Multifractal spectrum distribution based on detrending moving average

The time-singularity multifractal spectrum distribution (MFSD) has been proposed recently as a generalized singularity spectrum in a time varying framework. In this paper, we aim at putting forward a new algorithm i.e. MFSD based on detrending moving average (DMA-MFSD) to determine MFSD, which is also a generalization of multifractal detrending moving average (MF-DMA) method. We relate DMA-MFSD method to the MFSD based on the standard partition function, and prove that both approaches are equivalent for fractal time series with compact support. The performance of the DMA-MFSD methods with different moving windows is studied using synthetic fractional Gaussian noise (fGn), binomial multiplicative cascades (BMC) with analytical solutions and real sea clutter data. We find that the estimated DMA-MFSD is in good accordance with the detrended fluctuation analysis based multifractal spectrum distribution (DFA-MFSD) and the theoretical analysis. Overall, the backward DMA-MFSD method has the best performance, which provides the most accurate estimates of the time-singularity MFSD, while the centered DMA-MFSD method performs worse. In addition we find that the backward DMA-MFSD algorithm even outperforms the DFA-MFSD method in the computational complexity and precision.     

Small and Large Time Scale Analysis of a Network Traffic Model

Empirical studies of the internet and WAN traffic data have observed multifractal behavior at time scales below a few hundred milliseconds. There have been some attempts to model this phenomenon, but there is no model to connect the small time scale behavior with behavior observed at large time scales of bigger than a few hundred milliseconds. There have been separate analyses of models for high speed data transmissions, which show that appropriate approximations to large time scale behavior of cumulative traffic are either fractional Brownian motion or stable Lévy motion, depending on the input rates assumed. This paper tries to bridge this gap and develops and analyzes a model offering an explanation of both the small and large time scale behavior of a network traffic model based on the infinite source Poisson model. Previous studies of this model have usually assumed that transmission rates are constant and deterministic. We consider a nonconstant, multifractal, random transmission rate at the user level which results in cumulative traffic exhibiting multifractal behavior on small time scales and self-similar behavior on large time scales.     

Generation of Over-Dispersed and Under-Dispersed Binomial Variates

Abstract

This article proposes an algorithm for generating over-dispersed and under-dispersed binomial variates with specified mean and variance. The over-dispersed/under-dispersed distributions are derived from correlated binary variables with an underlying continuous multivariate distribution. Different multivariate distributions or different correlation matrices result in different over-dispersed (or under-dispersed) distributions. The over-dispersed binomial distributions that are generated from three different correlation matrices of a multivariate normal are compared with the beta-binomial distribution for various mean and over-dispersion parameters by quantile-quantile (Q-Q) plots. The two distributions appear to be similar. The under-dispersed binomial distribution is simulated to model an example data set that exhibits under-dispersed binomial variation.     

北京交通流序列的重分形扩散熵分析

运用重分形扩散熵分析方法来分析北京交通拥堵指数的长程相关性和重分形特征.方法综合使用了扩散技术和Renyi熵来研究北京交通拥堵指数的标度行为.由于交通拥堵指数序列具有明显的周期性,故先选用傅里叶滤波去除序列的周期性,再进行重分形扩散熵分析.实验结果表明北京交通拥堵指数序列的极端波动显示出反相关性,同时拥堵指数序列具有较弱的重分形特征.     

Optimal routing of vehicles with communication capabilities in disasters

Major emergencies and disasters such as acts of terrorism, acts of nature, or human-caused accidents may lead to disruptions in traffic flow. Minimizing the negative effects of such disruptions is critical for a nation’s economy and security. A decision support system that is capable of gathering (real-time) information about the traffic conditions following a disaster and utilizing this information to generate alternative routes for vehicles would benefit the government, industry, and the public. For this purpose, we develop a mathematical programming model to minimize the delay for vehicles with communication capabilities following a disaster. Most commercial trucks and public buses utilize QUALCOMM as a communication tool. We also develop a prediction model for vehicles that do not have any communication capabilities. Although the problem is inherently integer we developed a linear program to reduce the computational burden caused by the large size of the problem. An algorithm is proposed to update the parameters of the linear program based on a duality analysis in order to obtain better results. A monotonic speed–density relationship is embedded in the model to capture high traffic congestion that occurs after a disaster. The model and the algorithm are tested using a simulated disaster scenario. The results indicate that the proposed model improves system performance measures such as mobility and average speed.     

