ORCID Profile
0000-0002-2725-353X
Current Organisations
China Ship Scientific Research Center
,
City University of Hong Kong
,
Tsinghua University
,
Shanghai International Studies University
,
Zhejiang University
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Publisher: Hindawi Limited
Date: 2012
DOI: 10.1155/2012/863707
Abstract: The statistics of sea level is essential in the field of geosciences, ranging from ocean dynamics to climates. The fractal properties of sea level, such as long-range dependence (LRD) or long memory, 1 / f noise behavior, and self-similarity (SS), are known. However, the description of its multiscale behavior as well as local roughness with the Hölder exponent h ( t ) from a view of multifractional Brownian motion (mBm) is rarely reported, to the best of our knowledge. In this research, we will exhibit that there is the multiscale property of sea level based on h ( t ) s of sea level data recorded by the National Data Buoy Center (NDBC) at six stations in the Florida and Eastern Gulf of Mexico. The contributions of this paper are twofold as follows. (i) Hölder exponent of sea level may not change with time considerably at small time scale, for ex le, daily time scale, but it varies significantly at large time scale, such as at monthly time scale. (ii) The dispersion of the Hölder exponents of sea level may be different at different stations. This implies that the Hölder roughness of sea level may be spatial dependent.
Publisher: IEEE
Date: 2000
Publisher: Elsevier BV
Date: 12-2012
Publisher: IEEE Comput. Soc
Date: 2000
Publisher: Hindawi Limited
Date: 2013
DOI: 10.1155/2013/471963
Abstract: We contribute the quantitative descriptions of the large time scales for the Ethernet traffic to be Gaussian. We focus on the normality property of the accumulated traffic data under different time scales. The investigation is carried out graphically by the quantile-quantile (QQ) plots and numerically by statistical tests. The present results indicate that the larger the time scale, the more normal the Ethernet traffic.
Publisher: Hindawi Limited
Date: 2013
DOI: 10.1155/2013/767502
Abstract: This paper provides the fluctuation analysis of random functions with the Pareto distribution. By the introduced concept of wild fluctuations, we give an alternative way to classify the fluctuations from those with light-tailed distributions. Moreover, the suggested term wildest fluctuation may be used to classify random functions with infinite variance from those with finite variances.
Publisher: Hindawi Limited
Date: 2013
DOI: 10.1155/2013/157636
Abstract: Delay analysis plays a role in real-time systems in computer communication networks. This paper gives our results in the aspect of delay analysis of fractal traffic passing through servers. There are three contributions presented in this paper. First, we will explain the reasons why conventional theory of queuing systems ceases in the general sense when arrival traffic is fractal. Then, we will propose a concise method of delay computation for hard real-time systems as shown in this paper. Finally, the delay computation of fractal traffic passing through severs is presented.
Publisher: Elsevier BV
Date: 05-2019
DOI: 10.1016/J.WATRES.2019.01.056
Abstract: We are still facing the knowledge gap of how the water-quality extremes (i.e. phytoplankton blooms), their causes, severity or occurrence could be directly related to the climatic oscillation. Considering that the climatic and phytoplankton concentration time series are highly non-stationary, we applied the advanced time-frequency analysis - Ensemble Empirical Mode Decomposition (EEMD), Hilbert-Huang Spectrum (HHS) and Wavelet Analysis (WA) - to examine the variability of long term phytoplankton dynamics from 1986 to 2014 in five North Temperate Lakes (NTLs). These analysis techniques isolated five separate time series for the surface Chlorophyll a concentrations (CHL) of the five NTLs and a time series for the global climate oscillation (denoted by multivariate ENSO index, MEI), and showed that these time series generally operated at similar time scales. The long-term residual trends of decreasing were found in three lakes (i.e., BM, SP and TR lakes), which are the same to global climate dynamics (MEI). The wavelet analysis reveals strong coherency between MEI and CHL data sets for all lakes, with a periodicity of 64-months. Intuitive associations between the CHL and MEI data set showed that two types of ENSO (El Nino and La Nina) differ in their influences to CHL. Potential mechanisms relating the phytoplankton dynamics in NTLs to climatic oscillation (ENSO) were also discussed.
