Complex Matrix Models and Statistics of Branched Coverings of 2D Surfaces

We present a complex matrix gauge model defined on an arbitrary two-dimensional orientable lattice. We rewrite the model's partition function in terms of a sum over representations of the group U(N). The model solves the general combinatorial problem of counting branched covers of orientable Riemann surfaces with any given, fixed branch point structure. We then define an appropriate continuum limit allowing the branch points to freely float over the surface. The simplest such limit reproduces two-dimensional chiral U(N) Yang-Mills theory and its string description due to Gross and Taylor.Comment: 21 pages, 2 figures, TeX, harvmac.tex, epsf.tex, TeX "big

Almost Flat Planar Diagrams

We continue our study of matrix models of dually weighted graphs. Among the attractive features of these models is the possibility to interpolate between ensembles of regular and random two-dimensional lattices, relevant for the study of the crossover from two-dimensional flat space to two-dimensional quantum gravity. We further develop the formalism of large $N$ character expansions. In particular, a general method for determining the large $N$ limit of a character is derived. This method, aside from being potentially useful for a far greater class of problems, allows us to exactly solve the matrix models of dually weighted graphs, reducing them to a well-posed Cauchy-Riemann problem. The power of the method is illustrated by explicitly solving a new model in which only positive curvature defects are permitted on the surface, an arbitrary amount of negative curvature being introduced at a single insertion.Comment: harvmac.tex and pictex.tex. Must be compiled "big". Diagrams are written directly into the text in pictex command

Advances in large N group theory and the solution of two-dimensional R2^{2} gravity

We review the recent exact solution of a matrix model which interpolates between flat and random lattices. The importance of the results is twofold: Firstly, we have developed a new large N technique capable of treating a class of matrix models previously thought to be unsolvable. Secondly, we are able to make a first precise statement about two-dimensional R^2 gravity. These notes are based on a lecture given at the Cargese summer school 1995. They contain some previously unpublished results

Interrogational Torture in Criminal Proceedings - Reflections on Legal History -, Vol. 2

Subject of this publication is torture as an interrogational instrument in criminal proceedings from a legal history point of view. Thereby, the author makes a distinction between torturing the accused on the one hand and, on the other hand, torture as an instrument to force a witness’ incriminating testimony against third parties (in German: Zeugenfolter), torture as a means to avert dangers (lifesaving torture), torture as an additional cruelty to the accused’s punishment (in German: Straffolter), and corporal punishment for lying in court. Only the first manifestation, namely torturing the accused intending to extort his confession, is the real subject of this paper. Volume I covers the following historical periods: Code of Hammurabi; Germanic Law; Roman Law; Age of the Kingdom of the Franks; High Middle Ages

Interrogational Torture in Criminal Proceedings - Reflections on Legal History -, Vol. 1

Subject of this publication is torture as an interrogational instrument in criminal proceedings from a legal history point of view. Thereby, the author makes a distinction between torturing the accused on the one hand and, on the other hand, torture as an instrument to force a witness’ incriminating testimony against third parties (in German: Zeugenfolter), torture as a means to avert dangers (lifesaving torture), torture as an additional cruelty to the accused’s punishment (in German: Straffolter), and corporal punishment for lying in court. Only the first manifestation, namely torturing the accused intending to extort his confession, is the real subject of this paper. Volume I covers the following historical periods: Code of Hammurabi; Germanic Law; Roman Law; Age of the Kingdom of the Franks; High Middle Ages

On the breakdown of perturbative integrability in large N matrix models

We study the perturbative integrability of the planar sector of a massive SU(N) matrix quantum mechanical theory with global SO(6) invariance and Yang-Mills-like interaction. This model arises as a consistent truncation of maximally supersymmetric Yang-Mills theory on a three-sphere to the lowest modes of the scalar fields. In fact, our studies mimic the current investigations concerning the integrability properties of this gauge theory. Like in the field theory we can prove the planar integrability of the SO(6) model at first perturbative order. At higher orders we restrict ourselves to the widely studied SU(2) subsector spanned by two complexified scalar fields of the theory. We show that our toy model satisfies all commonly studied integrability requirements such as degeneracies in the spectrum, existence of conserved charges and factorized scattering up to third perturbative order. These are the same qualitative features as the ones found in super Yang-Mills theory, which were enough to conjecture the all-loop integrability of that theory. For the SO(6) model, however, we show that these properties are not sufficient to predict higher loop integrability. In fact, we explicitly demonstrate the breakdown of perturbative integrability at fourth order.Comment: 27 page

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.

Field thermal monitoring during the August 2003 eruption at Piton de la Fournaise (La Réunion )

International audience[1] A detailed set of thermal images collected during the last day of the August 2003 eruption of Piton de la Fournaise (La Réunion), clearly revealed several dynamic processes associated with a spatter cone containing a lava pond and feeding a channelized lava flow. Periods of steady effusion were interrupted by brief pulses of lava effusion that closely coincide with peaks in seismic tremor amplitude. The thermal measurements show that roofing of a lava channel during steady effusion and cooling of surface flows decrease thermal radiance in two different ways. Here we show that the decrease in thermal radiance because of channel roofing is not related to a decrease in volcanic activity, as might be interpreted from satellite data. In addition, we introduce a new method of representing thermal data (hereby named ''Radiative Thermogramme'') that successfully describes thermal patterns produced by distinct eruptive processes within the same span of time. This graphic solution can be directly correlated with volcanic field processes and provides a useful tool for interpreting a high number of thermal data in a wide range of volcanic activities

Sudden cardiac death while waiting: do we need the wearable cardioverter-defibrillator?

Sudden cardiac death (SCD) is the most frequent cause of cardiovascular death in industrialized nations. Patients with cardiomyopathy are at increased risk for SCD and may benefit from an implantable cardioverter-defibrillator (ICD). The risk of SCD is highest in the first months after myocardial infarction or first diagnosis of severe non-ischemic cardiomyopathy. On the other hand, left ventricular function may improve in a subset of patients to such an extent that an ICD might no longer be needed. To offer protection from a transient risk of SCD, the wearable cardioverter-defibrillator (WCD) is available. Results of the first randomized clinical trial investigating the role of the WCD after myocardial infarction were recently published. This review is intended to provide insight into data from the VEST trial, and to put these into perspective with studies and clinical experience. As a non-invasive, temporary therapy, the WCD may offer advantages over early ICD implantation. However, recent data demonstrate that patient compliance and education play a crucial role in this new concept of preventing SCD