Fractional Brownian Motion Model Research Articles

METHOD FOR AUTOMATIC SPEAKER RECOGNITION WITH HURST PARAMETER BASED FEATURES AND METHOD FOR SPEAKER CLASSIFICATION BASED ON FRACTIONAL BROWNIAN MOTION CLASSIFIERS

It is proposed a text-independent automatic speaker recognition (ASkR) system which employs a new speech feature and a new classifier. The statistical feature pH is a vector of Hurst parameters obtained by applying a wavelet-based multi-dimensional estimator (M dim wavelets) to the windowed short-time segments of speech. The proposed classifier for the speaker identification and verification tasks is based on the multi-dimensional fBm (fractional Brownian motion) model, denoted by M dim fBm. For a given sequence of input speech features, the speaker model is obtained from the sequence of vectors of H parameters, means and variances of these features.

Optimal space–time adaptive wavelet methods for degenerate parabolic PDEs

We analyze parabolic PDEs with certain type of weakly singular or degenerate time-dependent coefficients and prove existence and uniqueness of weak solutions in an appropriate sense. A localization of the PDEs to a bounded spatial domain is justified. For the numerical solution a space–time wavelet discretization is employed. An optimality result for the iterative solution of the arising systems can be obtained. Finally, applications to fractional Brownian motion models in option pricing are presented.

How Performing a Repetitive One-Legged Stance Modifies Two-Legged Postural Control

The proprioceptive cues in the control of movement is recognized as playing a major role in postural control. However, little is known about its possible increased contribution to postural control consecutive to repetitive muscular activations. To test this, the short-term effects induced by a 1-legged exercise on 2-legged postural control with the eyes closed were assessed in healthy subjects. The center-of-pressure (CP) displacements obtained using a force platform were split into 2 elementary movements: center-of-gravity vertical projection (CGv) and the difference (CP - CGv). These movements assessed the net postural performance and the level of neuromuscular activity, respectively, and were processed afterward (a) through variances, mean velocity, and the average surface covered by the trajectories and (b) a fractional Brownian motion (fBm) modeling. The latter provides further information about how much the subject controls the movements and the spatiotemporal relation between the successive control mechanisms. No difference was found using the classical parameters. In contrast, fBm parameters showed statistically significant changes in postural control after 1-legged exercises: The spatial and temporal coordinates of the transition points for the CG movements along the anteroposterior axis are decreased. Because the body movement control does not rely on visual or vestibular cues, this ability to trigger the corrective process of the CG movements more quickly in the postexercise condition and once a more reduced distance has been covered emphasizes how prior muscular activation improves body movement detection. As a general rule, these data show that the motor systems control body motions better after repetitive stimulation of the sensory cues. These insights should be of interest in physical activities based on a precise muscular length control.

Effets posturaux induits par le port d’une orthèse de genou chez des patients opérés d’une ligamentoplastie du LCA en cours de rééducation

The purpose of this study was to assess the effects of an orthosis wearing on the postural capacities of patients undergoing a knee ligamentary surgery. The experimental task was carried out with fourteen patients at the end of their program of rehabilitation. The displacements of the centre of pressure (CP) were recorded during four conditions performed during one-legged stance, alternating the wearing or not of the orthosis as well as the involved leg (sound or operated). The patients were required to maintain a light flexion of the knee and minimising the body motions. Traditional parameters and other issued from fractional Brownian motion modelling were used to assess the postural behaviour. No significant difference was observed, depending on the orthosis was worn or not, nor its interaction with the involved leg. This lack of distinction between the two legs would suggest a complete recovery of proprioceptive capacities of the operated leg after rehabilitation. Our results highlight the uselessness of prophylactic orthosis prescription for a way of life with little soliciting when post-surgery rehabilitation was carried out.

Image Informative Maps for Estimating Noise Standard Deviation and Texture Parameters

The problem of automatic detection of image areas appropriate for accurate estimation of additive noise standard deviation (STD) irrespectively to processed image properties is considered in this paper. For accurate estimation of either image texture or noise STD, we distinguish two complementary informative maps: noise- (NI-) and texture- (TI-) informative ones. The NI map is determined and iteratively upgraded based on the Fisher information on noise STD calculated in scanning window (SW) fashion. Fractional Brownian motion (fBm) model for image texture is used to derive the required Fisher information. To extract final noise STD from NI map, fBm- and DCT-based estimators are implemented. The performance of these two estimators is comparatively assessed on large image database for different noise levels. It is also compared with performance of two competitive state-of-the-art estimators recently published. Utilizing NI map along with DCT-based noise STD estimator has proved to be significantly more efficient.