Publisher: Hindawi Limited
Date: 2013
DOI: 10.1155/2013/130258
Abstract: von Karman originally deduced his spectrum of wind speed fluctuation based on the Stokes-Navier equation. Taking into account, the practical issues of measurement and/or computation errors, we suggest that the spectrum can be described from the point of view of the golden ratio. We call it the golden ratio phenomenon of the von Karman spectrum. To depict that phenomenon, we derive the von Karman spectrum based on fractional differential equations, which bridges the golden ratio to the von Karman spectrum and consequently provides a new outlook of random data following the von Karman spectrum in turbulence. In addition, we express the fractal dimension, which is a measure of local self-similarity, using the golden ratio, of random data governed by the von Karman spectrum.
Publisher: Elsevier BV
Date: 03-2003
Publisher: Institution of Engineering and Technology (IET)
Date: 2000
DOI: 10.1049/EL:20001183
Publisher: Hindawi Limited
Date: 2012
DOI: 10.1155/2012/821215
Abstract: Self-similar process with long-range dependence (LRD), that is, fractional Gaussian noise (fGn) with LRD is a widely used model of Internet traffic. It is indexed by its Hurst parameter H fGn that linearly relates to its fractal dimension D f G n . Note that, on the one hand, the fractal dimension D of traffic measures local self-similarity. On the other hand, LRD is a global property of traffic, which is characterized by its Hurst parameter H . However, by using fGn, both the self-similarity and the LRD of traffic are measured by H f G n . Therefore, there is a limitation for fGn to accurately model traffic. Recently, the generalized Cauchy (GC) process was introduced to model traffic with the flexibility to separately measure the fractal dimension D G C and the Hurst parameter H G C of traffic. However, there is a fundamental problem whether or not there exists the generality that the GC model is more conformable with real traffic than single parameter models, such as fGn, irrelevant of traffic traces used in experimental verification . The solution to that problem remains unknown but is desired for model evaluation in traffic theory or for model selection against specific issues, such as queuing analysis relating to the autocorrelation function (ACF) of arrival traffic. The key contribution of this paper is our solution to that fundamental problem (see Theorem 3.17) with the following features in analysis. (i) Set-valued analysis of the traffic of the fGn type. (ii) Set-valued analysis of the traffic of the GC type. (iii) Revealing the generality previously mentioned by comparing metrics of the traffic of the fGn type to that of the GC type.
Publisher: Elsevier BV
Date: 05-2013
Publisher: Hindawi Limited
Date: 2012
DOI: 10.1155/2012/843676
Abstract: We study the Cauchy-Matern (CM) process with long-range dependence (LRD). The closed form of its power spectrum density (PSD) function is given. We apply it to model the autocovariance function (ACF) and the PSD of the sea surface wind speed (wind speed for short) observed in the Lake Worth, Florida, over the 1984–2006 period. The present results exhibit that the wind speed at the Lake Worth over 1984–2006 is of LRD. The present results exhibit that the CM process may yet be a novel model to fit the wind speed there.
Publisher: Hindawi Limited
Date: 2013
DOI: 10.1155/2013/680678
Abstract: The golden ratio is an astonishing number in high-energy physics, neutrino physics, and cosmology. The Kolmogorov −5/3 law plays a role in describing energy transfer of random data or random functions. The contributions of this essay are in twofold. One is to express the Kolmogorov −5/3 law by using the golden ratio. The other is to represent the fractal dimension of random data following the Kolmogorov −5/3 law with the golden ratio. It is our hope that this essay may be helpful to provide a new outlook of the Kolmogorov −5/3 law from the point of view of the golden ratio.
