184,580 research outputs found
Anomalous Dimension in the Solution of the Barenblatt's Equation
A new method is presented to obtain the anomalous dimension in the solution
of the Barenblatt's equation. The result is the same as that in the
renormalization group (RG) approach. It gives us insight on the perturbative
solution of the Barenblatt's equation in the RG approach. Based on this
discussion, an improvement is made to take into account, in more complete way,
the nonlinear effect, which is included in the Heaviside function in higher
orders. This improved result is better than that in RG approach.Comment: 17 pages, LaTex, no figur
Reconstruction of sparse wavelet signals from partial Fourier measurements
In this paper, we show that high-dimensional sparse wavelet signals of finite
levels can be constructed from their partial Fourier measurements on a
deterministic sampling set with cardinality about a multiple of signal
sparsity
Simultaneous Amplitude and Phase Measurement for Periodic Optical Signals Using Time-Resolved Optical Filtering
Time-resolved optical filtering (TROF) measures the spectrogram or sonogram
by a fast photodiode followed a tunable narrowband optical filter. For periodic
signal and to match the sonogram, numerical TROF algorithm is used to find the
original complex electric field or equivalently both the amplitude and phase.
For phase-modulated optical signals, the TROF algorithm is initiated using the
craters and ridges of the sonogram.Comment: 10 pages, 5 figure
Asymmetry Helps: Eigenvalue and Eigenvector Analyses of Asymmetrically Perturbed Low-Rank Matrices
This paper is concerned with the interplay between statistical asymmetry and
spectral methods. Suppose we are interested in estimating a rank-1 and
symmetric matrix , yet only a
randomly perturbed version is observed. The noise matrix
is composed of zero-mean independent (but not
necessarily homoscedastic) entries and is, therefore, not symmetric in general.
This might arise, for example, when we have two independent samples for each
entry of and arrange them into an {\em asymmetric} data
matrix . The aim is to estimate the leading eigenvalue and
eigenvector of . We demonstrate that the leading eigenvalue
of the data matrix can be times more accurate --- up
to some log factor --- than its (unadjusted) leading singular value in
eigenvalue estimation. Further, the perturbation of any linear form of the
leading eigenvector of --- say, entrywise eigenvector perturbation
--- is provably well-controlled. This eigen-decomposition approach is fully
adaptive to heteroscedasticity of noise without the need of careful bias
correction or any prior knowledge about the noise variance. We also provide
partial theory for the more general rank- case. The takeaway message is
this: arranging the data samples in an asymmetric manner and performing
eigen-decomposition could sometimes be beneficial.Comment: accepted to Annals of Statistics, 2020. 37 page
The fragmentation instability of a black hole with global monopole under GUP
The fragmentation of black hole containing global monopole under GUP
is studied. We focus on that the black hole breaks into two parts. We derive
the entropies of the initial black hole and the broken parts while the
generalization of Heisenberg's uncertainty principle is introduced. We find
that the global monopole black hole keeps stable instead of breaking
because the entropy difference is negative without the generalization. The
fragmentation of the black hole will happen if the black hole entropies are
limited by the GUP and the considerable deviation from the general relativity
leads the case that the mass of one fragmented black hole is extremely small
and the other one is extremely large.Comment: 9 pages, 4 figure
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