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The disadvantages of particle swarm optimization (PSO) algorithm are that it is easy to fall into local optimum in high-dimensional space and has a low convergence rate in the iterative process. To deal with these problems, an adaptive particle swarmoptimization algorithm based on directed weighted complex network (DWCNPSO) is proposed. Particles can be scattered uniformly over the search space by using the topology of small-world network to initialize the particles position. At the same time, an evolutionary mechanism of the directed dynamic network is employed to make the particles evolve into the scale-free network when the indegree obeys power-law distribution. In the proposed method, not only the diversity of the algorithm was improved, but also particles' falling into local optimum was avoided. The simulation results indicate that the proposed algorithm can effectively avoid the premature convergence problem. Compared with other algorithms, the convergence rate is faster. [ABSTRACT FROM AUTHOR]

The selection of a design for the given product is a critical problem in product design development. Focuses of the designers and customers on the design are not identical. In order to bridge the gap and provide a more relaxing way to select the design, a new method based on quality function deployment (QFD) is proposed. In such amethod, customers are required to give their linguistic preferences on the design with respect to the customer requirements (CRs). In the rating of the weight of CRs, they are allowed to provide incomplete linguistic weight information and the objective optimization model is proposed to derive the exact linguistic weight information. Designers are required to rate the correlation between design requirements (DRs) and the relationship between the CRs and DRs to construct the house of quality. Opinions given by the customers are translated into the opinions with respect to the DRs based on the QFD. Afterwards, the priorities of the designs and design requirements are determined. The assessment results not only show the contribution of each design requirement to the customer satisfaction but also show the advantages and disadvantages of each design fromthe designers' perspective clearly and directly. An example is provided to validate the applicability of the proposed method. [ABSTRACT FROM AUTHOR]

This paper clarifies that the fractional Brownian motion, BH(t), is of long-range dependence (LRD) for the Hurst parameter 0 < H < 1 except H = 1/2. In addition, we note that the fractional Brownian motion is positively correlated for 0 < H < 1 except H = 1/2. Moreover, we present a theorem to state that the differential or integral of a random function, X(t), may substantially change the statistical dependence of BH(t). One example is that the differential of BH(t), in the domain of generalized functions, changes the LRD of BH(t) to be of short-range dependence (SRD) when 0

Axiomatic Design (AD) principles have been used to resolve themulticriteria decision making (MCDM) problems in engineering. With respect to MCDM problems in intuitionistic fuzzy environment, in which the criteria values take the form of intuitionistic fuzzy numbers, a new MCDM method is developed. Firstly, the approach proposed by Chen is extended to aggregate the decision makers' opinions in intuitionistic fuzzy environment. Secondly, membership common area and nonmembership common area are derived from the membership probability density function and the nonmembership probability density function, respectively. Then the membership information content and nonmembership information content are obtained based on the basic ideal of axiomatic design principles. Afterwards, the score function S and accuracy function H in intuitionistic fuzzy sets are extended with the information content to compare the alternatives. The alternatives that have the lowest values of functions of S and H are the best. Finally, a numerical example is used to illustrate the availability of the proposed method. [ABSTRACT FROM AUTHOR]

We depict our work on a fundamental issue in the theory of long-range dependent traffic in the aspect of the convergence of sample autocorrelation function (ACF) of real traffic. The present results suggest that the sample ACF of traffic is convergent. In addition, we show that the sample size has considerable effects in estimating the sample ACF of traffic. More precisely, a sample ACF of traffic tends to be smoother when the sample size increases. [ABSTRACT FROM AUTHOR]

This paper depicts our work in smoothing the sample autocorrelation function (ACF) of traffic. The experimental results exhibit that the sample ACF of traffic may be smoothed by the way of average. In addition, the results imply that the sum of sample 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. [ABSTRACT FROM AUTHOR]

