399 research outputs found
Quantifying and containing the curse of high resolution coronal imaging
Future missions such as Solar Orbiter (SO), InterHelioprobe, or Solar Probe
aim at approaching the Sun closer than ever before, with on board some high
resolution imagers (HRI) having a subsecond cadence and a pixel area of about
at the Sun during perihelion. In order to guarantee their scientific
success, it is necessary to evaluate if the photon counts available at these
resolution and cadence will provide a sufficient signal-to-noise ratio (SNR).
We perform a first step in this direction by analyzing and characterizing the
spatial intermittency of Quiet Sun images thanks to a multifractal analysis.
We identify the parameters that specify the scale-invariance behavior. This
identification allows next to select a family of multifractal processes, namely
the Compound Poisson Cascades, that can synthesize artificial images having
some of the scale-invariance properties observed on the recorded images.
The prevalence of self-similarity in Quiet Sun coronal images makes it
relevant to study the ratio between the SNR present at SoHO/EIT images and in
coarsened images. SoHO/EIT images thus play the role of 'high resolution'
images, whereas the 'low-resolution' coarsened images are rebinned so as to
simulate a smaller angular resolution and/or a larger distance to the Sun. For
a fixed difference in angular resolution and in Spacecraft-Sun distance, we
determine the proportion of pixels having a SNR preserved at high resolution
given a particular increase in effective area. If scale-invariance continues to
prevail at smaller scales, the conclusion reached with SoHO/EIT images can be
transposed to the situation where the resolution is increased from SoHO/EIT to
SO/HRI resolution at perihelion.Comment: 25 pages, 1 table, 7 figure
Intermittent process analysis with scattering moments
Scattering moments provide nonparametric models of random processes with
stationary increments. They are expected values of random variables computed
with a nonexpansive operator, obtained by iteratively applying wavelet
transforms and modulus nonlinearities, which preserves the variance. First- and
second-order scattering moments are shown to characterize intermittency and
self-similarity properties of multiscale processes. Scattering moments of
Poisson processes, fractional Brownian motions, L\'{e}vy processes and
multifractal random walks are shown to have characteristic decay. The
Generalized Method of Simulated Moments is applied to scattering moments to
estimate data generating models. Numerical applications are shown on financial
time-series and on energy dissipation of turbulent flows.Comment: Published in at http://dx.doi.org/10.1214/14-AOS1276 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Quantifying origin and character of long-range correlations in narrative texts
In natural language using short sentences is considered efficient for
communication. However, a text composed exclusively of such sentences looks
technical and reads boring. A text composed of long ones, on the other hand,
demands significantly more effort for comprehension. Studying characteristics
of the sentence length variability (SLV) in a large corpus of world-famous
literary texts shows that an appealing and aesthetic optimum appears somewhere
in between and involves selfsimilar, cascade-like alternation of various
lengths sentences. A related quantitative observation is that the power spectra
S(f) of thus characterized SLV universally develop a convincing `1/f^beta'
scaling with the average exponent beta =~ 1/2, close to what has been
identified before in musical compositions or in the brain waves. An
overwhelming majority of the studied texts simply obeys such fractal attributes
but especially spectacular in this respect are hypertext-like, "stream of
consciousness" novels. In addition, they appear to develop structures
characteristic of irreducibly interwoven sets of fractals called multifractals.
Scaling of S(f) in the present context implies existence of the long-range
correlations in texts and appearance of multifractality indicates that they
carry even a nonlinear component. A distinct role of the full stops in inducing
the long-range correlations in texts is evidenced by the fact that the above
quantitative characteristics on the long-range correlations manifest themselves
in variation of the full stops recurrence times along texts, thus in SLV, but
to a much lesser degree in the recurrence times of the most frequent words. In
this latter case the nonlinear correlations, thus multifractality, disappear
even completely for all the texts considered. Treated as one extra word, the
full stops at the same time appear to obey the Zipfian rank-frequency
distribution, however.Comment: 28 pages, 8 figures, accepted for publication in Information Science
Wavelet and Multiscale Analysis of Network Traffic
The complexity and richness of telecommunications traffic is such that one may despair to find any regularity or explanatory principles. Nonetheless, the discovery of scaling behaviour in tele-traffic has provided hope that parsimonious models can be found. The statistics of scaling behavior present many challenges, especially in non-stationary environments. In this paper we describe the state of the art in this area, focusing on the capabilities of the wavelet transform as a key tool for unravelling the mysteries of traffic statistics and dynamics
Combining local regularity estimation and total variation optimization for scale-free texture segmentation
Texture segmentation constitutes a standard image processing task, crucial to
many applications. The present contribution focuses on the particular subset of
scale-free textures and its originality resides in the combination of three key
ingredients: First, texture characterization relies on the concept of local
regularity ; Second, estimation of local regularity is based on new multiscale
quantities referred to as wavelet leaders ; Third, segmentation from local
regularity faces a fundamental bias variance trade-off: In nature, local
regularity estimation shows high variability that impairs the detection of
changes, while a posteriori smoothing of regularity estimates precludes from
locating correctly changes. Instead, the present contribution proposes several
variational problem formulations based on total variation and proximal
resolutions that effectively circumvent this trade-off. Estimation and
segmentation performance for the proposed procedures are quantified and
compared on synthetic as well as on real-world textures
Bio-inspired route estimation in cognitive radio networks
Cognitive radio is a technique that was originally created for the proper use of the radio electric spectrum due its underuse. A few methods were used to predict the network traffic to determine the occupancy of the spectrum and then use the ‘holes’ between the transmissions of primary users. The goal is to guarantee a complete transmission for the second user while not interrupting the trans-mission of primary users. This study seeks the multifractal generation of traffic for a specific radio electric spectrum as well as a bio-inspired route estimation for secondary users. It uses the MFHW algorithm to generate multifractal traces and two bio-inspired algo-rithms: Ant Colony Optimization and Max Feeding to calculate the secondary user’s path. Multifractal characteristics offer a predic-tion, which is 10% lower in comparison with the original traffic values and a complete transmission for secondary users. In fact, a hybrid strategy combining both bio-inspired algorithms promise a reduction in handoff. The purpose of this research consists on deriving future investigation in the generation of multifractal traffic and a mobility spectrum using bio-inspired algorithms
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