73,598,999 research outputs found

### Texture transitions in binary mixtures of 6OBAC with compounds of its homologous series

Recently we have observed in compounds of the 4,n-alkyloxybenzoic acid
series, with the homologous index n ranging from 6 to 9, a texture transition
in the nematic range which subdivides the nematic phase in two sub-phases
displaying different textures in polarised light analysis. To investigate a
persistence of texture transitions in nematic phases, we prepared binary
mixtures of 4,6-alkyloxybenzoic acid (6OBAC) with other members (7-,8-,9-,12-,
16OBAC) of its homologous series. Binary mixtures exhibit a broadening in the
temperature ranges of both smectic and nematic phases. A nematic temperature
range of 75 C is observed. In the nematic phase, in spite of the microscopic
disorder introduced by mixing two components, the polarised light optics
analysis of the liquid crystal cells reveals a texture transition. In the case
of the binary mixture of 6OBAC with 12OBAC and with 16OBAC, that is of
compounds with monomers of rather different lengths, the texture transition
temperature is not homogeneous in the cell, probably due to a local variation
in the relative concentrations of compounds.Comment: 13 pages, 9 figure

### Approximate Near Neighbors for General Symmetric Norms

We show that every symmetric normed space admits an efficient nearest
neighbor search data structure with doubly-logarithmic approximation.
Specifically, for every $n$, $d = n^{o(1)}$, and every $d$-dimensional
symmetric norm $\|\cdot\|$, there exists a data structure for
$\mathrm{poly}(\log \log n)$-approximate nearest neighbor search over
$\|\cdot\|$ for $n$-point datasets achieving $n^{o(1)}$ query time and
$n^{1+o(1)}$ space. The main technical ingredient of the algorithm is a
low-distortion embedding of a symmetric norm into a low-dimensional iterated
product of top-$k$ norms.
We also show that our techniques cannot be extended to general norms.Comment: 27 pages, 1 figur

### The gamma-ray burst monitor for Lobster-ISS

Lobster-ISS is an X-ray all-sky monitor experiment selected by ESA two years
ago for a Phase A study (now almost completed) for a future flight (2009)
aboard the Columbus Exposed Payload Facility of the International Space
Station. The main instrument, based on MCP optics with Lobster-eye geometry,
has an energy passband from 0.1 to 3.5 keV, an unprecedented daily sensitivity
of 2x10^{-12} erg cm^{-2}s$^{-1}, and it is capable to scan, during each orbit,
the entire sky with an angular resolution of 4--6 arcmin. This X-ray telescope
is flanked by a Gamma Ray Burst Monitor, with the minimum requirement of
recognizing true GRBs from other transient events. In this paper we describe
the GRBM. In addition to the minimum requirement, the instrument proposed is
capable to roughly localize GRBs which occur in the Lobster FOV (162x22.5
degrees) and to significantly extend the scientific capabilities of the main
instrument for the study of GRBs and X-ray transients. The combination of the
two instruments will allow an unprecedented spectral coverage (from 0.1 up to
300/700 keV) for a sensitive study of the GRB prompt emission in the passband
where GRBs and X-Ray Flashes emit most of their energy. The low-energy spectral
band (0.1-10 keV) is of key importance for the study of the GRB environment and
the search of transient absorption and emission features from GRBs, both goals
being crucial for unveiling the GRB phenomenon. The entire energy band of
Lobster-ISS is not covered by either the Swift satellite or other GRB missions
foreseen in the next decade.Comment: 6 pages, 4 figures. Paper presented at the COSPAR 2004 General
Assembly (Paris), accepted for publication in Advances in Space Research in
June 2005 and available on-line at the Journal site
(http://www.sciencedirect.com/science/journal/02731177), section "Articles in
press

