The matrix model version of AGT conjecture and CIV-DV prepotential

Recently exact formulas were provided for partition function of conformal (multi-Penner) beta-ensemble in the Dijkgraaf-Vafa phase, which, if interpreted as Dotsenko-Fateev correlator of screenings and analytically continued in the number of screening insertions, represents generic Virasoro conformal blocks. Actually these formulas describe the lowest terms of the q_a-expansion, where q_a parameterize the shape of the Penner potential, and are exact in the filling numbers N_a. At the same time, the older theory of CIV-DV prepotential, straightforwardly extended to arbitrary beta and to non-polynomial potentials, provides an alternative expansion: in powers of N_a and exact in q_a. We check that the two expansions coincide in the overlapping region, i.e. for the lowest terms of expansions in both q_a and N_a. This coincidence is somewhat non-trivial, since the two methods use different integration contours: integrals in one case are of the B-function (Euler-Selberg) type, while in the other case they are Gaussian integrals.Comment: 27 pages, 1 figur

Matrix Model Conjecture for Exact BS Periods and Nekrasov Functions

We give a concise summary of the impressive recent development unifying a number of different fundamental subjects. The quiver Nekrasov functions (generalized hypergeometric series) form a full basis for all conformal blocks of the Virasoro algebra and are sufficient to provide the same for some (special) conformal blocks of W-algebras. They can be described in terms of Seiberg-Witten theory, with the SW differential given by the 1-point resolvent in the DV phase of the quiver (discrete or conformal) matrix model (\beta-ensemble), dS = ydz + O(\epsilon^2) = \sum_p \epsilon^{2p} \rho_\beta^{(p|1)}(z), where \epsilon and \beta are related to the LNS parameters \epsilon_1 and \epsilon_2. This provides explicit formulas for conformal blocks in terms of analytically continued contour integrals and resolves the old puzzle of the free-field description of generic conformal blocks through the Dotsenko-Fateev integrals. Most important, this completes the GKMMM description of SW theory in terms of integrability theory with the help of exact BS integrals, and provides an extended manifestation of the basic principle which states that the effective actions are the tau-functions of integrable hierarchies.Comment: 14 page

Boundary operators in minimal Liouville gravity and matrix models

We interpret the matrix boundaries of the one matrix model (1MM) recently constructed by two of the authors as an outcome of a relation among FZZT branes. In the double scaling limit, the 1MM is described by the (2,2p+1) minimal Liouville gravity. These matrix operators are shown to create a boundary with matter boundary conditions given by the Cardy states. We also demonstrate a recursion relation among the matrix disc correlator with two different boundaries. This construction is then extended to the two matrix model and the disc correlator with two boundaries is compared with the Liouville boundary two point functions. In addition, the realization within the matrix model of several symmetries among FZZT branes is discussed.Comment: 26 page

Perturbative quantum gravity with the Immirzi parameter

We study perturbative quantum gravity in the first-order tetrad formalism. The lowest order action corresponds to Einstein-Cartan plus a parity-odd term, and is known in the literature as the Holst action. The coupling constant of the parity-odd term can be identified with the Immirzi parameter of loop quantum gravity. We compute the quantum effective action in the one-loop expansion. As in the metric second-order formulation, we find that in the case of pure gravity the theory is on-shell finite, and the running of Newton's constant and the Immirzi parameter is inessential. In the presence of fermions, the situation changes in two fundamental aspects. First, non-renormalizable logarithmic divergences appear, as usual. Second, the Immirzi parameter becomes a priori observable, and we find that it is renormalized by a four-fermion interaction generated by radiative corrections. We compute its beta function and discuss possible implications. The sign of the beta function depends on whether the Immirzi parameter is larger or smaller than one in absolute value, and the values plus or minus one are UV fixed-points (we work in Euclidean signature). Finally, we find that the Holst action is stable with respect to radiative corrections in the case of minimal coupling, up to higher order non-renormalizable interactions.Comment: v2 minor amendment

HRDetect is a predictor of BRCA1 and BRCA2 deficiency based on mutational signatures.

