On the Distribution Properties of BitTorrent Seeds

2011 ◽  
Vol 186 ◽  
pp. 510-514
Author(s):  
Hong Tang ◽  
Lu Wang ◽  
Ding Huang
Keyword(s):  
Lyapunov Exponent ◽  
Gini Coefficient ◽  
Web Server ◽  
Largest Lyapunov Exponent ◽  
The Gini Coefficient ◽  
Seed Distribution ◽  
Emergent Structure ◽  
The Stability ◽  
P2p Applications ◽  
The Web

The P2P applications tend to be important in nowadays Internet, and BitTorrent(BT) is one of the most popular P2P applications. This paper analyzes the distribution of BitTorrent seeds and its properties with the data measured from the Web server of BitTorrent. The Gini coefficient is introduced as the index of the distribution of the seeds in BitTorrent system to demonstrate the evolution of the seed distribution. The Largest Lyapunov exponent is also employed to analyze the stability of the emergent structure of the seeds. The results show that in a BitTorrent system the seed distribution is not inequality, but its evolution is steady and the inequality doesn’t enlarge with the participants’ increasing.

Stochastic Stability of a Universal-Joint Driven Torsional System

1999 ◽  
Author(s):  
S. F. Asokanthan ◽  
Xiao-Hui Wang
Keyword(s):  
Lyapunov Exponent ◽  
Excitation Frequency ◽  
Excitation Amplitude ◽  
Angular Speed ◽  
Analytical Models ◽  
Largest Lyapunov Exponent ◽  
Deterministic Case ◽  
Speed Fluctuation ◽  
The Difference ◽  
The Stability

Abstract Torsional instabilities in a two-degree-of-freedom system driven by a Hooke’s joint due to random input angular speed fluctuation are investigated. Linearised analytical models are used for calculating the largest Lyapunov exponent. Instability behaviour is then characterised by examining the sign of this exponent. Conditions for the onset of instability via sub-harmonic parametric resonances has been shown to coincide with those for the deterministic case. However, the onset of instability via sum as well as the difference type combination resonance is found to be different from that of the deterministic case. The instability conditions for the system under input angular speed fluctuation have been presented graphically in the excitation frequency-excitation amplitude-top Lyapunov exponent space. Predictions for the deterministic and the stochastic cases are compared. The effect of fluctuation probability density as well as that of inertia loads on the stability behaviour of the system has been examined.

scholarly journals Stochastic Stability of Coupled Viscoelastic Systems Excited by Real Noise

2018 ◽  
Vol 2018 ◽  
pp. 1-14 ◽  
Author(s):  
Jian Deng
Keyword(s):  
Lyapunov Exponent ◽  
Lyapunov Exponents ◽  
Stochastic Stability ◽  
Random Fluctuation ◽  
Largest Lyapunov Exponent ◽  
Real Noise ◽  
The Largest Lyapunov Exponent ◽  
The Stability ◽  
The Moment ◽  
Moment Lyapunov Exponents

The moment stochastic stability and almost-sure stochastic stability of two-degree-of-freedom coupled viscoelastic systems, under the parametric excitation of a real noise, are investigated through the moment Lyapunov exponents and the largest Lyapunov exponent, respectively. The real noise is also called the Ornstein-Uhlenbeck stochastic process. For small damping and weak random fluctuation, the moment Lyapunov exponents are determined approximately by using the method of stochastic averaging and a formulated eigenvalue problem. The largest Lyapunov exponent is calculated through its relation with moment Lyapunov exponents. The stability index, the stability boundaries, and the critical excitation are obtained analytically. The effects of various parameters on the stochastic stability of the system are then discussed in detail. Monte Carlo simulation is carried out to verify the approximate results of moment Lyapunov exponents. As an application example, the stochastic stability of a flexural-torsional viscoelastic beam is studied.

scholarly journals Alternative Methods of the Largest Lyapunov Exponent Estimation with Applications to the Stability Analyses Based on the Dynamical Maps—Introduction to the Method

Materials ◽  
2021 ◽  
Vol 14 (23) ◽  
pp. 7197
Author(s):  
Artur Dabrowski ◽  
Tomasz Sagan ◽  
Volodymyr Denysenko ◽  
Marek Balcerzak ◽  
Sandra Zarychta ◽  
...  
Keyword(s):  
Lyapunov Exponent ◽  
Numerical Algorithms ◽  
Alternative Methods ◽  
Largest Lyapunov Exponent ◽  
Continuous Systems ◽  
Science And Engineering ◽  
Stability Of Dynamical Systems ◽  
The Largest Lyapunov Exponent ◽  
The Stability ◽  
Mathematical Operations

Controlling stability of dynamical systems is one of the most important challenges in science and engineering. Hence, there appears to be continuous need to study and develop numerical algorithms of control methods. One of the most frequently applied invariants characterizing systems’ stability are Lyapunov exponents (LE). When information about the stability of a system is demanded, it can be determined based on the value of the largest Lyapunov exponent (LLE). Recently, we have shown that LLE can be estimated from the vector field properties by means of the most basic mathematical operations. The present article introduces new methods of LLE estimation for continuous systems and maps. We have shown that application of our approaches will introduce significant improvement of the efficiency. We have also proved that our approach is simpler and more efficient than commonly applied algorithms. Moreover, as our approach works in the case of dynamical maps, it also enables an easy application of this method in noncontinuous systems. We show comparisons of efficiencies of algorithms based our approach. In the last paragraph, we discuss a possibility of the estimation of LLE from maps and for noncontinuous systems and present results of our initial investigations.

