Maximum pseudo-likelihood estimator for nearest-neighbours Gibbs point processes

This paper is devoted to the estimation of a vector parametrizing an energy function associated to some "Nearest-Neighbours" Gibbs point process, via the pseudo-likelihood method. We present some convergence results concerning this estimator, that is strong consistency and asymptotic normality, when only a single realization is observed. Sufficient conditions are expressed in terms of the local energy function and are verified on some examples.Comment: 29 pages - 2 figure

On uniqueness of the q-state Potts model on a self-dual family of graphs

This paper deals with the location of the complex zeros of the Tutte polynomial for a class of self-dual graphs. For this class of graphs, as the form of the eigenvalues is known, the regions of the complex plane can be focused on the sets where there is only one dominant eigenvalue in particular containing the positive half plane. Thus, in these regions, the analyticity of the pressure can be derived easily. Next, some examples of graphs with their Tutte polynomial having a few number of eigenvalues are given. The cases of the strip of triangles with a double edge, the wheel and the cycle with an edge having a high order of multiplicity are presented. In particular, for this last example, we remark that the well known conjecture of Chen et al. is false in the finite case

Continuum Percolation in the Relative Neighborhood Graph

In the present study, we establish the existence of nontrivial site percolation threshold in the Relative Neighborhood Graph (RNG) for Poisson stationary point process with unit intensity in the plane

Maximum pseudolikelihood estimator for exponential family models of marked Gibbs point processes

This paper is devoted to the estimation of a vector $\bm {\theta}$ parametrizing an energy function of a Gibbs point process, via the maximum pseudolikelihood method. Strong consistency and asymptotic normality results of this estimator depending on a single realization are presented. In the framework of exponential family models, sufficient conditions are expressed in terms of the local energy function and are verified on a wide variety of examples.Comment: Published in at http://dx.doi.org/10.1214/07-EJS160 the Electronic Journal of Statistics (http://www.i-journals.org/ejs/) by the Institute of Mathematical Statistics (http://www.imstat.org

Continuum percolation in proximity graphs

14 pagesWe establish a sufficient condition to obtain continuum percolation on a class of proximity graphs when their vertices are distributed under a stationary Poisson point process with unit intensity in the plane. We apply this result on a family of graphs which generalizes $\beta$-skeleton graphs

Une approche récursive pour construire des polynômes à racines réelles

In the present study, we propose necessary and sufficient assumptions on the coefficients in order to only get distinct real roots of polynomials.Dans cette étude, nous donnons des conditions nécessaires et suffisantes sur les coefficients d'un polynôme de manière à ce que ce denier n'ait que des racines réelles

R-local Delaunay inhibition model

Let us consider the local specification system of Gibbs point process with inhib ition pairwise interaction acting on some Delaunay subgraph specifically not con taining the edges of Delaunay triangles with circumscribed circle of radius grea ter than some fixed positive real value $R$. Even if we think that there exists at least a stationary Gibbs state associated to such system, we do not know yet how to prove it mainly due to some uncontrolled "negative" contribution in the expression of the local energy needed to insert any number of points in some large enough empty region of the space. This is solved by introducing some subgraph, called the $R$-local Delaunay graph, which is a slight but tailored modification of the previous one. This kind of model does not inherit the local stability property but satisfies s ome new extension called $R$-local stability. This weakened property combined with the local property provides the existence o f Gibbs state.Comment: soumis \`{a} Journal of Statistical Physics 27 page

Superconducting routing platform for large-scale integration of quantum technologies

To reach large-scale quantum computing, three-dimensional integration of scalable qubit arrays and their control electronics in multi-chip assemblies is promising. Within these assemblies, the use of superconducting interconnections, as routing layers, offers interesting perspective in terms of (1) thermal management to protect the qubits from control electronics self-heating, (2) passive device performance with significant increase of quality factors and (3) density rise of low and high frequency signals thanks to minimal dispersion. We report on the fabrication, using 200 mm silicon wafer technologies, of a multi-layer routing platform designed for the hybridization of spin qubit and control electronics chips. A routing level couples the qubits and the control circuits through one layer of Al0.995Cu0.005 and superconducting layers of TiN, Nb or NbN, connected between them by W-based vias. Wafer-level parametric tests at 300 K validate the yield of these technologies and low temperature electrical measurements in cryostat are used to extract the superconducting properties of the routing layers. Preliminary low temperature radio-frequency characterizations of superconducting passive elements, embedded in these routing levels, are presented

Discussion of "modern statistics of spatial point processes"

International audienceThe paper 'Modern statistics for spatial point processes' by Jesper Møller and Rasmus P. Waagepetersen is based on a special invited lecture given by the authors at the 21st Nordic Conference on Mathematical Statistics, held at Rebild, Denmark, in June 2006. At the conference, Antti Penttinen and Eva B. Vedel Jensen were invited to discuss the paper. We here present the comments from the two invited discussants and from a number of other scholars, as well as the authors' responses to these comments

Estimation d'interactions et étude symptotique pour les processus ponctuels de Gibbs

* INRA Centre de Recherche d'Avignon, Unité de Biométrie, Domaine St Paul, Site Agroparc, 84914 Avignon cedex 9 Diffusion du document : INRA Centre de Recherche d'Avignon, Unité de Biométrie, Domaine St Paul, Site Agroparc, 84914 Avignon cedex 9 Diplôme : Dr. d'Universit