桂花叶片的分形特征

提供了一种叶片分形维数的测定方法,并用其测定了桂花(Osmanthus fragrans Lour)的叶片分形维数。通过分析发现：(1)桂花叶片具有典型的分形特征并且这种分形特征可以用分形理论的一般方法加以研究;(2)同一株桂花树的成熟叶片在统计意义上具有相同的分形维数;(3)对于桂花这个物种的成熟叶片在统计意义上具有相同的分形维数。由此推测同一种植物的成熟叶片(或者其他构件)具有相同分形维数。最后提出创建植物分形分类学的设想。     

桂花叶片的分形特征

提供了一种叶片分形维数的测定方法,并用其测定了桂花(Osmanthus fragrans Lour)的叶片分形维数。通过分析发现:(1)桂花叶片具有典型的分形特征并且这种分形特征可以用分形理论的一般方法加以研究;(2)同一株桂花树的成熟叶片在统计意义上具有相同的分形维数;(3)对于桂花这个物种的成熟叶片在统计意义上具有相同的分形维数。由此推测同一种植物的成熟叶片(或者其他构件)具有相同分形维数。最后提出创建植物分形分类学的设想。     

海南东寨港红树林土壤粒径分布的分形特征及其影响因素

应用分形理论分析了海南东寨港红树林土壤粒径分布的分形特征及其影响因素,海南东寨港土壤的分形维数为2．302—2．575,分形维数的大小与土壤中的粘粒、盐分、有机质、全氮含量呈显著正相关,外滩红树林土壤的分形维数低于中滩和内滩;随着土壤质地由砂壤土、轻壤土、中壤土、重壤土的变化,分形维数逐渐增大;从陆到海土壤分形维数逐渐减小。群落类型、土壤质地、滩位、含盐量、有机质、全氮含量等是影响海南东寨港红树林土壤分形维数的主要因子。     

英罗港红树林土壤粒径分布的分形特征

应用分形理论分析了英罗港红树林土壤粒径分布的分形特征。结果表明,红树林土壤的分形维数为2.6837-2.8834,不同质地土壤的分形维数呈现砂壤土＜轻壤土＜中壤土＜重壤土＜轻粘土的规律,外滩红树林土壤的分形维数低于中滩和内滩。土壤分形维数与其盐分和有机质含量呈显著正相关。群落类型、土壤质地、滩位、含盐量、有机质含量等是影响英罗港红树林土壤分形维数的主要因子。     

退化沙质草地开垦和围封过程中的土壤颗粒分形特征

研究了科尔沁退化沙质草地开垦和围封过程中土壤颗粒分形维数的变化特征,以及分形维数与土壤性状的关系.结果表明,不同开垦和围封年限的土壤颗粒分形维数(0～30cm)介于2.387～2.588之间.随着开垦年限的增加,0～15 cm层土壤颗粒分形维数从2.441降至2.387;围封11年后,0～15 cm层土壤颗粒分形维数增加到2.588.15～30 cm层土壤颗粒分形维数无明显变化.土壤颗粒分形维数是反映土壤质地的一个较好指标,重点反映粘粒含量,其次是粉粒含量.分形维数的变化能够很好地表征退化沙质草地土壤的化学、物理和生物学性状的变化趋势,可以作为评价退化沙质草地土壤性状的一个综合指标.     

科尔沁沙地农田沙漠化演变中土壤颗粒分形特征

研究了科尔沁沙地农田沙漠化过程中土壤的粗粒化和养分的贫瘠化特征 ,土壤颗粒分形维数的变化特征 ,以及分形维数与土壤性状的关系。结果表明 :土壤沙粒含量越高 ,土壤分形维数越低 ,表征农田沙漠化程度越高 ;土壤颗粒分形维数与土壤有机 C、全 N、粘粉粒含量之间存在显著的线性关系。说明分形维数能很好地表征农田沙漠化演变中土壤结构和养分状况以及沙漠化的程度 ,可作为评价土壤沙漠化演变的一项综合性定量指标。     

九龙江流域杉木混交林土壤结构的分形研究

运用分形理论对九龙江流域4种类型杉木混交林土壤粒径的分形维数与土壤水稳性团聚体、团聚体含量及结构体破坏率关系进行研究,比较分析了不同类型杉木混交林土壤结构的分形维数,建立了土壤结构分形维数与土壤理化性质的回归模型.研究结果表明,杉木混交林土壤分形维数与土壤水稳性团聚体、团聚体含量、结构体破坏率及土壤理化性质呈显著回归关系,分形维数与0.25mm土壤颗粒含量线性负相关,与结构体破坏率呈线性正相关.杉木米老排混交林土壤团粒结构的分形维数最小,土壤结构、稳定性及肥力状况最好,而杉木巨尾按混交林土壤自我培肥能力最差.分形理论在林地土壤肥力研究上的应用为林地评价提供了新方法.     

