pediatric Nephrology received two questionnaires about urine collection methods used for non-toilet-trained children, distinguishing between male and female patients, and about the corresponding analgesic protocols used in their pediatric emergency departments. Results - In total, 26 centers completed questionnaires concerning female patients. UC was performed in cases of fever associated with urinary tract malformations in 14 of 26 centers (54%). UB was used in cases of fever of unknown origin lasting for more than 48h in 17 of 26 centers (65%), in cases of fever associated with UTI symptoms in 14 of 26 centers (54%), and in cases of fever in infants under 3 months of age in 16 of 26 centers (61%). The questionnaires concerning male patients were completed by 30 centers. UB was the initially used urine collection method in all situations with, respectively, 22 of 30 (73%), 27 of 30 (90%), 23 of 30 (77%), and 22 of 30 (73%) centers. The analgesic protocol for urine collection is not well established in France. Conclusion - UC for urine collection in pediatric emergency departments in France is underused despite the national recommendations and the greater diagnostic power of this method compared with UB