Move ordering and communities in complex networks describing the game of go

We analyze the game of go from the point of view of complex networks. We construct three different directed networks of increasing complexity, defining nodes as local patterns on plaquettes of increasing sizes, and links as actual successions of these patterns in databases of real games. We discuss the peculiarities of these networks compared to other types of networks. We explore the ranking vectors and community structure of the networks and show that this approach enables to extract groups of moves with common strategic properties. We also investigate different networks built from games with players of different levels or from different phases of the game. We discuss how the study of the community structure of these networks may help to improve the computer simulations of the game. More generally, we believe such studies may help to improve the understanding of human decision process.Comment: 14 pages, 21 figure

Eigenfunction entropy and spectral compressibility for critical random matrix ensembles

Based on numerical and perturbation series arguments we conjecture that for certain critical random matrix models the information dimension of eigenfunctions D_1 and the spectral compressibility chi are related by the simple equation chi+D_1/d=1, where d is the system dimensionality.Comment: 4 pages, 3 figure

Etude d'outils pour la conception d'un électro-aimant

rapport Janus, responsable de stage : H. Fonvieill

Eigenmodes of Decay and Discrete Fragmentation Processes

Linear rate equations are used to describe the cascading decay of an initial heavy cluster into fragments. This representation is based upon a triangular matrix of transition rates. We expand the state vector of mass multiplicities, which describes the process, into the biorthonormal basis of eigenmodes provided by the triangular matrix. When the transition rates have a scaling property in terms of mass ratios at binary fragmentation vertices, we obtain solvable models with explicit mathematical properties for the eigenmodes. A suitable continuous limit provides an interpolation between the solvable models. It gives a general relationship between the decay products and the elementary transition rates.Comment: 6 pages, plain TEX, 2 figures available from the author

Phenomenological discussion of B→PVB\to P V decays in QCD improved factorization approach

Trying a global fit of the experimental branching ratios and CP-asymmetries of the charmless $B\to PV$ decays according to QCD factorization, we find it impossible to reach a satisfactory agreement, the confidence level (CL) of the best fit is smaller than .1 %. This failure reflects the difficulty to accommodate several large experimental branching ratios of the strange channels. Furthermore, experiment was not able to exclude a large direct CP asymmetry in $\bar {B}^0\to\rho^+ \pi^-$, which is predicted very small by QCD factorization. Proposing a fit with QCD factorization complemented by a charming-penguin inspired model we reach a best fit which is not excluded by experiment (CL of about 8 %) but is not fully convincing. These negative results must be tempered by the remark that some of the experimental data used are recent and might still evolve significantly.Comment: 8 pages, 2 figures (requires epsfig, psfrag),talk presented at the XXXVIIIth Rencontres de Moriond: Electroweak Interactions and Unified Theories,Les Arcs, France, March 15-22, 2003. To be published in the Proceeding

Schr\"odinger equations for the square root density of an eigenmixture and % the square root of an eigendensity spin matrix

We generalize a "one eigenstate" theorem of Levy, Perdew and Sahni (LPS) to the case of densities coming from eigenmixture density operators. The generalization is of a special interest for the radial density functional theory (RDFT) for nuclei, a consequence of the rotational invariance of the nuclear Hamiltonian; when nuclear ground states (GSs) have a finite spin, the RDFT uses eigenmixture density operators to simplify predictions of GS energies into one-dimensional, radial calculations. We also study Schr\"odinger equations governing spin eigendensity matrices.Comment: 8 page

MRI/TRUS data fusion for brachytherapy

BACKGROUND: Prostate brachytherapy consists in placing radioactive seeds for tumour destruction under transrectal ultrasound imaging (TRUS) control. It requires prostate delineation from the images for dose planning. Because ultrasound imaging is patient- and operator-dependent, we have proposed to fuse MRI data to TRUS data to make image processing more reliable. The technical accuracy of this approach has already been evaluated. METHODS: We present work in progress concerning the evaluation of the approach from the dosimetry viewpoint. The objective is to determine what impact this system may have on the treatment of the patient. Dose planning is performed from initial TRUS prostate contours and evaluated on contours modified by data fusion. RESULTS: For the eight patients included, we demonstrate that TRUS prostate volume is most often underestimated and that dose is overestimated in a correlated way. However, dose constraints are still verified for those eight patients. CONCLUSIONS: This confirms our initial hypothesis

Crossed Module Bundle Gerbes; Classification, String Group and Differential Geometry

We discuss nonabelian bundle gerbes and their differential geometry using simplicial methods. Associated to any crossed module there is a simplicial group NC, the nerve of the 1-category defined by the crossed module and its geometric realization |NC|. Equivalence classes of principal bundles with structure group |NC| are shown to be one-to-one with stable equivalence classes of what we call crossed module gerbes bundle gerbes. We can also associate to a crossed module a 2-category C'. Then there are two equivalent ways how to view classifying spaces of NC-bundles and hence of |NC|-bundles and crossed module bundle gerbes. We can either apply the W-construction to NC or take the nerve of the 2-category C'. We discuss the string group and string structures from this point of view. Also a simplicial principal bundle can be equipped with a simplicial connection and a B-field. It is shown how in the case of a simplicial principal NC-bundle these simplicial objects give the bundle gerbe connection and the bundle gerbe B-field

Intermediate statistics in quantum maps

We present a one-parameter family of quantum maps whose spectral statistics are of the same intermediate type as observed in polygonal quantum billiards. Our central result is the evaluation of the spectral two-point correlation form factor at small argument, which in turn yields the asymptotic level compressibility for macroscopic correlation lengths