Random Euclidean embeddings in spaces of bounded volume ratio

Let $\text{(}\text{R}{}^{\mathrm{N}}\text{,6·6)}$ be the space $\text{R}{}^{\mathrm{N}}$ equipped with a norm 6·6 whose unit ball has a bounded volume ratio with respect to the Euclidean unit ball. Let Γ be any random N×n matrix with N>n, whose entries are independent random variables satisfying some moment assumptions. We show that with high probability Γ is a good isomorphism from the n-dimensional Euclidean space $\text{(}\text{R}{}^{\mathrm{n}}\text{,|·|)}$ onto its image in $\text{(}\text{R}{}^{\mathrm{N}}\text{,6·6)}$: there exist α,β>0 such that for all $\text{x∈}\text{R}{}^{\mathrm{n}}$, $\text{α}\text{N}\text{|x|?6Γx6?β}\text{N}\text{|x|}$. This solves a conjecture of Schechtman on random embeddings of ?₂ⁿ into ?₁^N. To cite this article: A. Litvak et al., C. R. Acad. Sci. Paris, Ser. I 339 (2004).     

Immersions with fractal set of points of zero Gauss-Kronecker curvature

We construct, for any good Cantor set F of S ^n-1, an immersion of the sphere S ⁿ with set of points of zero Gauss-Kronecker curvature equal to F × D ¹, where D ¹ is the 1-dimensional disk. In particular these examples show that the theorem of Matheus-Oliveira strictly extends two results by do Carmo-Elbert and Barbosa-Fukuoka-Mercuri.To professor João Lucas Barbosa, in occasion of his 60th birthday. Supported by CNPq/Brazil. Supported by Faperj/Brazil.     

On almost hyperHermitian structures on Riemannian manifolds and tangent bundles

Some results concerning almost hyperHermitian structures are considered, using the notions of the canonical connection and the second fundamental tensor field h of a structure on a Riemannian manifold which were introduced by the second author. With the help of any metric connection on an almost Hermitian manifold M an almost hyperHermitian structure can be constructed in the defined way on the tangent bundle TM. A similar construction was considered in [6], [7]. This structure includes two basic anticommutative almost Hermitian structures for which the second fundamental tensor fields h ¹ and h ² are computed. It allows us to consider various classes of almost hyperHermitian structures on TM. In particular, there exists an infinite-dimensional set of almost hyperHermitian structures on TTM where M is any Riemannian manifold.     

Noise spectroscopy and interlayer phase coherence in bilayer quantum Hall systems

Bilayer quantum Hall systems develop strong interlayer phase coherence when the distance between layers is comparable to the typical distance between electrons within a layer. The phase-coherent state has until now been investigated primarily via transport measurements. We argue here that interlayer current and charge-imbalance noise studies in these systems will be able to address some of the key experimental questions. We show that the characteristic frequency of current noise is that of the zero wave vector collective mode, which is sensitive to the degree of order in the system. Local electric potential noise measured in a plane above the bilayer system, on the other hand, is sensitive to finite-wave-vector collective modes and, hence, to the soft-magnetoroton picture of the order-disorder phase transition.     

Distribution of the local density of states, reflection coefficient, and Wigner delay time in absorbing ergodic systems at the point of chiral symmetry

Employing the chiral Gaussian unitary ensemble of random matrices, we calculate the probability distribution of the local density of states for zero-dimensional ("quantum chaotic") two-sublattice systems at the point of chiral symmetry E=0 and in the presence of uniform absorption. The obtained result can be used to find the distributions of the reflection coefficient and of the Wigner time delay for such systems.     

Affine registration: a comparison of several programs

Several registration programs with an affine model for the displacement field were tested on various 2D and 3D MRI of the same modality. The following programs were considered: AIR 3.0 (Woods, J. Comp. Assist. Tomogr, 22(1): 139-152, 1998), COCGV (Ostuni, JMRI, 7(2): 410-415, 1997), FLIRT (Jenkinson, Med. Image Analysis, 5(2): 143-156, 2001), Intramodal Registration (Thevenaz, IEEE Trans. Image Proc., 7(1): 27-41, 1998), SPM (Friston, Human Brain Mapping, 2: 165-189, 1995), and Patch Algorithm (Zhilkin, MRI 18(9): 1143-1150, 2000). Although some of these programs can perform multimodal registration, none was used in such a mode. This paper attempts a fair comparison of the performance of the Patch Algorithm with other programs. However, different settings of the programs' parameters may further improve the quality of the registration and/or change execution speed. The registered images, the CPU time required to perform the registration, and the error between the registered and reference images, are presented. Most of the programs give comparable accuracies of registration, but their execution times vary considerably. In general the AIR and Patch Algorithm require the least time. The Patch Algorithm can be easily parallelizable on a multi-processor computer.     

The three-electron heteropoly blue [P6Mo18O73]11- with a basket-shaped skeleton

The novel basket-shaped three-electron-reduced heteropoly blue [H2dmpip]5[K [subset or is implied by] P6Mo18O73] was prepared and characterized; it shows reversible one-electron redox properties.     

Apparent clustering of intermediate-redshift galaxies as a probe of dark energy

We show that the apparent redshift-space clustering of galaxies in the redshift range of 0.2-0.4 provides surprisingly useful constraints on dark-energy components in the Universe, because of the right balance between the density of objects and the survey depth. We apply Fisher matrix analysis to the luminous red galaxies in the Sloan Digital Sky Survey, as a concrete example. Possible degeneracies in the evolution of the equation of state and the other cosmological parameters are clarified.     

Fluorescence tomography with simulated data based on the equation of radiative transfer

The quantification of a nonuniform quantum yield or fluorophore absorption distribution is of major interest in molecular imaging of biological tissue. We introduce what is believed to be the first fluorescence image reconstruction algorithm based on the equation of radiative transfer that recovers the spatial distribution of light-emitting fluorophores inside a highly scattering medium from measurements made on the surface of the medium. We obtain images of either the quantum yield or the fluorophore absorption.     

Edge effects on the order and freezing of a 2D array of block copolymer spheres

The order in a single layer of spherical domains of a block copolymer melt is investigated as a function of distance from the edges of the 15 microm wide, 30 nm deep wells that confine it along a substrate. At 255 degrees C the edge induces the formation of a hexatic phase whose orientational and translational order decreases slowly away from the edge until in the center of the well the block copolymer spheres have liquidlike order.