12,873 research outputs found
DeepSphere: Efficient spherical Convolutional Neural Network with HEALPix sampling for cosmological applications
Convolutional Neural Networks (CNNs) are a cornerstone of the Deep Learning
toolbox and have led to many breakthroughs in Artificial Intelligence. These
networks have mostly been developed for regular Euclidean domains such as those
supporting images, audio, or video. Because of their success, CNN-based methods
are becoming increasingly popular in Cosmology. Cosmological data often comes
as spherical maps, which make the use of the traditional CNNs more complicated.
The commonly used pixelization scheme for spherical maps is the Hierarchical
Equal Area isoLatitude Pixelisation (HEALPix). We present a spherical CNN for
analysis of full and partial HEALPix maps, which we call DeepSphere. The
spherical CNN is constructed by representing the sphere as a graph. Graphs are
versatile data structures that can act as a discrete representation of a
continuous manifold. Using the graph-based representation, we define many of
the standard CNN operations, such as convolution and pooling. With filters
restricted to being radial, our convolutions are equivariant to rotation on the
sphere, and DeepSphere can be made invariant or equivariant to rotation. This
way, DeepSphere is a special case of a graph CNN, tailored to the HEALPix
sampling of the sphere. This approach is computationally more efficient than
using spherical harmonics to perform convolutions. We demonstrate the method on
a classification problem of weak lensing mass maps from two cosmological models
and compare the performance of the CNN with that of two baseline classifiers.
The results show that the performance of DeepSphere is always superior or equal
to both of these baselines. For high noise levels and for data covering only a
smaller fraction of the sphere, DeepSphere achieves typically 10% better
classification accuracy than those baselines. Finally, we show how learned
filters can be visualized to introspect the neural network.Comment: arXiv admin note: text overlap with arXiv:astro-ph/0409513 by other
author
Improved microscopic-macroscopic approach incorporating the effects of continuum states
The Woods-Saxon-Strutinsky method (the microscopic-macroscopic method)
combined with Kruppa's prescription for positive energy levels, which is
necessary to treat neutron rich nuclei, is studied to clarify the reason for
its success and to propose improvements for its shortcomings. The reason why
the plateau condition is met for the Nilsson model but not for the Woods-Saxon
model is understood in a new interpretation of the Strutinsky smoothing
procedure as a low-pass filter. Essential features of Kruppa's level density is
extracted in terms of the Thomas-Fermi approximation modified to describe
spectra obtained from diagonalization in truncated oscillator bases. A method
is proposed which weakens the dependence on the smoothing width by applying the
Strutinsky smoothing only to the deviations from a reference level density. The
BCS equations are modified for the Kruppa's spectrum, which is necessary to
treat the pairing correlation properly in the presence of continuum. The
potential depth is adjusted for the consistency between the microscopic and
macroscopic Fermi energies. It is shown, with these improvements, that the
microscopic-macroscopic method is now capable to reliably calculate binding
energies of nuclei far from stability.Comment: 66 pages, 29 figures, 1 tabl
Novel Fourier Quadrature Transforms and Analytic Signal Representations for Nonlinear and Non-stationary Time Series Analysis
The Hilbert transform (HT) and associated Gabor analytic signal (GAS)
representation are well-known and widely used mathematical formulations for
modeling and analysis of signals in various applications. In this study, like
the HT, to obtain quadrature component of a signal, we propose the novel
discrete Fourier cosine quadrature transforms (FCQTs) and discrete Fourier sine
quadrature transforms (FSQTs), designated as Fourier quadrature transforms
(FQTs). Using these FQTs, we propose sixteen Fourier-Singh analytic signal
(FSAS) representations with following properties: (1) real part of eight FSAS
representations is the original signal and imaginary part is the FCQT of the
real part, (2) imaginary part of eight FSAS representations is the original
signal and real part is the FSQT of the real part, (3) like the GAS, Fourier
spectrum of the all FSAS representations has only positive frequencies, however
unlike the GAS, the real and imaginary parts of the proposed FSAS
representations are not orthogonal to each other. The Fourier decomposition
method (FDM) is an adaptive data analysis approach to decompose a signal into a
set of small number of Fourier intrinsic band functions which are AM-FM
components. This study also proposes a new formulation of the FDM using the
discrete cosine transform (DCT) with the GAS and FSAS representations, and
demonstrate its efficacy for improved time-frequency-energy representation and
analysis of nonlinear and non-stationary time series.Comment: 22 pages, 13 figure
