Multiproduct Uniform Polar Quantizer

The aim of this paper is to reduce the complexity of the unrestricted uniform polar quantizer (UUPQ), keeping its high performances. To achieve this, in this paper we propose the multiproduct uniform polar quantizer (MUPQ), where several consecutive magnitude levels are joined in segments and within each segment the uniform product quantization is performed (i.e. all levels within one segments have the same number of phase levels). MUPQ is much simpler for realization than UUPQ, but it achieves similar performances as UUPQ. Since MUPQ has low complexity and achieves much better performances than the scalar uniform quantizer, it can be widely used instead of scalar uniform quantizers to improve performances, for any signal with the Gaussian distribution

Continuous-feed nanocasting process for the synthesis of bismuth nanowire composites

We present a novel, continuous-feed nanocasting procedure for the synthesis of bismuth nanowire structures embedded in the pores of a mesoporous silica template. The immobilization of a bismuth salt inside the silica template from a diluted metal salt solution yields a sufficiently high loading to obtain electrically conducting bulk nanowire composite samples after reduction and sintering the nanocomposite powders. Electrical resistivity measurements of sintered bismuth nanowires embedded in the silica template reveal size-quantization effects

5D fuzzball geometries and 4D polar states

We analyze the map between a class of `fuzzball' solutions in five dimensions and four-dimensional multicentered solutions under the 4D-5D connection, and interpret the resulting configurations in the framework of Denef and Moore. In five dimensions, we consider Kaluza-Klein monopole supertubes with circular profile which represent microstates of a small black ring. The resulting four-dimensional configurations are, in a suitable duality frame, polar states consisting of stacks of D6 and anti-D6 branes with flux. We argue that these four-dimensional configurations represent zero-entropy constituents of a 2-centered configuration where one of the centers is a small black hole. We also discuss how spectral flow transformations in five dimensions, leading to configurations with momentum, give rise to four-dimensional D6 anti-D6 polar configurations with different flux distributions at the centers.Comment: Latex, 36 pages, 2 figures. v2: typos corrected, references added, published versio

Minimal geodesics along volume preserving maps, through semi-discrete optimal transport

We introduce a numerical method for extracting minimal geodesics along the group of volume preserving maps, equipped with the L2 metric, which as observed by Arnold solve Euler's equations of inviscid incompressible fluids. The method relies on the generalized polar decomposition of Brenier, numerically implemented through semi-discrete optimal transport. It is robust enough to extract non-classical, multi-valued solutions of Euler's equations, for which the flow dimension is higher than the domain dimension, a striking and unavoidable consequence of this model. Our convergence results encompass this generalized model, and our numerical experiments illustrate it for the first time in two space dimensions.Comment: 21 pages, 9 figure

Four-Dimensional Avatars of Two-Dimensional RCFT

We investigate a 4D analog of 2D WZW theory. The theory turns out to have surprising finiteness properties and an infinite-dimensional current algebra symmetry. Some correlation functions are determined by this symmetry. One way to define the theory systematically proceeds by the quantization of moduli spaces of holomorphic vector bundles over algebraic surfaces. We outline how one can define vertex operators in the theory. Finally, we define four-dimensional ``conformal blocks'' and present an analog of the Verlinde formula.Comment: 28pp. harvmac l-mode, Talk presented at Strings 95 and at the Trieste Conference on S-Duality and Mirror Symmetry. References added, misprints corrected, improved discussion of the gauged actio