WAVELET-BASED ESTIMATOR FOR THE HURST PARAMETERS OF FRACTIONAL BROWNIAN SHEET

It is proposed a class of statistical estimators H = （H1,… ,Hd） for the Hurst parameters H = （H1,… ,Hd） of fractional Brownian field via multi-dimensional wavelet analysis and least squares, which are asymptotically normal. These estimators can be used to detect self-similarity and long-range dependence in multi-dimensional signals, which is important in texture classification and improvement of diffusion tensor imaging （DTI） of nuclear magnetic resonance （NMR）. Some fractional Brownian sheets will be simulated and the simulated data are used to validate these estimators. We find that when Hi ≥ 1/2, the estimators are accurate, and when Hi 〈 1/2, there are some bias.

Another Important Parameter’s Research on Estimating Self-Similarity

It is convincingly demonstrated by numerous studies that the self-similarity of modern multimedia network traffic is presented by Hurst parameter (H). The specific performance is that the similar degree is higher along with the increase of H when H is between 0.5 and 1. However, it is doubtable that whether the complicated process of self-similarity can be described comprehensively by the parameter H only. Therefore, another important parameter cf has been proposed based on the discrete wavelet decomposition in this paper. The significance of the parameters is provided and the performance of the self-similarity process is described better.

Self Similarity Analysis of Web Users Arrival Pattern at Selected Web Centers

The paper focuses on measuring self-similarity using few techniques by an index called Hurst index which is a self-similarity parameter. It has been evident that Internet traffic exhibits self-similarity. Motivated by this fact, real time web users at various centers considered here as traffic and it has been examined by various methods to test the self-similarity. The results from the experiments carried out verify that the traffic examined in the present study is self similar using a new method based on some descriptive measures;for example percentiles have been applied to compute Hurst parameter which gives intensity of the self-similarity. Numerical results and analysis we discussed and presented here play a significant role to improve the services at web centers in the view of quality of service (QOS).

FRACTIONAL 2D-STOCHASTIC CURRENTS

Using multiple stochastic integrals and the stochastic calculus for the frac-tional Brownian sheet, we define and we analyze the 2D-fractional stochastic currents.

A statistical hiding algorithm based on self-similar network traffic

Although the encryption of network packets significantly increases privacy, the density of the traffic can still provide useful information to the observer, and maybe results in the breach of confidentiality. In this paper, we address issues related to hiding information in self-similar network, which is proved to be similar with modern communication network. And a statistical hiding algorithm is proposed for traffic padding. The figures and the comparison of Hurst Parameters before and after traffic padding, show the effective performance of the algorithm.

Network resource allocation attack detection with long range dependence

The approach of traffic abnormality detection of network resource allocation attack did not have reliable signatures to depict abnormality and identify them. However, it is crucial for us to detect attacks accurately. The technique that we adopted is inspired by long range dependence ideas. We use the number of packet arrivals of a flow in fixed-length time intervals as the signal and attempt to extend traffic invariant “self-similarity”. We validate the effectiveness of the approach with simulation and trace analysis.

Implementation of Efficient Burst Assembly Algorithm with Traffic Prediction

This paper reports on the implementation of efficient burst assembly algorithms and traffic prediction. The ultimate goal is to propose a new burst assembly algorithm which is based on time-burst length （hybrid） threshold with traffic prediction to reduce burst assembly delay in OBS （Optical Burst Switching） networks. Research has shown that traffic always change from time to time, hence, any measure that is put in place should be able to adapt to such changes. With our implemented burst assembly algorithm, the traffic rate is predicted and the predicted rate is used to dynamically adjust the burst assembly length. This work further investigates the impact of the proposed algorithm on traffic self similarity.

Forecasting Short Time Series with Missing Data by Means of Energy Associated to Series

In this work an algorithm to predict short times series with missing data by means energy associated of series using artificial neural networks (ANN) is presented. In order to give the prediction one step ahead, a comparison between this and previous work that involves a similar approach to test short time series with uncertainties on their data, indicates that a linear smoothing is a well approximation in order to employ a method for uncompleted datasets. Moreover, in function of the long- or short-term stochastic dependence of the short time series considered, the training process modifies the number of patterns and iterations in the topology according to a heuristic law, where the Hurst parameter H is related with the short times series, of which they are considered as a path of the fractional Brownian motion. The results are evaluated on high roughness time series from solutions of the Mackey-Glass Equation (MG) and cumulative monthly historical rainfall data from San Agustin, Cordoba. A comparison with ANN nonlinear filters is shown in order to see a better performance of the outcomes when the information is taken from geographical point observation.

Brain-inspired dual-pathway neural network architecture and its generalization analysis

In this study, we explored the neural mechanism of global topological perception in the human visual system. We showed strong evidence that the retinotectal pathway in the archicortex of the human brain is responsible for global topological perception, and for modulating the local feature processing in the classical ventral visual pathway. Inspired by this recent cognitive discovery,we developed a novel CogNet architecture to emulate the global-local dichotomy of human visual cognitive mechanisms. The thorough experimental results indicate that the proposed CogNet not only significantly improves image classification accuracies but also effectively addresses the texture bias problem observed in baseline CNN models. We have also conducted mathematical analysis for the generalization gap for general neural networks. Our theoretical derivations suggest that the Hurst parameter, a measure of the curvature of the loss landscape, can closely bind the generalization gap. A larger Hurst parameter corresponds to a better generalization ability. We found that our proposed CogNet achieves a lower test error and attains a larger Hurst parameter,strengthening its superiority over the baseline CNN models further.