BPS States of Exceptional Non-Critical Strings

We study the BPS states of non-critical strings which arise for zero size instantons of exceptional groups. This is accomplished by using F-theory and M-theory duals and by employing mirror symmetry to compute the degeneracy of membranes wrapped around 2-cycles of the Calabi-Yau threefold. We find evidence for a number of novel physical phenomena, including having infinitely many light states with the first lightest state including a nearly massless gravitino.Comment: 29 pages, 1 figure, references added, to appear in the proceedings of the conference "Advanced Quantum Field Theory'' (in memory of Claude Itzykson

K3--Fibrations and Heterotic-Type II String Duality

We analyze the map between heterotic and type II N=2 supersymmetric string theories for certain two and three moduli examples found by Kachru and Vafa. The appearance of elliptic j-functions can be traced back to specializations of the Picard-Fuchs equations to systems for $K_3$ surfaces. For the three-moduli example we write the mirror maps and Yukawa couplings in the weak coupling limit in terms of j-functions; the expressions agree with those obtained in perturbative calculations in the heterotic string in an impressive way. We also discuss symmetries of the world-sheet instanton numbers in the type II theory, and interpret them in terms of S--duality of the non-perturbative heterotic string.Comment: 16p, harvmac with hyperlink

Measuring Taxes on Income from Capital: Evidence from the UK

This paper explores the empirical properties of alternative measures of the taxation of income from capital, using UK data over the last thirty years. We analyse measures of effective marginal and average tax rates, based on applying the legal parameters of the tax system to a hypothetical investment; and also measures based on observed tax payments or liabilities, scaled by various measures of income. There is a significant difference between these measures, both in their level and in how they move over time. The implicit assumption in some empirical work that these measures are broadly comparable to each other is not justified.

Giving and Receiving Peer Advice in an Online Breast Cancer Support Group

People have access to experiential information and advice about health online. The types of advice exchanged affect the nature of online communities and potentially patient decision making. The aim of this study was to examine the ways in which peers exchange advice within an online health forum in order to better understand online groups as a resource for decision making. Messages collected over a one-month period from an online breast cancer support forum were analyzed for examples of advice exchange. The majority of the messages solicited advice through problem disclosure or requests for information and opinion. A novel form of advice solicitation—“anyone in the same boat as me”—was noted as was the use of personal experience as a form of advice giving. Women construct their advice requests to target like-minded people. The implications in terms of decision making and support are discussed

A Search for Non-Perturbative Dualities of Local N=2N=2 Yang--Mills Theories from Calabi--Yau Threefolds

The generalisation of the rigid special geometry of the vector multiplet quantum moduli space to the case of supergravity is discussed through the notion of a dynamical Calabi--Yau threefold. Duality symmetries of this manifold are connected with the analogous dualities associated with the dynamical Riemann surface of the rigid theory. N=2 rigid gauge theories are reviewed in a framework ready for comparison with the local case. As a byproduct we give in general the full duality group (quantum monodromy) for an arbitrary rigid $SU(r+1)$ gauge theory, extending previous explicit constructions for the $r=1,2$ cases. In the coupling to gravity, R--symmetry and monodromy groups of the dynamical Riemann surface, whose structure we discuss in detail, are embedded into the symplectic duality group $\Gamma_D$ associated with the moduli space of the dynamical Calabi--Yau threefold.Comment: Latex. Version of previous paper with enlarged and revised appendix 35 pages, plain LaTe

Mirror Symmetry, Mirror Map and Applications to Calabi-Yau Hypersurfaces

Mirror Symmetry, Picard-Fuchs equations and instanton corrected Yukawa couplings are discussed within the framework of toric geometry. It allows to establish mirror symmetry of Calabi-Yau spaces for which the mirror manifold had been unavailable in previous constructions. Mirror maps and Yukawa couplings are explicitly given for several examples with two and three moduli.Comment: 59 pages. Some changes in the references, a few minor points have been clarifie

Two antisymmetric hypermultiplets in N=2 SU(N) gauge theory: Seiberg-Witten curve and M-theory interpretation

The one-instanton contribution to the prepotential for N=2 supersymmetric gauge theories with classical groups exhibits a universality of form. We extrapolate the observed regularity to SU(N) gauge theory with two antisymmetric hypermultiplets and N_f \leq 3 hypermultiplets in the defining representation. Using methods developed for the instanton expansion of non-hyperelliptic curves, we construct an effective quartic Seiberg-Witten curve that generates this one-instanton prepotential. We then interpret this curve in terms of an M-theoretic picture involving NS 5-branes, D4-branes, D6-branes, and orientifold sixplanes, and show that for consistency, an infinite chain of 5-branes and orientifold sixplanes is required, corresponding to a curve of infinite order.Comment: 30 pages; 3 figures; LaTeX; minor typos correcte

Relating Query Popularity and File Replication in the Gnutella Peer-to-Peer Network

In this paper, we characterize the user behavior in a peer-to-peer (P2P) file sharing network. Our characterization is based on the results of an extensive passive measurement study of the messages exchanged in the Gnutella P2P file sharing system. Using the data recorded during this measurement study, we analyze which queries a user issues and which files a user shares. The investigation of users queries leads to the characterization of query popularity. Furthermore, the analysis of the files shared by the users leads to a characterization of file replication. As major contribution, we relate query popularity and file replication by an analytical formula characterizing the matching of files to queries. The analytical formula defines a matching probability for each pair of query and file, which depends on the rank of the query with respect query popularity, but is independent of the rank of the file with respect to file replication. We validate this model by conducting a detailed simulation study of a Gnutella-style overlay network and comparing simulation results to the results obtained from the measurement

GKZ-Generalized Hypergeometric Systems in Mirror Symmetry of Calabi-Yau Hypersurfaces

We present a detailed study of the generalized hypergeometric system introduced by Gel'fand, Kapranov and Zelevinski (GKZ-hypergeometric system) in the context of toric geometry. GKZ systems arise naturally in the moduli theory of Calabi-Yau toric varieties, and play an important role in applications of the mirror symmetry. We find that the Gr\"obner basis for the so-called toric ideal determines a finite set of differential operators for the local solutions of the GKZ system. At the special point called the large radius limit, we find a close relationship between the principal parts of the operators in the GKZ system and the intersection ring of a toric variety. As applications, we analyze general three dimensional hypersurfaces of Fermat and non-Fermat types with Hodge numbers up to $h^{1,1}=3$. We also find and analyze several non Landau-Ginzburg models which are related to singular models.Comment: 55 pages, 3 Postscript figures, harvma

Clustering properties of a generalised critical Euclidean network

Many real-world networks exhibit scale-free feature, have a small diameter and a high clustering tendency. We have studied the properties of a growing network, which has all these features, in which an incoming node is connected to its $i$th predecessor of degree $k_i$ with a link of length $\ell$ using a probability proportional to $k^\beta_i \ell^{\alpha}$. For $\alpha > -0.5$, the network is scale free at $\beta = 1$ with the degree distribution $P(k) \propto k^{-\gamma}$ and $\gamma = 3.0$ as in the Barab\'asi-Albert model ($\alpha =0, \beta =1$). We find a phase boundary in the $\alpha-\beta$ plane along which the network is scale-free. Interestingly, we find scale-free behaviour even for $\beta > 1$ for $\alpha < -0.5$ where the existence of a new universality class is indicated from the behaviour of the degree distribution and the clustering coefficients. The network has a small diameter in the entire scale-free region. The clustering coefficients emulate the behaviour of most real networks for increasing negative values of $\alpha$ on the phase boundary.Comment: 4 pages REVTEX, 4 figure