11,087 research outputs found
A causal multifractal stochastic equation and its statistical properties
Multiplicative cascades have been introduced in turbulence to generate random
or deterministic fields having intermittent values and long-range power-law
correlations. Generally this is done using discrete construction rules leading
to discrete cascades. Here a causal log-normal stochastic process is
introduced; its multifractal properties are demonstrated together with other
properties such as the composition rule for scale dependence and stochastic
differential equations for time and scale evolutions. This multifractal
stochastic process is continuous in scale ratio and in time. It has a simple
generating equation and can be used to generate sequentially time series of any
length.Comment: Eur. Phys. J. B (in press
Perturbation of the Eigenvectors of the Graph Laplacian: Application to Image Denoising
The original contributions of this paper are twofold: a new understanding of
the influence of noise on the eigenvectors of the graph Laplacian of a set of
image patches, and an algorithm to estimate a denoised set of patches from a
noisy image. The algorithm relies on the following two observations: (1) the
low-index eigenvectors of the diffusion, or graph Laplacian, operators are very
robust to random perturbations of the weights and random changes in the
connections of the patch-graph; and (2) patches extracted from smooth regions
of the image are organized along smooth low-dimensional structures in the
patch-set, and therefore can be reconstructed with few eigenvectors.
Experiments demonstrate that our denoising algorithm outperforms the denoising
gold-standards
Metrics for Graph Comparison: A Practitioner's Guide
Comparison of graph structure is a ubiquitous task in data analysis and
machine learning, with diverse applications in fields such as neuroscience,
cyber security, social network analysis, and bioinformatics, among others.
Discovery and comparison of structures such as modular communities, rich clubs,
hubs, and trees in data in these fields yields insight into the generative
mechanisms and functional properties of the graph.
Often, two graphs are compared via a pairwise distance measure, with a small
distance indicating structural similarity and vice versa. Common choices
include spectral distances (also known as distances) and distances
based on node affinities. However, there has of yet been no comparative study
of the efficacy of these distance measures in discerning between common graph
topologies and different structural scales.
In this work, we compare commonly used graph metrics and distance measures,
and demonstrate their ability to discern between common topological features
found in both random graph models and empirical datasets. We put forward a
multi-scale picture of graph structure, in which the effect of global and local
structure upon the distance measures is considered. We make recommendations on
the applicability of different distance measures to empirical graph data
problem based on this multi-scale view. Finally, we introduce the Python
library NetComp which implements the graph distances used in this work
Time dependent intrinsic correlation analysis of temperature and dissolved oxygen time series using empirical mode decomposition
In the marine environment, many fields have fluctuations over a large range
of different spatial and temporal scales. These quantities can be nonlinear
\red{and} non-stationary, and often interact with each other. A good method to
study the multiple scale dynamics of such time series, and their correlations,
is needed. In this paper an application of an empirical mode decomposition
based time dependent intrinsic correlation, \red{of} two coastal oceanic time
series, temperature and dissolved oxygen (saturation percentage) is presented.
The two time series are recorded every 20 minutes \red{for} 7 years, from 2004
to 2011. The application of the Empirical Mode Decomposition on such time
series is illustrated, and the power spectra of the time series are estimated
using the Hilbert transform (Hilbert spectral analysis). Power-law regimes are
found with slopes of 1.33 for dissolved oxygen and 1.68 for temperature at high
frequencies (between 1.2 and 12 hours) \red{with} both close to 1.9 for lower
frequencies (time scales from 2 to 100 days). Moreover, the time evolution and
scale dependence of cross correlations between both series are considered. The
trends are perfectly anti-correlated. The modes of mean year 3 and 1 year have
also negative correlation, whereas higher frequency modes have a much smaller
correlation. The estimation of time-dependent intrinsic correlations helps to
show patterns of correlations at different scales, for different modes.Comment: 35 pages with 22 figure
Lagrangian Cascade in Three-Dimensional Homogeneous and Isotropic Turbulence
In this work, the scaling statistics of the dissipation along Lagrangian
trajectories are investigated by using fluid tracer particles obtained from a
high resolution direct numerical simulation with . Both the
energy dissipation rate and the local time averaged
agree rather well with the lognormal distribution hypothesis.
Several statistics are then examined. It is found that the autocorrelation
function of and variance of
obey a log-law with scaling exponent
compatible with the intermittency parameter . The
th-order moment of has a clear power-law on the inertial
range . The measured scaling exponent agrees
remarkably with where is the scaling exponent
estimated using the Hilbert methodology. All these results suggest that the
dissipation along Lagrangian trajectories could be modelled by a multiplicative
cascade.Comment: 10 pages with 7 figures accepted for Journal of Fluid Mechanics as
Rapid
Noise Corruption of Empirical Mode Decomposition and Its Effect on Instantaneous Frequency
Huang's Empirical Mode Decomposition (EMD) is an algorithm for analyzing
nonstationary data that provides a localized time-frequency representation by
decomposing the data into adaptively defined modes. EMD can be used to estimate
a signal's instantaneous frequency (IF) but suffers from poor performance in
the presence of noise. To produce a meaningful IF, each mode of the
decomposition must be nearly monochromatic, a condition that is not guaranteed
by the algorithm and fails to be met when the signal is corrupted by noise. In
this work, the extraction of modes containing both signal and noise is
identified as the cause of poor IF estimation. The specific mechanism by which
such "transition" modes are extracted is detailed and builds on the observation
of Flandrin and Goncalves that EMD acts in a filter bank manner when analyzing
pure noise. The mechanism is shown to be dependent on spectral leak between
modes and the phase of the underlying signal. These ideas are developed through
the use of simple signals and are tested on a synthetic seismic waveform.Comment: 28 pages, 19 figures. High quality color figures available on Daniel
Kaslovsky's website: http://amath.colorado.edu/student/kaslovsk
PROMETHEUS Payment: What's the Score?
Explains the scorecard used in "Provider payment Reform for Outcomes, Margins, Evidence, Transparency, Hassle-reduction, Excellence, Understandability, and Sustainability" (PROMETHEUS) to determine provider payments based on evidence-informed case rates
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