小叶章种群分布格局的分形特征I计盒维数

应用分形理论（Ｆｒａｃｔａｌ ｔｈｅｏｒｙ）中的计盒维数（Ｂｏｘ－ｃｏｕｎｔｉｎｇ ｄｉｍｅｎｓｉｏｎ）对三江平原小叶章（Ｄｅｙｅｕｘｉａ ａｎｇｕｓｔｉｆｏｌｉａ）种群分布格局特征进行了研究。结果表明：三江平原小叶章种群分布格局具有分形特征。其计盒维数５－９月分别为１．５２４、１．７６９、１．７１１、１．６１５、１．７０１,表明其占据空间能力较强。季节动态自５月始至６月达到极大值,而后逐渐下降,     

小叶章种群分布格局的分形特征Ⅱ信息维数与关联维数

应用分形理论中的信息维数（Ｉｎｆｏｒｍａｔｉｏｎ ｄｉｍｅｎｓｏｉｎ）和关联维数（Ｃａｒｒｅｌａｔｉｏｎ ｄｉｍｅｎｓｏｉｎ）研究了三江平原小叶章（Ｄｅｙｅｕｘｉａ ａｎｇｕｓｔｉｆｌｏｉａ）种群分布格局特征。结果表明,信息维数在５～９月分别为１．４９４、１．７０９、１．６４２、１．５５３、１．６２５,表明其结构较复杂,格局强度较高。关联维数则为１．６６２、１．８６１、１．７６６、１．７５０、１．     

相关维数计算中的ln c(r)～ln r线性拟和

相关维数是定量描述非线性时间序列的一个重要参数,在脑电、心电等生物医学信号的特征描述方面得到了广泛地应用.相关维数的计算涉及到诸如延迟时间、嵌入维数等多个参数的选择,同时需要确定ln C_m(r)～ln r线性拟和的尺度区间.本文介绍了一种新的确定尺度区间的方法,利用该方法确定尺度区间能够保持计算结果的稳定性与一致性.     

睡眠脑电的分形维数分析

为了研究是否用维数来描述脑功能的复杂程序,我们计算了５例正常人整夜睡眠时不同阶段的ＥＥＧ资料维数。结果显示,随着睡眠深度的增加而维数降低。这一事实和生理概念及其他作者所报道的结果相一致,故我们考虑维数分析在表示脑功能状态上有一定的理论意义。如果我们用简化法来计算维数,此法就有可能实时地应用于临床诊断。     

经颅磁刺激对癫痫病灶脑电相关维数的影响

利用脑功能指标——大鼠病灶区脑电的相关维数,研究低频经颅磁刺激对慢性颞叶癫痫大鼠脑功能改善的作用。对一组颞叶癫痫大鼠施予频率为0．5Hz、强度为0．4T、20次／日、连续一周的低频重复性经颅磁刺激(rTMS)．在rTMS前后,分别测取颞叶癫痫大鼠责任病灶区皮层和海马区的脑电,重构时间延迟吸引子,用G-P算法估算反映对应脑区功能状态的相关维数。研究结果显示：施予适量的rTMS(0.4T、20次／日、连续一周),使颞叶癫痫大鼠海马和相应皮层脑电的相关维数比刺激前明显升高。研究表明适量的rTMS有抑制癫痫的作用。     

胃电的非线性动力学分析

我们用非线性动力学的方法分析了两例健康人的胃电图（Ｅｌｅｃｔｒｏｇａｓｔｒｏｇｒａｍ,简称ＥＧＧ）,得出它的功率谱、计算了它的关联维数和最大Ｌｙａｐｕｎｏｖ指数。结果显示：它的功率谱为一有尖峰的连续谱;其关联维数介于６和７之间;它的最大Ｌｖａａｕｎｏｖ指数大于０。由此,我们可以初步推知ＥＧＧ不是随机噪声,它服从确定性的动力学规律。     

山西七里峪油松种群空间格局的分形特征

油松(Pinus tabuliformis)耐低温、干旱和瘠薄,是我国温性针叶林中分布最广的树种,也是我国北方广大地区最主要的造林树种之一。2013年7月,在七里峪林场设置一块100 m×100 m的油松天然林样地,逐一测量并记录了每株油松的胸径、树高和冠幅,并确定它们的坐标位置。应用分形理论中的计盒维数、信息维数和关联维数研究了样地内油松种群空间格局的分形特征。结果表明,油松种群格局具有自相似性,其有较高的计盒维数(1.785)和关联维数(1.826),个体空间相关程度较高,种内竞争激烈,对空间有较强的占据能力。油松种群格局的信息维数较低(0.262),其格局强度尺度变化程度较低,个体分布比较均匀。3个分形维数相辅相承、相互影响,研究结果对全面准确地解释油松种群的空间格局特征具有重要意义。     

