9,813 research outputs found
Local-set-based Graph Signal Reconstruction
Signal processing on graph is attracting more and more attentions. For a
graph signal in the low-frequency subspace, the missing data associated with
unsampled vertices can be reconstructed through the sampled data by exploiting
the smoothness of the graph signal. In this paper, the concept of local set is
introduced and two local-set-based iterative methods are proposed to
reconstruct bandlimited graph signal from sampled data. In each iteration, one
of the proposed methods reweights the sampled residuals for different vertices,
while the other propagates the sampled residuals in their respective local
sets. These algorithms are built on frame theory and the concept of local sets,
based on which several frames and contraction operators are proposed. We then
prove that the reconstruction methods converge to the original signal under
certain conditions and demonstrate the new methods lead to a significantly
faster convergence compared with the baseline method. Furthermore, the
correspondence between graph signal sampling and time-domain irregular sampling
is analyzed comprehensively, which may be helpful to future works on graph
signals. Computer simulations are conducted. The experimental results
demonstrate the effectiveness of the reconstruction methods in various sampling
geometries, imprecise priori knowledge of cutoff frequency, and noisy
scenarios.Comment: 28 pages, 9 figures, 6 tables, journal manuscrip
Accuracy, Scalability, and Efficiency of Mixed-Element USM3D for Benchmark Three-Dimensional Flows
The unstructured, mixed-element, cell-centered, finite-volume flow solver USM3D is enhanced with new capabilities including parallelization, line generation for general unstructured grids, improved discretization scheme, and optimized iterative solver. The paper reports on the new developments to the flow solver and assesses the accuracy, scalability, and efficiency. The USM3D assessments are conducted using a baseline method and the recent hierarchical adaptive nonlinear iteration method framework. Two benchmark turbulent flows, namely, a subsonic separated flow around a three-dimensional hemisphere-cylinder configuration and a transonic flow around the ONERA M6 wing are considered
Cultural Values and Cross-cultural Video Consumption on YouTube
Video-sharing social media like YouTube provide access to diverse cultural
products from all over the world, making it possible to test theories that the
Web facilitates global cultural convergence. Drawing on a daily listing of
YouTube's most popular videos across 58 countries, we investigate the
consumption of popular videos in countries that differ in cultural values,
language, gross domestic product, and Internet penetration rate. Although
online social media facilitate global access to cultural products, we find this
technological capability does not result in universal cultural convergence.
Instead, consumption of popular videos in culturally different countries
appears to be constrained by cultural values. Cross-cultural convergence is
more advanced in cosmopolitan countries with cultural values that favor
individualism and power inequality
Non-Uniform Time Sampling for Multiple-Frequency Harmonic Balance Computations
A time-domain harmonic balance method for the analysis of almost-periodic (multi-harmonics) flows is presented. This method relies on Fourier analysis to derive an efficient alternative to classical time marching schemes for such flows. It has recently received significant attention, especially in the turbomachinery field where the flow spectrum is essentially a combination of the blade passing frequencies. Up to now, harmonic balance methods have used a uniform time sampling of the period of interest, but in the case of several frequencies, non-necessarily multiple of each other, harmonic balance methods can face stability issues due to a bad condition number of the Fourier operator. Two algorithms are derived to find a non-uniform time sampling in order to minimize this condition number. Their behavior is studied on a wide range of frequencies, and a model problem of a 1D flow with pulsating outlet pressure, which enables to prove their efficiency. Finally, the flow in a multi-stage axial compressor is analyzed with different frequency sets. It demonstrates the stability and robustness of the present non-uniform harmonic balance method regardless of the frequency set
The geometry of nonlinear least squares with applications to sloppy models and optimization
Parameter estimation by nonlinear least squares minimization is a common
problem with an elegant geometric interpretation: the possible parameter values
of a model induce a manifold in the space of data predictions. The minimization
problem is then to find the point on the manifold closest to the data. We show
that the model manifolds of a large class of models, known as sloppy models,
have many universal features; they are characterized by a geometric series of
widths, extrinsic curvatures, and parameter-effects curvatures. A number of
common difficulties in optimizing least squares problems are due to this common
structure. First, algorithms tend to run into the boundaries of the model
manifold, causing parameters to diverge or become unphysical. We introduce the
model graph as an extension of the model manifold to remedy this problem. We
argue that appropriate priors can remove the boundaries and improve convergence
rates. We show that typical fits will have many evaporated parameters. Second,
bare model parameters are usually ill-suited to describing model behavior; cost
contours in parameter space tend to form hierarchies of plateaus and canyons.
Geometrically, we understand this inconvenient parametrization as an extremely
skewed coordinate basis and show that it induces a large parameter-effects
curvature on the manifold. Using coordinates based on geodesic motion, these
narrow canyons are transformed in many cases into a single quadratic, isotropic
basin. We interpret the modified Gauss-Newton and Levenberg-Marquardt fitting
algorithms as an Euler approximation to geodesic motion in these natural
coordinates on the model manifold and the model graph respectively. By adding a
geodesic acceleration adjustment to these algorithms, we alleviate the
difficulties from parameter-effects curvature, improving both efficiency and
success rates at finding good fits.Comment: 40 pages, 29 Figure
- …