Bekenstein entropy bound for weakly-coupled field theories on a 3-sphere

We calculate the high temperature partition functions for SU(Nc) or U(Nc) gauge theories in the deconfined phase on S^1 x S^3, with scalars, vectors, and/or fermions in an arbitrary representation, at zero 't Hooft coupling and large Nc, using analytical methods. We compare these with numerical results which are also valid in the low temperature limit and show that the Bekenstein entropy bound resulting from the partition functions for theories with any amount of massless scalar, fermionic, and/or vector matter is always satisfied when the zero-point contribution is included, while the theory is sufficiently far from a phase transition. We further consider the effect of adding massive scalar or fermionic matter and show that the Bekenstein bound is satisfied when the Casimir energy is regularized under the constraint that it vanishes in the large mass limit. These calculations can be generalized straightforwardly for the case of a different number of spatial dimensions.Comment: 32 pages, 12 figures. v2: Clarifications added. JHEP versio

Direct Integration and Non-Perturbative Effects in Matrix Models

We show how direct integration can be used to solve the closed amplitudes of multi-cut matrix models with polynomial potentials. In the case of the cubic matrix model, we give explicit expressions for the ring of non-holomorphic modular objects that are needed to express all closed matrix model amplitudes. This allows us to integrate the holomorphic anomaly equation up to holomorphic modular terms that we fix by the gap condition up to genus four. There is an one-dimensional submanifold of the moduli space in which the spectral curve becomes the Seiberg--Witten curve and the ring reduces to the non-holomorphic modular ring of the group $\Gamma(2)$. On that submanifold, the gap conditions completely fix the holomorphic ambiguity and the model can be solved explicitly to very high genus. We use these results to make precision tests of the connection between the large order behavior of the 1/N expansion and non-perturbative effects due to instantons. Finally, we argue that a full understanding of the large genus asymptotics in the multi-cut case requires a new class of non-perturbative sectors in the matrix model.Comment: 51 pages, 8 figure

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

A cluster-randomized, placebo-controlled, maternal vitamin a or beta-carotene supplementation trial in bangladesh: design and methods

<p>Abstract</p> <p>Background</p> <p>We present the design, methods and population characteristics of a large community trial that assessed the efficacy of a weekly supplement containing vitamin A or beta-carotene, at recommended dietary levels, in reducing maternal mortality from early gestation through 12 weeks postpartum. We identify challenges faced and report solutions in implementing an intervention trial under low-resource, rural conditions, including the importance of population choice in promoting generalizability, maintaining rigorous data quality control to reduce inter- and intra- worker variation, and optimizing efficiencies in information and resources flow from and to the field.</p> <p>Methods</p> <p>This trial was a double-masked, cluster-randomized, dual intervention, placebo-controlled trial in a contiguous rural area of ~435 sq km with a population of ~650,000 in Gaibandha and Rangpur Districts of Northwestern Bangladesh. Approximately 120,000 married women of reproductive age underwent 5-weekly home surveillance, of whom ~60,000 were detected as pregnant, enrolled into the trial and gave birth to ~44,000 live-born infants. Upon enrollment, at ~ 9 weeks' gestation, pregnant women received a weekly oral supplement containing vitamin A (7000 ug retinol equivalents (RE)), beta-carotene (42 mg, or ~7000 ug RE) or a placebo through 12 weeks postpartum, according to prior randomized allocation of their cluster of residence. Systems described include enlistment and 5-weekly home surveillance for pregnancy based on menstrual history and urine testing, weekly supervised supplementation, periodic risk factor interviews, maternal and infant vital outcome monitoring, birth defect surveillance and clinical/biochemical substudies.</p> <p>Results</p> <p>The primary outcome was pregnancy-related mortality assessed for 3 months following parturition. Secondary outcomes included fetal loss due to miscarriage or stillbirth, infant mortality under three months of age, maternal obstetric and infectious morbidity, infant infectious morbidity, maternal and infant micronutrient status, fetal and infant growth and prematurity, external birth defects and postnatal infant growth to 3 months of age.</p> <p>Conclusion</p> <p>Aspects of study site selection and its "resonance" with national and rural qualities of Bangladesh, the trial's design, methods and allocation group comparability achieved by randomization, field procedures and innovative approaches to solving challenges in trial conduct are described and discussed. This trial is registered with <url>http://Clinicaltrials.gov</url> as protocol NCT00198822.</p

