北京东灵山地区辽东栎林种群空间分布分形分析

通过植物个体的坐标点与模拟冠幅的分形维数的分析,对辽东栎林内不同种群沿海拔梯度变化的空间分布格局和种群动态进行了比较和讨论。结果表明:模拟冠幅分形分析方法更适于分析具有大小不等、复杂多样的冠幅的植物个体空间分布格局。随着海拔的升高,不同种群的空间占据能力也随之变化。辽东栎种群的空间分布占绝对优势地位,分形维数可达1.9811;五角枫种群则逐步下降,分形维数最低为0.1170。低海拔山坡六道木种群空间占据能力较强,高海拔山坡照山白种群有较大的空间占据能力。在一定的环境条件下,不同的种群可能具有相近的空间占据能力,但对乔木层与灌木层来说,相同的分形维数的内涵是不同的。冠幅的分形维数作为表征植物种群空间占据能力的工具,是种群动态分析和种群分布格局研究的的重要指标之一。     

Fat fractal and multifractals for protein and enzyme surfaces.

The roughness and irregularity of the surfaces in the protein and enzyme are fractal features that may be characterized by fractal dimensions and mass exponents. The surface fractal dimensions calculated by the variation method are different from those obtained by other methods, since the former is applicable to the self-affine system. Thus the results reported here are reliable for the surfaces. However, the fat fractal and multifractal features of proteins and enzymes are studied by simulation. The surface mass exponents are regarded as another kind of scaling exponent, and the spectrum f(alpha) provides further detailed information about the surfaces of enzyme and protein. The applications of the spectrum f(alpha) to the enzymatic reactions is also discussed.     

红树植物木榄幼树斑块形状的分形分析

应用分形理论分析了山口国家级红树林自然保护区木榄幼树斑块形状的分形特征。木榄幼树斑块在整体水平上的分形维数为 1 .1 2 ,而单个斑块的分形维数介于 1 .1 7～ 1 .3 7之间。分形维数的大小与斑块形状的复杂程度密切相关。频谱法和周长 -面积法都适用于分析幼树斑块形状的分形特征。     

Stochastic fractal behavior in concentration fluctuation and fluorescence correlation spectroscopy.

Fluctuations in the concentration of Brownian particles in one and two dimensions, or any reasonable measurement of the concentration such as in fluorescence correlation spectroscopy, is shown to be a stochastic fractal with a long tail. Being singular at omega = 0, the power spectrum of the fluctuation S(omega) approximately omega-1/2 for diffusion in one dimension, approximately log omega in two dimensions, but non-singular in three dimensions. This discovery provides one simple physical mechanism for possible long-memory fractal behavior, and its implications to various biological processes are discussed.     

Analysis of fractal dimension of O2A glial cells differentiating in vitro

Fractal dimension is a quantitative measure of morphological complexity. Glial cells of the oligodendrocyte-type 2 astrocyte (O2A) lineage exhibit increasing morphological complexity as they differentiate in vitro. Enriched populations of O2A progenitor cells isolated from neonatal rat cerebral hemispheres or optic nerves were allowed to differentiate in vitro, and their fractal dimensions were measured over time. The fractal dimensions of the maturing cells correlated with perceived complexity; cells with elaborate process branching had larger fractal dimensions than cells with a simpler morphology. An analysis of changes in fractal dimension revealed distinct rates of growth for both oligodendrocytes and type 2 astrocytes. The fractal dimension remained constant over a 10-fold range in optical magnification, demonstrating that cultured O2A glial cells exhibit self-similarity, a defining characteristic of fractal objects. These results illustrate that fractal dimension analysis of maturing cell populations is a useful method for quantitatively describing the process of cell differentiation.     

分子进化研究：Ⅱ.5SrRNA序列的分形与分子进化的关系

本文根据分形理论的原理和方法,在对现行的计算核酸序列分维的方法进行修改的基础上,对各类生物的80余种5SrRNA序列的分维进行了计算,并结合耗散结构理论就其分维与分子进化的关系问题进行了研究和探讨。作者认为,5SrRNA序列的分维与其分子进化间的关系是一种复杂的非线性关系,在分子进化的过程中,序列的分维表现为随机涨落。     

A mathematical analysis using fractals for binding interactions of nuclear estrogen receptors occurring on biosensor surfaces

