Complex Line Bundles over Simplicial Complexes and their Applications

Discrete vector bundles are important in Physics and recently found remarkable applications in Computer Graphics. This article approaches discrete bundles from the viewpoint of Discrete Differential Geometry, including a complete classification of discrete vector bundles over finite simplicial complexes. In particular, we obtain a discrete analogue of a theorem of Andr\'e Weil on the classification of hermitian line bundles. Moreover, we associate to each discrete hermitian line bundle with curvature a unique piecewise-smooth hermitian line bundle of piecewise constant curvature. This is then used to define a discrete Dirichlet energy which generalizes the well-known cotangent Laplace operator to discrete hermitian line bundles over Euclidean simplicial manifolds of arbitrary dimension

A Note on the Equality of Algebraic and Geometric D-Brane Charges in WZW Models

The algebraic definition of charges for symmetry-preserving D-branes in Wess-Zumino-Witten models is shown to coincide with the geometric definition, for all simple Lie groups. The charge group for such branes is computed from the ambiguities inherent in the geometric definition.Comment: 12 pages, fixed typos, added references and a couple of remark

Romantic Partnerships and the Dispersion of Social Ties: A Network Analysis of Relationship Status on Facebook

A crucial task in the analysis of on-line social-networking systems is to identify important people --- those linked by strong social ties --- within an individual's network neighborhood. Here we investigate this question for a particular category of strong ties, those involving spouses or romantic partners. We organize our analysis around a basic question: given all the connections among a person's friends, can you recognize his or her romantic partner from the network structure alone? Using data from a large sample of Facebook users, we find that this task can be accomplished with high accuracy, but doing so requires the development of a new measure of tie strength that we term `dispersion' --- the extent to which two people's mutual friends are not themselves well-connected. The results offer methods for identifying types of structurally significant people in on-line applications, and suggest a potential expansion of existing theories of tie strength.Comment: Proc. 17th ACM Conference on Computer Supported Cooperative Work and Social Computing (CSCW), 201

Physical States at the Tachyonic Vacuum of Open String Field Theory

We illustrate a method for computing the number of physical states of open string theory at the stable tachyonic vacuum in level truncation approximation. The method is based on the analysis of the gauge-fixed open string field theory quadratic action that includes Fadeev-Popov ghost string fields. Computations up to level 9 in the scalar sector are consistent with Sen's conjecture about the absence of physical open string states at the tachyonic vacuum. We also derive a long exact cohomology sequence that relates relative and absolute cohomologies of the BRS operator at the non-perturbative vacuum. We use this exact result in conjunction with our numerical findings to conclude that the higher ghost number non-perturbative BRS cohomologies are non-empty.Comment: 43 pages, 16 eps figures, LaTe

RationalMaps, a package for Macaulay2

This paper describes the RationalMaps package for Macaulay2. This package provides functionality for computing several aspects of rational maps such as whether a map is birational, or a closed embedding.Comment: 8 pages. The current version of the package (and other necessary files) can be accessed at https://github.com/Macaulay2/Workshop-2016-Utah/tree/master/RationalMap

Chern-Simons Theory on S^1-Bundles: Abelianisation and q-deformed Yang-Mills Theory

We study Chern-Simons theory on 3-manifolds $M$ that are circle-bundles over 2-dimensional surfaces $\Sigma$ and show that the method of Abelianisation, previously employed for trivial bundles $\Sigma \times S^1$, can be adapted to this case. This reduces the non-Abelian theory on $M$ to a 2-dimensional Abelian theory on $\Sigma$ which we identify with q-deformed Yang-Mills theory, as anticipated by Vafa et al. We compare and contrast our results with those obtained by Beasley and Witten using the method of non-Abelian localisation, and determine the surgery and framing presecription implicit in this path integral evaluation. We also comment on the extension of these methods to BF theory and other generalisations.Comment: 37 pages; v2: references adde

Formation of Episodic Magnetically Driven Radiatively Cooled Plasma Jets in the Laboratory

We report on experiments in which magnetically driven radiatively cooled plasma jets were produced by a 1 MA, 250 ns current pulse on the MAGPIE pulsed power facility. The jets were driven by the pressure of a toroidal magnetic field in a ''magnetic tower'' jet configuration. This scenario is characterized by the formation of a magnetically collimated plasma jet on the axis of a magnetic ''bubble'', confined by the ambient medium. The use of a radial metallic foil instead of the radial wire arrays employed in our previous work allows for the generation of episodic magnetic tower outflows which emerge periodically on timescales of ~30 ns. The subsequent magnetic bubbles propagate with velocities reaching ~300 km/s and interact with previous eruptions leading to the formation of shocks.Comment: 6 pages, 5 figures. Accepted for publication in Astrophysics & Space Scienc

