Quantum superalgebras at roots of unity and non-abelian symmetries of integrable models

We consider integrable vertex models whose Boltzmann weights (R-matrices) are trigonometric solutions to the graded Yang-Baxter equation. As is well known the latter can be generically constructed from quantum affine superalgebras $U_{q}(\hat g)$. These algebras do not form a symmetry algebra of the model for generic values of the deformation parameter $q$ when periodic boundary conditions are imposed. If $q$ is evaluated at a root of unity we demonstrate that in certain commensurate sectors one can construct non-abelian subalgebras which are translation invariant and supercommute with the transfer matrix and therefore with all charges of the model. In the line of argument we introduce the restricted quantum superalgebra $U^{res}_q(\hat g)$ and investigate its root of unity limit. We prove several new formulas involving supercommutators of arbitrary powers of the Chevalley-Serre generators and derive higher order quantum Serre relations as well as an analogue of Lustzig's quantum Frobenius theorem for superalgebras.Comment: 31 pages, tcilatex (minor typos corrected

Transfer matrix eigenvalues of the anisotropic multiparametric U model

A multiparametric extension of the anisotropic U model is discussed which maintains integrability. The R-matrix solving the Yang-Baxter equation is obtained through a twisting construction applied to the underlying Uq(sl(2|1)) superalgebraic structure which introduces the additional free parameters that arise in the model. Three forms of Bethe ansatz solution for the transfer matrix eigenvalues are given which we show to be equivalent.Comment: 26 pages, no figures, LaTe

Expression of TopBP1 in hereditary breast cancer

TopBP1 protein displays structural as well as functional similarities to BRCA1 and is involved in DNA replication, DNA damage checkpoint response and transcriptional regulation. Aberrant expression of TopBP1 may lead to genomic instability and can have pathological consequences. In this study we aimed to investigate expression of TopBP1 gene at mRNA and protein level in hereditary breast cancer. Real-time quantitative PCR was performed in 127 breast cancer samples. Expression of TopBP1 mRNA in lobular carcinoma was significantly lower compared with ductal carcinoma (p < 0.05). The level of TopBP1 mRNA appeared to be lower in poorly differentiated (III grade) hereditary breast cancer in comparison with moderately (II grade) and well-differentiated cancer (I grade) (p < 0.05 and p < 0.001 respectively). We analyzed TopBP1 protein expression using immunohistochemistry and Western blot techniques. Expression of TopBP1 protein was found to be significantly increased in poorly differentiated breast cancer (III grade) (p < 0.05). The percentage of samples with cytoplasmic apart from nuclear staining increased with increasing histological grade. There was no significant association between level and intracellular localization of TopBP1 protein in hereditary breast cancer and other clinicopathological parameters such as estrogen and progesterone receptors status, appearance of metastasis in the axillary lymph nodes and type of cancer. Our data suggest that decreased level of TopBP1 mRNA and increased level of TopBP1 protein might be associated with progression of hereditary breast cancer

Intermediate phase, network demixing, boson and floppy modes, and compositional trends in glass transition temperatures of binary AsxS1-x system

The structure of binary As_xS_{1-x} glasses is elucidated using modulated-DSC, Raman scattering, IR reflectance and molar volume experiments over a wide range (8%<x<41%) of compositions. We observe a reversibility window in the calorimetric experiments, which permits fixing the three elastic phases; flexible at x<22.5%, intermediate phase (IP) in the 22.5%<x<29.5% range, and stressed-rigid at x>29.5%. Raman scattering supported by first principles cluster calculations reveal existence of both pyramidal (PYR, As(S1/2)3) and quasi-tetrahedral(QT, S=As(S1/2)3) local structures. The QT unit concentrations show a global maximum in the IP, while the concentration of PYR units becomes comparable to those of QT units in the phase, suggesting that both these local structures contribute to the width of the IP. The IP centroid in the sulfides is significantly shifted to lower As content x than in corresponding selenides, a feature identified with excess chalcogen partially segregating from the backbone in the sulfides, but forming part of the backbone in selenides. These ideas are corroborated by the proportionately larger free volumes of sulfides than selenides, and the absence of chemical bond strength scaling of Tgs between As-sulfides and As-selenides. Low-frequency Raman modes increase in scattering strength linearly as As content x of glasses decreases from x = 20% to 8%, with a slope that is close to the floppy mode fraction in flexible glasses predicted by rigidity theory. These results show that floppy modes contribute to the excess vibrations observed at low frequency. In the intermediate and stressed rigid elastic phases low-frequency Raman modes persist and are identified as boson modes. Some consequences of the present findings on the optoelectronic properties of these glasses is commented upon.Comment: Accepted for PR