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。     

铅染毒大鼠脑电信号的分形特性研究

利用混沌时间序列的分析方法,对铅中毒情况下的大鼠的脑电波进行了测试和分析,求出了其分形维数。从研究结果中得出了铅中毒情况与脑电信号的分形维数之间的关系,结果表明,铅中毒会引起脑电信号的分形维数的显著变化。通过这一工作,能够为临床上重金属中毒的早期诊断提供新的方便、灵敏的指标。     

小叶章种群分布格局的分形特征Ⅱ信息维数与关联维数

应用分形理论中的信息维数(Information dimension)和关联维数(Carrelation dimension)研究了三江平原小叶章(Deyeuxia angustifolia)种群分布格局特征。结果表明:信息维数在5~9月分别为1.494、1.709、1.642、1.553、1.625,表明其结构较复杂,格局强度较高。关联维数则为1.662、1.861、1.766、1.750、1.807,说明小叶章个体空间相关程度较高。种内竞争强烈,对空间有较强的占据能力。两个维数的季节动态均自5月至6月达到极大值,而后逐渐下降,至9月略有回升。     

高维混沌降维的投影追踪主分量分析法

一些生理信号,例如脑电是源自于高维混沌系统,因此低维混沌理论和方法不适用于分析这类高维混沌。采用投影追踪主分量分析法（Princiopal Component Analysis based on Projection Pursuit,PP PCA）对高维Lorenz模型系统进行了降维的研究。在用上述方法成功地对线性和非线性噪声－周期模型分别进行了PP PCA分析的基础上,对Lorenz高维混沌系统进行了PPPCA降维的研究。结果表明,正确选用非线性的投影追踪主分量分析法,可以通过简化原系统达到降维的目的,并能保留研究所关心的原系统的主要动态特性。同时也阐明了方法的稳定性和将该方法应用于高维脑电降维的可行性。     

EEG动力学模型中混沌现象的研究

通过对脑电图（electroencephalogram,EEG）动力学模型模拟出的EEG信号的相图、分岔图、功率谱、关联维数和Lyapunov指数的对比研究,得出如下结论：1）该模型是按周期行为与混沌现象交替出现的间歇突发通向混沌的,且该间歇性与Hopf分岔、倍周期分岔和逆分岔有关;2）支持了EEG中存在混沌运动的观点。     

Correlation dimension based lossless compression of EEG signals

Transmission of long duration EEG signals without loss of information is essential for telemedicine based applications. In this work, a lossless compression scheme for EEG signals based on neural network predictors using the concept of correlation dimension (CD) is proposed. EEG signals which are considered as irregular time series of chaotic processes can be characterized by the non-linear dynamic parameter CD which is a measure of the correlation among the EEG samples. The EEG samples are first divided into segments of 1 s duration and for each segment, the value of CD is calculated. Blocks of EEG samples are then constructed such that each block contains segments with closer CD values. By arranging the EEG samples in this fashion, the accuracy of the predictor is improved as it makes use of highly correlated samples. As a result, the magnitude of the prediction error decreases leading to less number of bits for transmission. Experiments are conducted using EEG signals recorded under different physiological conditions. Different neural network predictors as well as classical predictors are considered. Experimental results show that the proposed CD based preprocessing scheme improves the compression performance of the predictors significantly.     

Nonlinear analysis of EEG signals: Surrogate data analysis

ObjectivesThe electroencephalogram (EEG) signal contains information about the state and condition of the brain. The aim of the study is to conduct a nonlinear analysis of the EEG signals and to compare the differences in the nonlinear characteristics of the EEG during normal state and the epileptic state.DataThe EEG data used for this study – which consisted of epileptic EEG and normal EEG – were obtained from the EEG database available with the Bonn University, Germany.ResultsThe attractors seen in normal and epileptic human brain dynamics were studied and compared. Surrogate data analyses were conducted on two nonlinear measures, namely the largest Lyapunov exponent and the correlation dimension, to test the hypothesis whether EEG signals were in accordance with linear stochastic models.DiscussionsThe existence of deterministic chaos in brain activity is confirmed by the existence of a chaotic attractor; also, saturation of the correlation dimension towards a definite value is the manifestation of a deterministic dynamics. Also a reduction is observed between the dimensionalities of the brain attractors from normal state to the epileptic state. The evaluation of the largest Lyapunov exponent also confirms the lowering of complexity during an episode of seizure.ConclusionIn case of Lyapunov exponent of EEG data, the change due to surrogating is small suggesting that it is not representing the system complexity properly but there is a marked change in the case of correlation dimension value due to surrogating.     

