The first Hochschild cohomology group of a schurian cluster-tilted algebra

Given a cluster-tilted algebra B we study its first Hochschild cohomology group HH1(B) with coefficients in the B-B-bimodule B. We find several consequences when B is representation-finite, and also in the case where B is cluster-tilted of type Ã.Fil: Assem, Ibrahim. University of Sherbrooke; CanadáFil: Redondo, Maria Julia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; Argentin

mm-cluster categories and mm-replicated algebras

Let A be a hereditary algebra over an algebraically closed field. We prove that an exact fundamental domain for the m-cluster category of A is the m-left part of the m-replicated algebra $A^{(m)}$ of A. Moreover, we obtain a one-to-one correspondence between the tilting objects in the m-cluster category (that is, the m-clusters) and those tilting $A^{(m)}$-modules for which all non projective-injective direct summands lie in the m-left part of $A^{(m)}$.Comment: 28 pages, 2 figure

Cycle-finite module categories

We describe the structure of module categories of finite dimensional algebras over an algebraically closed field for which the cycles of nonzero nonisomorphisms between indecomposable finite dimensional modules are finite (do not belong to the infinite Jacobson radical of the module category). Moreover, geometric and homological properties of these module categories are exhibited

The Intrinsic Fundamental Group of a Linear Category

We provide an intrinsic definition of the fundamental group of a linear category over a ring as the automorphism group of the fibre functor on Galois coverings. If the universal covering exists, we prove that this group is isomorphic to the Galois group of the universal covering. The grading deduced from a Galois covering enables us to describe the canonical monomorphism from its automorphism group to the first Hochschild-Mitchell cohomology vector space.Comment: Final version, to appear in Algebras and Representation Theor

High Serine-arginine Protein Kinase 1 Expression with PTEN Loss Defines Aggressive Phenotype of Prostate Cancer Associated with Lethal Outcome and Decreased Overall Survival

Background: Serine-arginine protein kinase 1 (SRPK1) has been implicated in prostate cancer (PCa) progression. However, its prognostic value and association with ERG and PTEN expression, two of the most common genetic alterations, have not been explored fully. Objective: We assessed the prognostic value of SRPK1 in association with ERG and PTEN in a cohort of patients managed nonsurgically by androgen deprivation therapy (ADT) for advanced disease. Design, setting, and participants: The study cohort consisted of men diagnosed with PCa by transurethral resection of the prostate (TURP; n = 480). The patients were divided into three main groups: incidental (patients with Gleason score [GS] ≤7 with no prior ADT), advanced (patients with GS ≥8 with no prior ADT), and castrate-resistant PCa (patients with prior ADT). Outcome measurements and statistical analysis: A total of 480 TURP samples were assessed by immunohistochemistry for SRPK1, ERG, and PTEN, and results were correlated with Gleason grade group (GG), overall survival (OS), and PCa-specific mortality (PCSM). Results and limitations: High SRPK1 expression was noted in 105/455 (23%) available patient cores. Expression of SRPK1 was associated with Gleason grade grouping (p \u3c 0.0001) with high expression detected in 22/74 (33%) with GG 5. High SRPK1 was not associated with ERG positivity (p = 0.18) but was significantly associated with PTEN intensity (p = 0.001). High SRPK1 was associated with OS (hazard ratio [HR] 1.99; confidence interval [CI]: 1.57–2.54, p \u3c 0.0001) and PCSM (HR 1.64; CI: 1.19–2.26, p \u3c 0.002). Adjusting for Gleason score, patients with high SRPK1 and negative PTEN had the worst clinical outcome for both OS and PCSM compared with other patients (p \u3c 0.0001, HR: 3.02; CI: 1.87–4.88 and HR: 6.40, CI: 3.19–12.85, respectively). Conclusions: High SRPK1 is associated with worse OS and PCSM. Moreover, patients with high SRPK1 expression and loss of PTEN had the worst clinical outcome for OS and cancer-specific mortality. Combined status of SRPK1 and PTEN may provide added value in stratifying patients into various prognostic groups. Patient summary: The expression of serine-arginine protein kinase 1 (SRPK1) combined with PTEN has a significant prognostic role in prostate cancer patients. Patients with high SRPK1 expression and negative PTEN had the worst clinical outcome for overall survival and cancer-specific mortality

MicroRNAs as Potential Biomarkers for Childhood Epilepsy

BACKGROUND: Epilepsy is the most frequent chronic neurologic condition in childhood. Its clinical diagnosis is based on electroencephalograms (EEG) and neuroimaging techniques. MicroRNAs (miRNAs) modulate gene expression of several genes and are aberrantly expressed in several diseases. AIM: Evaluation of using circulating miR-106b and miR-146a as diagnostic and prognostic biomarkers in children patients with epilepsy. METHODS: Thirty epileptic children and twenty controls were enrolled in our study. They were assessed for the expression pattern of miR-106b and miR-146a in plasma using quantitative real-time PCR and determination of plasma Immunoglobulin levels. RESULTS: MiR-146a and miR-106b expression patterns were significantly up-regulated in children patients than that in normal controls. Plasma Immunoglobulins were differentially expressed in epileptic patients in comparison with healthy controls. No correlations were found between expression levels of miRNAs (miR-146a and miR-106b) and clinical data or immunoglobulin levels in children patients with epilepsy. CONCLUSION: Our findings suggest that up-regulated plasma miR-106b and miR-146a could be used as biomarkers for epilepsy evaluation

Tilted algebras and short chains of modules

We provide an affirmative answer for the question raised almost twenty years ago concerning the characterization of tilted artin algebras by the existence of a sincere finitely generated module which is not the middle of a short chain

On Arnold's 14 `exceptional' N=2 superconformal gauge theories

We study the four-dimensional superconformal N=2 gauge theories engineered by the Type IIB superstring on Arnold's 14 exceptional unimodal singularities (a.k.a. Arnold's strange duality list), thus extending the methods of 1006.3435 to singularities which are not the direct sum of minimal ones. In particular, we compute their BPS spectra in several `strongly coupled' chambers. From the TBA side, we construct ten new periodic Y-systems, providing additional evidence for the existence of a periodic Y-system for each isolated quasi-homogeneous singularity with $\hat c<2$ (more generally, for each N=2 superconformal theory with a finite BPS chamber whose chiral primaries have dimensions of the form N/l).Comment: 73 pages, 7 figure