Bending and Breaking of Stripes in a Charge-Ordered Manganite
In complex electronic materials, coupling between electrons and the atomic
lattice gives rise to remarkable phenomena, including colossal
magnetoresistance and metal-insulator transitions. Charge-ordered phases are a
prototypical manifestation of charge-lattice coupling, in which the atomic
lattice undergoes periodic lattice displacements (PLDs). Here we directly map
the picometer scale PLDs at individual atomic columns in the room temperature
charge-ordered manganite BiSrCaMnO using
aberration corrected scanning transmission electron microscopy (STEM). We
measure transverse, displacive lattice modulations of the cations, distinct
from existing manganite charge-order models. We reveal locally unidirectional
striped PLD domains as small as 5 nm, despite apparent bidirectionality
over larger length scales. Further, we observe a direct link between disorder
in one lattice modulation, in the form of dislocations and shear deformations,
and nascent order in the perpendicular modulation. By examining the defects and
symmetries of PLDs near the charge-ordering phase transition, we directly
visualize the local competition underpinning spatial heterogeneity in a complex
oxide.Comment: Main text: 20 pages, 4 figures. Supplemental Information: 27 pages,
14 figure
The Vanishing Role of Money in the Macroeconomy - An Empirical Investigation Based On Spectral and Wavelet Analysis
The recent de-emphasizing of the role of money in both theoretical macroeconomics as well as in the practical conduct of monetary policy sits uneasily with the idea that inflation is a monetary phenomenon. Empirical evidence has, however, been accumulating, pointing to an important leading indicator role for money and credit aggregates with respect to long term inflationary trends. Such a role could arise from monetary aggregates furnishing a nominal anchor for inflationary expectations, from their influence on the term structure of interest rates and from their affecting transactions costs in markets. Our paper attempts to assess the informational content role of money in the Indian economy by a separation of these effects across time scales and frequency bands, using the techniques of wavelet analysis and band spectral analysis respectively. Our results indicate variability of causal relations across frequency ranges and time scales, as also occasional causal reversals.Money, inflation, Cointegration, Causality, Decomposition, band spectra, wavelets
Convolutional Deblurring for Natural Imaging
In this paper, we propose a novel design of image deblurring in the form of
one-shot convolution filtering that can directly convolve with naturally
blurred images for restoration. The problem of optical blurring is a common
disadvantage to many imaging applications that suffer from optical
imperfections. Despite numerous deconvolution methods that blindly estimate
blurring in either inclusive or exclusive forms, they are practically
challenging due to high computational cost and low image reconstruction
quality. Both conditions of high accuracy and high speed are prerequisites for
high-throughput imaging platforms in digital archiving. In such platforms,
deblurring is required after image acquisition before being stored, previewed,
or processed for high-level interpretation. Therefore, on-the-fly correction of
such images is important to avoid possible time delays, mitigate computational
expenses, and increase image perception quality. We bridge this gap by
synthesizing a deconvolution kernel as a linear combination of Finite Impulse
Response (FIR) even-derivative filters that can be directly convolved with
blurry input images to boost the frequency fall-off of the Point Spread
Function (PSF) associated with the optical blur. We employ a Gaussian low-pass
filter to decouple the image denoising problem for image edge deblurring.
Furthermore, we propose a blind approach to estimate the PSF statistics for two
Gaussian and Laplacian models that are common in many imaging pipelines.
Thorough experiments are designed to test and validate the efficiency of the
proposed method using 2054 naturally blurred images across six imaging
applications and seven state-of-the-art deconvolution methods.Comment: 15 pages, for publication in IEEE Transaction Image Processin
Graph Spectral Image Processing
Recent advent of graph signal processing (GSP) has spurred intensive studies
of signals that live naturally on irregular data kernels described by graphs
(e.g., social networks, wireless sensor networks). Though a digital image
contains pixels that reside on a regularly sampled 2D grid, if one can design
an appropriate underlying graph connecting pixels with weights that reflect the
image structure, then one can interpret the image (or image patch) as a signal
on a graph, and apply GSP tools for processing and analysis of the signal in
graph spectral domain. In this article, we overview recent graph spectral
techniques in GSP specifically for image / video processing. The topics covered
include image compression, image restoration, image filtering and image
segmentation
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