21,651 research outputs found
Quantum Energy of Fuzzy Sphere: Gaussian Variational Method
The matrix model with mass term has a nontrivially classical solution which
is known to represent a noncommutative fuzzy sphere. The fuzzy sphere has a
lower energy then that of the trivial solution. In this letter we investigate
the quantum correction of the energy of the fuzzy sphere by using the Gaussian
variational technique, in contrast to the other studying in which only the
small fluctuation was considered. Our result, which only considering the boson
part, shows that the quantum correction does not change the stability of the
fuzzy sphere.Comment: Short summary of the Master-thesi
A numerical simulation of the backward Raman amplifying in plasma
This paper describe a numerical simulation method for the interaction between
laser pulses and low density plasmas based on hydrodynamic approximation. We
investigate Backward Raman Amplifying (BRA) experiments and their variants. The
numerical results are in good agreement with experiments.Comment: 11 pages, 4 figur
Joint Frequency Estimation with Two Sub-Nyquist Sampling Sequences
In many applications of frequency estimation, the frequencies of the signals
are so high that the data sampled at Nyquist rate are hard to acquire due to
hardware limitation. In this paper, we propose a novel method based on subspace
techniques to estimate the frequencies by using two sub-Nyquist sample
sequences, provided that the two under-sampled ratios are relatively prime
integers. We analyze the impact of under-sampling and expand the estimated
frequencies which suffer from aliasing. Through jointing the results estimated
from these two sequences, the frequencies approximate to the frequency
components really contained in the signals are screened. The method requires a
small quantity of hardware and calculation. Numerical results show that this
method is valid and accurate at quite low sampling rates.Comment: 10 pages, 7 figure
A family of spectral gradient methods for optimization
We propose a family of spectral gradient methods, whose stepsize is
determined by a convex combination of the long Barzilai-Borwein (BB) stepsize
and the short BB stepsize. Each member of the family is shown to share certain
quasi-Newton property in the sense of least squares. The family also includes
some other gradient methods as its special cases. We prove that the family of
methods is -superlinearly convergent for two-dimensional strictly convex
quadratics. Moreover, the family is -linearly convergent in the
any-dimensional case. Numerical results of the family with different settings
are presented, which demonstrate that the proposed family is promising.Comment: 22 pages, 2figure
A Class of Deterministic Sensing Matrices and Their Application in Harmonic Detection
In this paper, a class of deterministic sensing matrices are constructed by
selecting rows from Fourier matrices. These matrices have better performance in
sparse recovery than random partial Fourier matrices. The coherence and
restricted isometry property of these matrices are given to evaluate their
capacity as compressive sensing matrices. In general, compressed sensing
requires random sampling in data acquisition, which is difficult to implement
in hardware. By using these sensing matrices in harmonic detection, a
deterministic sampling method is provided. The frequencies and amplitudes of
the harmonic components are estimated from under-sampled data. The simulations
show that this under-sampled method is feasible and valid in noisy
environments.Comment: 12 pages, 6 figure
An algorithm of frequency estimation for multi-channel coprime sampling
In some applications of frequency estimation, it is challenging to sample at
as high as the Nyquist rate due to hardware limitations. An effective solution
is to use multiple sub-Nyquist channels with coprime undersampling ratios to
jointly sample. In this paper, an algorithm suitable for any number of channels
is proposed, which is based on subspace techniques. Numerical simulations show
that the proposed algorithm has high accuracy and good robustness.Comment: 2 pages, 3 figures. arXiv admin note: text overlap with
arXiv:1508.0572
Constrained and Preconditioned Stochastic Gradient Method
We consider stochastic approximations which arise from such applications as
data communications and image processing. We demonstrate why constraints are
needed in a stochastic approximation and how a constrained approximation can be
incorporated into a preconditioning technique to derive the pre-conditioned
stochastic gradient method (PSGM). We perform convergence analysis to show that
the PSGM converges to the theoretical best approximation under some simple
assumptions on the preconditioner and on the independence of samples drawn from
a stochastic process. Simulation results are presented to demonstrate the
effectiveness of the constrained and precondi-tioned stochastic gradient
method.Comment: 14 pages, 8 figure
Semi-Supervised Graph Classification: A Hierarchical Graph Perspective
Node classification and graph classification are two graph learning problems
that predict the class label of a node and the class label of a graph
respectively. A node of a graph usually represents a real-world entity, e.g., a
user in a social network, or a protein in a protein-protein interaction
network. In this work, we consider a more challenging but practically useful
setting, in which a node itself is a graph instance. This leads to a
hierarchical graph perspective which arises in many domains such as social
network, biological network and document collection. For example, in a social
network, a group of people with shared interests forms a user group, whereas a
number of user groups are interconnected via interactions or common members. We
study the node classification problem in the hierarchical graph where a `node'
is a graph instance, e.g., a user group in the above example. As labels are
usually limited in real-world data, we design two novel semi-supervised
solutions named \underline{SE}mi-supervised gr\underline{A}ph
c\underline{L}assification via \underline{C}autious/\underline{A}ctive
\underline{I}teration (or SEAL-C/AI in short). SEAL-C/AI adopt an iterative
framework that takes turns to build or update two classifiers, one working at
the graph instance level and the other at the hierarchical graph level. To
simplify the representation of the hierarchical graph, we propose a novel
supervised, self-attentive graph embedding method called SAGE, which embeds
graph instances of arbitrary size into fixed-length vectors. Through
experiments on synthetic data and Tencent QQ group data, we demonstrate that
SEAL-C/AI not only outperform competing methods by a significant margin in
terms of accuracy/Macro-F1, but also generate meaningful interpretations of the
learned representations.Comment: 12 pages, WWW-201
On-Line Choice Number of Complete Multipartite Graphs: an Algorithmic Approach
This paper studies the on-line choice number on complete multipartite graphs
with independence number . We give a unified strategy for every prescribed
. Our main result leads to several interesting consequences comparable to
known results. (1) If , where denotes the number of parts of cardinality , then is
on-line chromatic-choosable. (2) If , then is on-line
chromatic-choosable. (3) The on-line choice number of regular complete
multipartite graphs is at most
for
Intrinsic fluctuations of chemical reactions with different approaches
The Brusselator model are used for the study of the intrinsic fluctuations of
chemical reactions with different approaches. The equilibrium states of systems
are assumed to be spirally stable in mean-field description, and two
statistical measures of intrinsic fluctuations are analyzed by different
theoretical methods, namely, the master, the Langevin, and the linearized
Langevin equation. For systems far away from the Hopf bifurcation line, the
discrepancies between the results of different methods are insignificant even
for small system size. However, the discrepancies become noticeable even for
large system size when systems are closed to the bifurcation line. In
particular, the statistical measures possess singular structures for linearized
Langevin equation at the bifurcation line, and the singularities are absent
from the simulation results of the master and the Langevin equation.Comment: 3 figures, 20 page
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