The Matsumoto-Yor property and the structure of the Wishart distribution

This paper establishes a link between a generalized matrix Matsumoto-Yor (MY) property and the Wishart distribution. This link highlights certain conditional independence properties within blocks of the Wishart and leads to a new characterization of the Wishart distribution similar to the one recently obtained by Geiger and Heckerman but involving independences for only three pairs of block partitionings of the random matrix.In the process, we obtain two other main results. The first one is an extension of the MY independence property to random matrices of different dimensions. The second result is its converse. It extends previous characterizations of the matrix generalized inverse Gaussian and Wishart seen as a couple of distributions.We present two proofs for the generalized MY property. The first proof relies on a new version of Herz's identity for Bessel functions of matrix arguments. The second proof uses a representation of the MY property through the structure of the Wishart.     

CRYRING at the LSR at FLAIR

FLAIR will be the next-generation facility for physics with low-energy antiprotons, providing antiprotons at energies from tens of MeV down to rest. It will also offer unique possibilities for physics with highly charged ions at very low energies. The FLAIR facility will have two deceleration rings, the LSR which will decelerate antiprotons to 300 keV and the USR which will bring them down further to 20 keV. The LSR will consist of the present CRYRING at the Manne Siegbahn Laboratory. During the next few years, CRYRING will be modified with respect to injection and extraction, to allow injection of 30 MeV antiprotons and to provide it with both fast (single-turn) and slow (resonant) extraction at a variable energy. We here describe plans and preparations for the transfer of CRYRING to FLAIR, giving, in particular, an overview of new components for injection and extraction.     

Long alternating paths in bicolored point sets

Given n red and n blue points in convex position in the plane, we show that there exists a noncrossing alternating path of length . We disprove a conjecture of Erd?s by constructing an example without any such path of length greater than .     

The increment ratio statistic

We introduce a new statistic written as a sum of certain ratios of second-order increments of partial sums process of observations, which we call the increment ratio (IR) statistic. The IR statistic can be used for testing nonparametric hypotheses for d-integrated () behavior of time series X_t, including short memory (d=0), (stationary) long-memory and unit roots (d=1). If S_n behaves asymptotically as an (integrated) fractional Brownian motion with parameter , the IR statistic converges to a monotone function Λ(d) of as both the sample size N and the window parameter m increase so that N/m→∞. For Gaussian observations X_t, we obtain a rate of decay of the bias EIR-Λ(d) and a central limit theorem (N/m)^1/2(IR-EIR)→N(0,σ²(d)), in the region . Graphs of the functions Λ(d) and σ(d) are included. A simulation study shows that the IR test for short memory (d=0) against stationary long-memory alternatives has good size and power properties and is robust against changes in mean, slowly varying trends and nonstationarities. We apply this statistic to sequences of squares of returns on financial assets and obtain a nuanced picture of the presence of long-memory in asset price volatility.     

A Note on the Game Chromatic Index of Graphs

In this note we prove that the game chromatic index χ _g ^′(G) of a graph G of arboricity k is at most Δ + 3k − 1. This improves a bound obtained by Cai and Zhu [J. Graph Theory 36 (2001), 144–155] for k-degenerate graphs. Tomasz Bartnicki: Research of the first author is supported by a PhD grant from Polish Ministry of Science and Higher Education N201 2128 33. Received: November 1, 2006. Final version received: December 22, 2007.     

Feasibility of using ultrasound contrast agents to increase the size of thermal lesions induced by non-focused transducers: in vitro demonstration in tissue mimicking phantom