Research on the relation of EEG signal chaos characteristics with high-level intelligence activity of human brain

Using phase space reconstruct technique from one-dimensional and multi-dimensional time series and the quantitative criterion rule of system chaos, and combining the neural network; analyses, computations and sort are conducted on electroencephalogram (EEG) signals of five kinds of human consciousness activities (relaxation, mental arithmetic of multiplication, mental composition of a letter, visualizing a 3-dimensional object being revolved about an axis, and visualizing numbers being written or erased on a blackboard). Through comparative studies on the determinacy, the phase graph, the power spectra, the approximate entropy, the correlation dimension and the Lyapunov exponent of EEG signals of 5 kinds of consciousness activities, the following conclusions are shown: (1) The statistic results of the deterministic computation indicate that chaos characteristic may lie in human consciousness activities, and central tendency measure (CTM) is consistent with phase graph, so it can be used as a division way of EEG attractor. (2) The analyses of power spectra show that ideology of single subject is almost identical but the frequency channels of different consciousness activities have slight difference. (3) The approximate entropy between different subjects exist discrepancy. Under the same conditions, the larger the approximate entropy of subject is, the better the subject's innovation is. (4) The results of the correlation dimension and the Lyapunov exponent indicate that activities of human brain exist in attractors with fractional dimensions. (5) Nonlinear quantitative criterion rule, which unites the neural network, can classify different kinds of consciousness activities well. In this paper, the results of classification indicate that the consciousness activity of arithmetic has better differentiation degree than that of abstract.     

Fractal dimension of electroencephalographic time series and underlying brain processes

 Fractal dimension has been proposed as a useful measure for the characterization of electrophysiological time series. This paper investigates what the pointwise dimension of electroencephalographic (EEG) time series can reveal about underlying neuronal generators. The following theoretical assumptions concerning brain function were made (i) within the cortex, strongly coupled neural assemblies exist which oscillate at certain frequencies when they are active, (ii) several such assemblies can oscillate at a time, and (iii) activity flow between assemblies is minimal. If these assumptions are made, cortical activity can be considered as the weighted sum of a finite number of oscillations (plus noise). It is shown that the correlation dimension of finite time series generated by multiple oscillators increases monotonically with the number of oscillators. Furthermore, it is shown that a reliable estimate of the pointwise dimension of the raw EEG signal can be calculated from a time series as short as a few seconds. These results indicate that (i) The pointwise dimension of the EEG allows conclusions regarding the number of independently oscillating networks in the cortex, and (ii) a reliable estimate of the pointwise dimension of the EEG is possible on the basis of short raw signals. Received: 1 September 1994/Accepted in revised form: 16 May 1995     

Testing procedures for non-stationarity and non-linearity in physiological signals

Most of the physiological signals (EEG, ECG, blood flow, human gait, etc.) characterize by complex dynamics including both non-stationarities and non-linearities. These time series resemble red noise with long-range correlation and 1/(f beta) power spectrum. A question arises as to how to distinguish the characteristics of the process underlying the signal dynamics from the properties of the observed time series. The classical methods to determine possible non-linear (chaotic) dynamics (e.g. correlation dimension) often fail in such signals because of relatively short data records containing stochastic components and non-stationarities. We report an application of several approaches, aimed at (1) determining of the non-stationarities in the signals and (2) testing whether non-linear dynamics exists. Assessment of the intrinsic correlation properties of the dynamic process and distinguishing the same from external trends was performed using singular spectra and detrended fluctuation analysis. The existence of non-linear dynamics was tested by correlation dimension (modified algorithm of re-embedding) and by correlation integrals of real and surrogate data. The correlation integrals of real signal and surrogate data sets were statistically compared using Kolmogorov-Smirnov (K-S) test. The procedures were tested on EEG and laser-Doppler (LD) blood flow. Our suggestion is that no one approach taken alone is the best for our aims. Instead, a battery of methods should be used.     

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.