Publisher: IEEE
Date: 2001
Publisher: Hindawi Limited
Date: 2011
DOI: 10.1155/2011/389803
Abstract: Scaling phenomena of the Internet traffic gain people's interests, ranging from computer scientists to statisticians. There are two types of scales. One is small-time scaling and the other large-time one. Tools to separately describe them are desired in computer communications, such as performance analysis of network systems. Conventional tools, such as the standard fractional Brownian motion (fBm), or its increment process, or the standard multifractional fBm (mBm) indexed by the local Hölder function H ( t ) may not be enough for this purpose. In this paper, we propose to describe the local scaling of traffic by using D ( t ) on a point-by-point basis and to measure the large-time scaling of traffic by using E [ H ( t ) ] on an interval-by-interval basis, where E implies the expectation operator. Since E [ H ( t ) ] is a constant within an observation interval while D ( t ) is random in general, they are uncorrelated with each other. Thus, our proposed method can be used to separately characterize the small-time scaling phenomenon and the large one of traffic, providing a new tool to investigate the scaling phenomena of traffic.
Publisher: Hindawi Limited
Date: 2013
DOI: 10.1155/2013/806984
Abstract: This paper gives a novel explanation of the integral equation of Abel’s type from the point of view of Mikusinski’s operational calculus. The concept of the inverse of Mikusinski’s operator of fractional order is introduced for constructing a representation of the solution to the integral equation of Abel’s type. The proof of the existence of the inverse of the fractional Mikusinski operator is presented, providing an alternative method of treating the integral equation of Abel’s type.
Publisher: Hindawi Limited
Date: 2012
DOI: 10.1155/2012/673648
Abstract: Due to the fact that 1 / f noise gains the increasing interests in the field of biomedical signal processing and living systems, we present this introductive survey that may suffice to exhibit the elementary and the particularities of 1 / f noise in comparison with conventional random functions. Three theorems are given for highlighting the particularities of 1 / f noise. The first says that a random function with long-range dependence (LRD) is a 1 / f noise. The secondindicates that a heavy-tailed random function is in the class of 1 / f noise. The third provides a type of stochastic differential equations that produce 1 / f noise.
Publisher: Hindawi Limited
Date: 2008
DOI: 10.1155/2008/475878
Abstract: The aim of distributed denial-of-service (DDOS) flood attacks is to overwhelm the attacked site or to make its service performance deterioration considerably by sending flood packets to the target from the machines distributed all over the world. This is a kind of local behavior of traffic at the protected site because the attacked site can be recovered to its normal service state sooner or later even though it is in reality overwhelmed during attack. From a view of mathematics, it can be taken as a kind of short-range phenomenon in computer networks. In this paper, we use the Hurst parameter ( H ) to measure the local irregularity or self-similarity of traffic under DDOS flood attack provided that fractional Gaussian noise (fGn) is used as the traffic model. As flood attack packets of DDOS make the H value of arrival traffic vary significantly away from that of traffic normally arriving at the protected site, we discuss a method to statistically detect signs of DDOS flood attacks with predetermined detection probability and false alarm probability.
Publisher: Hindawi Limited
Date: 2013
DOI: 10.1155/2013/725730
Abstract: We depict our work on a fundamental issue in the theory of long-range dependent traffic in the aspect of the convergence of s le autocorrelation function (ACF) of real traffic. The present results suggest that the s le ACF of traffic is convergent. In addition, we show that the s le size has considerable effects in estimating the s le ACF of traffic. More precisely, a s le ACF of traffic tends to be smoother when the s le size increases.
Publisher: Hindawi Limited
Date: 2010
DOI: 10.1155/2010/560429
Abstract: This paper discusses the estimation of autocorrelation function (ACF) of fractional Gaussian noise (fGn) with long-range dependence (LRD). A variance bound of ACF estimation of one block of fGn with LRD for a given value of the Hurst parameter ( H ) is given. The present bound provides a guideline to require the block size to guarantee that the variance of ACF estimation of one block of fGn with LRD for a given H value does not exceed the predetermined variance bound regardless of the start point of the block. In addition, the present result implies that the error of ACF estimation of a block of fGn with LRD depends only on the number of data points within the s le and not on the actual s le length in time. For a given block size, the error is found to be larger for fGn with stronger LRD than that with weaker LRD.