We contribute the quantitative descriptions of the large time scales for the Ethernet traffic to beGaussian. We focus onthe normality property of the accumulated traffic data under different time scales. The investigation is carried out graphically by the quantilequantile (QQ) plots and numerically by statistical tests. The present results indicate that the larger the time scale, the more normal the Ethernet traffic. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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 randomdata following the von Karman spectrumin turbulence. In addition, we express the fractal dimension, which is a measure of local self-similarity, using the golden ratio, of randomdata governed by the von Karman spectrum. [ABSTRACT FROM AUTHOR]

Quality function deployment (QFD) is a customer-driven approach for product design and development. A QFD analysis process includes a series of subprocesses, such as determination of the importance of customer requirements (CRs), the correlation among engineering characteristics (ECs), and the relationship between CRs and ECs. Usually more than group of one decision makers are involved in the subprocesses to make the decision. In most decision making problems, they often provide their evaluation information in the linguistic form. Moreover, because of different knowledge, background, and discrimination ability, decision makers may express their linguistic preferences in multi-granularity linguistic information. Therefore, an effective approach to deal with the multi-granularity linguistic information in QFD analysis process is highly needed. In this study, the QFD methodology is extended with 2-tuple linguistic representation model under multi-granularity linguistic environment. The extended QFD methodology can cope with multi- granularity linguistic evaluation information and avoid the loss of information. The applicability of the proposed approach is demonstrated with a numerical example. [ABSTRACT FROM AUTHOR]

The extraction of affine invariant features plays an important role in many fields of image processing. In this paper, the original image is transformed into new images to extract more affine invariant features. To construct new images, the original image is cut in two areas by a closed curve, which is called general contour (GC). GC is obtained by performing projections along lines with different polar angles. New image is obtained by changing gray value of pixels in inside area. The traditional affine moment invariants (AMIs) method is applied to the new image. Consequently, cutting affine moment invariants (CAMIs) are derived. Several experiments have been conducted to evaluate the proposed method. Experimental results show that CAMIs can be used in object classification tasks. [ABSTRACT FROM AUTHOR]

Drought is part of natural climate variability and ranks the first natural disaster in the world. Drought forecasting plays an important role in mitigating impacts on agriculture and water resources. In this study, a drought forecast model based on the random forest method is proposed to predict the time series of monthly standardized precipitation index SPI. We demonstrate model application by four stations in the Haihe river basin, China. The random-forest-RF- based forecast model has consistently shown better predictive skills than the ARIMA model for both long and short drought forecasting. The confidence intervals derived from the proposed model generally have good coverage, but still tend to be conservative to predict some extreme drought events. [ABSTRACT FROM AUTHOR]

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 example, 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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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 HfGn that linearly relates to its fractal dimension DfGn. 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 HfGn . 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 DGC and the Hurst parameter HGC 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. [ABSTRACT FROM AUTHOR]

An introduction to a series of articles on nonlinear time series is presented.

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 second indicates 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. [ABSTRACT FROM AUTHOR]

Estimating power spectrum density (PSD) is essential in signal processing. This short paper gives a theorem to represent a smoothed PSD estimate with the Cauchy integral. It may be used for the approximation of the smoothed PSD estimate. [ABSTRACT FROM AUTHOR]