Integrable multiparametric quantum spin chains

Using Reshetikhin's construction for multiparametric quantum algebras we obtain the associated multiparametric quantum spin chains. We show that under certain restrictions these models can be mapped to quantum spin chains with twisted boundary conditions. We illustrate how this general formalism applies to construct multiparametric versions of the supersymmetric t-J and U models.Comment: 17 pages, RevTe

Eigenvalus of Casimir Invariants for Type-I Quantum Superalgebras

We present the eigenvalues of the Casimir invariants for the type I quantum superalgebras on any irreducible highest weight module.Comment: 13 pages, AmsTex file; to appear in Lett. Math. Phy

Structure of the string R-matrix

By requiring invariance directly under the Yangian symmetry, we rederive Beisert's quantum R-matrix, in a form that carries explicit dependence on the representation labels, the braiding factors, and the spectral parameters u_i. In this way, we demonstrate that there exist a rewriting of its entries, such that the dependence on the spectral parameters is purely of difference form. Namely, the latter enter only in the combination u_1-u_2, as indicated by the shift automorphism of the Yangian. When recasted in this fashion, the entries exhibit a cleaner structure, which allows to spot new interesting relations among them. This permits to package them into a practical tensorial expression, where the non-diagonal entries are taken care by explicit combinations of symmetry algebra generators.Comment: 9 pages, LaTeX; typos correcte

An essential function for the ATR-Activation-Domain (AAD) of TopBP1 in mouse development and cellular senescence

ATR activation is dependent on temporal and spatial interactions with partner proteins. In the budding yeast model, three proteins – Dpb11TopBP1, Ddc1Rad9 and Dna2 - all interact with and activate Mec1ATR. Each contains an ATR activation domain (ADD) that interacts directly with the Mec1ATR:Ddc2ATRIP complex. Any of the Dpb11TopBP1, Ddc1Rad9 or Dna2 ADDs is sufficient to activate Mec1ATR in vitro. All three can also independently activate Mec1ATR in vivo: the checkpoint is lost only when all three AADs are absent. In metazoans, only TopBP1 has been identified as a direct ATR activator. Depletion-replacement approaches suggest the TopBP1-AAD is both sufficient and necessary for ATR activation. The physiological function of the TopBP1 AAD is, however, unknown. We created a knock-in point mutation (W1147R) that ablates mouse TopBP1-AAD function. TopBP1-W1147R is early embryonic lethal. To analyse TopBP1-W1147R cellular function in vivo, we silenced the wild type TopBP1 allele in heterozygous MEFs. AAD inactivation impaired cell proliferation, promoted premature senescence and compromised Chk1 signalling following UV irradiation. We also show enforced TopBP1 dimerization promotes ATR-dependent Chk1 phosphorylation. Our data suggest that, unlike the yeast models, the TopBP1-AAD is the major activator of ATR, sustaining cell proliferation and embryonic development

Genome-Wide Studies of Histone Demethylation Catalysed by the Fission Yeast Homologues of Mammalian LSD1

In order to gain a more global view of the activity of histone demethylases, we report here genome-wide studies of the fission yeast SWIRM and polyamine oxidase (PAO) domain homologues of mammalian LSD1. Consistent with previous work we find that the two S. pombe proteins, which we name Swm1 and Swm2 (after SWIRM1 and SWIRM2), associate together in a complex. However, we find that this complex specifically demethylates lysine 9 in histone H3 (H3K9) and both up- and down-regulates expression of different groups of genes. Using chromatin-immunoprecipitation, to isolate fragments of chromatin containing either H3K4me2 or H3K9me2, and DNA microarray analysis (ChIP-chip), we have studied genome-wide changes in patterns of histone methylation, and their correlation with gene expression, upon deletion of the swm1+ gene. Using hyper-geometric probability comparisons we uncover genetic links between lysine-specific demethylases, the histone deacetylase Clr6, and the chromatin remodeller Hrp1. The data presented here demonstrate that in fission yeast the SWIRM/PAO domain proteins Swm1 and Swm2 are associated in complexes that can remove methyl groups from lysine 9 methylated histone H3. In vitro, we show that bacterially expressed Swm1 also possesses lysine 9 demethylase activity. In vivo, loss of Swm1 increases the global levels of both H3K9me2 and H3K4me2. A significant accumulation of H3K4me2 is observed at genes that are up-regulated in a swm1 deletion strain. In addition, H3K9me2 accumulates at some genes known to be direct Swm1/2 targets that are down-regulated in the swm1¿ strain. The in vivo data indicate that Swm1 acts in concert with the HDAC Clr6 and the chromatin remodeller Hrp1 to repress gene expression. In addition, our in vitro analyses suggest that the H3K9 demethylase activity requires an unidentified post-translational modification to allow it to act. Thus, our results highlight complex interactions between histone demethylase, deacetylase and chromatin remodelling activities in the regulation of gene expression