Approximately 1-5% of breast cancers are attributed to inherited mutations in BRCA1 or BRCA2 and are selectively sensitive to poly(ADP-ribose) polymerase (PARP) inhibitors. In other cancer types, germline and/or somatic mutations in BRCA1 and/or BRCA2 (BRCA1/BRCA2) also confer selective sensitivity to PARP inhibitors. Thus, assays to detect BRCA1/BRCA2-deficient tumors have been sought. Recently, somatic substitution, insertion/deletion and rearrangement patterns, or 'mutational signatures', were associated with BRCA1/BRCA2 dysfunction. Herein we used a lasso logistic regression model to identify six distinguishing mutational signatures predictive of BRCA1/BRCA2 deficiency. A weighted model called HRDetect was developed to accurately detect BRCA1/BRCA2-deficient samples. HRDetect identifies BRCA1/BRCA2-deficient tumors with 98.7% sensitivity (area under the curve (AUC) = 0.98). Application of this model in a cohort of 560 individuals with breast cancer, of whom 22 were known to carry a germline BRCA1 or BRCA2 mutation, allowed us to identify an additional 22 tumors with somatic loss of BRCA1 or BRCA2 and 47 tumors with functional BRCA1/BRCA2 deficiency where no mutation was detected. We validated HRDetect on independent cohorts of breast, ovarian and pancreatic cancers and demonstrated its efficacy in alternative sequencing strategies. Integrating all of the classes of mutational signatures thus reveals a larger proportion of individuals with breast cancer harboring BRCA1/BRCA2 deficiency (up to 22%) than hitherto appreciated (∼1-5%) who could have selective therapeutic sensitivity to PARP inhibition

The genomic evolution of human prostate cancer.

Prostate cancers are highly prevalent in the developed world, with inheritable risk contributing appreciably to tumour development. Genomic heterogeneity within individual prostate glands and between patients derives predominantly from structural variants and copy-number aberrations. Subtypes of prostate cancers are being delineated through the increasing use of next-generation sequencing, but these subtypes are yet to be used to guide the prognosis or therapeutic strategy. Herein, we review our current knowledge of the mutational landscape of human prostate cancer, describing what is known of the common mutations underpinning its development. We evaluate recurrent prostate-specific mutations prior to discussing the mutational events that are shared both in prostate cancer and across multiple cancer types. From these data, we construct a putative overview of the genomic evolution of human prostate cancer

Observation of a J^PC = 1-+ exotic resonance in diffractive dissociation of 190 GeV/c pi- into pi- pi- pi+

The COMPASS experiment at the CERN SPS has studied the diffractive dissociation of negative pions into the pi- pi- pi+ final state using a 190 GeV/c pion beam hitting a lead target. A partial wave analysis has been performed on a sample of 420000 events taken at values of the squared 4-momentum transfer t' between 0.1 and 1 GeV^2/c^2. The well-known resonances a1(1260), a2(1320), and pi2(1670) are clearly observed. In addition, the data show a significant natural parity exchange production of a resonance with spin-exotic quantum numbers J^PC = 1-+ at 1.66 GeV/c^2 decaying to rho pi. The resonant nature of this wave is evident from the mass-dependent phase differences to the J^PC = 2-+ and 1++ waves. From a mass-dependent fit a resonance mass of 1660 +- 10+0-64 MeV/c^2 and a width of 269+-21+42-64 MeV/c^2 is deduced.Comment: 7 page, 3 figures; version 2 gives some more details, data unchanged; version 3 updated authors, text shortened, data unchange

The Polarised Valence Quark Distribution from semi-inclusive DIS

The semi-inclusive difference asymmetry A^{h^{+}-h^{-}} for hadrons of opposite charge has been measured by the COMPASS experiment at CERN. The data were collected in the years 2002-2004 using a 160 GeV polarised muon beam scattered off a large polarised ^6LiD target and cover the range 0.006 < x < 0.7 and 1 < Q^2 < 100 (GeV/c)^2. In leading order QCD (LO) the asymmetry A_d^{h^{+}-h^{-}} measures the valence quark polarisation and provides an evaluation of the first moment of Delta u_v + Delta d_v which is found to be equal to 0.40 +- 0.07 (stat.) +- 0.05 (syst.) over the measured range of x at Q^2 = 10 (GeV/c)^2. When combined with the first moment of g_1^d previously measured on the same data, this result favours a non-symmetric polarisation of light quarks Delta u-bar = - Delta d-bar at a confidence level of two standard deviations, in contrast to the often assumed symmetric scenario Delta u-bar = Delta d-bar = Delta s-bar = Delta s.Comment: 7 pages, 3 figures, COMPASS, revised: details added, author list update

The Hubbard model within the equations of motion approach

The Hubbard model has a special role in Condensed Matter Theory as it is considered as the simplest Hamiltonian model one can write in order to describe anomalous physical properties of some class of real materials. Unfortunately, this model is not exactly solved except for some limits and therefore one should resort to analytical methods, like the Equations of Motion Approach, or to numerical techniques in order to attain a description of its relevant features in the whole range of physical parameters (interaction, filling and temperature). In this manuscript, the Composite Operator Method, which exploits the above mentioned analytical technique, is presented and systematically applied in order to get information about the behavior of all relevant properties of the model (local, thermodynamic, single- and two- particle ones) in comparison with many other analytical techniques, the above cited known limits and numerical simulations. Within this approach, the Hubbard model is shown to be also capable to describe some anomalous behaviors of the cuprate superconductors.Comment: 232 pages, more than 300 figures, more than 500 reference