Axiomatic design (AD) provides a framework to describe design objects and a set of axioms to evaluate relations between intended functions and means by which they are achieved. It has been extended to evaluate alternatives in engineering under fuzzy environment. With respect to multiple criteria group decision making (MCDM) with incomplete weight information under fuzzy linguistic environment, a new method is proposed. In the method, the fuzzy axiomatic design based on triangle representation model is used to aggregate the linguistic evaluating information. In order to get the weight vector of the criteria, we establish a nonlinear optimization model based on the basic ideal of fuzzy axiomatic design (FAD), by which the criteria weights can be determined. It is based on the concept that the optimal alternative should have the least weighted information content. Then, the weighted information content is derived by summing weighted information content for each criterion. The alternative that has the least total weighted information content is the best. Finally, a numerical example is used to illustrate the availability of the proposed method. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The Sauerbrey equation is a useful empirical model in material science to represent the dynamics of frequency change denoted by Δf in an area, denoted by A, of the electrode in terms of the increment of the mass, which is denoted by Δm, loaded on the surface of the crystal under a certain resonant frequency f0. For the purpose of studying Δf from the point of view of time series, we first propose two types of the modified representations of the Sauerbrey equation by taking time as an argument to represent Δf as a function expressed by x(t, f0, A, Δm), where t is time. Usually, Δf is studied experimentally for the performance evaluation of the tested quartz used in ammonia sensors. Its properties in time series, however, are rarely reported. This paper presents the fractal properties of Δf. We will show that Δf is long range dependent (LRD). Consequently, it is heavy tailed according to the Taqqu's theorem. The Hurst parameter (H) of Δf approaches one, implying its strong long memory, providing a new explanation of the repeatability of the experiments and novel point of view of the dynamics of Δf relating to the Sauerbrey equation in material science. [ABSTRACT FROM AUTHOR]

Oscillator of single-degree-freedom is a typical model in system analysis. Oscillations resulted from differential equations with fractional order attract the interests of researchers since such a type of oscillations may appear dramatic behaviors in system responses. However, a solution to the impulse response of a class of fractional oscillators studied in this paper remains unknown in the field. In this paper, we propose the solution in the closed form to the impulse response of the class of fractional oscillators. Based on it, we reveal the stability behavior of this class of fractional oscillators as follows. A fractional oscillator in this class may be strictly stable, nonstable, or marginally stable, depending on the ranges of its fractional order. [ABSTRACT FROM AUTHOR]

Sea level fluctuation gains increasing interests in several fields, such as geoscience and ocean dynamics. Recently, the long-range dependence (LRD) or long memory, which is measured by the Hurst parameter, denoted by H, of sea level was reported by Barbosa et al. (2006). However, reports regarding the local roughness of sea level, which is characterized by fractal dimension, denoted by D, of sea level, are rarely seen. Note that a common model describing a random function with LRD is fractional Gaussian noise (fGn), which is the increment process of fractional Brownian motion (fBm) (Beran (1994)). If using the model of fGn, D of a random function is greater than 1 and less than 2 because D is restricted by H with the restriction D = 2 - H. In this paper, we introduce the concept of one-dimensional random functions with LRD based on a specific class of processes called the Cauchy-class (CC) process, towards separately characterizing the local roughness and the long-range persistence of sea level. In order to achieve this goal, we present the power spectrum density (PSD) function of the CC process in the closed form. The case study for modeling real data of sea level collected by the National Data Buoy Center (NDBC) at six stations in the Florida and Eastern Gulf of Mexico demonstrates that the sea level may be one-dimensional but LRD. The case study also implies that the CC process might be a possible model of sea level. In addition to these, this paper also exhibits the yearly multiscale phenomenon of sea level. [ABSTRACT FROM AUTHOR]

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 (ffim), or its increment process, or the standard multifractional fBm (mBm) indexed by the local Holder 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(f)] on an interval-by-interval basis, where E implies the expectation operator. Since E[H(f)] 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. [ABSTRACT FROM AUTHOR]

