A crystal theoretic method for finding rigged configurations from paths

The Kerov--Kirillov--Reshetikhin (KKR) bijection gives one to one correspondences between the set of highest paths and the set of rigged configurations. In this paper, we give a crystal theoretic reformulation of the KKR map from the paths to rigged configurations, using the combinatorial R and energy functions. This formalism provides tool for analysis of the periodic box-ball systems.Comment: 24 pages, version for publicatio

Noncommutative Schur polynomials and the crystal limit of the U_q sl(2)-vertex model

Starting from the Verma module of U_q sl(2) we consider the evaluation module for affine U_q sl(2) and discuss its crystal limit (q=0). There exists an associated integrable statistical mechanics model on a square lattice defined in terms of vertex configurations. Its transfer matrix is the generating function for noncommutative complete symmetric polynomials in the generators of the affine plactic algebra, an extension of the finite plactic algebra first discussed by Lascoux and Sch\"{u}tzenberger. The corresponding noncommutative elementary symmetric polynomials were recently shown to be generated by the transfer matrix of the so-called phase model discussed by Bogoliubov, Izergin and Kitanine. Here we establish that both generating functions satisfy Baxter's TQ-equation in the crystal limit by tying them to special U_q sl(2) solutions of the Yang-Baxter equation. The TQ-equation amounts to the well-known Jacobi-Trudy formula leading naturally to the definition of noncommutative Schur polynomials. The latter can be employed to define a ring which has applications in conformal field theory and enumerative geometry: it is isomorphic to the fusion ring of the sl(n)_k -WZNW model whose structure constants are the dimensions of spaces of generalized theta-functions over the Riemann sphere with three punctures.Comment: 24 pages, 6 figures; v2: several typos fixe

Difference L operators related to q-characters

We introduce a factorized difference operator L(u) annihilated by the Frenkel-Reshetikhin screening operator for the quantum affine algebra U_q(C^{(1)}_n). We identify the coefficients of L(u) with the fundamental q-characters, and establish a number of formulas for their higher analogues. They include Jacobi-Trudi and Weyl type formulas, canceling tableau sums, Casorati determinant solution to the T-system, and so forth. Analogous operators for the orthogonal series U_q(B^{(1)}_n) and U_q(D^{(1)}_n) are also presented.Comment: 25 pages, LaTeX2e, no figur

Tetrahedron and 3D reflection equations from quantized algebra of functions

Soibelman's theory of quantized function algebra A_q(SL_n) provides a representation theoretical scheme to construct a solution of the Zamolodchikov tetrahedron equation. We extend this idea originally due to Kapranov and Voevodsky to A_q(Sp_{2n}) and obtain the intertwiner K corresponding to the quartic Coxeter relation. Together with the previously known 3-dimensional (3D) R matrix, the K yields the first ever solution to the 3D analogue of the reflection equation proposed by Isaev and Kulish. It is shown that matrix elements of R and K are polynomials in q and that there are combinatorial and birational counterparts for R and K. The combinatorial ones arise either at q=0 or by tropicalization of the birational ones. A conjectural description for the type B and F_4 cases is also given.Comment: 26 pages. Minor correction

Integrable structure of box-ball systems: crystal, Bethe ansatz, ultradiscretization and tropical geometry

The box-ball system is an integrable cellular automaton on one dimensional lattice. It arises from either quantum or classical integrable systems by the procedures called crystallization and ultradiscretization, respectively. The double origin of the integrability has endowed the box-ball system with a variety of aspects related to Yang-Baxter integrable models in statistical mechanics, crystal base theory in quantum groups, combinatorial Bethe ansatz, geometric crystals, classical theory of solitons, tau functions, inverse scattering method, action-angle variables and invariant tori in completely integrable systems, spectral curves, tropical geometry and so forth. In this review article, we demonstrate these integrable structures of the box-ball system and its generalizations based on the developments in the last two decades.Comment: 73 page