A mathematical approach using fractal concepts is presented for modeling the binding and dissociation interactions between analytes and nuclear estrogen receptors (ER) occurring on surface plasmon resonance biosensor chip surfaces. A kinetic knowledge of the binding interactions mediated by ER would help in better understanding the carcinogenicity of these steroidogenic compounds and assist in modulating these reactions. The fractal approach is applied to analyte-ER interaction data obtained from literature. Numerical values obtained for the binding and dissociation rate coefficients are linked to the degree of roughness or heterogeneity (fractal dimension, D(f)) present on the biosensor surface. For example, a single-fractal analysis is used to describe the binding and dissociation phases for the binding of estradiol and ERalpha in solution to clone 31 protein immobilized on a biosensor chip (C-S. Suen et al., 1998, J. Biol. Chem. 273(42), 27645-27653). The binding and the dissociation rate coefficients are 27.57 and 8.813, respectively, and the corresponding fractal dimensions are 1.986 and 2.268, respectively. In some examples dual-fractal models were employed to obtain a better fit of either the association or the dissociation phases or for both. Predictive relationships are developed for (a) the binding and the dissociation rate coefficients as a function of their respective fractal dimensions and (b) the ratio K(A) (= k/k(d)) as a function of the ratio of the fractal dimensions (D(f)/D(fd)). The analysis should provide further physical insights into the ER-mediated interactions occurring on biosensor and other surfaces.     

Fractal Feature of Particle-Size Distribution in the Rhizospheres and Bulk Soils during Natural Recovery on the Loess Plateau,China

The application of fractal geometry to describe soil structure is an increasingly useful tool for better understanding the performance of soil systems. Only a few studies, however, have focused on the structure of rhizospheric zones, where energy flow and nutrient recycling most frequently occur. We used fractal dimensions to investigate the characteristics of particle-size distribution (PSD) in the rhizospheres and bulk soils of six croplands abandoned for 1, 5, 10, 15, 20, and 30 years on the Loess Plateau of China and evaluated the changes over successional time. The PSDs of the rhizospheres and the fractal dimensions between rhizosphere soil and bulk soils during the natural succession differed significantly due to the influence of plant roots. The rhizospheres had higher sand (0.05–1.00 mm) contents, lower silt (<0.002 mm) contents, and lower fractal dimensions than the bulk soils during the early and intermediate successional stages (1–15 years). The fractal dimensions of the rhizosphere soil and bulk soil ranged from 2.102 to 2.441 and from 2.214 to 2.459, respectively, during the 30-year restoration. Rhizospheric clay and silt contents and fractal dimension tended to be higher and sand content tended to be lower as abandonment age increased, but the bulk soils had the opposite trend. Linear regression analysis indicated that the fractal dimensions of both the rhizospheres and bulk soils were significantly linearly correlated with clay, sand, organic-carbon, and total-nitrogen contents, with R ² ranging from 0.526 to 0.752 (P<0.001). In conclusion, PSD differed significantly between the rhizosphere soil and bulk soil. The fractal dimension was a sensitive and useful index for quantifying changes in the properties of the different soil zones. This study will greatly aid the application of the fractal method for describing soil structure and nutrient status and the understanding of the performance of rhizospheric zones during ecological restoration.     

Use of fractal dimensions to quantify coral shape

A morphometrical method to quantify and characterize coral corallites using Richardson Plots and Kaye’s notion of fractal dimensions is presented. A Jurassic coral species (Aplosmilia spinosa) and five Recent coral species were compared using the Box-Counting Method. This method enables the characterization of their morphologies at calicular and septal levels by their fractal dimensions (structural and textural). Moreover, it is possible to determine differences between species of Montastraea and to tackle the high phenotypic plasticity of Montastraea annularis. The use of fractal dimensions versus conventional methods (e.g., measurements of linear dimensions with a calliper, landmarks, Fourier analyses) to explore a rugged boundary object is discussed. It appears that fractal methods have the potential to considerably simplify the morphometrical and statistical approaches, and be a valuable addition to methods based on Euclidian geometry.     

Fractal characterisation of the effect of noise on biological oscillations: The biosynthesis of ethanol

Summary Biological reactions which interact with their environment are subject to the influx of noise. Noise introduces randomness and imparts fractal character to the deterministic behavior. A methodology is proposed to compute the fractal dimensions of such reactions. It is applied to the continuous culture of Zymomonas mobilis to produce ethanol. Results show that noise can change the nature of oscillations or induce oscillations in a stationary state. The noise-induced oscillations are aperiodic and fractal in nature. The variation of the fractal dimension with dilution rate and the initial ethanol concentration is presented and discussed in terms of the interaction between process kinetics and the incoming noise.     

