Connectedness of spheres in Cayley graphs

We introduce the notion of connection thickness of spheres in a Cayley graph, related to dead-ends and their retreat depth. It was well-known that connection thickness is bounded for finitely presented one-ended groups. We compute that for natural generating sets of lamplighter groups on a line or on a tree, connection thickness is linear or logarithmic respectively. We show that it depends strongly on the generating set. We give an example where the metric induced at the (finite) thickness of connection gives diameter of order n² to the sphere of radius n. We also discuss the rarity of dead-ends and the relationships of connection thickness with cut sets in percolation theory and with almost-convexity. Finally, we present a list of open questions about spheres in Cayley graphs

CONTRIBUIÇÃO AO ESTUDO CLINICO DOS ANTIESTREPTOCOCCICOS NÃO AZOICOS

Comentários sobre o trabalho "Contribuição ao estudo clínico dos antiestreptococcicos não azoicos", de J. J. Gournay e Y. Le Balc'h. "Biologie Médicale", Paris, ano 35, vol. 27, suplemento, 1937

Robots, computer algebra and eight connected components

Answering connectivity queries in semi-algebraic sets is a long-standing and challenging computational issue with applications in robotics, in particular for the analysis of kinematic singularities. One task there is to compute the number of connected components of the complementary of the singularities of the kinematic map. Another task is to design a continuous path joining two given points lying in the same connected component of such a set. In this paper, we push forward the current capabilities of computer algebra to obtain computer-aided proofs of the analysis of the kinematic singularities of various robots used in industry. We first show how to combine mathematical reasoning with easy symbolic computations to study the kinematic singularities of an infinite family (depending on paramaters) modelled by the UR-series produced by the company ``Universal Robots''. Next, we compute roadmaps (which are curves used to answer connectivity queries) for this family of robots. We design an algorithm for ``solving'' positive dimensional polynomial system depending on parameters. The meaning of solving here means partitioning the parameter's space into semi-algebraic components over which the number of connected components of the semi-algebraic set defined by the input system is invariant. Practical experiments confirm our computer-aided proof and show that such an algorithm can already be used to analyze the kinematic singularities of the UR-series family. The number of connected components of the complementary of the kinematic singularities of generic robots in this family is $8$

First step towards the new SPIRAL2 project control system

International audienceThe Spiral2 project at Ganil aims to produce rare ion beams using a Uranium carbide target fission process. The accelerator consists of a RFQ followed by a superconducting cavity linac and is designed to provide high intensity primary beams (deuterons, protons or heavy ions). The accelerator should be commissioned by the end of 2011; then, the first tests aiming to produce exotic beams are planned one year later. The control system will result of the collaboration between several institutes among which the Saclay Dapnia division yet having a good experience and knowledge with Epics. So and also because of its widely used functionalities, Epics has been chosen as the basic framework for the accelerator control and people from the other laboratories belonging to the collaboration are progressively acquiring a first experience with Epics. The paper first explains the organisation of the collaboration then it describes the basic hardware and software choices for the project. Some preliminary implementations are therefore given. As the project is still in its beginning phase, the paper ends by listing some interrogations not yet solved for the control system definition and opened for discussion

Uniform stability estimates for the discrete Calderon problems

In this article, we focus on the analysis of discrete versions of the Calderon problem in dimension d \geq 3. In particular, our goal is to obtain stability estimates for the discrete Calderon problems that hold uniformly with respect to the discretization parameter. Our approach mimics the one in the continuous setting. Namely, we shall prove discrete Carleman estimates for the discrete Laplace operator. A main difference with the continuous ones is that there, the Carleman parameters cannot be taken arbitrarily large, but should be smaller than some frequency scale depending on the mesh size. Following the by-now classical Complex Geometric Optics (CGO) approach, we can thus derive discrete CGO solutions, but with limited range of parameters. As in the continuous case, we then use these solutions to obtain uniform stability estimates for the discrete Calderon problems.Comment: 38 pages, 2 figure