Shaping black holes with free fields

Starting from a metric Ansatz permitting a weak version of Birkhoff's theorem we find static black hole solutions including matter in the form of free scalar and p-form fields, with and without a cosmological constant \Lambda. Single p-form matter fields permit multiple possibilities, including dyonic solutions, self-dual instantons and metrics with Einstein-Kaelher horizons. The inclusion of multiple p-forms on the other hand, arranged in a homogeneous fashion with respect to the horizon geometry, permits the construction of higher dimensional dyonic p-form black holes and four dimensional axionic black holes with flat horizons, when \Lambda<0. It is found that axionic fields regularize black hole solutions in the sense, for example, of permitting regular -- rather than singular -- small mass Reissner-Nordstrom type black holes. Their cosmic string and Vaidya versions are also obtained.Comment: 38 pages. v2: minor changes, published versio

Endomorphism algebras of Abelian varieties with special reference to superelliptic Jacobians

This is (mostly) a survey article. We use an information about Galois properties of points of small order on an Abelian variety in order to describe its endomorphism algebra over an algebraic closure of the ground field. We discuss in detail applications to jacobians of cyclic covers of the projective line

Landscape Encodings Enhance Optimization

Hard combinatorial optimization problems deal with the search for the minimum cost solutions (ground states) of discrete systems under strong constraints. A transformation of state variables may enhance computational tractability. It has been argued that these state encodings are to be chosen invertible to retain the original size of the state space. Here we show how redundant non-invertible encodings enhance optimization by enriching the density of low-energy states. In addition, smooth landscapes may be established on encoded state spaces to guide local search dynamics towards the ground state

Rotating black hole entropy from M5-branes

We compute the superconformal index of 3d N = 2 superconformal field theories obtained from N M5-branes wrapped on a hyperbolic 3-manifold. Exploiting the 3d-3d correspondence, we use perturbative invariants of SL(N, \u2102) Chern-Simons theory to determine the superconformal index in the large N limit, including corrections logarithmic in N. The leading order partition function provides a microscopic foundation for the entropy function of the dual rotating asymptotically AdS4 black holes. We also verify that the supergravity one-loop contribution to the log N term coincides with the field theoretic result. We propose a 3d-3d formulation for the refined topologically twisted index, and provide strong evidence in support of its vanishing \u2014 which agrees with the fact that the expected dual rotating magnetically-charged black hole does not exist. This provides an interesting link between gravity and a tantalizing mathematical result

The Interdomain Linker of AAV-2 Rep68 Is an Integral Part of Its Oligomerization Domain: Role of a Conserved SF3 Helicase Residue in Oligomerization

The four Rep proteins of adeno-associated virus (AAV) orchestrate all aspects of its viral life cycle, including transcription regulation, DNA replication, virus assembly, and site-specific integration of the viral genome into the human chromosome 19. All Rep proteins share a central SF3 superfamily helicase domain. In other SF3 members this domain is sufficient to induce oligomerization. However, the helicase domain in AAV Rep proteins (i.e. Rep40/Rep52) as shown by its monomeric characteristic, is not able to mediate stable oligomerization. This observation led us to hypothesize the existence of an as yet undefined structural determinant that regulates Rep oligomerization. In this document, we described a detailed structural comparison between the helicase domains of AAV-2 Rep proteins and those of the other SF3 members. This analysis shows a major structural difference residing in the small oligomerization sub-domain (OD) of Rep helicase domain. In addition, secondary structure prediction of the linker connecting the helicase domain to the origin-binding domain (OBD) indicates the potential to form α-helices. We demonstrate that mutant Rep40 constructs containing different lengths of the linker are able to form dimers, and in the presence of ATP/ADP, larger oligomers. We further identified an aromatic linker residue (Y224) that is critical for oligomerization, establishing it as a conserved signature motif in SF3 helicases. Mutation of this residue critically affects oligomerization as well as completely abolishes the ability to produce infectious virus. Taken together, our data support a model where the linker residues preceding the helicase domain fold into an α-helix that becomes an integral part of the helicase domain and is critical for the oligomerization and function of Rep68/78 proteins through cooperative interaction with the OBD and helicase domains