退化沙质草地开垦和围封过程中的土壤颗粒分形特征

研究了科尔沁退化沙质草地开垦和围封过程中土壤颗粒分形维数的变化特征,以及分形维数与土壤性状的关系.结果表明,不同开垦和围封年限的土壤颗粒分形维数(0～30cm)介于2.387～2.588之间.随着开垦年限的增加,0～15 cm层土壤颗粒分形维数从2.441降至2.387;围封11年后,0～15 cm层土壤颗粒分形维数增加到2.588.15～30 cm层土壤颗粒分形维数无明显变化.土壤颗粒分形维数是反映土壤质地的一个较好指标,重点反映粘粒含量,其次是粉粒含量.分形维数的变化能够很好地表征退化沙质草地土壤的化学、物理和生物学性状的变化趋势,可以作为评价退化沙质草地土壤性状的一个综合指标.     

基于盒维数的心音信号分形特征研究

在传统盒维数的基础上,从尺度变化的角度,提出一种计算心音信号时域波形分形维数的新的二进盒维数算法,并给出了算法思想和估算方法;然后用该方法对正常心音和几种典型的病态心音的分形维数进行计算,并对其分形特征进行了研究．研究结果表明：心音信号具有明显的分形特征,分形维数能够反映心音信号的复杂程度,并且能够明显地区分正常心音和病态心音．     

脑电信息处理

脑电信息处理是脑功能研究重要组成部分。本文介绍了脑电信息处理的前沿领域,包括诱发电位、事件相关电位（ＥＲＰ）、正弦调制光（声）诱发脑电、４０ＨｚＥＲＰ和脑电非线笥动力学研究,并论及了认知活动与分形维数的关系。     

Fractal diagnostics of disturbances in the alpha-rhythm dynamics in patients with epilepsy

A new method for analyzing the chaotic component of EEG is proposed. The method is based on estimating the fractal dimension of fluctuations of alpha-rhythm power (the square of amplitude). It is shown that the dimensions of the background EEG fragments for epilepsy patients is significantly higher than that in norm, indicating a disbalance of cerebral mechanisms that control the alpha-activity in this disease. A tendency toward the disturbance of the normal fractal structure of EEG in a group of patients with initial signs of epilepsy was revealed. This suggests that the method is of considerable promise for setting the individual long-term prognosis of the development of the epileptic syndrome.     

Use of the fractal dimension for the analysis of electroencephalographic time series

 Electroencephalogram (EEG) traces corresponding to different physiopathological conditions can be characterized by their fractal dimension, which is a measure of the signal complexity. Generally this dimension is evaluated in the phase space by means of the attractor dimension or other correlated parameters. Nevertheless, to obtain reliable values, long duration intervals are needed and consequently only long-term events can be analysed; also much calculation time is required. To analyse events of brief duration in real-time mode and to apply the results obtained directly in the time domain, thus providing an easier interpretation of fractal dimension behaviour, in this work we optimize and propose a new method for evaluating the fractal dimension. Moreover, we study the robustness of this evaluation in the presence of white or line noises and compare the results with those obtained with conventional spectral methods. The non-linear analysis carried out allows us to investigate relevant EEG events shorter than those detectable by means of other linear and non-linear techniques, thus achieving a better temporal resolution. An interesting link between the spectral distribution and the fractal dimension value is also pointed out. Received: 21 November 1996 / Accepted in revised form: 1 July 1997     

Modeling of movement-related potentials using a fractal approach

In bio-signal applications, classification performance depends greatly on feature extraction, which is also the case for electroencephalogram (EEG) based applications. Feature extraction, and consequently classification of EEG signals is not an easy task due to their inherent low signal-to-noise ratios and artifacts. EEG signals can be treated as the output of a non-linear dynamical (chaotic) system in the human brain and therefore they can be modeled by their dimension values. In this study, the variance fractal dimension technique is suggested for the modeling of movement-related potentials (MRPs). Experimental data sets consist of EEG signals recorded during the movements of right foot up, lip pursing and a simultaneous execution of these two tasks. The experimental results and performance tests show that the proposed modeling method can efficiently be applied to MRPs especially in the binary approached brain computer interface applications aiming to assist severely disabled people such as amyotrophic lateral sclerosis patients in communication and/or controlling devices.     