### Stochastic velocity motions and processes with random time

The aim of this paper is to analyze a class of random motions which models
the motion of a particle on the real line with random velocity and subject to
the action of the friction. The speed randomly changes when a Poissonian event
occurs. We study the characteristic and the moment generating function of the
position reached by the particle at time $t>0$. We are able to derive the
explicit probability distributions in few cases for which discuss the
connections with the random flights. The moments are also widely analyzed.
For the random motions having an explicit density law, further interesting
probabilistic interpretations emerge if we deal with them varying up a random
time. Essentially, we consider two different type of random times, namely
Bessel and Gamma times, which contain, as particular cases, some important
probability distributions (e.g. Gaussian, Exponential). In particular, for the
random processes built by means of these compositions, we derive the
probability distributions fixed the number of Poisson events.
Some remarks on the possible extensions to the random motions in higher
spaces are proposed. We focus our attention on the persistent planar random
motion

### On a generalization of iterated and randomized rounding

We give a general method for rounding linear programs that combines the
commonly used iterated rounding and randomized rounding techniques. In
particular, we show that whenever iterated rounding can be applied to a problem
with some slack, there is a randomized procedure that returns an integral
solution that satisfies the guarantees of iterated rounding and also has
concentration properties. We use this to give new results for several classic
problems where iterated rounding has been useful

### Dietary patterns of school-age children in Scotland : association with socio-economic indicators, physical activity and obesity

Peer reviewedPublisher PD

### Improved Distributed Algorithms for Exact Shortest Paths

Computing shortest paths is one of the central problems in the theory of
distributed computing. For the last few years, substantial progress has been
made on the approximate single source shortest paths problem, culminating in an
algorithm of Becker et al. [DISC'17] which deterministically computes
$(1+o(1))$-approximate shortest paths in $\tilde O(D+\sqrt n)$ time, where $D$
is the hop-diameter of the graph. Up to logarithmic factors, this time
complexity is optimal, matching the lower bound of Elkin [STOC'04].
The question of exact shortest paths however saw no algorithmic progress for
decades, until the recent breakthrough of Elkin [STOC'17], which established a
sublinear-time algorithm for exact single source shortest paths on undirected
graphs. Shortly after, Huang et al. [FOCS'17] provided improved algorithms for
exact all pairs shortest paths problem on directed graphs.
In this paper, we present a new single-source shortest path algorithm with
complexity $\tilde O(n^{3/4}D^{1/4})$. For polylogarithmic $D$, this improves
on Elkin's $\tilde{O}(n^{5/6})$ bound and gets closer to the
$\tilde{\Omega}(n^{1/2})$ lower bound of Elkin [STOC'04]. For larger values of
$D$, we present an improved variant of our algorithm which achieves complexity
$\tilde{O}\left( n^{3/4+o(1)}+ \min\{ n^{3/4}D^{1/6},n^{6/7}\}+D\right)$, and
thus compares favorably with Elkin's bound of $\tilde{O}(n^{5/6} +
n^{2/3}D^{1/3} + D )$ in essentially the entire range of parameters. This
algorithm provides also a qualitative improvement, because it works for the
more challenging case of directed graphs (i.e., graphs where the two directions
of an edge can have different weights), constituting the first sublinear-time
algorithm for directed graphs. Our algorithm also extends to the case of exact
$\kappa$-source shortest paths...Comment: 26 page

### Constitutional Analogies in the International Legal System

This Article explores issues at the frontier of international law and constitutional law. It considers five key structural and systemic challenges that the international legal system now faces: (1) decentralization and disaggregation; (2) normative and institutional hierarchies; (3) compliance and enforcement; (4) exit and escape; and (5) democracy and legitimacy. Each of these issues raises questions of governance, institutional design, and allocation of authority paralleling the questions that domestic legal systems have answered in constitutional terms. For each of these issues, I survey the international legal landscape and consider the salience of potential analogies to domestic constitutions, drawing upon and extending the writings of international legal scholars and international relations theorists. I also offer some preliminary thoughts about why some treaties and institutions, but not others, more readily lend themselves to analysis in constitutional terms. And I distinguish those legal and political issues that may generate useful insights for scholars studying the growing intersections of international and constitutional law from other areas that may be more resistant to constitutional analogies

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