5,666 research outputs found
Perturbative analysis of generally nonlocal spatial optical solitons
In analogy to a perturbed harmonic oscillator, we calculate the fundamental
and some other higher order soliton solutions of the nonlocal nonlinear
Schroedinger equation (NNLSE) in the second approximation in the generally
nonlocal case. Comparing with numerical simulations we show that soliton
solutions in the 2nd approximation can describe the generally nonlocal soliton
states of the NNLSE more exactly than that in the zeroth approximation. We show
that for the nonlocal case of an exponential-decay type nonlocal response the
Gaussian-function-like soliton solutions can't describe the nonlocal soliton
states exactly even in the strongly nonlocal case. The properties of such
nonlocal solitons are investigated. In the strongly nonlocal limit, the
soliton's power and phase constant are both in inverse proportion to the 4th
power of its beam width for the nonlocal case of a Gaussian function type
nonlocal response, and are both in inverse proportion to the 3th power of its
beam width for the nonlocal case of an exponential-decay type nonlocal
response.Comment: 13 pages, 16 figures, accepted by Phys. Rev.
Optimal sequencing of a set of positive numbers with the variance of the sequence's partial sums maximized
We consider the problem of sequencing a set of positive numbers. We try to
find the optimal sequence to maximize the variance of its partial sums. The
optimal sequence is shown to have a beautiful structure. It is interesting to
note that the symmetric problem which aims at minimizing the variance of the
same partial sums is proved to be NP-complete in the literature.Comment: 12 pages;Accepted for publication in Optimization Lette
Lack of sufficiently strong informative features limits the potential of gene expression analysis as predictive tool for many clinical classification problems
<p>Abstract</p> <p>Background</p> <p>Our goal was to examine how various aspects of a gene signature influence the success of developing multi-gene prediction models. We inserted gene signatures into three real data sets by altering the expression level of existing probe sets. We varied the number of probe sets perturbed (signature size), the fold increase of mean probe set expression in perturbed compared to unperturbed data (signature strength) and the number of samples perturbed. Prediction models were trained to identify which cases had been perturbed. Performance was estimated using Monte-Carlo cross validation.</p> <p>Results</p> <p>Signature strength had the greatest influence on predictor performance. It was possible to develop almost perfect predictors with as few as 10 features if the fold difference in mean expression values were > 2 even when the spiked samples represented 10% of all samples. We also assessed the gene signature set size and strength for 9 real clinical prediction problems in six different breast cancer data sets.</p> <p>Conclusions</p> <p>We found sufficiently large and strong predictive signatures only for distinguishing ER-positive from ER-negative cancers, there were no strong signatures for more subtle prediction problems. Current statistical methods efficiently identify highly informative features in gene expression data if such features exist and accurate models can be built with as few as 10 highly informative features. Features can be considered highly informative if at least 2-fold expression difference exists between comparison groups but such features do not appear to be common for many clinically relevant prediction problems in human data sets.</p
Coexistence of hexatic and isotropic phases in two-dimensional Yukawa systems
We have performed Brownian dynamics simulations on melting of two-dimensional
colloidal crystal in which particles interact with Yukawa potential. The pair
correlation function and bond-orientational correlation function was calculated
in the Yukawa system. An algebraic decay of the bond orientational correlation
function was observed. By ruling out the coexistence region, only a unstable
hexatic phase was found in the Yukawa systems. But our work shows that the
melting of the Yukawa systems is a two-stage melting not consist with the KTHNY
theory and the isotropic liquid and the hexatic phase coexistence region was
found. Also we have studied point defects in two-dimensional Yukawa systems.Comment: 9 pages, 8 figures. any comments are welcom
A genuine maximally seven-qubit entangled state
Contrary to A.Borras et al.'s [1] conjecture, a genuine maximally seven-qubit
entangled state is presented. We find a seven-qubit state whose marginal
density matrices for subsystems of 1,2- qubits are all completely mixed and for
subsystems of 3-qubits is almost completely mixed
Attacking practical quantum key distribution system with wavelength dependent beam splitter and multi-wavelength sources
Unconditional security of quantum key distribution protocol can be guaranteed
by the basic property of quantum mechanics. Unfortunately, the practical
quantum key distribution system always have some imperfections, and the
practical system may be attacked if the imperfection can be controlled by the
eavesdropper Eve. Applying the fatal security loophole introduced by the
imperfect beam splitter's wavelength dependent optical property, we propose
wavelength-dependent attacking model, which can be applied to almost all
practical quantum key distribution systems with the passive state modulation
and photon state detection after the practical beam splitter. Utilizing our
attacking model, we experimentally demonstrate the attacking system based on
practical polarization encoding quantum key distribution system with almost
100% success probability. Our result demonstrate that all practical devices
require tightened security inspection for avoiding side channel attacks in
practical quantum key distribution experimental realizations
Active optical clock based on four-level quantum system
Active optical clock, a new conception of atomic clock, has been proposed
recently. In this report, we propose a scheme of active optical clock based on
four-level quantum system. The final accuracy and stability of two-level
quantum system are limited by second-order Doppler shift of thermal atomic
beam. To three-level quantum system, they are mainly limited by light shift of
pumping laser field. These limitations can be avoided effectively by applying
the scheme proposed here. Rubidium atom four-level quantum system, as a typical
example, is discussed in this paper. The population inversion between
and states can be built up at a time scale of s.
With the mechanism of active optical clock, in which the cavity mode linewidth
is much wider than that of the laser gain profile, it can output a laser with
quantum-limited linewidth narrower than 1 Hz in theory. An experimental
configuration is designed to realize this active optical clock.Comment: 5 page
Bridgeness: A Local Index on Edge Significance in Maintaining Global Connectivity
Edges in a network can be divided into two kinds according to their different
roles: some enhance the locality like the ones inside a cluster while others
contribute to the global connectivity like the ones connecting two clusters. A
recent study by Onnela et al uncovered the weak ties effects in mobile
communication. In this article, we provide complementary results on document
networks, that is, the edges connecting less similar nodes in content are more
significant in maintaining the global connectivity. We propose an index named
bridgeness to quantify the edge significance in maintaining connectivity, which
only depends on local information of network topology. We compare the
bridgeness with content similarity and some other structural indices according
to an edge percolation process. Experimental results on document networks show
that the bridgeness outperforms content similarity in characterizing the edge
significance. Furthermore, extensive numerical results on disparate networks
indicate that the bridgeness is also better than some well-known indices on
edge significance, including the Jaccard coefficient, degree product and
betweenness centrality.Comment: 10 pages, 4 figures, 1 tabl
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