Fractal Binding and Dissociation Kinetics of Heart-Related Compounds on Biosensor Surfaces

A fractal analysis is presented for the binding and dissociation of different heart-related compounds in solution to receptors immobilized on biosensor surfaces. The data analyzed include LCAT (lecithin cholesterol acyl transferase) concentrations in solution to egg white apoA-I rHDL immobilized on a biosensor chip surface (), native, mildly oxidized, and strongly oxidized LDL in solution to a heparin-modified Au-surface of a surface plasmon resonance (SPR) biosensor (), and TRITC-labeled HDL in solution to a bare optical fiber surface (). Single-and dual-fractal models were used to fit the data. Values of the binding and the dissociation rate coefficient(s), affinity values, and the fractal dimensions were obtained from the regression analysis provided by Corel Quattro Pro 8.0 (). The binding rate coefficients are quite sensitive to the degree of heterogeneity on the sensor chip surface. Predictive equations are developed for the binding rate coefficient as a function of the degree of heterogeneity present on the sensor chip surface and on the LCAT concentration in solution and for the affinity as a function of the ratio of fractal dimensions present in the binding and the dissociation phases. The analysis presented provided physical insights into these analyte-receptor reactions occurring on different biosensor surfaces.     

三峡库区次生柏木林中物种分布格局的分形特征

应用非线性科学中的分形几何理论,以三峡库区一移民安置示范区次生柏木林为对象,研究该群落中物种在中、小尺度上水平分布格局的分形特征,主要应用计盒维数计算群落中一些重要物种分布格局的分维值,如柏木为1.588,地枇杷为1.617,莎草为1.627.得到的结果与用经典群落分析方法所得结果相符,表明分维计算在本研究中是一种有效的手段;对一些物种分布分维值的进一步分析还能说明人类活动对物种分布格局或空间占有程度的影响.     

Fractal properties of forest spatial structure

The definition of fractal dimension of natural objects, which enables to deal with scale dependence of fractal dimension is discussed. Abrupt changes of fractal dimension of spatial structure of terrestrial ecosystems are considered in the context of hierarchical paradigm. On this ground the procedure is proposed for segmentation of a territory, which takes into account the scale dependence of spatial variability of ecological parameters. Using remotely sensed data — normalized difference vegetation index (NDVI) and thermal radiation in the infrared band — fractal dimensions and critical scales are evaluated for different forest types with the help of software, developed for this purpose. The results obtained corroborate the potentialities of fractal approach in ecology. These methods and results can be used for discrimination of remotely sensed data; but further investigations, including detailed comparison of fractal characteristics of remotely sensed forest images with results of on-site field studies are necessary to validate them.     

Fractal binding and dissociation kinetics of heart-related compounds on biosensor surfaces

A fractal analysis is presented for the binding and dissociation of different heart-related compounds in solution to receptors immobilized on biosensor surfaces. The data analyzed include LCAT (lecithin cholesterol acyl transferase) concentrations in solution to egg white apoA-I rHDL immobilized on a biosensor chip surface (1), native, mildly oxidized, and strongly oxidized LDL in solution to a heparin-modified Au-surface of a surface plasmon resonance (SPR) biosensor (2), and TRITC-labeled HDL in solution to a bare optical fiber surface (3). Single-and dual-fractal models were used to fit the data. Values of the binding and the dissociation rate coefficient(s), affinity values, and the fractal dimensions were obtained from the regression analysis provided by Corel Quattro Pro 8.0 (4). The binding rate coefficients are quite sensitive to the degree of heterogeneity on the sensor chip surface. Predictive equations are developed for the binding rate coefficient as a function of the degree of heterogeneity present on the sensor chip surface and on the LCAT concentration in solution and for the affinity as a function of the ratio of fractal dimensions present in the binding and the dissociation phases. The analysis presented provided physical insights into these analyte-receptor reactions occurring on different biosensor surfaces.     

