基于RS和GIS的开封市土地覆盖分形

以RS和GIS为技术手段,利用开封市0.61m空间分辨率的QuickBird卫星遥感数据,采用分形几何方法研究了斑块的面积效应和覆盖类型分形的关系,并对覆盖类型的分形特征差异等进行了分析。结果表明,开封市防护林地和农田的平均斑块面积较大,分维数也较大,而水体的分维数较小,说明防护林和农田斑块的边界结构特征比水体更为复杂。斑块的分维值具有尺度依赖性,同一类型中大的斑块往往具有较大的分维值,其原因是大斑块经常出现不同类型的斑块相互嵌套,小斑块则很少出现甚至不出现这种现象。     

高寒草地甘肃臭草根系分形结构的坡向差异性

根系分形结构是植物根系构型应对环境异质性的表型可塑性结果, 可反映植物对生长环境的适应策略。利用ArcGIS建立研究区域的数字高程模型, 并提取坡向数据, 采用全根挖掘和Win-RHIZO根系分析仪相结合的方法, 研究了祁连山北坡高寒退化草地不同坡向甘肃臭草(Melica przewalskyi)的根系分形结构。结果表明: 随着坡向由北坡向东坡、西坡、南坡转变, 草地群落的密度、高度和土壤含水量逐渐减小, 甘肃臭草种群的密度、高度以及根系分形丰度呈逐渐增大的趋势、分形维数逐渐减小; 不同坡向甘肃臭草根系分形维数和分形丰度间的相关性存在差异(p < 0.05), 南坡和北坡甘肃臭草根系分形维数分形丰度之间存在极显著负相关关系(p < 0.01), 东坡和西坡之间存在显著负相关关系(p < 0.05), 甘肃臭草根系分形维数和分形丰度存在着“此消彼长”的权衡关系; 随着坡向由北坡向东坡、西坡、南坡转变, 甘肃臭草根系分形维数和分形丰度回归方程的标准化主轴(SMA)斜率逐渐增大(p < 0.05), 说明在干旱的南坡, 根系所开发利用的相同体积的土壤内, 根系分支更少、更稀疏。不同坡向甘肃臭草合理权衡根系分形维数和分形丰度的资源配置模式, 体现了植物根系构型构建的资源投资权衡机制。     

Fractal geometry of root systems: Field observations of contrasting genotypes of common bean (Phaseolus vulgaris L.) grown under different phosphorus regimes

Root growth and architecture are important for phosphorus acquisition due to the relative immobility of P in the soil. Fractal geometry is a potential new approach to the analysis of root architecture. Substantial genetic variation in root growth and architecture has been observed in common bean. Common bean (Phaseolus vulgaris L.) genotypes with contrasting root architecture were grown under moderate and low P conditions in a field experiment. Linear and planar fractal dimension were measured by tracing root intercepts with vertical planes. Linear fractal dimension increased over time in efficient genotypes, but remained fairly constant over time in inefficient genotypes. Planar fractal dimension increased over time for all genotypes, but was higher in efficient than inefficient genotypes at the end of the experiment. Planar fractal dimension of medium P plants was found to correlate with shoot P content indicating fractal dimension to be a possible indicator for root P uptake. The increasing fractal dimension over time indicates that fractal analysis is a sensitive measure of root branching intensity. A less destructive method for acquisition of data that allows for continuous analysis of fractal geometry and thereby screening for more P efficient genotypes in the field is suggested. This method will allow the researcher to conduct fractal analysis and still complete field trials with final yield evaluation.     