Determining Optical Flow of Natural Scene Based on the Fractal Brownian Motion Model

This study proposes to determine optical flow using the fractal Brownian motion (FBM) model instead of the traditional brightness conservation (BC) model which is recently argued not tenable to describe natural scenes. We firstly construct basic flow equation according to the FBM model, then regularize it by introducing the local smoothness constraint, and finally, determine the flow values by solving the regularized basic equation. Test results show that the proposed method makes a significant improvement on the famous Lucas-Kanade method using BC model, which illustrates that the FBM model outperforms the BC model in determining natural scene flow.

股指的分形布朗运动模型和Hurst指数与转移概率 Fractal Brownian Motion Model and Its Hurst Exponent and Transition Probability

股指时间序列被发现具有分形特性，基于分形市场假说，本文将建立一个分形布朗运动模型来描述股指的波动，通过比较模拟时间序列与实际股指序列的Hurst指数，估算出股指序列的转移概率。 The stock index sequence was discovered to have fractal Brownian properties. We propose a fractal Brownian motion model to describe the stock index fluctuation based on the fractal market hypothesis. Through comparing the Hurst exponents of the fractal simulation sequence and the realistic stock index se-quence, we obtain the transition probability of the stock index sequence.

Applying multifractal spectrum combined with fractal discrete Brownian motion model to wood defects recognition

Wood nondestructive testing technology is a new and multidisciplinary industry scientific research. It has attained fast development and achievements in recent years. X-ray computed tomography (CT) scanning technology is a kind of wood nondestructive testing technology in practice. CT scanning technology has been applied to the detection of internal defects in the logs for the purpose of obtaining prior information, which can be used to reach better wood sawing decision. Fractal geometry and its extension multifractal are used for describing, modeling, analyzing, and processing of different complex shapes and images. A method in CT image edge detection using multifractal theory combined with fractal Brownian motion is applied in the paper. First, its multifractal spectrum is estimated. Then, different types of pixels are classified by the spectrum; they are smoothing edge points and singular edge points. From the images processed by multifractal spectrum theory and compared with each image by different spectrum values, it can be seen that the larger the range of threshold is set, the more exact the edge can be detected. The paper provides a new method to recognize the defect information and to saw it in the condition of nondestructive wood.

Multiscale flow and transport model in three-dimensional fractal porous media

This paper proposes a multiscale flow and transport model which can be used in three-dimensional fractal random fields. The fractal random field effectively describes a field with a high degree of variability to satisfy the one-point statistics of Levy-stable distribution and the two-point statistics of fractional Levy motion (fLm). To overcome the difficulty of using infinite variance of Levy-stable distribution and to provide the physical meaning of a finite domain in real space, truncated power variograms are utilized for the fLm fields. The fLm model is general in the sense that both stationary and commonly used fractional Brownian motion (fBm) models are its special cases. When the upper cutoff of the truncated power variogram is close to the lower cutoff, the stationary model is well approximated. The commonly used fBm model is recovered when the Levy index of fLm is 2. Flow and solute transport were analyzed using the first-order perturbation method. Mean velocity, velocity covariance, and effective hydraulic conductivity in a three-dimensional fractal random field were derived. Analytical results for particle displacement covariance and macrodispersion coefficients are also presented. The results show that the plume in an fLm field moves slower at early time and has more significant long-tailing behavior at late time than in fBm or stationary exponential fields. The proposed fractal transport model has broader applications than those of stationary and fBm models. Flow and solute transport can be simulated for various scenarios by adjusting the Levy index and cutoffs of fLm to yield more accurate modeling results.

Effects of visual feedback of center-of-pressure displacements on undisturbed upright postural control of hemiparetic stroke patients

To assess whether insights from postural control without additional visual feedback (VFB) could be gained to explain the possible VFB effects (or non-effects) on upright stance performance. The center-of-pressure (CP) displacements of 39 patients with a recent hemispheric stroke (93 days ± 56; mean ± s.d.) were analyzed in two conditions (eyes open and VFB) through various classical parameters and fractional Brownian motion (fBm) modeling. Correlations between their ability to use the VFB technique appropriately and parameters assessing the eyes open condition were also computed. The fBm modeling showed that the VFB technique improves the control of the CP trajectories over the longer time intervals. In both conditions, the patients with right hemiparesis, compared to those with left hemiparesis, demonstrated improved control of their CP displacement along the AP axis over the shortest time intervals. Overall, 28% of the patients did not use the VFB technique. The correlation analysis indicated that the larger the spontaneous CP movements in the eyes open condition, the greater the effect of the VFB technique. By emphasizing its particular effects and the profile of the patients who used the technique, these data specify the conditions allowing hemiparetic patients to use the VFB technique appropriately and immediately.

