Semi-invariants of symmetric quivers of tame type

A symmetric quiver $(Q,\sigma)$ is a finite quiver without oriented cycles $Q=(Q_0,Q_1)$ equipped with a contravariant involution $\sigma$ on $Q_0\sqcup Q_1$. The involution allows us to define a nondegenerate bilinear form on a representation $V$ of $Q$. We shall say that $V$ is orthogonal if is symmetric and symplectic if $$ is skew-symmetric. Moreover, we define an action of products of classical groups on the space of orthogonal representations and on the space of symplectic representations. So we prove that if $(Q,\sigma)$ is a symmetric quiver of tame type then the rings of semi-invariants for this action are spanned by the semi-invariants of determinantal type $c^V$ and, when matrix defining $c^V$ is skew-symmetric, by the Pfaffians $pf^V$. To prove it, moreover, we describe the symplectic and orthogonal generic decomposition of a symmetric dimension vector

Unusual Formation of Point-Defect Complexes in the Ultrawide-Band-Gap Semiconductor β-Ga2 O3

Understanding the unique properties of ultra-wide band gap semiconductors requires detailed information about the exact nature of point defects and their role in determining the properties. Here, we report the first direct microscopic observation of an unusual formation of point defect complexes within the atomic-scale structure of β-Ga2O3 using high resolution scanning transmission electron microscopy (STEM). Each complex involves one cation interstitial atom paired with two cation vacancies. These divacancy-interstitial complexes correlate directly with structures obtained by density functional theory, which predicts them to be compensating acceptors in β-Ga2O3. This prediction is confirmed by a comparison between STEM data and deep level optical spectroscopy results, which reveals that these complexes correspond to a deep trap within the band gap, and that the development of the complexes is facilitated by Sn doping through increased vacancy concentration. These findings provide new insight on this emerging material's unique response to the incorporation of impurities that can critically influence their properties

Semi-invariants of symmetric quivers of finite type

Let $(Q,\sigma)$ be a symmetric quiver, where $Q=(Q_0,Q_1)$ is a finite quiver without oriented cycles and $\sigma$ is a contravariant involution on $Q_0\sqcup Q_1$. The involution allows us to define a nondegenerate bilinear form on a representation $V$ of $Q$. We shall call the representation orthogonal if is symmetric and symplectic if $$ is skew-symmetric. Moreover we can define an action of products of classical groups on the space of orthogonal representations and on the space of symplectic representations. For symmetric quivers of finite type, we prove that the rings of semi-invariants for this action are spanned by the semi-invariants of determinantal type $c^V$ and, in the case when matrix defining $c^V$ is skew-symmetric, by the Pfaffians $pf^V$

4d N=2 Gauge Theories and Quivers: the Non-Simply Laced Case

We construct the BPS quivers with superpotential for the 4d N=2 gauge theories with non-simply laced Lie groups (B_n, C_n, F_4 and G_2). The construction is inspired by the BIKMSV geometric engineering of these gauge groups as non-split singular elliptic fibrations. From the categorical viewpoint of arXiv:1203.6743, the fibration of the light category L(g) over the (degenerate) Gaiotto curve has a monodromy given by the action of the outer automorphism of the corresponding unfolded Lie algebra. In view of the Katz--Vafa `matter from geometry' mechanism, the monodromic idea may be extended to the construction of (Q, W) for SYM coupled to higher matter representations. This is done through a construction we call specialization.Comment: 42 pages, 2 figure

Counting the number of τ-exceptional sequences over Nakayama algebras

The notion of a τ-exceptional sequence was introduced by Buan and Marsh in (2018) as a generalisation of an exceptional sequence for finite dimensional algebras. We calculate the number of complete τ-exceptional sequences over certain classes of Nakayama algebras. In some cases, we obtain closed formulas which also count other well known combinatorial objects, and exceptional sequences of path algebras of Dynkin quivers

Src tyrosine kinase augments taxotere-induced apoptosis through enhanced expression and phosphorylation of Bcl-2

