SQCD: A Geometric Apercu

We take new algebraic and geometric perspectives on the old subject of SQCD. We count chiral gauge invariant operators using generating functions, or Hilbert series, derived from the plethystic programme and the Molien-Weyl formula. Using the character expansion technique, we also see how the global symmetries are encoded in the generating functions. Equipped with these methods and techniques of algorithmic algebraic geometry, we obtain the character expansions for theories with arbitrary numbers of colours and flavours. Moreover, computational algebraic geometry allows us to systematically study the classical vacuum moduli space of SQCD and investigate such structures as its irreducible components, degree and syzygies. We find the vacuum manifolds of SQCD to be affine Calabi-Yau cones over weighted projective varieties.Comment: 49 pages, 1 figur

M2-Branes and Fano 3-folds

A class of supersymmetric gauge theories arising from M2-branes probing Calabi-Yau 4-folds which are cones over smooth toric Fano 3-folds is investigated. For each model, the toric data of the mesonic moduli space is derived using the forward algorithm. The generators of the mesonic moduli space are determined using Hilbert series. The spectrum of scaling dimensions for chiral operators is computed.Comment: 128 pages, 39 figures, 42 table

Brane Tilings and Specular Duality

We study a new duality which pairs 4d N=1 supersymmetric quiver gauge theories. They are represented by brane tilings and are worldvolume theories of D3 branes at Calabi-Yau 3-fold singularities. The new duality identifies theories which have the same combined mesonic and baryonic moduli space, otherwise called the master space. We obtain the associated Hilbert series which encodes both the generators and defining relations of the moduli space. We illustrate our findings with a set of brane tilings that have reflexive toric diagrams.Comment: 42 pages, 16 figures, 5 table

New results for the SQCD Hilbert series

We derive new explicit results for the Hilbert series of N=1 supersymmetric QCD with U(N_c) and SU(N_c) color symmetry. We use two methods which have previously been applied to similar computational problems in the analysis of decay of unstable D-branes: expansions using Schur polynomials, and the log-gas approach related to random matrix theory.Comment: 33 pages, 2 figures; v2: references and comments on the 3rd order phase transition added; v3: refs. correcte

Counting Chiral Operators in Quiver Gauge Theories

We discuss in detail the problem of counting BPS gauge invariant operators in the chiral ring of quiver gauge theories living on D-branes probing generic toric CY singularities. The computation of generating functions that include counting of baryonic operators is based on a relation between the baryonic charges in field theory and the Kaehler moduli of the CY singularities. A study of the interplay between gauge theory and geometry shows that given geometrical sectors appear more than once in the field theory, leading to a notion of "multiplicities". We explain in detail how to decompose the generating function for one D-brane into different sectors and how to compute their relevant multiplicities by introducing geometric and anomalous baryonic charges. The Plethystic Exponential remains a major tool for passing from one D-brane to arbitrary number of D-branes. Explicit formulae are given for few examples, including C^3/Z_3, F_0, and dP_1.Comment: 75 pages, 22 figure

Neu3 Activity Enhances Egfr Activation Without Affecting Egfr Expression

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A-D-E Quivers and Baryonic Operators

We study baryonic operators of the gauge theory on multiple D3-branes at the tip of the conifold orbifolded by a discrete subgroup Gamma of SU(2). The string theory analysis predicts that the number and the order of the fixed points of Gamma acting on S^2 are directly reflected in the spectrum of baryonic operators on the corresponding quiver gauge theory constructed from two Dynkin diagrams of the corresponding type. We confirm the prediction by developing techniques to enumerate baryonic operators of the quiver gauge theory which includes the gauge groups with different ranks. We also find that the Seiberg dualities act on the baryonic operators in a non-Abelian fashion.Comment: 46 pages, 17 figures; v2: minor corrections, note added in section 1, references adde

Functional Characterization of a CRH Missense Mutation Identified in an ADNFLE Family

Nocturnal frontal lobe epilepsy has been historically considered a channelopathy caused by mutations in subunits of the neuronal nicotinic acetylcholine receptor or in a recently reported potassium channel. However, these mutations account for only a minority of patients, and the existence of at least a new locus for the disease has been demonstrated. In 2005, we detected two nucleotide variations in the promoter of the CRH gene coding for the corticotropin releasing hormone in 7 patients. These variations cosegregated with the disease and were demonstrated to alter the cellular levels of this hormone. Here, we report the identification in an Italian affected family of a novel missense mutation (hpreproCRH p.Pro30Arg) located in the region of the CRH coding for the protein pro-sequence. The mutation was detected in heterozygosity in the two affected individuals. In vitro assays demonstrated that this mutation results in reduced levels of protein secretion in the short time thus suggesting that mutated people could present an altered capability to respond immediately to stress agents

Counting Exceptional Instantons

We show how to obtain the instanton partition function of N=2 SYM with exceptional gauge group EFG using blow-up recursion relations derived by Nakajima and Yoshioka. We compute the two instanton contribution and match it with the recent proposal for the superconformal index of rank 2 SCFTs with E6, E7 global symmetry.Comment: 16 pages, references adde

Nutritional status and body composition by bioelectrical impedance vector analysis : a cross sectional study in mild cognitive impairment and Alzheimer's disease

Aims Analysis of nutritional status and body composition in Alzheimer's disease (AD) and Mild Cognitive Impairment (MCI). Methods A cross-sectional study was performed in a University-Hospital setting, recruiting 59 patients with AD, 34 subjects with MCI and 58 elderly healthy controls (HC). Nutritional status was assessed by anthropometric parameters (body mass index; calf, upper arm and waist circumferences), Mini Nutritional Assessment (MNA) and body composition by bioelectrical impedance vector analysis (BIVA). Variables were analyzed by analysis of variance and subjects were grouped by cognitive status and gender. Results Sociodemographic variables did not differ among the three groups (AD, MCI and HC), except for females' age, which was therefore used as covariate in a general linear multivariate model. MNA score was significantly lower in AD patients than in HC; MCI subjects achieved intermediate scores. AD patients (both sexes) had significantly (p<0.05) higher height-normalized impedance values and lower phase angles (body cell mass) compared with HC; a higher ratio of impedance to height was found in men with MCI with respect to HC. With BIVA method, MCI subjects showed a significant displacement on the RXc graph on the right side indicating lower soft tissues (Hotelling's T2 test: men = 10.6; women = 7.9;p < 0,05) just like AD patients (Hotelling's T2 test: men = 18.2; women = 16.9; p<0,001). Conclusion Bioelectrical parameters significantly differ from MCI and AD to HC; MCI showed an intermediate pattern between AD and HC. Longitudinal studies are required to investigate if BIVA could reflect early AD-changes in body composition in subjects with MCI