Miniature flat ultrasound transducers have shown to be effective for a large variety of thermal therapies, but the associated superficial heating implicates developing original strategies in order to extend therapeutic depth. The goal of the present paper is to use ultrasound contrast agents (UCA) to increase remote attenuation and heating. Theoretical simulations demonstrated that increasing attenuation from 0.27 to 0.8 Np/cm at 10 MHz beyond a distance of 18 mm from the transducer should result in longer thermal damages due to protein coagulation in a tissue mimicking phantom. Contrast agents (BR14, Bracco, Plan-les-Ouates, Switzerland) were embedded in thermo-sensitive gel and attenuations ranging from 0.27 to 1.33 Np/cm were measured at 10 MHz for concentrations of BR14 between 0 and 4.8%. Thermal damages were then induced in several gels, which had different layering configurations. Thermal damages, 12.8 mm in length, were obtained in homogeneous gels. When mixing contrast agents at a concentration of 3.2% beyond a first 18 mm-thick layer of homogeneous gel, the thermal damages reached 21.5 mm in length. This work demonstrated that contrast agents can be used for increasing attenuation remotely and extending therapeutic depth induced by a non-focused transducer. Additional work must be done in vivo in order to verify the remote-only distribution of bubbles and associated increase in attenuation.     

Link Homologies and the Refined Topological Vertex

We establish a direct map between refined topological vertex and sl(N) homological invariants of the of Hopf link, which include Khovanov-Rozansky homology as a special case. This relation provides an exact answer for homological invariants of the Hopf link, whose components are colored by arbitrary representations of sl(N). At present, the mathematical formulation of such homological invariants is available only for the fundamental representation (the Khovanov-Rozansky theory) and the relation with the refined topological vertex should be useful for categorizing quantum group invariants associated with other representations (R ₁, R ₂). Our result is a first direct verification of a series of conjectures which identifies link homologies with the Hilbert space of BPS states in the presence of branes, where the physical interpretation of gradings is in terms of charges of the branes ending on Lagrangian branes.     

GaN-nanowire-based dye-sensitized solar cells

GaN nanowires typically exhibit high electron mobility and excellent chemical stability. However, stability of GaN is detrimental for successful attachment of dye molecules and its application in dye-sensitized solar cells (DSSCs). Here we demonstrate DSSCs based on GaN/gallium oxide and GaN/TiO _x core–shell structures, and we show that coating of GaN nanowires with a TiO _x shell significantly increases dye adsorption and consequently photovoltaic performance. The best cells exhibited short circuit current density of 1.83 mA/cm² and power conversion efficiency of 0.44% under AM 1.5 simulated solar illumination.     

Structure–conductivity relations of simulated highly porous nanoparticle aggregate films

Electrical conductivity of porous films composed of nanoparticle aggregates is theoretically evaluated with respect to aggregate structure and film packing density. The aggregates are fractals composed of 5–30 primary particles with diameter of 10 nm. The film properties are derived from simulated boxes in the range of 0.5–1 μm. The electrical conductivity across the films of packing densities ranging from 0.01 to 0.15 was studied. All films prepared by an aerosol deposition technique, which uses nanoparticle aggregates, exhibited percolation behavior between planes parallel to the moving direction of the aggregates. They also followed the classical percolation relation for electrical conductivity while the critical percolation packing density depends on the aggregate size and structure used to build the films. Films using larger aggregates as building blocks have higher electrical conductance than smaller aggregates close to the percolation limit. For validation and supplementary information, two independent models are developed: one model follows the percolation theory to get detailed physical insights and another one computes the exact conductivities but at the cost of some details. This analysis gives new insights into the conduction backbone structures of these films with regard to neck contacts within an aggregate and grain boundary contacts between aggregates. The results shown are important for solar application of these films and especially for gas sensors where high sensitivity is often counteracted by low conductivity.     

Parity violation effects in hydrogen atom in forbidden magnetic-dipole transitions

General expressions for the probability of all strongly forbidden magnetic-dipole transitions between states njl and n′jl in the hydrogen atom and light hydrogen-like ions are derived in the lowest order in the parameter (αZ) in the form W _n′jl;njl ^(Ml) = D _n′n ^lj αm _e (αZ)¹⁰ (in relativistic units), where m _e is the electron mass, α is the fine-structure constant, Z is the nuclear charge, and the constants D _n′n ^lj are presented in an analytical form. Using these expressions, the dependence of the degree of parity violation on the principal quantum numbers n and n′ of the lower and upper states in the ns _1/2-n′s _1/2 and np _1/2-n′p _1/2 M1 transitions is systematically analyzed. The results obtained can be used in designing experiments on parity violation in the hydrogen atom.