Exactly solvable D_N-type quantum spin models with long-range interaction

We derive the spectra of the D_N-type Calogero (rational) su(m) spin model, including the degeneracy factors of all energy levels. By taking the strong coupling limit of this model, in which its spin and dynamical degrees of freedom decouple, we compute the exact partition function of the su(m) Polychronakos-Frahm spin chain of D_N type. With the help of this partition function we study several statistical properties of the chain's spectrum, such as the density of energy levels and the distribution of spacings between consecutive levels.Comment: 12 pages, 2 figure

New spin Calogero-Sutherland models related to B_N-type Dunkl operators

We construct several new families of exactly and quasi-exactly solvable BC_N-type Calogero-Sutherland models with internal degrees of freedom. Our approach is based on the introduction of two new families of Dunkl operators of B_N type which, together with the original B_N-type Dunkl operators, are shown to preserve certain polynomial subspaces of finite dimension. We prove that a wide class of quadratic combinations involving these three sets of Dunkl operators always yields a spin Calogero-Sutherland model, which is (quasi-)exactly solvable by construction. We show that all the spin Calogero-Sutherland models obtainable within this framework can be expressed in a unified way in terms of a Weierstrass P function with suitable half-periods. This provides a natural spin counterpart of the well-known general formula for a scalar completely integrable potential of BC_N type due to Olshanetsky and Perelomov. As an illustration of our method, we exactly compute several energy levels and their corresponding wavefunctions of an elliptic quasi-exactly solvable potential for two and three particles of spin 1/2.Comment: 18 pages, typeset in LaTeX 2e using revtex 4.0b5 and the amslatex package Minor changes in content, one reference adde

Spin dependent extension of Calogero-Sutherland model through anyon like representations of permutation operators

We consider a $A_{N-1}$ type of spin dependent Calogero-Sutherland model, containing an arbitrary representation of the permutation operators on the combined internal space of all particles, and find that such a model can be solved as easily as its standard $su(M)$ invariant counterpart through the diagonalisation of Dunkl operators. A class of novel representations of the permutation operator $P_{ij}$, which pick up nontrivial phase factors along with interchanging the spins of $i$-th and $j$-th particles, are subsequently constructed. These `anyon like' representations interestingly lead to different variants of spin Calogero-Sutherland model with highly nonlocal interactions. We also explicitly derive some exact eigenfunctions as well as energy eigenvalues of these models and observe that the related degeneracy factors crucially depend on the choice of a few discrete parameters which characterise such anyon like representations.Comment: 25 pages, plain LaTex file, the results of sec.4 are presented in a more explicit way, to appear in Nucl. Phys.

An affective disorder in zebrafish with mutation of the glucocorticoid receptor

Upon binding of cortisol, the glucocorticoid receptor (GR) regulates the transcription of specific target genes, including those that encode the stress hormones corticotropin-releasing hormone (CRH) and adrenocorticotropic hormone. Dysregulation of the stress axis is a hallmark of major depression in human patients. However, it is still unclear how glucocorticoid signaling is linked to affective disorders. We identified an adult-viable zebrafish mutant in which the negative feedback on the stress response is disrupted, due to abolition of all transcriptional activity of GR. As a consequence, cortisol is elevated, but unable to signal through GR. When placed into an unfamiliar aquarium ('novel tank'), mutant fish become immobile ('freeze'), show reduced exploratory behavior and do not habituate to this stressor upon repeated exposure. Addition of the antidepressant fluoxetine to the holding water and social interactions restore normal behavior, followed by a delayed correction of cortisol levels. Fluoxetine does not affect the overall transcription of CRH, the mineralocorticoid receptor (MR), the serotonin transporter (Serta) or GR itself. Fluoxetine, however, suppresses the stress-induced upregulation of MR and Serta in both wild-type fish and mutants. Our studies show a conserved, protective function of glucocorticoid signaling in the regulation of emotional behavior and reveal novel molecular aspects of how chronic stress impacts vertebrate brain physiology and behavior. Importantly, the zebrafish model opens up the possibility of high-throughput drug screens in search of new classes of antidepressants

