Clinical evidence suggest astrocytic abnormality in major depression (MD) while treatment with anti-psychotic drugs affects astroglial functions. Astroglial cells are involved in pH homeostasis of the brain by transporting protons (through sodium-proton transporter 1, NHE1, glutamate transporters EAAT1/2 and proton-lactate co-transporter MCT1) and bicarbonate (through the sodium-bicarbonate co-...

The Burge correspondence yields a bijection between simple labelled graphs and semistandard Young tableaux of threshold shape. We characterize the hook shape by peak valley conditions on arrays. This is first step towards an analogue Schensted’s result for RSK insertion which states that length longest increasing subword word largest row tableau under correspondence. Furthermore, we give crysta...

We give a new combinatorial interpretation of Howe dual pairs the form $(\g,{\rm Sp}_{2\ell})$, where $\g$ is Lie (super)algebra classical type. This done by establishing symplectic analogue RSK algorithm associated to this pair, in uniform way which does not depend on $\g$. introduce an jeu de taquin sliding for spinor model irreducible characters superalgebra define $P$-tableau and show that ...

In this paper, a nonlinear stiff differential equation is solved by using the Rosenbrock iterative method, modified homotpy analysis method and power series method. The approximate solution of this equation is calculated in the form of series which its components are computed by applying a recursive relations. Some numerical examples are studied to demonstrate the accuracy of the presented meth...

We prove that the Robinson-Schensted-Knuth correspondence is a gl∞-crystal isomorphism between two realizations of the crystal graph of a generalized Verma module with respect to a maximal parabolic subalgebra of gl∞. A flagged version of the RSK correspondence is derived in a natural way by computing a Demazure crystal graph of a generalized Verma module. As an application, we discuss a relati...

Other names: HU-1; MAPKAPK1A; RSK; RSK1; p90S6K; pp90RSK1 HGNC (Hugo): RPS6KA1 Location: 1p36.11 Local order: Information about the local order of the human RPS6KA1 locus can be found at ensembl.org. Human RPS6KA1 is found on chromosome 1, position 26,744,930-26,774,107, between genes coding for HMGN2 (High-mobility group nucleosome-binding domain-containing protein 2) and ARID1A (AT-rich inter...

T Cell Receptor (TCR) engagement, co-stimulatory signals, and the presence of inflammatory cytokines. These signals are sensed by mTOR. Once activated, mTOR interacts with and influences T cell signaling pathways essential in regulating cell differentiation, proliferation, survival and metabolism. Multiple agonists (TCR engagement and co-stimulation, growths factors, and cytokines) regulate T c...

Schützenberger’s theorem for the ordinary RSK correspondence naturally extends to Chen et. al’s correspondence for matchings and partitions. Thus the counting of bilaterally symmetric k-noncrossing partitions naturally arises as an analogue for involutions. In obtaining the analogous result for 3-noncrossing partitions, we use a different technique to develop a MAPLE package for 2-dimensional v...

This paper describes a family of Hecke algebras Hμ = EndG(Ind G U (ψμ)), where U is the subgroup of unipotent upper-triangular matrices of G = GLn(Fq) and ψμ is a linear character of U . The main results combinatorially index a basis of Hμ, provide a large commutative subalgebra of Hμ, and after describing the combinatorics associated with the representation theory ofHμ, generalize the RSK corr...