The analysis of oligonucleotide preparations by fractal measures

In this paper we put forward improved mathematical methods for detecting synthesis parameters in connection with analyzing crude products of chemically synthesized oligonucleotides. The crude products experimentally sampled are separated by high-performance capillary electrophoresis and ion-exchange high-performance liquid chromatography. The measured separation profiles of experimental syntheses can be expressed as target and nontarget yields; they are characterized by a few parameters. These parameters account for nonlinear synthesis equations that are solvable by employing iteration procedures. We provide here a theoretical as well as computational analysis based upon specific models for stepwise chain growth. Under nonconstant (nonuniform) conditions we use here an exponential form of growth, with different expressions for calculating the fractal dimension of the biochemical process under study. Step lengths of parameter variations in an interval of finite length have to be adjusted properly to find convergent solutions in a mathematical, regularly four-dimensional parameter space. It is conceivable to have most, if not all, of the calculating and plotting carefully done by a computer. This analysis represents the experimental situation up to 65-mer target oligonucleotides analyzed so far. We thus obtain the dynamics of the polymerization process limited in number by fractal models. The advantage, calculating these new methods as compared to qualitatively judged experimental methods, lies in the satisfactory evaluation of crude products, also of large amounts, of syntheses of these biopolymers. © 1998 John Wiley & Sons, Inc. Biopoly 45: 361–379, 1998     

The imaging and the fractal metrology of chimeric liposomal Drug Delivery nano Systems: the role of macromolecular architecture of polymeric guest

The major advance of mixed liposomes (the so-called chimeric systems) is to control the size, structure, and morphology of these nanoassemblies, and therefore, system colloidal properties, with the aid of a large variety of parameters, such as chemical architecture and composition. The goal of this study is to investigate the alterations of the physicochemical and morphological characteristics of chimeric dipalmitoylphosphatidylcholine (DPPC) liposomes, caused by the incorporation of block and gradient copolymers (different macromolecular architecture) with different chemical compositions (different amounts of hydrophobic component). Light scattering techniques were utilized in order to characterize physicochemically and to delineate the fractal morphology of chimeric liposomes. In this study, we also investigated the structural differences between the prepared chimeric liposomes as are visualized by scanning electron microscopy (SEM). It could be concluded that all the chimeric liposomes have regular structure, as SEM images revealed, while their fractal dimensionality was found to be dependent on the macromolecular architecture of the polymeric guest.     

Fibonacci,quasicrystals and the beauty of flowers

The appearance of Fibonacci sequences and the golden ratio in plant structures is one of the great outstanding puzzles of biology. Here I suggest that quasicrystals, which naturally pack in the golden ratio, may be ubiquitous in biological systems and introduce the golden ratio into plant phyllotaxy. The appearance of golden ratio-based structures as beautiful indicates that the golden ratio may play a role in the development of consciousness and lead to the aesthetic natural selection of flowering plants.     

An automated framework to quantify areas of regional ischemia in retinal vascular diseases with OCT angiography

In this observational and cross‐sectional study, capillary nonperfusion (CNP) and vascular changes in branch retinal vein occlusion (BRVO, sample size [n] = 26) and choroidal neovascularization (CNV, n = 29) were evaluated. Subjects underwent imaging using Optical coherence tomography angiography (Angiovue OCTA, RTVue XR, Optovue Inc., Fremont, California). Local fractal analysis was applied to the OCTA images of superficial, deep and choriocapillaris layer. CNP area (BRVO eyes) and vascular parameters were computed using local fractal‐based method. Sensitivity and specificity of vascular parameters were assessed with receiver operating characteristics curve. Automated CNP area showed excellent agreement with manually quantified CNP areas in both superficial (intraclass coefficient [ICC] = 0.96) and deep (ICC = 0.96) layers. BRVO eyes showed significantly altered (P < .05) vascular parameters in both superficial and deep layer as compared to normal eyes (n = 30). CNVM eyes had significantly higher capillary free zones (P < .001) as compared to normal eyes. In normal vs BRVO eyes, vessel density and spacing between the large vessels had similar area under the curve (AUC) (P > .05) in both superficial (0.97 and 0.97, respectively) and deep layer (0.99 and 0.98, respectively). Further, capillary free zones showed high AUC (0.92) in differentiating CNV eyes from normal eyes.