Spectral properties of a class of random walks on locally finite groups

We study some spectral properties of random walks on infinite countable amenable groups with an emphasis on locally finite groups, e.g. the infinite symmetric group. On locally finite groups, the random walks under consideration are driven by infinite divisible distributions. This allows us to embed our random walks into continuous time L\'evy processes whose heat kernels have shapes similar to the ones of alpha-stable processes. We obtain examples of fast/slow decays of return probabilities, a recurrence criterion, exact values and estimates of isospectral profiles and spectral distributions, formulae and estimates for the escape rates and for heat kernels.Comment: 62 pages, 1 figure, 2 table

Guidelines for a Dynamic Ontology - Integrating Tools of Evolution and Versioning in Ontology

Ontologies are built on systems that conceptually evolve over time. In addition, techniques and languages for building ontologies evolve too. This has led to numerous studies in the field of ontology versioning and ontology evolution. This paper presents a new way to manage the lifecycle of an ontology incorporating both versioning tools and evolution process. This solution, called VersionGraph, is integrated in the source ontology since its creation in order to make it possible to evolve and to be versioned. Change management is strongly related to the model in which the ontology is represented. Therefore, we focus on the OWL language in order to take into account the impact of the changes on the logical consistency of the ontology like specified in OWL DL

Connected Lie groups and property RD

For a locally compact group, property RD gives a control on the convolution norm of any compactly supported measure in terms of the $L^2$-norm of its density and the diameter of its support. We give a complete classification of those Lie groups with property RD.Comment: 29 page

Bounded characteristic classes and flat bundles

Let G be a connected Lie group, G^d the underlying discrete group, and BG, BG^d their classifying spaces. Let R denote the radical of G. We show that all classes in the image of the canonical map in cohomology H^*(BG,R)->H^*(BG^d,R) are bounded if and only if the derived group [R,R] is simply connected. We also give equivalent conditions in terms of stable commutator length and distortion.Comment: 12 pages, no figur

Six-axis decentralized control design for spacecraft formation flying mission

This contribution addresses the control design for the three-spacecraft formation flying interferometry mission Pegase. The operational mode considered is the high-precision nulling phase. The control design has as major objective the minimization of the variance of the controlled outputs, e.g. the optical path difference. The payload performance demands are shown to be fulfilled in spite of orbital disturbances, solar radiation pressure as well as sensor and actuator noise. Furthermore, a novel iterative algorithm is proposed, capable of designing decentralized H2-suboptimal controllers. These controllers consist of a set of individual closed loops on board the different spacecraft which only use locally available measurements, forces and torques. This approach reduces communication bandwidth and enhances robustness concerning faulty communication links. Finally, the performance loss due to decentralization is investigated