Study on network traffic forecast model of SVR optimized by GAFSA

There are some problems, such as low precision, on existing network traffic forecast model. In accordance with these problems, this paper proposed the network traffic forecast model of support vector regression (SVR) algorithm optimized by global artificial fish swarm algorithm (GAFSA). GAFSA constitutes an improvement of artificial fish swarm algorithm, which is a swarm intelligence optimization algorithm with a significant effect of optimization. The optimum training parameters used for SVR could be calculated by optimizing chosen parameters, which would make the forecast more accurate. With the optimum training parameters searched by GAFSA algorithm, a model of network traffic forecast, which greatly solved problems of great errors in SVR improved by others intelligent algorithms, could be built with the forecast result approaching stability and the increased forecast precision. The simulation shows that, compared with other models (e.g. GA-SVR, CPSO-SVR), the forecast results of GAFSA-SVR network traffic forecast model is more stable with the precision improved to more than 89%, which plays an important role on instructing network control behavior and analyzing security situation.     

Estimation of parameters in latent class models using fuzzy clustering algorithms

A mixture approach to clustering is an important technique in cluster analysis. A mixture of multivariate multinomial distributions is usually used to analyze categorical data with latent class model. The parameter estimation is an important step for a mixture distribution. Described here are four approaches to estimating the parameters of a mixture of multivariate multinomial distributions. The first approach is an extended maximum likelihood (ML) method. The second approach is based on the well-known expectation maximization (EM) algorithm. The third approach is the classification maximum likelihood (CML) algorithm. In this paper, we propose a new approach using the so-called fuzzy class model and then create the fuzzy classification maximum likelihood (FCML) approach for categorical data. The accuracy, robustness and effectiveness of these four types of algorithms for estimating the parameters of multivariate binomial mixtures are compared using real empirical data and samples drawn from the multivariate binomial mixtures of two classes. The results show that the proposed FCML algorithm presents better accuracy, robustness and effectiveness. Overall, the FCML algorithm has the superiority over the ML, EM and CML algorithms. Thus, we recommend FCML as another good tool for estimating the parameters of mixture multivariate multinomial models.     

Phase and multifractality analyses of random price time series by finite-range interacting biased voter system

A random financial price process which is developed by mechanisms of finite-range interacting biased voter model is considered in the present paper. Voter model is one of statistical physics systems as well as a continuous time Markov process, which originally represents a voter’s attitude on a particular topic, namely, voters reconsider their opinions at times distributed according to independent exponential random variables. The empirical mode decomposition method is employed to analyze the behaviors of logarithmic returns for the simulation data of the model and the two real market indexes, Shanghai Composite Index and Deutscher Aktien Index. The multifractal characteristics of the original returns and first 3 intrinsic mode functions (IMFs) after empirical mode decomposition are explored by the multifractal detrended function analysis. The instantaneous phase, amplitude probability distribution of first 4 IMFs, and the multifractal properties of instantaneous amplitude are investigated.     

Resource allocation in state-dependent emergency evacuation networks

Most of the previous studies on the Emergency Evacuation Problem (EEP) assume that the length and widths of the circulation spaces are fixed. This assumption is only true if one is evaluating facilities that are already built. However, when designing the network for the first time, the size of the circulation space is not known to the designer, in fact it is one of several design parameters. After the routes have been established, it seems that the next logical question is to find out whether or not the system circulation spaces are capable of accommodating the traffic for both normal circulation and in an emergency. The problem of designing emergency evacuation networks is very complex and it is only recently that queueing networks are now being used to model this problem. Recent advances include state-dependent queueing network models that incorporate the mean value analysis algorithm to capture the non-linearities in the problem. We extend these models by incorporating the mean value analysis algorithm within Powell's derivative free unconstrained optimization algorithm. The effect of varying circulation widths on throughput will be discussed and a methodology for solving the resource allocation problem is proposed and demonstrated on several examples. The computational experience of the new methodology illustrates its usefulness in network design problems.     

