Loop Equations and the Topological Phase of Multi-Cut Matrix Models

We study the double scaling limit of mKdV type, realized in the two-cut Hermitian matrix model. Building on the work of Periwal and Shevitz and of Nappi, we find an exact solution including all odd scaling operators, in terms of a hierarchy of flows of $2\times 2$ matrices. We derive from it loop equations which can be expressed as Virasoro constraints on the partition function. We discover a ``pure topological" phase of the theory in which all correlation functions are determined by recursion relations. We also examine macroscopic loop amplitudes, which suggest a relation to 2D gravity coupled to dense polymers.Comment: 24p

Archeological Survey Of The Proposed State Highway 288 Access Road Bridges, In Harris And Brazoria Counties, Texas

On February 22, 2005 a crew from Moore Archeological Consulting, Inc. performed a shovel test survey of the proposed State Highway 288 Access Road Bridges Project in Harris and Brazoria Counties, Texas. This was performed for S&B Infrastructure and the Texas Department of Transportation (TxDOT) under Antiquities Permit Number 3681. The results will be subject to review by TxDOT, S&B and the Texas Historical Commission. A total of 10 shovel tests were excavated in the Project Area which totaled approximately 2 acres. The Project Corridor was entirely within the existing, state-owned, right-of-way. No prehistoric or historic resources or features were found. The soils in all ten shovel tests were observed to contain disturbed and/or fill soils over truncated natural soils. All but one shovel test reached basal clay subsoils. No artifacts were observed or recovered. The recommendation of Moore Archeological Consulting is that this project should be allowed to proceed without further investigation

Character Expansion Methods for Matrix Models of Dually Weighted Graphs

We consider generalized one-matrix models in which external fields allow control over the coordination numbers on both the original and dual lattices. We rederive in a simple fashion a character expansion formula for these models originally due to Itzykson and Di Francesco, and then demonstrate how to take the large N limit of this expansion. The relationship to the usual matrix model resolvent is elucidated. Our methods give as a by-product an extremely simple derivation of the Migdal integral equation describing the large $N$ limit of the Itzykson-Zuber formula. We illustrate and check our methods by analyzing a number of models solvable by traditional means. We then proceed to solve a new model: a sum over planar graphs possessing even coordination numbers on both the original and the dual lattice. We conclude by formulating equations for the case of arbitrary sets of even, self-dual coupling constants. This opens the way for studying the deep problem of phase transitions from random to flat lattices.Comment: 22 pages, harvmac.tex, pictex.tex. All diagrams written directly into the text in Pictex commands. (Two minor math typos corrected. Acknowledgements added.

Open String Star as a Continuous Moyal Product

We establish that the open string star product in the zero momentum sector can be described as a continuous tensor product of mutually commuting two dimensional Moyal star products. Let the continuous variable $\kappa \in [~0,\infty)$ parametrize the eigenvalues of the Neumann matrices; then the noncommutativity parameter is given by $\theta(\kappa) =2\tanh(\pi\kappa/4)$. For each $\kappa$, the Moyal coordinates are a linear combination of even position modes, and the Fourier transform of a linear combination of odd position modes. The commuting coordinate at $\kappa=0$ is identified as the momentum carried by half the string. We discuss the relation to Bars' work, and attempt to write the string field action as a noncommutative field theory.Comment: 30 pages, LaTeX. One reference adde

Bayesian Spatiotemporal Pattern and Eco-climatological Drivers of Striped Skunk Rabies in the North Central Plains