Let x(t) be a locally self-similar Gaussian random function. Denote by rxx(τ) the autocorrelation function (ACF) of x(t). For x(t) that is sufficiently smooth on (0, ∞), there is an asymptotic expression given by rxx(0) - rxx(τ) ~ c|τ|α for |τ| → 0, where c is a constant and α is the fractal index of x(t). If the above is true, the fractal dimension of x(t), denoted by D, is given by D = D(α) = 2 - α/2. Conventionally, α is strictly restricted to 0 < α ≤ 2 so as to make sure that D ∈ [1,2). The generalized Cauchy (GC) process is an instance of this type of random functions. Another instance is fractional Brownian motion (fBm) and its increment process, that is, fractional Gaussian noise (fGn), which strictly follow the case of D ∈ [1,2) or 0 < α ≤ 2. In this paper, I claim that the fractal index α of x(t) may be relaxed to the range α > 0 as long as its ACF keeps valid for α > 0. With this claim, I extend the GC process to allow α > 0 and call this extension, for simplicity, the extended GC (EGC for short) process. I will address that there are dimensions 0 ≤ D(α) < 1 for 2 < α < 4 and further D(α) < 0 for 4 < α for the EGC processes. I will explain that x(t) with 1 ≤ D < 2 is locally rougher than that with 0 ≤ D < 1. Moreover, x(t) with D < 0 is locally smoother than that with 0 ≤ D < 1. The local smoothest x(t) occurs in the limit D → - ∞. The focus of this paper is on the fractal dimensions of random functions. The EGC processes presented in this paper can be either long-range dependent (LRD) or short-range dependent (SRD). Though applications of such class of random functions for D < 1 remain unknown, I will demonstrate the realizations of the EGC processes for D < 1. The above result regarding negatively fractal dimension on random functions can be further extended to describe a class of random fields with negative dimensions, which are also briefed in this paper. [ABSTRACT FROM AUTHOR]

Time-frequency distribution has received a growing utilization for analysis and interpretation of nonlinear and nonstationary processes in a variety of fields. Among them, two methods, such as, the empirical mode decomposition (EMD) with Hilbert transform (HT) which is termed as the Hilbert-Huang Transform (HHT) and the Hilbert spectrum based on maximal overlap discrete wavelet package transform (MODWPT), are fairly noteworthy. Comparisons of HHT and MODWPT in analyzing several typical nonlinear systems and examinations of the effectiveness using these two methods are illustrated. This study demonstrates that HHT can provide comparatively more accurate identifications of nonlinear systems than MODWPT. [ABSTRACT FROM AUTHOR]

In various network attacks, the Distributed Denial-of-Service (DDoS) attack is a severe threat. In order to deal with this kind of attack in time, it is necessary to establish a special type of defense system to change strategy dynamically against attacks. In this paper, we introduce an adaptive approach, which is used for defending against DDoS attacks, based on normal traffic analysis. The approach can check DDoS attacks and adaptively adjust its configurations according to the network condition and attack severity. In order to insure the common users to visit the victim server that is being attacked, we provide a nonlinear traffic control formula for the system. Our simulation test indicates that the nonlinear control approach can prevent the malicious attack packets effectively while making legitimate traffic flows arrive at the victim. [ABSTRACT FROM AUTHOR]

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 sample and not on the actual sample 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. [ABSTRACT FROM AUTHOR]

This paper points out that the predictability analysis of conventional time series may in general be invalid for long-range dependent (LRD) series since the conventional mean-square error (MSE) may generally not exist for predicting LRD series. To make the MSE of LRD series prediction exist, we introduce a generalized MSE. With that, the proof of the predictability of LRD series is presented in Hilbert space. [ABSTRACT FROM AUTHOR]

Fractal time series substantially differs from conventional one in its statistic properties. For instance, it may have a heavy-tailed probability distribution function (PDF), a slowly decayed autocorrelation function (ACF), and a power spectrum function (PSD) of 1/f type. It may have the statistical dependence, either long-range dependence (LRD) or short-range dependence (SRD), and global or local self-similarity. This article will give a tutorial review about those concepts. Note that a conventional time series can be regarded as the solution to a differential equation of integer order with the excitation of white noise in mathematics. In engineering, such as mechanical engineering or electronics engineering, engineers may usually consider it as the output or response of a differential system or filter of integer order under the excitation of white noise. In this paper, a fractal time series is taken as the solution to a differential equation of fractional order or a response of a fractional system or a fractional filter driven with a white noise in the domain of stochastic processes. [ABSTRACT FROM AUTHOR]

The article discusses various reports published within the issue including one by Li on the fractal time series from the point of view of systems of fractional order, article by Liu on the chaotic time series and an article by Cattani on the fractal shapes and the symmetries of DNA from a view of fractal time series.

