70,970 research outputs found
The source-lens clustering effect in the context of lensing tomography and its self-calibration
Cosmic shear can only be measured where there are galaxies. This source-lens
clustering (SLC) effect has two sources, intrinsic source clustering and cosmic
magnification (magnification/size bias). Lensing tomography can suppress the
former. However, this reduction is limited by the existence of photo-z error
and nonzero redshift bin width. Furthermore, SLC induced by cosmic
magnification cannot be reduced by lensing tomography. Through N-body
simulations, we quantify the impact of SLC on the lensing power spectrum in the
context of lensing tomography. We consider both the standard estimator and the
pixel-based estimator. We find that none of them can satisfactorily handle both
sources of SLC. (1) For the standard estimator, SLC induced by both sources can
bias the lensing power spectrum by O(1)-O(10)%. Intrinsic source clustering
also increases statistical uncertainties in the measured lensing power
spectrum. However, the standard estimator suppresses intrinsic source
clustering in the cross-spectrum. (2) In contrast, the pixel-based estimator
suppresses SLC through cosmic magnification. However, it fails to suppress SLC
through intrinsic source clustering and the measured lensing power spectrum can
be biased low by O(1)-O(10)%. In short, for typical photo-z errors
(sigma_z/(1+z)=0.05) and photo-z bin sizes (Delta_z^P=0.2), SLC alters the
lensing E-mode power spectrum by 1-10%, with ell~10^3$ and z_s~1 being of
particular interest to weak lensing cosmology. Therefore the SLC is a severe
systematic for cosmology in Stage-IV lensing surveys. We present useful scaling
relations to self-calibrate the SLC effect.Comment: 13 pages, 10 figures, Accepted by AP
Towards efficient SimRank computation on large networks
SimRank has been a powerful model for assessing the similarity of pairs of vertices in a graph. It is based on the concept that two vertices are similar if they are referenced by similar vertices. Due to its self-referentiality, fast SimRank computation on large graphs poses significant challenges. The state-of-the-art work [17] exploits partial sums memorization for computing SimRank in O(Kmn) time on a graph with n vertices and m edges, where K is the number of iterations. Partial sums memorizing can reduce repeated calculations by caching part of similarity summations for later reuse. However, we observe that computations among different partial sums may have duplicate redundancy. Besides, for a desired accuracy ϵ, the existing SimRank model requires K = [logC ϵ] iterations [17], where C is a damping factor. Nevertheless, such a geometric rate of convergence is slow in practice if a high accuracy is desirable. In this paper, we address these gaps. (1) We propose an adaptive clustering strategy to eliminate partial sums redundancy (i.e., duplicate computations occurring in partial sums), and devise an efficient algorithm for speeding up the computation of SimRank to 0(Kdn2) time, where d is typically much smaller than the average in-degree of a graph. (2) We also present a new notion of SimRank that is based on a differential equation and can be represented as an exponential sum of transition matrices, as opposed to the geometric sum of the conventional counterpart. This leads to a further speedup in the convergence rate of SimRank iterations. (3) Using real and synthetic data, we empirically verify that our approach of partial sums sharing outperforms the best known algorithm by up to one order of magnitude, and that our revised notion of SimRank further achieves a 5X speedup on large graphs while also fairly preserving the relative order of original SimRank scores
On the Number of Positive Solutions to a Class of Integral Equations
By using the complete discrimination system for polynomials, we study the
number of positive solutions in {\small } to the integral equation
{\small }, where {\small
} are continuous functions on {\small }, {\small } is
a positive integer. We prove the following results: when {\small },
either there does not exist, or there exist infinitely many positive solutions
in {\small }; when {\small }, there exist at least {\small 1},
at most {\small } positive solutions in {\small }. Necessary and
sufficient conditions are derived for the cases: 1) {\small }, there
exist positive solutions; 2) {\small }, there exist exactly {\small
} positive solutions. Our results generalize the
existing results in the literature, and their usefulness is shown by examples
presented in this paper.Comment: 9 page
Joint Quantization and Diffusion for Compressed Sensing Measurements of Natural Images
Recent research advances have revealed the computational secrecy of the
compressed sensing (CS) paradigm. Perfect secrecy can also be achieved by
normalizing the CS measurement vector. However, these findings are established
on real measurements while digital devices can only store measurements at a
finite precision. Based on the distribution of measurements of natural images
sensed by structurally random ensemble, a joint quantization and diffusion
approach is proposed for these real-valued measurements. In this way, a
nonlinear cryptographic diffusion is intrinsically imposed on the CS process
and the overall security level is thus enhanced. Security analyses show that
the proposed scheme is able to resist known-plaintext attack while the original
CS scheme without quantization cannot. Experimental results demonstrate that
the reconstruction quality of our scheme is comparable to that of the original
one.Comment: 4 pages, 4 figure
Quantum Phase Transition in the Sub-Ohmic Spin-Boson Model: Extended Coherent-state Approach
We propose a general extended coherent state approach to the qubit (or
fermion) and multi-mode boson coupling systems. The application to the
spin-boson model with the discretization of a bosonic bath with arbitrary
continuous spectral density is described in detail, and very accurate solutions
can be obtained. The quantum phase transition in the nontrivial sub-Ohmic case
can be located by the fidelity and the order-parameter critical exponents for
the bath exponents can be correctly given by the fidelity
susceptibility, demonstrating the strength of the approach.Comment: 4 pages, 3 figure
Gaussianizing the non-Gaussian lensing convergence field I: the performance of the Gaussianization
Motivated by recent works of Neyrinck et al. 2009 and Scherrer et al. 2010,
we proposed a Gaussianization transform to Gaussianize the non-Gaussian lensing
convergence field . It performs a local monotonic transformation
pixel by pixel to make the unsmoothed one-point
probability distribution function of the new variable Gaussian. We tested
whether the whole field is Gaussian against N-body simulations. (1) We
found that the proposed Gaussianization suppresses the non-Gaussianity by
orders of magnitude, in measures of the skewness, the kurtosis, the 5th- and
6th-order cumulants of the field smoothed over various angular scales
relative to that of the corresponding smoothed field. The residual
non-Gaussianities are often consistent with zero within the statistical errors.
(2) The Gaussianization significantly suppresses the bispectrum. Furthermore,
the residual scatters around zero, depending on the configuration in the
Fourier space. (3) The Gaussianization works with even better performance for
the 2D fields of the matter density projected over \sim 300 \mpch distance
interval centered at , which can be reconstructed from the weak
lensing tomography. (4) We identified imperfectness and complexities of the
proposed Gaussianization. We noticed weak residual non-Gaussianity in the
field. We verified the widely used logarithmic transformation as a good
approximation to the Gaussianization transformation. However, we also found
noticeable deviations.Comment: 13 pages, 15 figures, accepted by PR
Image Type Water Meter Character Recognition Based on Embedded DSP
In the paper, we combined DSP processor with image processing algorithm and
studied the method of water meter character recognition. We collected water
meter image through camera at a fixed angle, and the projection method is used
to recognize those digital images. The experiment results show that the method
can recognize the meter characters accurately and artificial meter reading is
replaced by automatic digital recognition, which improves working efficiency
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