Citation: Raghavan, R. K., Hanlon, C. A., Goodin, D. G., Davis, R., Moore, M., Moore, S., & Anderson, G. A. (2016). Bayesian Spatiotemporal Pattern and Eco-climatological Drivers of Striped Skunk Rabies in the North Central Plains. Plos Neglected Tropical Diseases, 10(4), 16. doi:10.1371/journal.pntd.0004632Striped skunks are one of the most important terrestrial reservoirs of rabies virus in North America, and yet the prevalence of rabies among this host is only passively monitored and the disease among this host remains largely unmanaged. Oral vaccination campaigns have not efficiently targeted striped skunks, while periodic spillovers of striped skunk variant viruses to other animals, including some domestic animals, are routinely recorded. In this study we evaluated the spatial and spatio-temporal patterns of infection status among striped skunk cases submitted for rabies testing in the North Central Plains of US in a Bayesian hierarchical framework, and also evaluated potential eco-climatological drivers of such patterns. Two Bayesian hierarchical models were fitted to point-referenced striped skunk rabies cases [n = 656 (negative), and n = 310 (positive)] received at a leading rabies diagnostic facility between the years 2007-2013. The first model included only spatial and temporal terms and a second covariate model included additional covariates representing eco-climatic conditions within a 4km(2) home-range area for striped skunks. The better performing covariate model indicated the presence of significant spatial and temporal trends in the dataset and identified higher amounts of land covered by low-intensity developed areas [Odds ratio (OR) = 3.41; 95% Bayesian Credible Intervals (CrI) = 2.08, 3.85], higher level of patch fragmentation (OR = 1.70; 95% CrI = 1.25, 2.89), and diurnal temperature range (OR = 0.54; 95% CrI = 0.27, 0.91) to be important drivers of striped skunk rabies incidence in the study area. Model validation statistics indicated satisfactory performance for both models; however, the covariate model fared better. The findings of this study are important in the context of rabies management among striped skunks in North America, and the relevance of physical and climatological factors as risk factors for skunk to human rabies transmission and the space-time patterns of striped skunk rabies are discussed

Massive IIA flux compactifications and U-dualities

We attempt to find a rigorous formulation for the massive type IIA orientifold compactifications of string theory introduced in hep-th/0505160. An approximate double T-duality converts this background into IIA string theory on a twisted torus, but various arguments indicate that the back reaction of the orientifold on this geometry is large. In particular, an AdS calculation of the entropy suggests a scaling appropriate for N M2-branes, in a certain limit of the compactification, though not the one studied in hep-th/0505160. The M-theory lift of this specific regime is not 4 dimensional. We suggest that the generic limit of the background corresponds to a situation analogous to F-theory, where the string coupling is small in some regions of a compact geometry, and large in others, so that neither a long wavelength 11D SUGRA expansion, nor a world sheet expansion exists for these compactifications. We end with a speculation on the nature of the generic compactification.Comment: JHEP3 LaTeX - 34 pages - 3 figures; v2: Added references; v3: mistake in entropy scaling corrected, major changes in conclusions; v4: changed claims about original DeWolfe et al. setup, JHEP versio

Marginal and Relevant Deformations of N=4 Field Theories and Non-Commutative Moduli Spaces of Vacua

We study marginal and relevant supersymmetric deformations of the N=4 super-Yang-Mills theory in four dimensions. Our primary innovation is the interpretation of the moduli spaces of vacua of these theories as non-commutative spaces. The construction of these spaces relies on the representation theory of the related quantum algebras, which are obtained from F-term constraints. These field theories are dual to superstring theories propagating on deformations of the AdS_5xS^5 geometry. We study D-branes propagating in these vacua and introduce the appropriate notion of algebraic geometry for non-commutative spaces. The resulting moduli spaces of D-branes have several novel features. In particular, they may be interpreted as symmetric products of non-commutative spaces. We show how mirror symmetry between these deformed geometries and orbifold theories follows from T-duality. Many features of the dual closed string theory may be identified within the non-commutative algebra. In particular, we make progress towards understanding the K-theory necessary for backgrounds where the Neveu-Schwarz antisymmetric tensor of the string is turned on, and we shed light on some aspects of discrete anomalies based on the non-commutative geometry.Comment: 60 pages, 4 figures, JHEP format, amsfonts, amssymb, amsmat

The Solution Space of the Unitary Matrix Model String Equation and the Sato Grassmannian

The space of all solutions to the string equation of the symmetric unitary one-matrix model is determined. It is shown that the string equation is equivalent to simple conditions on points $V_1$ and $V_2$ in the big cell \Gr of the Sato Grassmannian $Gr$. This is a consequence of a well-defined continuum limit in which the string equation has the simple form \lb \cp ,\cq_- \rb =\hbox{\rm 1}, with \cp and \cq_- $2\times 2$ matrices of differential operators. These conditions on $V_1$ and $V_2$ yield a simple system of first order differential equations whose analysis determines the space of all solutions to the string equation. This geometric formulation leads directly to the Virasoro constraints \L_n\,(n\geq 0), where \L_n annihilate the two modified-KdV \t-functions whose product gives the partition function of the Unitary Matrix Model.Comment: 21 page