3,005 research outputs found
Fast, Approximate Synthesis of Fractional Gaussian Noise for Generating Self-Similar Network Traffic
Recent network traffic studies argue that network arrival processes are much
more faithfully modeled using statistically self-similar processes instead of
traditional Poisson processes [LTWW94,PF95]. One difficulty in dealing with
self-similar models is how to efficiently synthesize traces (sample paths)
corresponding to self-similar traffic. We present a fast Fourier transform
method for synthesizing approximate self-similar sample paths for one type of
self-similar process, Fractional Gaussian Noise, and assess its performance and
validity. We find that the method is as fast or faster than existing methods
and appears to generate close approximations to true self-similar sample paths.
We also discuss issues in using such synthesized sample paths for simulating
network traffic, and how an approximation used by our method can dramatically
speed up evaluation of Whittle's estimator for H, the Hurst parameter giving
the strength of long-range dependence present in a self-similar time series.Comment: 14 page
A Large Sky Simulation of the Gravitational Lensing of the Cosmic Microwave Background
Large scale structure deflects cosmic microwave background (CMB) photons.
Since large angular scales in the large scale structure contribute
significantly to the gravitational lensing effect, a realistic simulation of
CMB lensing requires a sufficiently large sky area. We describe simulations
that include these effects, and present both effective and multiple plane
ray-tracing versions of the algorithm, which employs spherical harmonic space
and does not use the flat sky approximation. We simulate lensed CMB maps with
an angular resolution of ~0.9 arcmin. The angular power spectrum of the
simulated sky agrees well with analytical predictions. Maps generated in this
manner are a useful tool for the analysis and interpretation of upcoming CMB
experiments such as PLANCK and ACT.Comment: 14 pages, 12 figures, replaced with version accepted for publication
by the AP
Wavelet Multiresolution Analysis of High-Frequency FX Rates, Summer 1997
FX pricing processes are nonstationary and their frequency characteristics are time-dependent. Most do not conform to geometric Brownian motion, since they exhibit a scaling law with a Hurst exponent between zero and 0.5 and fractal dimensions between 1.5 and 2. This paper uses wavelet multiresolution analysis, with Haar wavelets, to analyze the nonstationarity (time-dependence) and self-similarity (scale-dependence) of intra-day Asian currency spot exchange rates.foreign exchange, anti-persistence, multi-resolution analysis, wavelets, Asia
Wavelet Multiresolution Analysis of High-Frequency Asian FX Rates, Summer 1997
FX pricing processes are nonstationary and their frequency characteristics are time-dependent. Most do not conform to geometric Brownian motion, since they exhibit a scaling law with a Hurst exponent between zero and 0.5 and fractal dimensions between 1.5 and 2. This paper uses wavelet multiresolution analysis, with Haar wavelets, to analyze the nonstationarity (time-dependence) and self-similarity (scale-dependence) of intra-day Asian currency spot exchange rates. These are the ask and bid quotes of the currencies of eight Asian countries (Japan, Hong Kong, Indonesia, Malaysia, Philippines, Singapore, Taiwan, Thailand), and of Germany for comparison, for the crisis period May 1, 1998 - August 31, 1997, provided by Telerate (U.S. dollar is the numeraire). Their time-scale dependent spectra, which are localized in time, are observed in wavelet based scalograms. The FX increments can be characterized by the irregularity of their singularities. This degrees of irregularity are measured by homogeneous Hurst exponents. These critical exponents are used to identify the fractal dimension, relative stability and long term dependence of each Asian FX series. The invariance of each identified Hurst exponent is tested by comparing it at varying time and scale (frequency) resolutions. It appears that almost all FX markets show anti-persistent pricing behavior. The anchor currencies of the D-mark and Japanese Yen are ultra-efficient in the sense of being most anti-persistent. The Taiwanese dollar is the most persistent, and thus unpredictable, most likely due to administrative control. FX markets exhibit these non- linear, non-Gaussian dynamic structures, long term dependence, high kurtosis, and high degrees of non-informational (noise) trading, possibly because of frequent capital flows induced by non-synchronized regional business cycles, rapidly changing political risks, unexpected informational shocks to investment opportunities, and, in particular, investment strategies synthesizing interregional claims using cash swaps with different duration horizons.foreign exchange markets, anti-persistence, long-term dependence, multi-resolution analysis, wavelets, time-scale analysis, scaling laws, irregularity analysis, randomness, Asia
Models of statistical self-similarity for signal and image synthesis
Statistical self-similarity of random processes in continuous-domains is defined through invariance of their statistics to time or spatial scaling. In discrete-time, scaling by an arbitrary factor of signals can be accomplished through frequency warping, and statistical self-similarity is defined by the discrete-time continuous-dilation scaling operation. Unlike other self-similarity models mostly relying on characteristics of continuous self-similarity other than scaling, this model provides a way to express discrete-time statistical self-similarity using scaling of discrete-time signals. This dissertation studies the discrete-time self-similarity model based on the new scaling operation, and develops its properties, which reveals relations with other models. Furthermore, it also presents a new self-similarity definition for discrete-time vector processes, and demonstrates synthesis examples for multi-channel network traffic. In two-dimensional spaces, self-similar random fields are of interest in various areas of image processing, since they fit certain types of natural patterns and textures very well. Current treatments of self-similarity in continuous two-dimensional space use a definition that is a direct extension of the 1-D definition. However, most of current discrete-space two-dimensional approaches do not consider scaling but instead are based on ad hoc formulations, for example, digitizing continuous random fields such as fractional Brownian motion. The dissertation demonstrates that the current statistical self-similarity definition in continuous-space is restrictive, and provides an alternative, more general definition. It also provides a formalism for discrete-space statistical self-similarity that depends on a new scaling operator for discrete images. Within the new framework, it is possible to synthesize a wider class of discrete-space self-similar random fields
Project Slope - A study of lunar orbiter photographic evaluation secondary analysis tasks Final report
Project SLOPE /Study of Lunar Orbiter Photographic Evaluation/ techniques, implementation and accurac
The global picture of self-similar and not self-similar decay in Burgers Turbulence
This paper continue earlier investigations on the decay of Burgers turbulence
in one dimension from Gaussian random initial conditions of the power-law
spectral type . Depending on the power , different
characteristic regions are distinguished. The main focus of this paper is to
delineate the regions in wave-number and time in which self-similarity
can (and cannot) be observed, taking into account small- and large-
cutoffs. The evolution of the spectrum can be inferred using physical arguments
describing the competition between the initial spectrum and the new frequencies
generated by the dynamics. For large wavenumbers, we always have
region, associated to the shocks. When is less than one, the large-scale
part of the spectrum is preserved in time and the global evolution is
self-similar, so that scaling arguments perfectly predict the behavior in time
of the energy and of the integral scale. If is larger than two, the
spectrum tends for long times to a universal scaling form independent of the
initial conditions, with universal behavior at small wavenumbers. In the
interval the leading behaviour is self-similar, independent of and
with universal behavior at small wavenumber. When , the spectrum
has three scaling regions : first, a region at very small \ms1 with
a time-independent constant, second, a region at intermediate
wavenumbers, finally, the usual region. In the remaining interval,
the small- cutoff dominates, and also plays no role. We find also
(numerically) the subleading term in the evolution of the spectrum
in the interval . High-resolution numerical simulations have been
performed confirming both scaling predictions and analytical asymptotic theory.Comment: 14 pages, 19 figure
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