Almost sure and moment stability properties of fractional order Black-Scholes model

2013 ◽  
Vol 16 (2) ◽  
Author(s):  
Caibin Zeng ◽  
YangQuan Chen ◽  
Qigui Yang
Keyword(s):  
Lyapunov Exponent ◽  
Asymptotic Stability ◽  
Large Deviations ◽  
Fractional Order ◽  
Sufficient Conditions ◽  
Largest Lyapunov Exponent ◽  
Model Driven ◽  
Black Scholes Model ◽  
Black Scholes ◽  
The Stability

AbstractWe deal with the stability problem of the fractional order Black-Scholes model driven by fractional Brownian motion (fBm). First, necessary and sufficient conditions are established for almost sure asymptotic stability and pth moment asymptotic stability by means of the largest Lyapunov exponent and the pth moment Lyapunov exponent, respectively. Moreover, we are able to present large deviations results for this fractional process. In particular, for the first time it is found that the Hurst parameter affects both stability conclusions and large deviations. Interestingly, large deviations always happen for the considered system when 1/2 < H < 1. This fact is due to the long-range dependence (LRD) property of the fBm. Numerical simulation results are presented to illustrate the above findings.

APLIKASI PENCARI INFORMASI PERMINTAAN LAYANAN WEB YANG ERROR MENGGUNAKAN ALGORITMA BOYER-MOORE

2016 ◽  
Vol 1 (1) ◽  
pp. 001
Author(s):  
Harry Setya Hadi
Keyword(s):  
Data Storage ◽  
Computer Network ◽  
Web Server ◽  
Access Methods ◽  
Ip Address ◽  
String Searching ◽  
Common Process ◽  
Web Server Logs ◽  
Different Parts ◽  
The Web

String searching is a common process in the processes that made the computer because the text is the main form of data storage. Boyer-Moore is the search string from right to left is considered the most efficient methods in practice, and matching string from the specified direction specifically an algorithm that has the best results theoretically. A system that is connected to a computer network that literally pick a web server that is accessed by multiple users in different parts of both good and bad aim. Any activity performed by the user, will be stored in Web server logs. With a log report contained in the web server can help a web server administrator to search the web request error. Web server log is a record of the activities of a web site that contains the data associated with the IP address, time of access, the page is opened, activities, and access methods. The amount of data contained in the resulting log is a log shed useful information.

EFFECTS OF TREND AND PERIODICITY ON THE CORRELATION DIMENSION AND THE LYAPUNOV EXPONENTS

2008 ◽  
Vol 18 (12) ◽  
pp. 3679-3687 ◽  
Author(s):  
AYDIN A. CECEN ◽  
CAHIT ERKAL
Keyword(s):  
Time Series ◽  
Lyapunov Exponent ◽  
Lyapunov Exponents ◽  
Correlation Dimension ◽  
Time Series Data ◽  
Logistic Map ◽  
Model Identification ◽  
Series Data ◽  
Largest Lyapunov Exponent ◽  
The Impact

We present a critical remark on the pitfalls of calculating the correlation dimension and the largest Lyapunov exponent from time series data when trend and periodicity exist. We consider a special case where a time series Zi can be expressed as the sum of two subsystems so that Zi = Xi + Yi and at least one of the subsystems is deterministic. We show that if the trend and periodicity are not properly removed, correlation dimension and Lyapunov exponent estimations yield misleading results, which can severely compromise the results of diagnostic tests and model identification. We also establish an analytic relationship between the largest Lyapunov exponents of the subsystems and that of the whole system. In addition, the impact of a periodic parameter perturbation on the Lyapunov exponent for the logistic map and the Lorenz system is discussed.

The Lyapunov Exponent Variance of an Electronic Manufacturing Enterprise’s Daily Qualified Rate Time Series by Improved Small Data Sets Approach

2012 ◽  
Vol 197 ◽  
pp. 271-277
Author(s):  
Zhu Ping Gong
Keyword(s):  
Time Series ◽  
Lyapunov Exponent ◽  
Chaotic Time Series ◽  
Quality System ◽  
Quality Level ◽  
Largest Lyapunov Exponent ◽  
Small Data ◽  
Data Set ◽  
Electronic Manufacturing ◽  
Small Data Set

Small data set approach is used for the estimation of Largest Lyapunov Exponent (LLE). Primarily, the mean period drawback of Small data set was corrected. On this base, the LLEs of daily qualified rate time series of HZ, an electronic manufacturing enterprise, were estimated and all positive LLEs were taken which indicate that this time series is a chaotic time series and the corresponding produce process is a chaotic process. The variance of the LLEs revealed the struggle between the divergence nature of quality system and quality control effort. LLEs showed sharp increase in getting worse quality level coincide with the company shutdown. HZ’s daily qualified rate, a chaotic time series, shows us the predictable nature of quality system in a short-run.

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