Constraints on Low-Dimensional String Compactifications

We study the restrictions imposed by cancellation of the tadpoles for two, three, and four-form gauge fields in string theory, M-theory and F-theory compactified to two, three and four dimensions, respectively. For a large class of supersymmetric vacua, turning on a sufficient number of strings, membranes and three-branes, respectively, can cancel the tadpoles, and preserve supersymmetry. However, there are cases where the tadpole cannot be removed in this way, either because the tadpole is fractional, or because of its sign. For M-theory and F-theory compactifications, we also explore the relation of the membranes and three-branes to the nonperturbative space-time superpotential.Comment: 16 pages, harvma

Vascular Endothelial Growth Factor and Kinase Domain Region Receptor Are Involved in Both Seminiferous Cord Formation and Vascular Development During Testis Morphogenesis in the Rat

Morphological male sex determination is dependent on migration of endothelial and preperitubular cells from the adjacent mesonephros into the developing testis. Our hypothesis is that VEGFA and its receptor KDR are necessary for both testicular cord formation and neovascularization. The Vegfa gene has 8 exons with many splice variants. Vegfa120, Vegfa164, and Vegfa188 mRNA isoforms were detected on Embryonic Day (E) 13.5 (plug date = E0) in the rat. Vegfa120, Vegfa144, Vegfa164, Vegfa188, and Vegfa205 mRNA were detected at E18 and Postnatal Day 3 (P3). Kdr mRNA was present on E13.5, whereas Fms-like tyrosine kinase 1 receptor (Flt1) mRNA was not detected until E18. VEGFA protein was localized to Sertoli cells at cord formation and KDR to germ and interstitial cells. The VEGFA signaling inhibitors SU1498 (40 μM) and VEGFR-TKI (8 μM) inhibited cord formation in E13 testis cultures with 90% reduced vascular density (P \u3c 0.01) in VEGFR-TKI-treated organs. Furthermore, Je-11 (10 μM), an antagonist to VEGFA, also perturbed cord formation and inhibited vascular density by more than 50% (P \u3c 0.01). To determine signal transduction pathways involved in VEGFA’s regulation of testis morphogenesis, E13 testis were treated with LY 294002 (15 μM), a phosphoinositide 3-kinase (PI3K) pathway inhibitor, resulting in inhibition of both vascular density (46%) and cord formation. Thus, we support our hypothesis and conclude that VEGFA, secreted by the Sertoli cell, is involved in both neovascularization and cord formation and potentially acts through the PI3K pathway during testis morphogenesis to elicit its effects

Vascular Endothelial Growth Factor and Kinase Domain Region Receptor Are Involved in Both Seminiferous Cord Formation and Vascular Development During Testis Morphogenesis in the Rat

Morphological male sex determination is dependent on migration of endothelial and preperitubular cells from the adjacent mesonephros into the developing testis. Our hypothesis is that VEGFA and its receptor KDR are necessary for both testicular cord formation and neovascularization. The Vegfa gene has 8 exons with many splice variants. Vegfa120, Vegfa164, and Vegfa188 mRNA isoforms were detected on Embryonic Day (E) 13.5 (plug date = E0) in the rat. Vegfa120, Vegfa144, Vegfa164, Vegfa188, and Vegfa205 mRNA were detected at E18 and Postnatal Day 3 (P3). Kdr mRNA was present on E13.5, whereas Fms-like tyrosine kinase 1 receptor (Flt1) mRNA was not detected until E18. VEGFA protein was localized to Sertoli cells at cord formation and KDR to germ and interstitial cells. The VEGFA signaling inhibitors SU1498 (40 μM) and VEGFR-TKI (8 μM) inhibited cord formation in E13 testis cultures with 90% reduced vascular density (P \u3c 0.01) in VEGFR-TKI-treated organs. Furthermore, Je-11 (10 μM), an antagonist to VEGFA, also perturbed cord formation and inhibited vascular density by more than 50% (P \u3c 0.01). To determine signal transduction pathways involved in VEGFA’s regulation of testis morphogenesis, E13 testis were treated with LY 294002 (15 μM), a phosphoinositide 3-kinase (PI3K) pathway inhibitor, resulting in inhibition of both vascular density (46%) and cord formation. Thus, we support our hypothesis and conclude that VEGFA, secreted by the Sertoli cell, is involved in both neovascularization and cord formation and potentially acts through the PI3K pathway during testis morphogenesis to elicit its effects