Fractal-feature distance analysis of contrast-detail phantom image and meaning of pseudo fractal dimension and complexity

The purposes of our studies are to examine whether or not fractal-feature distance deduced from virtual volume method can simulate observer performance indices and to investigate the physical meaning of pseudo fractal dimension and complexity. Contrast-detail (C-D) phantom radiographs were obtained at various mAs values (0.5 - 4.0 mAs) and 140 kVp with a computed radiography system, and the reference image was acquired at 13 mAs. For all C-D images, fractal analysis was conducted using the virtual volume method that was devised with a fractional Brownian motion model. The fractal-feature distances between the considered and reference images were calculated using pseudo fractal dimension and complexity. Further, we have performed the C-D analysis in which ten radiologists participated, and compared the fractal-feature distances with the image quality figures (IQF). To clarify the physical meaning of the pseudo fractal dimension and complexity, contrast-to-noise ratio (CNR) and standard deviation (SD) of images noise were calculated for each mAs and compared with the pseudo fractal dimension and complexity, respectively. A strong linear correlation was found between the fractal-feature distance and IQF. The pseudo fractal dimensions became large as CNR increased. Further, a linear correlation was found between the exponential complexity and image noise SD.

Rapid, man-made object morphological segmentation for aerial images using a multi-scaled, geometric image analysis

This paper describes a man-made object segmentation method for aerial images based on a modified watershed segmentation algorithm. Our segmentation procedure includes three steps: (1) a multi-scaled geometric image analysis of aerial images by the non-subsampled contourlet transform (NSCT) method, (2) watershed segmentation, and (3) region classification of man-made objects. First, background of multi-scaled geometric image analysis is introduced briefly, and NSCT is used to represent the features for the purpose of man-made object segmentation. Thanks to the properties of NSCT, it not only avoids pseudo-Gibbs phenomena around singularities in image de-noising with regard to shift invariance, but it also enriches the set of basis functions, which makes it possible to extract orientational contour of man-made objects more effectively. In the NSCT decomposition step, the best basis selection is employed for ensuring maximum information content. Second, the “texture gradient” of combined features is calculated based on the first NSCT decomposition step and the resulting best basis selection, afterward the watershed transform is applied. According to their feature values, the aerial images are divided into several homogenous regions. Third, the fractional Brownian motion (fBm) model is used to determine the man-made object regions. Last, the experimental results show that the outcome of man-made object segmentation becomes more continuous and satisfying as a result of the homogenous texture-regions extraction and the modified watershed procedure.

Modeling and Pricing of Swaps for Stochastic Volatilities with Delay and Jumps

The jumps in stock market volatility are found to be so active that this discredits many recently proposed stochastic volatility models without jumps (Bollerslev et al (2008)). The most convincing evidence comes from recent nonparametric work using high-frequency data as in Barndorff-Nielsen and Shephard (2007) and Ait-Sahalia and Jacod (2008) among others. From the other side, some statistical studies of stock prices (see Sheinkman and LeBaron (1989), and Akgiray (1989)) indicate the dependence on past returns. In this paper, we incorporate a jump part into the stochastic volatility model with delay and without jumps proposed by Swishchuk (2005). Our model of stochastic volatility exhibits jumps and also past-dependence: the behavior of a stock price right after a given time t not only depends on the situation at t, but also on the whole past (history) of the process S(t) up to time t. This draws some similarities with fractional Brownian motion models (see Mandelbrot (1997)) due to a long-range dependence property. Another advantage of this model is mean-reversion. This model is also a continuous-time version of GARCH(1,1) model (see Bollerslev (1986)) with jumps.The valuation of the variance swaps for stochastic volatility with delay and jumps is discussed in this paper. A variance swap is a forward contract on realized variance, the square of the realized volatility. We provide some analytical closed forms for the expectation of the realized variance for the stochastic volatility with delay and jumps. Besides, we also present a lower bound for delay as a measure of risk. We also discuss the approaches for calculating of other swaps such as volatility, covariance, correlation swaps. As applications of our analytical solutions, a numerical example using S&P60 Canada Index (1998-2002) is then provided to price variance swaps with delay and jumps.

Stochastic Fractal Dimension Image

Fractal analysis for medical image classification and analysis was introduced in cite{Chen1989}. According to the authors, when viewed as an intensity surface, Mandelbrot's fractal theory provides an informative framework for characterizing such a surface. Using the fractional Brownian motion model, the authors provide an algorithm for converting a scalar image to a fractal dimension image for classification purposes or edge enhancement. This submission constitutes a report on the ITK implementation of this algorithm.