This paper provides the fluctuation analysis of random functions with the Pareto distribution. By the introduced concept of wild fluctuations, we give an alternativeway to classify the fluctuations fromthosewith light-tailed distributions. Moreover, the suggested term wildest fluctuation may be used to classify random functions with infinite variance from those with finite variances. [ABSTRACT FROM AUTHOR]

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 resultmay 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. [ABSTRACT FROM AUTHOR]

Extreme learning machine (ELM) is a fast learning algorithm of single-hidden layer feedforward neural networks (SLFNs). Compared with the traditional neural networks, the ELM algorithm has the advantages of fast learning speed and good generalization. At the same time, an ordinal logistic regression (LR) is a statisticalmethod which is conceptually simple and algorithmically fast. In this paper, in order to improve the real-time performance, a flare forecasting method is introduced which is the combination of the LR model and the ELM algorithm. The predictive variables are three photospheric magnetic parameters, that is, the total unsigned magnetic flux, length of the strong-gradient magnetic polarity inversion line, and total magnetic energy dissipation. The LR model is used to map these three magnetic parameters of each active region into four probabilities. Consequently, the ELM is used to map the four probabilities into a binary label which is the final output. The proposed model is used to predict the occurrence of flares with a certain level over 24 hours following the time when the magnetogram is recorded. The experimental results show that the cascade algorithm not only improves learning speed to realize timely prediction but also has higher accuracy of X-class flare prediction in comparison with other methods. [ABSTRACT FROM AUTHOR]

Accurate estimation of the Fourier transform in log-polar coordinates is a major challenge for phase-correlation based motion estimation. To acquire better image registration accuracy, a method is proposed to estimate the log-polar coordinates coefficients using multilayer pseudopolar fractional Fourier transform (MPFFT). The MPFFT approach encompasses pseudopolar and multilayer techniques and provides a grid which is geometrically similar to the log-polar grid. At low coordinates coefficients the multilayer pseudopolar grid is dense, and at high coordinates coefficients the grid is sparse. As a result, large scalings in images can be estimated, and better image registration accuracy can be achieved. Experimental results demonstrate the effectiveness of the presented method. [ABSTRACT FROM AUTHOR]

We present a new method to estimate noise for a single-slice sinogram of low- dose CT based on the homogenous patches centered at a special pixel, called center point, which has the smallest variance among all sinogram pixels. The homogenous patch, composed by homogenous points, is formed by the points similar to the center point using similarity sorting, similarity decreasing searching, and variance analysis in a very large neighborhood (VLN) to avoid manual selection of parameter for similarity measures.Homogenous pixels in the VLN allow us find the largest number of samples, who have the highest similarities to the center point, for noise estimation, and the noise level can be estimated according to unbiased estimation. Experimental results show that for the simulated noisy sinograms, the method proposed in this paper can obtain satisfied noise estimation results, especially for sinograms with relatively serious noises. [ABSTRACT FROM AUTHOR]

In order to organically combine the minimum-energy frame with the significant properties of multiwavelets, minimum-energy multiwavelet frames with arbitrary integer dilation factor are studied. Firstly, we define the concept of minimum-energy multiwavelet frame with arbitrary dilation factor and present its equivalent characterizations. Secondly, some necessary conditions and sufficient conditions for minimum-energy multiwavelet frame are given. Thirdly, the decomposition and reconstruction formulas of minimum-energy multiwavelet frame with arbitrary integer dilation factor are deduced. Finally, we give several numerical examples based on B- spline functions. [ABSTRACT FROM AUTHOR]

An introduction to articles published within the issue is presented, including one by M. Li on negatively fractal dimensional Gaussian random functions, another by M. M. Kader on waves propagating along the interface between air-water, and one by I. Bochicchio et al on the application of Saint Venant's theory to Volterra's distortions.