Activation of Src, which has an intrinsic protein tyrosine kinase activity, has been demonstrated in many human tumours, such as colorectal and breast cancers, and is closely associated with the pathogenesis and metastatic potential of these cancers. In this study, we have examined the effect of activated Src on the sensitivity to taxotere, an anticancer drug targeting microtubules, using v-src-transfected HAG-1 human gall bladder epithelial cells. As compared with parental HAG-1 cell line, v-src-transfected HAG/src3-1 cells became 5.9 and 7.0-fold sensitive to taxotere for 2 and 24-h exposure, respectively. By contrast, HAG-1 cells transfected with activated Ras, which acts downstream of Src, acquired approximately 2.5∼4.8-fold taxotere resistance. The taxotere sensitivity in HAG/src3-1 cells was reversed, if not completely, by herbimycin A, a specific inhibitor of Src family protein tyrosine kinase, indicating that Src protein tyrosine kinase augments sensitivity to taxotere. Treatment of HAG/src3-1 cells with taxotere resulted in phosphorylation of Bcl-2 and subsequent induction of apoptotic cell death, whereas neither Bcl-2 phosphorylation nor apoptosis occurred in parental or c-H-ras-transfected HAG-1 cells. Interestingly, the Bcl-2 protein is overexpressed in v-src-transfected cell line, compared to those in parental or Ras-transfected cell line. Treatment of HAG/src3-1 cells with herbimycin A significantly reduced the expression and phosphorylation of Bcl-2, and abrogated taxotere-induced apoptosis, suggesting a potential role for Src protein tyrosine kinase in the taxotere-induced apoptotic events. H-7, a protein kinase C inhibitor and wortmannin, a phosphatidylinositol-3 kinase (PI-3 kinase) inhibitor, neither altered taxotere sensitivity nor inhibited taxotere-induced apoptosis in these cells. These data indicate that the ability of activated Src to increase taxotere sensitivity would be mediated by apoptotic events occurring through Src to downstream signal transduction pathways toward Bcl-2 phosphorylation, but not by activated Ras, PI-3 kinase or protein kinase C

Superconformal index, BPS monodromy and chiral algebras

We show that specializations of the 4d N = 2 superconformal index labeled by an integer N is given by Tr M-N where M is the Kontsevich-Soibelman monodromy operator for BPS states on the Coulomb branch. We provide evidence that the states enumerated by these limits of the index lead to a family of 2d chiral algebras A(N). This generalizes the recent results for the N = -1 case which corresponds to the Schur limit of the superconformal index. We show that this specialization of the index leads to the same integrand as that of the elliptic genus of compactification of the superconformal theory on S-2 x T-2 where we turn on 1/2 N units of U(1)(r) flux on S-2

Enhanced Discrimination of Malignant from Benign Pancreatic Disease by Measuring the CA 19-9 Antigen on Specific Protein Carriers

The CA 19-9 assay detects a carbohydrate antigen on multiple protein carriers, some of which may be preferential carriers of the antigen in cancer. We tested the hypothesis that the measurement of the CA 19-9 antigen on individual proteins could improve performance over the standard CA 19-9 assay. We used antibody arrays to measure the levels of the CA 19-9 antigen on multiple proteins in serum or plasma samples from patients with pancreatic adenocarcinoma or pancreatitis. Sample sets from three different institutions were examined, comprising 531 individual samples. The measurement of the CA 19-9 antigen on any individual protein did not improve upon the performance of the standard CA 19-9 assay (82% sensitivity at 75% specificity for early-stage cancer), owing to diversity among patients in their CA 19-9 protein carriers. However, a subset of cancer patients with no elevation in the standard CA 19-9 assay showed elevations of the CA 19-9 antigen specifically on the proteins MUC5AC or MUC16 in all sample sets. By combining measurements of the standard CA 19-9 assay with detection of CA 19-9 on MUC5AC and MUC16, the sensitivity of cancer detection was improved relative to CA 19-9 alone in each sample set, achieving 67–80% sensitivity at 98% specificity. This finding demonstrates the value of measuring glycans on specific proteins for improving biomarker performance. Diagnostic tests with improved sensitivity for detecting pancreatic cancer could have important applications for improving the treatment and management of patients suffering from this disease