Multifractality in relativistic charged particles produced at SPS energies

The multifractal analysis of relativistic shower particles produced in ³²S–emulsion interactions at 200 AGeV has been investigated using the method of modified multifractal moments, G_q, in pseudo-rapidity space. The anomalous fractal dimension, d_q, and generalized fractal dimensions, D_q, are determined for the present data for different order of moment. The experimental data reflects multifractal geometry in a multipion production process. The downward concave shape of the multifractal spectral function, f(α_q), gives an evidence for self-similar cascade mechanism. The multifractal specific heat has also been evaluated for the present data using the generalized fractal dimensions, D_q. We compared our experimental results with those obtained from simulated events of the Lund Monte Carlo Code FRITIOF and uncorrelated Monte Carlo events, (MC-RAND) generated randomly in pseudorapidity space based on the assumption of independent emission of particles. The experimental data on multifractality has been found to exhibit a remarkable proximity to the analogous data obtained from the FRITIOF code and the uncorrelated Monte Carlo events.     

Multiscale Analysis and Data Networks

The empirical finding of self-similarity in data network traffic over many time scales motivates the need for analysis tools that are particularly well adapted for identifying structures in network traffic. These structures span a range of time scales or are scale-dependent. Wavelet-based scaling analysis methods are especially successful, both collecting summary statistics from scale to scale and probing the local structure of packet traces. They include both spectral density estimation to identify large time-scale features and multifractal estimation for small time-scale bursts. While these methods are primarily statistical in nature, we may also adapt them to visualize the “burstiness” or the instantaneous scaling features of network traffic. This expository paper discusses the theoretical and implementation issues of wavelet-based scaling analysis for network traffic. Because data network traffic research does not consist solely of analysis, we show how these wavelet-based methods may be used to monitor and infer network properties (in conjunction with on-line algorithms and careful network experimentation). More importantly, we address what types of networking questions we can and cannot investigate with such tools.     

A traffic shaping model for optimizing network operations

The management of technology in multi-service computer networks, such as university networks, has become a challenge with the explosive growth of entertainment oriented peer-to-peer (P2P) traffic. Traffic shaping is one of the tools used to manage bandwidth to improve system performance by allocating bandwidth between P2P and non-peer-to-peer (NP2P) traffic. We present a model for traffic shaping and bandwidth management that considers the trade-offs from allocating different amounts of bandwidths for different application categories and use data from a university network. The current policy allocates varying bandwidths over the day to P2P and NP2P traffic to reflect the importance of not letting entertainment based traffic choke the network during the day time at the expense of the more important traffic, such as Web traffic. We highlight the difficulties in obtaining data in the form required for analysis, and the need to estimate demand for allocations not covered by current policy. We present a goal programming model for this estimation task. We also model the traffic shaping problem as a Markov decision process and develop an algorithm for determining the optimal bandwidth allocation to maximize the utility of all users. Finally we use a numerical example to illustrate our approach.     

Parameter estimation of the WMTD model

The MTD （mixture transition distribution） model based on Weibull distribution （WMTD model） is proposed in this paper, which is aimed at its parameter estimation. An EM algorithm for estimation is given and shown to work well by some simulations. And bootstrap method is used to obtain confidence regions for the parameters. Finally, the results of a real example--predicting stock prices--show that the WMTD model proposed is able to capture the features of the data from thick-tailed distribution better than GMTD （mixture transition distribution） model.     

An Online Expectation–Maximization Algorithm for Changepoint Models

Changepoint models are widely used to model the heterogeneity of sequential data. We present a novel sequential Monte Carlo (SMC) online expectation–maximization (EM) algorithm for estimating the static parameters of such models. The SMC online EM algorithm has a cost per time which is linear in the number of particles and could be particularly important when the data is representable as a long sequence of observations, since it drastically reduces the computational requirements for implementation. We present an asymptotic analysis for the stability of the SMC estimates used in the online EM algorithm and demonstrate the performance of this scheme by using both simulated and real data originating from DNA analysis. The supplementary materials for the article are available online.     