Conformal algebra: R-matrix and star-triangle relation

The main purpose of this paper is the construction of the R-operator which acts in the tensor product of two infinite-dimensional representations of the conformal algebra and solves Yang-Baxter equation. We build the R-operator as a product of more elementary operators S_1, S_2 and S_3. Operators S_1 and S_3 are identified with intertwining operators of two irreducible representations of the conformal algebra and the operator S_2 is obtained from the intertwining operators S_1 and S_3 by a certain duality transformation. There are star-triangle relations for the basic building blocks S_1, S_2 and S_3 which produce all other relations for the general R-operators. In the case of the conformal algebra of n-dimensional Euclidean space we construct the R-operator for the scalar (spin part is equal to zero) representations and prove that the star-triangle relation is a well known star-triangle relation for propagators of scalar fields. In the special case of the conformal algebra of the 4-dimensional Euclidean space, the R-operator is obtained for more general class of infinite-dimensional (differential) representations with nontrivial spin parts. As a result, for the case of the 4-dimensional Euclidean space, we generalize the scalar star-triangle relation to the most general star-triangle relation for the propagators of particles with arbitrary spins.Comment: Added references and corrected typo

Common Promoter Elements in Odorant and Vomeronasal Receptor Genes

In mammals, odorants and pheromones are detected by hundreds of odorant receptors (ORs) and vomeronasal receptors (V1Rs and V2Rs) expressed by sensory neurons that are respectively located in the main olfactory epithelium and in the vomeronasal organ. Even though these two olfactory systems are functionally and anatomically separate, their sensory neurons show a common mechanism of receptor gene regulation: each neuron expresses a single receptor gene from a single allele. The mechanisms underlying OR and VR gene expression remain unclear. Here we investigated if OR and V1R genes share common sequences in their promoter regions

C-jun Inhibits Mammary Apoptosis In Vivo

c-Jun mediates ROS production and apoptosis

Gene Expression Changes in the Motor Cortex Mediating Motor Skill Learning

The primary motor cortex (M1) supports motor skill learning, yet little is known about the genes that contribute to motor cortical plasticity. Such knowledge could identify candidate molecules whose targeting might enable a new understanding of motor cortical functions, and provide new drug targets for the treatment of diseases which impair motor function, such as ischemic stroke. Here, we assess changes in the motor-cortical transcriptome across different stages of motor skill acquisition. Adult rats were trained on a gradually acquired appetitive reach and grasp task that required different strategies for successful pellet retrieval, or a sham version of the task in which the rats received pellet reward without needing to develop the reach and grasp skill. Tissue was harvested from the forelimb motor-cortical area either before training commenced, prior to the initial rise in task performance, or at peak performance. Differential classes of gene expression were observed at the time point immediately preceding motor task improvement. Functional clustering revealed that gene expression changes were related to the synapse, development, intracellular signaling, and the fibroblast growth factor (FGF) family, with many modulated genes known to regulate synaptic plasticity, synaptogenesis, and cytoskeletal dynamics. The modulated expression of synaptic genes likely reflects ongoing network reorganization from commencement of training till the point of task improvement, suggesting that motor performance improves only after sufficient modifications in the cortical circuitry have accumulated. The regulated FGF-related genes may together contribute to M1 remodeling through their roles in synaptic growth and maturation.McGovern Institute for Brain Research at MITNational Institutes of Health (U.S.) ((NIH grant 1-RC1-NS068103-01)National Institutes of Health (U.S.) (NIH grant R01-MH084966)Roberto Rocca Education Program (Fellowship)Massachusetts Institute of Technology. Undergraduate Research Opportunities Program (Fellowship)Italy. Ministero dell'istruzione, dell'università e della ricerca (MIUR grant RBIN04H5AS)Italy. Ministero dell'istruzione, dell'università e della ricerca (MIUR grant RBLA03FLJC)Italy. Ministero dell'istruzione, dell'università e della ricerca (FIRB n. RBAP10L8TY

Serum from Calorie-Restricted Rats Activates Vascular Cell eNOS through Enhanced Insulin Signaling Mediated by Adiponectin

eNOS activation resulting in mitochondrial biogenesis is believed to play a central role in life span extension promoted by calorie restriction (CR). We investigated the mechanism of this activation by treating vascular cells with serum from CR rats and found increased Akt and eNOS phosphorylation, in addition to enhanced nitrite release. Inhibiting Akt phosphorylation or immunoprecipitating adiponectin (found in high quantities in CR serum) completely prevented the increment in nitrite release and eNOS activation. Overall, we demonstrate that adiponectin in the serum from CR animals increases NO• signaling by activating the insulin pathway. These results suggest this hormone may be a determinant regulator of the beneficial effects of CR