Exact dynamical structure factor of the degenerate Haldane-Shastry model

The dynamical structure factor $S(q,\omega)$ of the K-component (K = 2,3,4) spin chain with the 1/r^2 exchange is derived exactly at zero temperature for arbitrary size of the system. The result is interpreted in terms of a free quasi-particle picture which is generalization of the spinon picture in the SU(2) case; the excited states consist of K quasi-particles each of which is characterized by a set of K-1 quantum numbers. Divergent singularities of $S(q,\omega)$ at the spectral edges are derived analytically. The analytic result is checked numerically for finite systems.Comment: 4 pages, 1 figure, accepted for publication in Phys. Rev. Let

Crohn's disease activity index and Vienna classification - Is it worthwhile to calculate before surgery?

Background: Crohn's disease (CD) patients with increased disease activity may reveal an increased risk for perioperative complications. The `Crohn's disease activity index' (CDAI) and the `Vienna classification' (VC) were developed for standardized disease activity estimations. The significance of these scores to predict extent, type and early outcome of surgery in CD patients was analyzed. Methods: In 179 surgically treated CD patients, the CDAI and VC were assessed from a prospective database. Relations of the scores with CD risk factors, type, number, location and complications of surgery were analyzed. Results: VC behavior and location subtypes were associated with distinct types of surgery (i.e. `strictureplasty' in `stricturing disease', `colon surgery' in `colon involvement'), but not with surgery type and extent or outcome. Surgery extent (i.e. with 5 vs. 3 `surgical sites' 425 +/- 25 vs. 223.3 +/- 25) and complications (357.1 +/- 36.9 (with) vs. 244.4 +/- 13 (without)) were associated with elevated CDAI levels; however, nicotine abuse remained the only significant risk factor for perioperative complications after multiple logistic regression. Conclusion: The significance of VC or CDAI for predicting the extent of surgery or complications is limited. None of the tested variables except preoperative nicotine abuse influenced the likelihood for perioperative complications. Copyright (c) 2006 S. Karger AG, Base

Mammalian target of rapamycin complex 1 signaling opposes the effects of anchorage loss, leading to activation of Cdk4 and Cdc6 stabilization

AbstractWhen deprived of an anchorage to the extracellular matrix, fibroblasts arrest in the G1 phase with inactivation of Cdk4/6 and Cdk2 and destruction of Cdc6, the assembler of prereplicative complexes essential for S phase onset. How cellular anchorages control these kinases and Cdc6 stability is poorly understood. Here, we report that in rat embryonic fibroblasts, activation of mammalian target of rapamycin complex 1 by a Tsc2 mutation or overexpression of a constitutively active mutant Rheb overrides the absence of the anchorage and stabilizes Cdc6 at least partly via activating Cdk4/6 that induces Emi1, an APC/CCdh1 ubiquitin ligase inhibitor.Structured summaryMINT-7890626: cdc27 (uniprotkb:Q4V8A2) physically interacts (MI:0915) with Cyclin-A (uniprotkb:Q6AY13) by anti bait coimmunoprecipitation (MI:0006

Rodrigues Formula for the Nonsymmetric Multivariable Hermite Polynomial

Applying a method developed by Takamura and Takano for the nonsymmetric Jack polynomial, we present the Rodrigues formula for the nonsymmetric multivariable Hermite polynomial.Comment: 5 pages, LaTe

Inozemtsev's hyperbolic spin model and its related spin chain

In this paper we study Inozemtsev's su(m) quantum spin model with hyperbolic interactions and the associated spin chain of Haldane-Shastry type introduced by Frahm and Inozemtsev. We compute the spectrum of Inozemtsev's model, and use this result and the freezing trick to derive a simple analytic expression for the partition function of the Frahm-Inozemtsev chain. We show that the energy levels of the latter chain can be written in terms of the usual motifs for the Haldane-Shastry chain, although with a different dispersion relation. The formula for the partition function is used to analyze the behavior of the level density and the distribution of spacings between consecutive unfolded levels. We discuss the relevance of our results in connection with two well-known conjectures in quantum chaos.Comment: 22 pages, RevTeX, 7 figure