LpL^p-Spectral theory of locally symmetric spaces with QQ-rank one

We study the $L^p$-spectrum of the Laplace-Beltrami operator on certain complete locally symmetric spaces $M=\Gamma\backslash X$ with finite volume and arithmetic fundamental group $\Gamma$ whose universal covering $X$ is a symmetric space of non-compact type. We also show, how the obtained results for locally symmetric spaces can be generalized to manifolds with cusps of rank one

Bound states in N = 4 SYM on T^3: Spin(2n) and the exceptional groups

The low energy spectrum of (3+1)-dimensional N=4 supersymmetric Yang-Mills theory on a spatial three-torus contains a certain number of bound states, characterized by their discrete abelian magnetic and electric 't Hooft fluxes. At weak coupling, the wave-functions of these states are supported near points in the moduli space of flat connections where the unbroken gauge group is semi-simple. The number of such states is related to the number of normalizable bound states at threshold in the supersymmetric matrix quantum mechanics with 16 supercharges based on this unbroken group. Mathematically, the determination of the spectrum relies on the classification of almost commuting triples with semi-simple centralizers. We complete the work begun in a previous paper, by computing the spectrum of bound states in theories based on the even-dimensional spin groups and the exceptional groups. The results satisfy the constraints of S-duality in a rather non-trivial way.Comment: 20 page

On the bounded cohomology of semi-simple groups, S-arithmetic groups and products

We prove vanishing results for Lie groups and algebraic groups (over any local field) in bounded cohomology. The main result is a vanishing below twice the rank for semi-simple groups. Related rigidity results are established for S-arithmetic groups and groups over global fields. We also establish vanishing and cohomological rigidity results for products of general locally compact groups and their lattices

Contacts homme-eau et schistosomiase urinaire dans un village mauritanien = Water contact and urinary schistosomiasis in a Mauritanian village

Huit jours d'observations directes, de septembre à décembre 1985, dans un village d'endémie bilharzienne à #S. haematobium$ situé en zone sahélienne ont permis d'enregistrer 1226 contacts homme-eau dans la mare du village et d'analyser la responsabilité des diverses activités dans la transmission. Un indice d'exposition, intégrant la durée du contact, la surface corporelle exposée et la probabilité de présence de cercaires dans l'eau a été calculé pour chaque contact. Les activités domestiques, essentiellement féminines, ont représenté 62 % des contacts mais seulement 15 % de l'exposition totale. La situation est inverse pour les activités récréatives qui, impliquant principalement de jeunes garçons, n'étaient responsables que de 14 % des contacts mais de 70 % de l'exposition totale. Entre 6 et 20 ans l'exposition moyenne par contact est plus importante pour le sexe masculin. Une politique de prévention de la maladie par une action sur les contacts semble irréaliste dans le contexte étudié et le traitement sélectif des enfants ou des sujets fortement infectés apparaît comme la stratégie de lutte la mieux adaptée. (Résumé d'auteur

Growth in solvable subgroups of GL_r(Z/pZ)

Let $K=Z/pZ$ and let $A$ be a subset of \GL_r(K) such that is solvable. We reduce the study of the growth of $A$ under the group operation to the nilpotent setting. Specifically we prove that either $A$ grows rapidly (meaning $|A\cdot A\cdot A|\gg |A|^{1+\delta}$), or else there are groups $U_R$ and $S$, with $S/U_R$ nilpotent such that $A_k\cap S$ is large and $U_R\subseteq A_k$, where $k$ is a bounded integer and $A_k = \{x_1 x_2...b x_k : x_i \in A \cup A^{-1} \cup {1}}$. The implied constants depend only on the rank $r$ of $\GL_r(K)$. When combined with recent work by Pyber and Szab\'o, the main result of this paper implies that it is possible to draw the same conclusions without supposing that is solvable.Comment: 46 pages. This version includes revisions recommended by an anonymous referee including, in particular, the statement of a new theorem, Theorem

Berry's phase for compact Lie groups

The Lie group adiabatic evolution determined by a Lie algebra parameter dependent Hamiltonian is considered. It is demonstrated that in the case when the parameter space of the Hamiltonian is a homogeneous K\"ahler manifold its fundamental K\"ahler potentials completely determine Berry geometrical phase factor. Explicit expressions for Berry vector potentials (Berry connections) and Berry curvatures are obtained using the complex parametrization of the Hamiltonian parameter space. A general approach is exemplified by the Lie algebra Hamiltonians corresponding to SU(2) and SU(3) evolution groups.Comment: 24 pages, no figure

Isohemagglutinins of Graft Origin after ABO-Unmatched Liver Transplantation

THE increasing success of liver transplantation in recent years has provided an experimental model to study and document the hepatic synthesis of many plasma proteins.12345 The normal hepatobiliary tract has not been regarded as a major source of antibody,6,7 aside from the enteric IgA secreted from plasma into the biliary tree.8 Liver transplantation affords the opportunity to study the production of antibody to red cells. Recipient ABO incompatibility to the donor (a mismatched transplant, e.g., a group A liver transplanted into a group B recipient), although not absolutely contraindicated in liver transplantation, is avoided when possible. However, ABO-unmatched transplants (defined. © 1984, Massachusetts Medical Society. All rights reserved

BPS states in (2,0) theory on R x T5

We consider $(2, 0)$ theory on a space-time of the form $R \times T^5$, where the first factor denotes time, and the second factor is a flat spatial five-torus. In addition to their energy, quantum states are characterized by their spatial momentum, 't Hooft flux, and $Sp (4)$ $R$-symmetry representation. The momentum obeys a shifted quantization law determined by the 't Hooft flux. By supersymmetry, the energy is bounded from below by the magnitude of the momentum. This bound is saturated by BPS states, that are annihilated by half of the supercharges. The spectrum of such states is invariant under smooth deformations of the theory, and can thus be studied by exploiting the interpretation of $(2, 0)$ theory as an ultra-violet completion of maximally supersymmetric Yang-Mills theory on $R \times T^4$. Our main example is the $A$-series of $(2,0)$ theories, where such methods allow us to study the spectrum of BPS states for many values of the momentum and the 't Hooft flux. In particular, we can describe the $R$-symmetry transformation properties of these states by determining the image of their $Sp (4)$ representation in a certain quotient of the $Sp (4)$ representation ring.Comment: 22 page

Universal statistical properties of poker tournaments

We present a simple model of Texas hold'em poker tournaments which retains the two main aspects of the game: i. the minimal bet grows exponentially with time; ii. players have a finite probability to bet all their money. The distribution of the fortunes of players not yet eliminated is found to be independent of time during most of the tournament, and reproduces accurately data obtained from Internet tournaments and world championship events. This model also makes the connection between poker and the persistence problem widely studied in physics, as well as some recent physical models of biological evolution, and extreme value statistics.Comment: Final longer version including data from Internet and WPT tournament

Branching processes, the max-plus algebra and network calculus

Branching processes can describe the dynamics of various queueing systems, peer-to-peer systems, delay tolerant networks, etc. In this paper we study the basic stochastic recursion of multitype branching processes, but in two non-standard contexts. First, we consider this recursion in the max-plus algebra where branching corresponds to finding the maximal offspring of the current generation. Secondly, we consider network-calculus-type deterministic bounds as introduced by Cruz, which we extend to handle branching-type processes. The paper provides both qualitative and quantitative results and introduces various applications of (max-plus) branching processes in queueing theory