Fractal geometry and root system structures of heterogeneous plant communities

Above-ground plant growth is widely known in terms of structural diversity. Likewise, the below-ground growth presents a mosaic of heterogeneous structures of differing complexity. In this study, root system structures of heterogeneous plant communities were recorded as integral systems by using the trench profile method. Fractal dimensions of the root images were calculated from image files by the box-counting method. This method allows the structural complexity of such associations to be compared between plant communities, with regard to their potentials for soil resource acquisition and utilization. Distinct and partly significant differences are found (fractal dimension between 1.46±0.09 and 1.71±0.05) in the below-ground structural complexity of plant communities, belonging to different biotope types. The size of the heterogeneous plant community to be examined has an crucial influence on the fractal dimension of the root system structures. The structural heterogeneity becomes particularly evident (fractal dimensions between 1.32 and 1.77) when analysing many small units of a complex root system association. In larger plant communities, a broad variety of below-ground structures is recorded in its entirety, integrating the specific features of single sub-structures. In that way, extreme fractal dimensions are lost and the diversity decreases. Therefore, the analysis of larger units of root system associations provides a general knowledge of the complexity of root system structures for heterogeneous plant communities.     

From Hutchinsonian ratios to spatial scaling theory: the interplay among limiting similarity,body size and landscape structure

Spatial scaling theory (SST) relates the physical structure of the environment to species coexistence and community assembly. Although SST is a recognized theory in ecology, few studies have evaluated its predictions, producing contradictory results and frequently failing to meet its assumptions. In addition, the ‘risk predictions’ of SST regarding an increase in species similarity with body size and the dependence of this pattern on the landscape and food fractal dimensions have not been evaluated. This study attempted to account for previous limitations, analyzing these predictions in coleopteran guilds that inhabit 18 temporary ponds. This metacommunity covers a large gradient of environmental variables, including food density, the landscape fractal dimension, the food fractal dimensions and other indicators of pond heterogeneity. Average similarity in carnivorous and herbivorous body sizes systematically increased with guild richness, fulfilling classical predictions of niche theory. Species similarity was associated with body size, but the association reverts from negative to positive as the landscape fractal dimension and heterogeneity increases, a pattern further supported by null model analyses. Several nonexclusive mechanisms may account for this pattern: 1) the body size-dependent landscape perception, through which small animals detect more heterogeneity than larger animals; 2) the reaching of landscape limits by larger species, which prevents them from accessing novel largest clusters; 3) the large differences between the landscape and food fractal dimensions; and 4) the homogenization of the landscape when an integer fractal dimension is reached. These mechanisms may dictate that smaller organisms are more able to capitalize on heterogeneity or available resources than larger organisms, thus promoting increased similarity among smaller species. The presented results support the connection between landscape spatial structure and biodiversity and a mechanistic understanding of this connection from the SST.     

植被格局的分形模型：植被格局的分形特征

 目前植被格局研究存在一些问题,分形模型是解决这些问题的有力工具。选择从分枝到景观的各个等级层次上若干有代表性的研究实例进行介绍,给出了尺度、自相似性和分形维数在植被格局研究中的应用方法,说明了分形模型描述植被格局的实用性和优越性。在此基础上提出植被格局的分形机制,认为植被格局是具有自组织特征的分形体。最后对植被格局的分形模型进行了评价,提出研究中需要注意的若干问题以及未来的发展方向。     

植被格局的分形特征

目前植被格局研究存在一些问题,分形模型是解决这些问题的有力工具。选择从分枝到景观的各个等级层次上若干有代表性的研究实例进行介绍。给出了尺度,自相似性和分形维数在植被格局研究中的应用方法,说明了分形模型描述植被格局的实用性和优越性。在此基础上提出了植被格局的分形机制,认为植被格局是具有自组织特征的分形体。最后对植被格局的分形模型进行了评价,提出了研究中需要注意的若干问题以及未来的发展方向。     

The Fractal Patterns of Words in a Text: A Method for Automatic Keyword Extraction

A text can be considered as a one dimensional array of words. The locations of each word type in this array form a fractal pattern with certain fractal dimension. We observe that important words responsible for conveying the meaning of a text have dimensions considerably different from one, while the fractal dimensions of unimportant words are close to one. We introduce an index quantifying the importance of the words in a given text using their fractal dimensions and then ranking them according to their importance. This index measures the difference between the fractal pattern of a word in the original text relative to a shuffled version. Because the shuffled text is meaningless (i.e., words have no importance), the difference between the original and shuffled text can be used to ascertain degree of fractality. The degree of fractality may be used for automatic keyword detection. Words with the degree of fractality higher than a threshold value are assumed to be the retrieved keywords of the text. We measure the efficiency of our method for keywords extraction, making a comparison between our proposed method and two other well-known methods of automatic keyword extraction.