262 research outputs found
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
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
Amenability of groups and -sets
This text surveys classical and recent results in the field of amenability of
groups, from a combinatorial standpoint. It has served as the support of
courses at the University of G\"ottingen and the \'Ecole Normale Sup\'erieure.
The goals of the text are (1) to be as self-contained as possible, so as to
serve as a good introduction for newcomers to the field; (2) to stress the use
of combinatorial tools, in collaboration with functional analysis, probability
etc., with discrete groups in focus; (3) to consider from the beginning the
more general notion of amenable actions; (4) to describe recent classes of
examples, and in particular groups acting on Cantor sets and topological full
groups
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