Bacillus amyloliquefaciens ribonuclease Barnase (RNase Ba) is a 12 kD (kilodalton) small extracellular ribonuclease. It has broad application prospects in agriculture, clinical medicine, pharmaceutical, and so forth. In this work, the thermal stability of Barnase has been studied using molecular dynamics simulation at different temperatures. The present study focuses on the contribution of noncovalent intramolecular interaction to protein stability and how they affect the thermal stability of the enzyme. Profiles of root mean square deviation and root mean square fluctuation identify thermostable and thermosensitive regions of Barnase. Analyses of trajectories in terms of secondary structure content, intramolecular hydrogen bonds and salt bridge interactions indicate distinct differences in different temperature simulations. In the simulations, Four three-member salt bridge networks (Asp8-Arg110-Asp12, Arg83-Asp75-Arg87, Lys66-Asp93-Arg69, and Asp54-Lys27-Glu73) have been identified as critical salt bridges for thermostability which are maintained stably at higher temperature enhancing stability of three hydrophobic cores. The study may help enlighten our knowledge of protein structural properties, noncovalent interactions which can stabilize secondary peptide structures or promote folding, and also help understand their actions better. Such an understanding is required for designing efficient enzymes with characteristics for particular applications at desired working temperatures. [ABSTRACT FROM AUTHOR]

A new operational matrix of fractional order integration for Legendre wavelets is derived. Block pulse functions and collocation method are employed to derive a general procedure for forming this matrix. Moreover, a computational method based on wavelet expansion together with this operational matrix is proposed to obtain approximate solution of the fractional population growth model of a species within a closed system. The main characteristic of the new approach is to convert the problem under study to a nonlinear algebraic equation. [ABSTRACT FROM AUTHOR]

A new direct operational inversion method is introduced for solving coupled linear systems of ordinary fractional differential equations. The solutions so-obtained can be expressed explicitly in terms of multivariate Mittag-Leffler functions. In the case where the multiorders are multiples of a common real positive number, the solutions can be reduced to linear combinations of Mittag- Leffler functions of a single variable. The solutions can be shown to be asymptotically oscillatory under certain conditions. This technique is illustrated in detail by two concrete examples, namely, the coupled harmonic oscillator and the fractional Wien bridge circuit. Stability conditions and simulations of the corresponding solutions are given. [ABSTRACT FROM AUTHOR]

A key requirement of lunar rover autonomous navigation is to acquire state information accurately in real-time during its motion and set up a gradual parameter- based nonlinear kinematics model for the rover. In this paper, we propose a dual- extended-Kalman-filter- (dual-EKF-) based realtime celestial navigation (RCN) method. The proposed method considers the rover position and velocity on the lunar surface as the system parameters and establishes a constant velocity (CV) model. In addition, the attitude quaternion is considered as the system state, and the quaternion differential equation is established as the state equation, which incorporates the output of angular rate gyroscope. Therefore, the measurement equation can be established with sun direction vector from the sun sensor and speed observation from the speedometer. The gyro continuous output ensures the algorithm real-time operation. Finally,we use the dual-EKF method to solve the system equations. Simulation results show that the proposed method can acquire the rover position and heading information in real time and greatly improve the navigation accuracy. Our method overcomes the disadvantage of the cumulative error in inertial navigation. [ABSTRACT FROM AUTHOR]

Generalized belief propagation (GBP) is a region-based belief propagation algorithm which can get good convergence in Markov random fields. However, the computation time is too heavy to use in practical engineering applications. This paper proposes a method to accelerate the efficiency of GBP. A caching technique and chessboard passing strategy are used to speed up algorithm. Then, the direction set method which is used to reduce the complexity of computing clique messages from quadric to cubic. With such a strategy the processing speed can be greatly increased. Besides, it is the first attempt to apply GBP for solving the stereomatching problem. Experiments show that the proposed algorithm can speed up by 15+ times for typical stereo matching problem and infer a more plausible result. [ABSTRACT FROM AUTHOR]

An introduction is presented in which the editor discusses various reports within the issue on topics including a fractal approach for oscillation, propagation and diffusion properties of low-scale structures, specific methods for analysis of complex movements and mathematical models for propagation phenomena.