Methods of non-linear dynamics in estimation of electroencephalograms of healthy people and of patients with epilepsy

A possibility is discussed of use of methods of non-linear dynamics for analysis of spontaneous EEG and if the EEG caused by low acoustic stimuli in healthy people and in patients with epilepsy. A use of methods of non-linear dynamics--the fractal dimension of EEG--in clinical practice and in research is described.     

Application of competitive Hopfield neural network to brain-computer interface systems

We propose an unsupervised recognition system for single-trial classification of motor imagery (MI) electroencephalogram (EEG) data in this study. Competitive Hopfield neural network (CHNN) clustering is used for the discrimination of left and right MI EEG data posterior to selecting active segment and extracting fractal features in multi-scale. First, we use continuous wavelet transform (CWT) and Student's two-sample t-statistics to select the active segment in the time-frequency domain. The multiresolution fractal features are then extracted from wavelet data by means of modified fractal dimension. At last, CHNN clustering is adopted to recognize extracted features. Due to the characteristic of non-supervision, it is proper for CHNN to classify non-stationary EEG signals. The results indicate that CHNN achieves 81.9% in average classification accuracy in comparison with self-organizing map (SOM) and several popular supervised classifiers on six subjects from two data sets.     

Methods of nonlinear dynamics in estimation of electroencephalograms of healthy people and of patients with epilepsy

A possibility is discussed of use of methods of nonlinear dynamics for analysis of spontaneous EEG and of the EEG caused by low acoustic stimuli in healthy people and in patients with epilepsy. The use of methods of nonlinear dynamics—the fractal dimension of EEG—in clinical and scientific practice is described.     

The dynamics of EEG entropy

The scaling properties of human EEG have so far been analyzed predominantly in the framework of detrended fluctuation analysis (DFA). In particular, these studies suggested the existence of power-law correlations in EEG. In DFA, EEG time series are tacitly assumed to be made up of fluctuations, whose scaling behavior reflects neurophysiologically important information and polynomial trends. Even though these trends are physiologically irrelevant, they must be eliminated (detrended) to reliably estimate such measures as Hurst exponent or fractal dimension. Here, we employ the diffusion entropy method to study the scaling behavior of EEG. Unlike DFA, this method does not rely on the assumption of trends superposed on EEG fluctuations. We find that the growth of diffusion entropy of EEG increments of awake subjects with closed eyes is arrested only after approximately 0.5 s. We demonstrate that the salient features of diffusion entropy dynamics of EEG, such as the existence of short-term scaling, asymptotic saturation, and alpha wave modulation, may be faithfully reproduced using a dissipative, first-order, stochastic differential equation—an extension of the Langevin equation. The structure of such a model is utterly different from the “noise+trend” paradigm of DFA. Consequently, we argue that the existence of scaling properties for EEG dynamics is an open question that necessitates further studies.     

Fractal analysis of the uterine contractions.

The fractal dimension D may be calculated in many ways, since its strict definition, the Hausdorff definition is too complicated for practical estimation. In this paper we perform a comparative study often methods of fractal analysis of time series. In Benoit, a commercial program for fractal analysis, five methods of computing fractal dimension of time series (rescaled range analysis, power spectral analysis, roughness-length, variogram methods and wavelet method) are available. We have implemented some other algorithms for calculating D: Higuchi's fractal dimension, relative dispersion analysis, running fractal dimension, method based on mathematical morphology and method based on intensity differences. For biomedical signals results obtained by means of different algorithms are different, but consistent.     

遗传算法支持下土地利用空间分形特征尺度域的识别

针对土地利用空间分形特征只存在于有限尺度域的现象,采用无标度区内离散点拟合的离差平方和平均值最小作为目标函数,提出了一种基于遗传算法的土地利用空间分形特征尺度域的识别方法,用于准确计算分形维数的有效区间范围。以武汉市武昌区水域空间分形特征为例,利用Quickbird多光谱遥感影像提取土地利用空间信息,重点讨论了基于遗传算法识别土地利用空间分形特征尺度域范围的总体思路、适应度函数和遗传算子等环节;然后分别从测定系数、标准差和无标度区间3个角度,将其同人工判断法、相关系数法以及强化系数法进行对比讨论;并结合研究区域实际的水域空间分布格局,分析不同方法计算所得半径维数的合理性。结果表明,土地利用分形特征尺度域的范围对分形维数计算结果有较大影响;相对于传统计算方法来说,遗传算法在尺度无标度区间识别上具有更高的精度,可以为土地利用空间格局分形特征的研究提供客观指导意见。