456 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
The Dynamics of Internet Traffic: Self-Similarity, Self-Organization, and Complex Phenomena
The Internet is the most complex system ever created in human history.
Therefore, its dynamics and traffic unsurprisingly take on a rich variety of
complex dynamics, self-organization, and other phenomena that have been
researched for years. This paper is a review of the complex dynamics of
Internet traffic. Departing from normal treatises, we will take a view from
both the network engineering and physics perspectives showing the strengths and
weaknesses as well as insights of both. In addition, many less covered
phenomena such as traffic oscillations, large-scale effects of worm traffic,
and comparisons of the Internet and biological models will be covered.Comment: 63 pages, 7 figures, 7 tables, submitted to Advances in Complex
System
A Multifractal Description of Wind Speed Records
In this paper, a systematic analysis of hourly wind speed data obtained from
four potential wind generation sites in North Dakota is conducted. The power
spectra of the data exhibited a power law decay characteristic of
processes with possible long range correlations. The temporal
scaling properties of the records were studied using multifractal detrended
fluctuation analysis {\em MFDFA}. It is seen that the records at all four
locations exhibit similar scaling behavior which is also reflected in the
multifractal spectrum determined under the assumption of a binomial
multiplicative cascade model
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
A critical look at power law modelling of the Internet
This paper takes a critical look at the usefulness of power law models of the
Internet. The twin focuses of the paper are Internet traffic and topology
generation. The aim of the paper is twofold. Firstly it summarises the state of
the art in power law modelling particularly giving attention to existing open
research questions. Secondly it provides insight into the failings of such
models and where progress needs to be made for power law research to feed
through to actual improvements in network performance.Comment: To appear Computer Communication
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
The pseudo-self-similar traffic model: application and validation
Since the early 1990¿s, a variety of studies has shown that network traffic, both for local- and wide-area networks, has self-similar properties. This led to new approaches in network traffic modelling because most traditional traffic approaches result in the underestimation of performance measures of interest. Instead of developing completely new traffic models, a number of researchers have proposed to adapt traditional traffic modelling approaches to incorporate aspects of self-similarity. The motivation for doing so is the hope to be able to reuse techniques and tools that have been developed in the past and with which experience has been gained. One such approach for a traffic model that incorporates aspects of self-similarity is the so-called pseudo self-similar traffic model. This model is appealing, as it is easy to understand and easily embedded in Markovian performance evaluation studies. In applying this model in a number of cases, we have perceived various problems which we initially thought were particular to these specific cases. However, we recently have been able to show that these problems are fundamental to the pseudo self-similar traffic model. In this paper we review the pseudo self-similar traffic model and discuss its fundamental shortcomings. As far as we know, this is the first paper that discusses these shortcomings formally. We also report on ongoing work to overcome some of these problems
-variations for multifractal fractional random walks
A multifractal random walk (MRW) is defined by a Brownian motion subordinated
by a class of continuous multifractal random measures . In
this paper we obtain an extension of this process, referred to as multifractal
fractional random walk (MFRW), by considering the limit in distribution of a
sequence of conditionally Gaussian processes. These conditional processes are
defined as integrals with respect to fractional Brownian motion and convergence
is seen to hold under certain conditions relating the self-similarity (Hurst)
exponent of the fBm to the parameters defining the multifractal random measure
. As a result, a larger class of models is obtained, whose fine scale
(scaling) structure is then analyzed in terms of the empirical structure
functions. Implications for the analysis and inference of multifractal
exponents from data, namely, confidence intervals, are also provided.Comment: Published in at http://dx.doi.org/10.1214/07-AAP483 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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