Fractal asset returns, arbitrage and option pricing

In the discrete-time fractional random walk model a market with one risky asset affords an arbitrage opportunity as described by Cutland et al. [Cutland NJ, Kopp PE, Willinger W. Stock price returns and the Joseph effect: a fractional version of the Black–Scholes model. In: Russo Francesco, Bolthausen Erwin, Dozzi Marco, editors. Seminar on 6 stochastic analysis, random fields and applications, pp. 327–351. Seminar on stochastic analysis, random fields and applications. Ascona: Centro Stefano Franscini; 1993, Progress in probability 36. Birkhauser Verlag; 1995.] and Sottinen [Sottinen Tommi. Fractional Brownian motion, random walks and binary market models. Finance Stoch 2001;5(3):343–355]. We briefly discuss these results and compute a numerical example in a fractional binomial model as illustration and mention an option pricing model for assets the returns of which are driven by a fractional Brownian motion [Yaozhong Hu, Bernt Øksendal. Fractional white noise calculus and applications to finance. Infin Dimens Anal Quant Probability Rel Top 2003;6:1–32, ISSN 0219-0257; Fajardo J, Cajueiro DO. Volatility estimation and option pricing with fractional Brownian motion, October 2003. Available from: http://ideas.repec.org/p/ibm/finlab/flwp53.html].

Relation between postural control assessment with eyes open and centre of pressure visual feedback effects in healthy individuals

Visual feedback (VFB) of the resultant centre of pressure (CP(Res)) is a potentially interesting technique for rehabilitation purposes. However, all past studies have not been unanimous in supporting its utility in a physical therapy program. The present study was therefore undertaken with the main aim of assessing whether insights from postural control without additional feedback could be gained to explain the possible VFB effects. The CP(Res) displacements of 65 healthy adults were analysed in two conditions (eyes-open and VFB) through various classical parameters (including surface and variances along each medio-lateral and antero-posterior axes) and fractional Brownian motion (fBm) modelling. The results indicate that 69% of the sample were dependent on VFB, i.e. that the surface covered by the CP(Res) displacements was smaller during VFB than in the eyes-open condition. The comparison of the two subgroups (i.e. those who were dependant on VFB and those who were not) brought out significant differences in many classical and fBm parameters. In addition, the correlation between the degree of VFB dependency and the values measured during the eyes-open condition indicates that the more the subjects are VFB-dependent, the less they lean forward, the smaller the variance and the better the CP(Res) displacements are controlled over the longest time intervals. By specifying the links between the postural performance in an eyes-open standard condition and the degree of VFB dependency, a number of clues help identify the reasons for which some subjects do not succeed in using this technique, hence explaining the controversy about its use as a rehabilitation tool.

Minimax estimation of linear functionals under squared error loss

Under a very general setting, we consider the problem of estimating a linear functional of an unknown vector in a Hilbert space from indirect data contaminated by noise. We then discuss two situations in detail: estimating the signal function in the fractional Brownian motion model and the regression model with correlated errors. In the fractional Brownian motion model, we observe the process which is the sum of a fractional Brownian motion with Hurst index between ( 1 2 , 1 ) and a drift function that is determined by the signal function. In the regression model with correlated errors, we assume that the errors have long memory. For both estimation problems, we obtain the asymptotic rate for the minimax affine risks over certain types of parameter spaces. In each case, we also show that the minimax affine risk is bounded by 1.25 times the minimax risk.

What insights can be gained when analysing the resultant centre of pressure trajectory?

This article reviews the main aspects of the interpretation of centre of pressure trajectories measured from a force platform during undisturbed upright stance control. This objective measure has been used for more than 40 years by both clinicians and fundamental scientists to assess the postural stability of both healthy and disabled individuals. Besides rough summary statistics, which provide global information on the position of the body relative to the base of support, various techniques have been proposed such as frequency analysis, fractional Brownian motion modelling, and chaos systems, to give more relevant insights from neurophysiological and biomechanical points of view. Concurrently, the contribution of the joints and muscles of the lower legs has been studied trough EMG measures as well as indices computed from data from separate measures under each foot.

基于分数布朗运动模型的激光雷达目标检测

基于分数布朗运动模型的激光雷达目标检测

Towards an FBM Model Based Network Calculus Framework with Service Differentiation

In this paper, we exploit traffic modeling with the fractional Brownian motion (FBM) process to develop a network calculus framework for end-to-end performance analysis over a network provisioning differentiated services (DiffServ). The fundamental elements constituting the framework include accurate single-hop queueing analysis and three network calculuses that describe the stochastic behaviors when the traffic process is multiplexed, randomly split, or goes through a buffering system, respectively. Specifically, we develop a generic FBM based analysis for multiclass single-hop analysis where both inter-buffer priority and intra-buffer priority are used for service differentiation. Moreover, we present both theoretical and simulation studies to demonstrate that the output from the multiplexing, splitting, and buffering calculuses can still be modeled or well approximated by a properly parameterized FBM process. It is such preservation of the FBM characteristics that enables the concatenation of FBM based single-hop analysis into a network-wide performance analysis.