Preliminary implementation for the new SPIRAL2 project control system

International audienceThe Spiral2 project consists of a new facility to provide high intensity rare ions beams. It is based on a primary beam driver accelerator (RFQ followed by a superconducting linac) and a rare ion production process delivering the beam either to a low energy experimental area or to the existing Ganil facility. From October this year, one ion source coupled with a first beam line section will be in test; then, the injector (ion and deuteron sources, RFQ) will be tested by the end of 2010 so the whole accelerator should be commissioned by the end of 2011; the first exotic beams being planned one year later. The accelerator control system design results from the collaboration between several institutes and Epics has been chosen as the basic framework. The paper therefore presents the main choices: MVME5500 CPUs, VME I/O boards, VxWorks, Siemens PLCs, Modbus field buses, EDM screens and Java applications, Linux PCs, use of a LabView/Epics gateway... Specific topics are the evaluation of the XAL environment, an Epics design to address the power supplies, an emittance measurement system, the development of a beam profiler interface and the investigation for a triggered acquisition system

The SPIRAL2 control system progress towards the commissioning phase

MOCOAAB03, http://accelconf.web.cern.ch/AccelConf/ICALEPCS2013/papers/mocoaab03.pdfInternational audienceThe commissioning of the first phase of the Spiral2 Radioactive Ion Beams facility at Ganil will soon start, so requiring the control system components to be delivered in time. Yet, parts of the system were validated during preliminary tests performed with ions and deuterons beams at low energy. The control system development results from the collaboration between Ganil, CEA-IRFU, CNRS-IPHC laboratories, using appropriate tools and approach. Based on Epics, the control system follows a classical architecture. At the lowest level, Modbus/TCP protocol is considered as a field bus. Then, equipment are handled by IOCs (soft or VME/VxWorks) with a software standardized interface between IOCs and clients applications on top. This last upper layer consists of Epics standard tools, CSS/BOY user interfaces within the socalled CSSop Spiral2 context suited for operation and, for machine tunings, high level applications implemented by Java programs developed within a Spiral2 framework derived from the open-Xal one. Databases are used for equipment data and alarms archiving, to configure equipment and to manage the machine lattice and beam settings. A global overview of the system is therefore here proposed

Shape optimization for the generalized Graetz problem

We apply shape optimization tools to the generalized Graetz problem which is a convection-diffusion equation. The problem boils down to the optimization of generalized eigen values on a two phases domain. Shape sensitivity analysis is performed with respect to the evolution of the interface between the fluid and solid phase. In particular physical settings, counterexamples where there is no optimal domains are exhibited. Numerical examples of optimal domains with different physical parameters and constraints are presented. Two different numerical methods (level-set and mesh-morphing) are show-cased and compared

A Small but Efficient Collaboration for the Spiral2 Control System Development

http://accelconf.web.cern.ch/AccelConf/ICALEPCS2013/papers/tucobab01.pdfThe Spiral2 radioactive ion beam facility to be commissioned in 2014 at Ganil (Caen) is built within international collaborations. This also concerns the control system development shared by three laboratories: Ganil has to coordinate the control and automated systems work packages, CEA/IRFU is in charge of the "injector" (sources and low energy beam lines) and the LLRF, CNRS/IPHC provides the emittancemeters and a beam diagnostics platform. Besides the technology Epics based, this collaboration, although being handled with a few people, nevertheless requires an appropriate and tight organization to reach the objectives given by the project. This contribution describes how, started in 2006, the collaboration for controls has been managed both from the technological point of view and the organizational one, taking into account not only the previous experience, technical background or skill of each partner, but also their existing working practices and "cultural" approaches. A first feedback comes from successful beam tests carried out at Saclay and Grenoble; a next challenge is the migration to operation, Ganil having to run Spiral2 as the other members are moving to new projects

Background Light in Potential Sites for the ANTARES Undersea Neutrino Telescope

The ANTARES collaboration has performed a series of {\em in situ} measurements to study the background light for a planned undersea neutrino telescope. Such background can be caused by $^{40}$K decays or by biological activity. We report on measurements at two sites in the Mediterranean Sea at depths of 2400~m and 2700~m, respectively. Three photomultiplier tubes were used to measure single counting rates and coincidence rates for pairs of tubes at various distances. The background rate is seen to consist of three components: a constant rate due to $^{40}$K decays, a continuum rate that varies on a time scale of several hours simultaneously over distances up to at least 40~m, and random bursts a few seconds long that are only correlated in time over distances of the order of a meter. A trigger requiring coincidences between nearby photomultiplier tubes should reduce the trigger rate for a neutrino telescope to a manageable level with only a small loss in efficiency.Comment: 18 pages, 8 figures, accepted for publication in Astroparticle Physic