Box ball system associated with antisymmetric tensor crystals

A new box ball system associated with an antisymmetric tensor crystal of the quantum affine algebra of type A is considered. This includes the so-called colored box ball system with capacity 1 as the simplest case. Infinite number of conserved quantities are constructed and the scattering rule of two olitons are given explicitly.Comment: 15 page

Stable Grothendieck polynomials and K-theoretic factor sequences

We formulate a nonrecursive combinatorial rule for the expansion of the stable Grothendieck polynomials of [Fomin-Kirillov '94] in the basis of stable Grothendieck polynomials for partitions. This gives a common generalization, as well as new proofs of the rule of [Fomin-Greene '98] for the expansion of the stable Schubert polynomials into Schur polynomials, and the K-theoretic Grassmannian Littlewood-Richardson rule of [Buch '02]. The proof is based on a generalization of the Robinson-Schensted and Edelman-Greene insertion algorithms. Our results are applied to prove a number of new formulas and properties for K-theoretic quiver polynomials, and the Grothendieck polynomials of [Lascoux-Schutzenberger '82]. In particular, we provide the first $K$-theoretic analogue of the factor sequence formula of [Buch-Fulton '99] for the cohomological quiver polynomials

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

Crystal isomorphisms in Fock spaces and Schensted correspondence in affine type A

We are interested in the structure of the crystal graph of level $l$ Fock spaces representations of $\mathcal{U}_q (\widehat{\mathfrak{sl}_e})$. Since the work of Shan [26], we know that this graph encodes the modular branching rule for a corresponding cyclotomic rational Cherednik algebra. Besides, it appears to be closely related to the Harish-Chandra branching graph for the appropriate finite unitary group, according to [8]. In this paper, we make explicit a particular isomorphism between connected components of the crystal graphs of Fock spaces. This so-called "canonical" crystal isomorphism turns out to be expressible only in terms of: - Schensted's classic bumping procedure, - the cyclage isomorphism defined in [13], - a new crystal isomorphism, easy to describe, acting on cylindric multipartitions. We explain how this can be seen as an analogue of the bumping algorithm for affine type $A$. Moreover, it yields a combinatorial characterisation of the vertices of any connected component of the crystal of the Fock space

Schubert Polynomials for the affine Grassmannian of the symplectic group

We study the Schubert calculus of the affine Grassmannian Gr of the symplectic group. The integral homology and cohomology rings of Gr are identified with dual Hopf algebras of symmetric functions, defined in terms of Schur's P and Q-functions. An explicit combinatorial description is obtained for the Schubert basis of the cohomology of Gr, and this is extended to a definition of the affine type C Stanley symmetric functions. A homology Pieri rule is also given for the product of a special Schubert class with an arbitrary one.Comment: 45 page

Portopulmonary Hypertension

Portopulmonary hypertension (PPH) is characterized by the development of pulmonary arterial hypertension (PAH) associated with portal hypertension, with or without liver disease. It is defined as a mean pulmonary artery pressure (MPAP) greater than 25 mmHg, pulmonary vascular resistance (PVR) above 240 dynes.s.cm-5, pulmonary artery occlusion pressure (PAOP) normal when less than 15 mmHg or transpulmonary gradient (TPG) > 10 mmHg. In the pulmonary hypertension classification PPH is classified in Group I. Pulmonary arterial hypertension in association with cirrhosis and portal hypertension is underdiagnosed. Epidemiological studies estimated that about 2–6% of patients with portal hypertension develop PPH. Mortality is directly proportional to measured MPAP and PVR. Mean pulmonary artery pressure is an independent predictor of mortality, and many centers consider that values greater than 50 mmHg is an absolute contraindication to liver transplantation (LT). The aim of the review is to explore the current aspects of PPH relative to concept, diagnosis, and treatment

Cardiac-Specific SOCS3 Deletion Prevents In Vivo Myocardial Ischemia Reperfusion Injury through Sustained Activation of Cardioprotective Signaling Molecules.

Myocardial ischemia reperfusion injury (IRI) adversely affects cardiac performance and the prognosis of patients with acute myocardial infarction. Although myocardial signal transducer and activator of transcription (STAT) 3 is potently cardioprotective during IRI, the inhibitory mechanism responsible for its activation is largely unknown. The present study aimed to investigate the role of the myocardial suppressor of cytokine signaling (SOCS)-3, an intrinsic negative feedback regulator of the Janus kinase (JAK)-STAT signaling pathway, in the development of myocardial IRI. Myocardial IRI was induced in mice by ligating the left anterior descending coronary artery for 1 h, followed by different reperfusion times. One hour after reperfusion, the rapid expression of JAK-STAT-activating cytokines was observed. We precisely evaluated the phosphorylation of cardioprotective signaling molecules and the expression of SOCS3 during IRI and then induced myocardial IRI in wild-type and cardiac-specific SOCS3 knockout mice (SOCS3-CKO). The activation of STAT3, AKT, and ERK1/2 rapidly peaked and promptly decreased during IRI. This decrease correlated with the induction of SOCS3 expression up to 24 h after IRI in wild-type mice. The infarct size 24 h after reperfusion was significantly reduced in SOCS3-CKO compared with wild-type mice. In SOCS3-CKO mice, STAT3, AKT, and ERK1/2 phosphorylation was sustained, myocardial apoptosis was prevented, and the expression of anti-apoptotic Bcl-2 family member myeloid cell leukemia-1 (Mcl-1) was augmented. Cardiac-specific SOCS3 deletion led to the sustained activation of cardioprotective signaling molecules including and prevented myocardial apoptosis and injury during IRI. Our findings suggest that SOCS3 may represent a key factor that exacerbates the development of myocardial IRI

On the uniqueness of promotion operators on tensor products of type A crystals

The affine Dynkin diagram of type $A_n^{(1)}$ has a cyclic symmetry. The analogue of this Dynkin diagram automorphism on the level of crystals is called a promotion operator. In this paper we show that the only irreducible type $A_n$ crystals which admit a promotion operator are the highest weight crystals indexed by rectangles. In addition we prove that on the tensor product of two type $A_n$ crystals labeled by rectangles, there is a single connected promotion operator. We conjecture this to be true for an arbitrary number of tensor factors. Our results are in agreement with Kashiwara's conjecture that all `good' affine crystals are tensor products of Kirillov-Reshetikhin crystals.Comment: 31 pages; 8 figure