Publisher: ASTM International
Date: 2000
DOI: 10.1520/JTE12129J
Publisher: Hindawi Limited
Date: 2013
DOI: 10.1155/2013/631498
Abstract: This paper depicts our work in smoothing the s le autocorrelation function (ACF) of traffic. The experimental results exhibit that the s le ACF of traffic may be smoothed by the way of average. In addition, the results imply that the sum of s le ACFs of traffic convergences. Considering that the traffic data used in this research is long-range dependent (LRD), the latter may be meaningful for the theoretical research of LRD traffic.
Publisher: Hindawi Limited
Date: 2013
DOI: 10.1155/2013/635412
Abstract: This paper presents the representation of the fractional Riemann-Liouville integral by using the Mikusinski operators. The Mikusinski operators discussed in the paper may yet provide a new view to describe and study the fractional Riemann-Liouville integral operator. The present result may be useful for applying the Mikusinski operational calculus to the study of fractional calculus in mathematics and to the theory of filters of fractional order in engineering.
Publisher: Hindawi Limited
Date: 2012
DOI: 10.1155/2012/302786
Abstract: Cyber-physical networking systems (CPNSs) are made up of various physical systems that are heterogeneous in nature. Therefore, exploring universalities in CPNSs for either data or systems is desired in its fundamental theory. This paper is in the aspect of data, aiming at addressing that power laws may yet be a universality of data in CPNSs. The contributions of this paper are in triple folds. First, we provide a short tutorial about power laws. Then, we address the power laws related to some physical systems. Finally, we discuss that power-law-type data may be governed by stochastically differential equations of fractional order. As a side product, we present the point of view that the upper bound of data flow at large-time scaling and the small one also follows power laws.
Publisher: Hindawi Limited
Date: 2012
DOI: 10.1155/2012/154038
Abstract: Network calculus is a theory initiated primarily in computer communication networks, especially in the aspect of real-time communications, where min-plus algebra plays a role. Cyber-physical networking systems (CPNSs) are recently developing fast and models in data flows as well as systems in CPNS are, accordingly, greatly desired. Though min-plus algebra may be a promising tool to linearize any node in CPNS as can be seen from its applications to the Internet computing, there are tough problems remaining unsolved in this regard. The identity in min-plus algebra is one problem we shall address. We shall point out the confusions about the conventional identity in the min-plus algebra and present an analytical expression of the asymptotic identity that may not cause confusions.
Publisher: MDPI AG
Date: 25-05-2021
DOI: 10.3390/FRACTALFRACT5020049
Abstract: Phytoplankton movement patterns and swimming behavior are important and basic topics in aquatic biology. Heavy tail distribution exists in erse taxa and shows theoretical advantages in environments. The fat tails in the movement patterns and swimming behavior of phytoplankton in response to the food supply were studied. The log-normal distribution was used for fitting the probability density values of the movement data of Oxyrrhis marina. Results showed that obvious fat tails exist in the movement patterns of O. marina without and with positive stimulations of food supply. The algal cells tended to show a more chaotic and disorderly movement, with shorter and neat steps after adding the food source. At the same time, the randomness of turning rate, path curvature and swimming speed increased in O. marina cells with food supply. Generally, the responses of phytoplankton movement were stronger when supplied with direct prey cells rather than the cell-free filtrate. The scale-free random movements are considered to benefit the adaption of the entire phytoplankton population to varied environmental conditions. Inferentially, the movement pattern of O. marina should also have the characteristics of long-range dependence, local self-similarity and a system of fractional order.
Publisher: Hindawi Limited
Date: 2012
DOI: 10.1155/2012/419319
Abstract: This paper gives a novel traffic feature for identifying abnormal variation of traffic under DDOS flood attacks. It is the histogram of the maxima of the bounded traffic rate on an interval-by-interval basis. We use it to experiment on the traffic data provided by MIT Lincoln Laboratory under Defense Advanced Research Projects Agency (DARPA) in 1999. The experimental results profitably enhance the evidences that traffic rate under DDOS attacks is statistically higher than that of normal traffic considerably. They show that the pattern of the histogram of the maxima of bounded rate of attack-contained traffic greatly differs from that of attack-free traffic. Besides, the present traffic feature is simple in mathematics and easy to use in practice.