基于多分辨率分析的股票市场预测模型研究

采用多分辨率分析技术将深证成指收盘数据序列分解为多个子序列,然后采用神经网络技术对每个子序列分别建立预测模型,将各个预测结果叠加后得到最终预测结果.研究首先发现多分辨率技术可以有效提高预测模型的预测精度,表明分析我国股市波动时应该按照不同因素对股市影响大小及周期的差异分别研究,才能更有效分析股市运行状况及对其预测;其次结果表明不同类型神经网络预测模型预测性能差异明显,在选择股市预测模型的神经网络类型时应该注意其学习算法及收敛过程,以便能更好捕获股市变化规律.     

Multifractal characteristics of palmprint and its extracted algorithm

The palmprint is one of the most reliable physiological characteristics that can be used to distinguish between individuals. In this paper, we propose a palmprint recognition method based on multifractal spectrum technology using statistical moment approaches. The multifractal spectrum of palmprint is calculated by developing an algorithm for extracting palmprint characteristics. The three parameters proposed as the distinguishing palmprint features include the width spread and maximum of multifractal spectrum, and a parameter which describes the asymmetry of the spectrum curve. The identification process can be divided into the following main steps: (1) capturing palmprint image, extracting and normalizing the subimages; (2) defining a coordinate system and calculating partition function; (3) estimating multifractal spectrum; (4) extracting the three parameters and, finally, (5) the feature matching and palmprint identification. The experimental results demonstrate the feasibility of the proposed method.     

Role Analysis in Networks Using Mixtures of Exponential Random Graph Models

This article introduces a novel and flexible framework for investigating the roles of actors within a network. Particular interest is in roles as defined by local network connectivity patterns, identified using the ego-networks extracted from the network. A mixture of exponential-family random graph models (ERGM) is developed for these ego-networks to cluster the nodes into roles. We refer to this model as the ego-ERGM. An expectation-maximization algorithm is developed to infer the unobserved cluster assignments and to estimate the mixture model parameters using a maximum pseudo-likelihood approximation. We demonstrate the flexibility and utility of the method using examples of simulated and real networks.     

Genetic Tabu search for robust fixed channel assignment under dynamic traffic data

The contribution of this work is twofold. Firstly, we introduce a new channel assignment model for GSM radio networks. In this model both spatial and temporal variations of traffic are taken into account in order to improve network capacity and robustness. Secondly, using this model, we develop an original and effective hybrid algorithm to get high quality frequency plans. This algorithm combines a problem specific crossover and a Tabu search procedure. The proposed model and hybrid algorithm are evaluated using both artificial and real data. Computational results allow us to confirm the effectiveness of the proposed approach.     

Computation of M. L. estimates for the parameters of a negative binomial distribution from grouped data. A comparison of the scoring,Newton—Raphson and E-M algorithms

Computation of M. L. estimates for the parameters of a negative binomial distribution from grouped data is considered. For this problem the Scoring, Newton—Raphson and E-M algorithm is derived. Using simulated data the performance of the algorithms is compared with respect to convergence, number of iterations and computing time. Finally an empirical example drawn from actuarial science is given.     

A class of bivariate negative binomial distributions with different index parameters in the marginals

In this paper, we consider a new class of bivariate negative binomial distributions having marginal distributions with different index parameters. This feature is useful in statistical modelling and simulation studies, where different marginal distributions and a specified correlation are required. This feature also makes it more flexible than the existing bivariate generalizations of the negative binomial distribution, which have a common index parameter in the marginal distributions. Various interesting properties, such as canonical expansions and quadrant dependence, are obtained. Potential application of the proposed class of bivariate negative binomial distributions, as a bivariate mixed Poisson distribution, and computer generation of samples are examined. Numerical examples as well as goodness-of-fit to simulated and real data are also given here in order to illustrate the application of this family of bivariate negative binomial distributions.