Wavelet-based density estimation for noise reduction in plasma simulations using particles

For given computational resources, the accuracy of plasma simulations using particles is mainly held back by the noise due to limited statistical sampling in the reconstruction of the particle distribution function. A method based on wavelet analysis is proposed and tested to reduce this noise. The method, known as wavelet based density estimation (WBDE), was previously introduced in the statistical literature to estimate probability densities given a finite number of independent measurements. Its novel application to plasma simulations can be viewed as a natural extension of the finite size particles (FSP) approach, with the advantage of estimating more accurately distribution functions that have localized sharp features. The proposed method preserves the moments of the particle distribution function to a good level of accuracy, has no constraints on the dimensionality of the system, does not require an a priori selection of a global smoothing scale, and its able to adapt locally to the smoothness of the density based on the given discrete particle data. Most importantly, the computational cost of the denoising stage is of the same order as one time step of a FSP simulation. The method is compared with a recently proposed proper orthogonal decomposition based method, and it is tested with three particle data sets that involve different levels of collisionality and interaction with external and self-consistent fields

Approximation algorithms for wavelet transform coding of data streams

This paper addresses the problem of finding a B-term wavelet representation of a given discrete function $f \in \real^n$ whose distance from f is minimized. The problem is well understood when we seek to minimize the Euclidean distance between f and its representation. The first known algorithms for finding provably approximate representations minimizing general $\ell_p$ distances (including $\ell_\infty$) under a wide variety of compactly supported wavelet bases are presented in this paper. For the Haar basis, a polynomial time approximation scheme is demonstrated. These algorithms are applicable in the one-pass sublinear-space data stream model of computation. They generalize naturally to multiple dimensions and weighted norms. A universal representation that provides a provable approximation guarantee under all p-norms simultaneously; and the first approximation algorithms for bit-budget versions of the problem, known as adaptive quantization, are also presented. Further, it is shown that the algorithms presented here can be used to select a basis from a tree-structured dictionary of bases and find a B-term representation of the given function that provably approximates its best dictionary-basis representation.Comment: Added a universal representation that provides a provable approximation guarantee under all p-norms simultaneousl

Fuzzy rule based multiwavelet ECG signal denoising

Since different multiwavelets, pre- and post-filters have different impulse responses and frequency responses, different multiwavelets, pre- and post-filters should be selected and applied at different noise levels for signal denoising if signals are corrupted by additive white Gaussian noises. In this paper, some fuzzy rules are formulated for integrating different multiwavelets, pre- and post-filters together so that expert knowledge on employing different multiwavelets, pre- and post-filters at different noise levels on denoising performances is exploited. When an ECG signal is received, the noise level is first estimated. Then, based on the estimated noise level and our proposed fuzzy rules, different multiwavelets, pre- and post-filters are integrated together. A hard thresholding is applied on the multiwavelet coefficients. According to extensive numerical computer simulations, our proposed fuzzy rule based multiwavelet denoising algorithm outperforms traditional multiwavelet denoising algorithms by 30%

Wavelet transform for the evaluation of peak intensities in flow-injection analysis

The application of the wavelet transform in the determination of peak intensities in flow-injection analysis was studied with regard to its properties of minimizing the effects of noise and baseline drift. The results indicate that for white noise and a favourable peak shape a signal-to-noise ratio of 2 can be tolerated at the 5% error level, which means that a significant reduction in the detection limit can be obtained in comparison with the classical signal-processing methods. With regard to the influence of a changing baseline it was found that its d.c. level has a negligible effect, but a linear or exponentially rising baseline introduces an error that depends on the chosen frequency of the wavelet that is used to determine the peak intensity. The optimum choice of this frequency, in turn, depends on the shape of the peak that is studied. In this respect significant differences were observed for pure Gaussian and exponentially modified Gaussian peaks

Cross-Layer Peer-to-Peer Track Identification and Optimization Based on Active Networking

P2P applications appear to emerge as ultimate killer applications due to their ability to construct highly dynamic overlay topologies with rapidly-varying and unpredictable traffic dynamics, which can constitute a serious challenge even for significantly over-provisioned IP networks. As a result, ISPs are facing new, severe network management problems that are not guaranteed to be addressed by statically deployed network engineering mechanisms. As a first step to a more complete solution to these problems, this paper proposes a P2P measurement, identification and optimisation architecture, designed to cope with the dynamicity and unpredictability of existing, well-known and future, unknown P2P systems. The purpose of this architecture is to provide to the ISPs an effective and scalable approach to control and optimise the traffic produced by P2P applications in their networks. This can be achieved through a combination of different application and network-level programmable techniques, leading to a crosslayer identification and optimisation process. These techniques can be applied using Active Networking platforms, which are able to quickly and easily deploy architectural components on demand. This flexibility of the optimisation architecture is essential to address the rapid development of new P2P protocols and the variation of known protocols