1,601 research outputs found
Local Search in Unstructured Networks
We review a number of message-passing algorithms that can be used to search
through power-law networks. Most of these algorithms are meant to be
improvements for peer-to-peer file sharing systems, and some may also shed some
light on how unstructured social networks with certain topologies might
function relatively efficiently with local information. Like the networks that
they are designed for, these algorithms are completely decentralized, and they
exploit the power-law link distribution in the node degree. We demonstrate that
some of these search algorithms can work well on real Gnutella networks, scale
sub-linearly with the number of nodes, and may help reduce the network search
traffic that tends to cripple such networks.Comment: v2 includes minor revisions: corrections to Fig. 8's caption and
references. 23 pages, 10 figures, a review of local search strategies in
unstructured networks, a contribution to `Handbook of Graphs and Networks:
From the Genome to the Internet', eds. S. Bornholdt and H.G. Schuster
(Wiley-VCH, Berlin, 2002), to be publishe
Spectral Dynamics of the Velocity Gradient Field in Restricted Flows
We study the velocity gradients of the fundamental Eulerian equation,
, which shows up in different contexts
dictated by the different modeling of 's. To this end we utilize a basic
description for the spectral dynamics of , expressed in terms of the
(possibly complex) eigenvalues, , which are shown to
be governed by the Ricatti-like equation .
We address the question of the time regularity of four prototype models
associated with different forcing . Using the spectral dynamics as our
essential tool in these investigations, we obtain a simple form of a critical
threshold for the linear damping model and we identify the 2D vanishing
viscosity limit for the viscous irrotational dusty medium model. Moreover, for
the -dimensional restricted Euler equations we obtain global
invariants, interesting for their own sake, which enable us to precisely
characterize the local topology at breakdown time, extending previous studies
in the -dimensional case. Finally, as a forth model we introduce the
-dimensional restricted Euler-Poisson (REP)system, identifying a set of
global invariants, which in turn yield (i) sufficient conditions for
finite time breakdown, and (ii) characterization of a large class of
2-dimensional initial configurations leading to global smooth solutions.
Consequently, the 2D restricted Euler-Poisson equations are shown to admit a
critical threshold
Fastest mixing Markov chain on graphs with symmetries
We show how to exploit symmetries of a graph to efficiently compute the
fastest mixing Markov chain on the graph (i.e., find the transition
probabilities on the edges to minimize the second-largest eigenvalue modulus of
the transition probability matrix). Exploiting symmetry can lead to significant
reduction in both the number of variables and the size of matrices in the
corresponding semidefinite program, thus enable numerical solution of
large-scale instances that are otherwise computationally infeasible. We obtain
analytic or semi-analytic results for particular classes of graphs, such as
edge-transitive and distance-transitive graphs. We describe two general
approaches for symmetry exploitation, based on orbit theory and
block-diagonalization, respectively. We also establish the connection between
these two approaches.Comment: 39 pages, 15 figure
LSST: from Science Drivers to Reference Design and Anticipated Data Products
(Abridged) We describe here the most ambitious survey currently planned in
the optical, the Large Synoptic Survey Telescope (LSST). A vast array of
science will be enabled by a single wide-deep-fast sky survey, and LSST will
have unique survey capability in the faint time domain. The LSST design is
driven by four main science themes: probing dark energy and dark matter, taking
an inventory of the Solar System, exploring the transient optical sky, and
mapping the Milky Way. LSST will be a wide-field ground-based system sited at
Cerro Pach\'{o}n in northern Chile. The telescope will have an 8.4 m (6.5 m
effective) primary mirror, a 9.6 deg field of view, and a 3.2 Gigapixel
camera. The standard observing sequence will consist of pairs of 15-second
exposures in a given field, with two such visits in each pointing in a given
night. With these repeats, the LSST system is capable of imaging about 10,000
square degrees of sky in a single filter in three nights. The typical 5
point-source depth in a single visit in will be (AB). The
project is in the construction phase and will begin regular survey operations
by 2022. The survey area will be contained within 30,000 deg with
, and will be imaged multiple times in six bands, ,
covering the wavelength range 320--1050 nm. About 90\% of the observing time
will be devoted to a deep-wide-fast survey mode which will uniformly observe a
18,000 deg region about 800 times (summed over all six bands) during the
anticipated 10 years of operations, and yield a coadded map to . The
remaining 10\% of the observing time will be allocated to projects such as a
Very Deep and Fast time domain survey. The goal is to make LSST data products,
including a relational database of about 32 trillion observations of 40 billion
objects, available to the public and scientists around the world.Comment: 57 pages, 32 color figures, version with high-resolution figures
available from https://www.lsst.org/overvie
Dynamical control of qubit coherence: Random versus deterministic schemes
We revisit the problem of switching off unwanted phase evolution and
decoherence in a single two-state quantum system in the light of recent results
on random dynamical decoupling methods [L. Viola and E. Knill, Phys. Rev. Lett.
{\bf 94}, 060502 (2005)]. A systematic comparison with standard cyclic
decoupling is effected for a variety of dynamical regimes, including the case
of both semiclassical and fully quantum decoherence models. In particular,
exact analytical expressions are derived for randomized control of decoherence
from a bosonic environment. We investigate quantitatively control protocols
based on purely deterministic, purely random, as well as hybrid design, and
identify their relative merits and weaknesses at improving system performance.
We find that for time-independent systems, hybrid protocols tend to perform
better than pure random and may improve over standard asymmetric schemes,
whereas random protocols can be considerably more stable against fluctuations
in the system parameters. Beside shedding light on the physical requirements
underlying randomized control, our analysis further demonstrates the potential
for explicit control settings where the latter may significantly improve over
conventional schemes.Comment: 21 pages, 15 figures, to appear in Physical Review A, 72 (2005
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