Publisher: Hindawi Limited
Date: 2012
DOI: 10.1155/2012/860569
Abstract: Reliable distinguishing DDOS flood traffic from aggregated traffic is desperately desired by reliable prevention of DDOS attacks. By reliable distinguishing, we mean that flood traffic can be distinguished from aggregated one for a predetermined probability. The basis to reliably distinguish flood traffic from aggregated one is reliable detection of signs of DDOS flood attacks. As is known, reliably distinguishing DDOS flood traffic from aggregated traffic becomes a tough task mainly due to the effects of flash-crowd traffic. For this reason, this paper studies reliable detection in the underlying DiffServ network to use static-priority schedulers. In this network environment, we present a method for reliable detection of signs of DDOS flood attacks for a given class with a given priority. There are two assumptions introduced in this study. One is that flash-crowd traffic does not have all priorities but some. The other is that attack traffic has all priorities in all classes, otherwise an attacker cannot completely achieve its DDOS goal. Further, we suppose that the protected site is equipped with a sensor that has a signature library of the legitimate traffic with the priorities flash-crowd traffic does not have. Based on those, we are able to reliably distinguish attack traffic from aggregated traffic with the priorities that flash-crowd traffic does not have according to a given detection probability.
Publisher: Institute of Electrical and Electronics Engineers (IEEE)
Date: 09-2010
Publisher: IOP Publishing
Date: 2023
Abstract: The timeliness of monitoring is essential to algal bloom management. However, acquiring algal bio-indicators can be time-consuming and laborious, and bloom biomass data often contain a large proportion of extreme values limiting the predictive models. Therefore, to predict algal blooms from readily water quality parameters (i.e. dissolved oxygen, pH, etc), and to provide a novel solution to the modeling challenges raised by the extremely distributed biomass data, a Bayesian scale-mixture of skew-normal (SMSN) model was proposed. In this study, our SMSN model accurately predicted over-dispersed biomass variations with skewed distributions in both rivers and lakes (in-s le and out-of-s le prediction R 2 ranged from 0.533 to 0.706 and 0.412 to 0.742, respectively). Moreover, we successfully achieve a probabilistic assessment of algal blooms with the Bayesian framework (accuracy .77 and macro- F 1 score .72), which robustly decreased the classic point-prediction-based inaccuracy by up to 34%. This work presented a promising Bayesian SMSN modeling technique, allowing for real-time prediction of algal biomass variations and in-situ probabilistic assessment of algal bloom.
Publisher: Hindawi Limited
Date: 2013
DOI: 10.1155/2013/217213
Abstract: We investigate the stationarity property of the accumulated Ethernet traffic series. We applied several widely used stationarity and unit root tests, such as Dickey-Fuller test and its augmented version, Phillips-Perron test, as well as the Kwiatkowski-Phillips-Schmidt-Shin test and some of its generalizations, to the assessment of the stationarity of the traffic traces at the different time scales. The quantitative results in this research provide evidence that when the time scale increases, the accumulated traffic series are more stationary.
Publisher: Hindawi Limited
Date: 10-07-2018
DOI: 10.1155/2018/7402764
Abstract: We consider a class of stochastic fractional heat equations driven by fractional noises. A central limit theorem is given, and a moderate deviation principle is established.
Publisher: IEEE
Date: 2001
Publisher: Hindawi Limited
Date: 2012
DOI: 10.1155/2012/291510
Abstract: A fractal signal x ( t ) in biomedical engineering may be characterized by 1 / f noise, that is, the power spectrum density (PSD) ergences at f = 0 . According the Taqqu’s law, 1 / f noise has the properties of long-range dependence and heavy-tailed probability density function (PDF). The contribution of this paper is to exhibit that the prediction error of a biomedical signal of 1 / f noise type is long-range dependent (LRD). Thus, it is heavy-tailed and of 1 / f noise. Consequently, the variance of the prediction error is usually large or may not exist, making predicting biomedical signals of 1 / f noise type difficult.
No related grants have been discovered for Ming Li.