Origination of Pareto distribution in complex dynamic systems

The Pareto distribution, whose probability density function can be approximated at sufficiently great chi as rho(chi) - chi(-alpha), where alpha > or = 2, is of crucial importance from both the theoretical and practical point of view. The main reason is its qualitative distinction from the normal (Gaussian) distribution. Namely, the probability of high deviations appears to be significantly higher. The conception of the universal applicability of the Gauss law remains to be widely distributed despite the lack of objective confirmation of this notion in a variety of application areas. The origin of the Pareto distribution in dynamic systems located in the gaussian noise field is considered. A simple one-dimensional model is discussed where the system response in a rather wide interval of the variable can be quite precisely approximated by this distribution.     

Coaxial lines for multiphase power distribution

A coaxial cable can be used to reduce the magnetic and electric fields that extend into environments in the vicinity of transmission lines and distribution lines and in-house or building wiring for power distribution systems. The use of the coaxial geometry may prove useful in cases where there are environmental concerns with respect to health effects and in cases where there is a need to run high-speed data communications in close proximity to power distribution systems. © 1996 Wiley-Liss, Inc.     

Modeling menstrual cycle length using a mixture distribution

In reproductive health studies, epidemiologists are often interested in examining the effects of covariates on menstrual cycle length which is a convenient, noninvasive measure of women's ovarian and reproductive function. Previous literature (Harlow and Zeger, 1991) suggests that the distribution of cycle length is a mixture of a major symmetric distribution and a component featuring a long right tail. Motivated by the shape of this marginal distribution, we propose a mixture distribution for cycle length, representing standard cycles from a Normal distribution and nonstandard cycles from a shifted Weibull distribution. The parameters are estimated using an estimating equation derived from the score function of an independence working model. The fitted mixture distribution agrees well with the distribution estimated using nonparametric approaches. We propose two measures to help determine whether a cycle is standard or nonstandard, developing tools necessary to identify characteristics of the menstrual cycles that are biologically indicative of ovarian dysfunction. We model the effect of a woman's age on the mean and variation of both standard and nonstandard cycle lengths using multiple measurements of women.     

Global asymptotic stability of the size distribution in probabilistic models of the cell cycle

Probabilistic models of the cell cycle maintain that cell generation time is a random variable given by some distribution function, and that the probability of cell division per unit time is a function only of cell age (and not, for instance, of cell size). Given the probability density, f(t), for time spent in the random compartment of the cell cycle, we derive a recursion relation for _n(x), the probability density for cell size at birth in a sample of cells in generation n. For the case of exponential growth of cells, the recursion relation has no steady-state solution. For the case of linear cell growth, we show that there exists a unique, globally asymptotically stable, steady-state birth size distribution, _*(x). For the special case of the transition probability model, we display _*(x) explicitly.This work was supported by the National Science Foundation under grants MCS8301104 (to J.J.T.) and MCS8300559 (to K.B.H.), and by the National Institutes of Health under grant GM27629 (to J.J.T.).     

Abundance, spatial variance and occupancy: arthropod species distribution in the Azores

1. The positive abundance-occupancy and abundance-variance relationships are two of the most widely documented patterns in population and community ecology. 2. Recently, a general model has been proposed linking the mean abundance, the spatial variance in abundance, and the occupancy of species. A striking feature of this model is that it consists explicitly of the three variables abundance, variance and occupancy, and no extra parameters are involved. However, little is known about how well the model performs. 3. Here, we show that the abundance-variance-occupancy model fits extremely well to data on the abundance, variance and occupancy of a large number of arthropod species in natural forest patches in the Azores, at three spatial extents, and distinguishing between species of different colonization status. Indeed, virtually all variation about the bivariate abundance-occupancy and abundance-variance relationships is effectively explained by the third missing variable (variance in abundance in the case of the abundance-occupancy relationship, and occupancy in the case of the abundance-variance relationship). 4. Introduced species tend to exhibit lower densities, less spatial variance in these densities, and occupy fewer sites than native and endemic species. None the less, they all lie on the same bivariate abundance-occupancy and abundance-variance, and trivariate abundance-variance-occupancy, relationships. 5. Density, spatial variance in density, and occupancy appear to be all the things one needs to know to describe much of the spatial distribution of species.     

红棕象甲幼虫空间格局研究

【背景】红棕象甲是外来危险I生有害生物,近十年来在我国南方严重危害棕榈科植物。[方法】为了确定其调查抽样方法、准确获得虫情,应用聚集度指标法和回归模型分析法等,对红棕象甲幼虫的空间格局进行了研究。【结果】在lwao模型中,α=0．4208〉0,β=1.5133〉1,这说明了红棕象甲幼虫的种群空间格局的分布图式为聚集型;用马占山重新解释的Taylor幂法则分析表明,红棕象甲幼虫的空间格局归属于聚集型,个体之间相互吸引。【结论与意义】红棕象甲幼虫在林内呈聚集型分布,分布的基本成分为个体群;运用1wao法确定了林间最适理论抽样数和序贯抽样模型,为该虫的监测与防治提供了依据。     

Fractal bird nest distribution produces scale-free colony sizes

The spatial distribution of organisms often differs across scales. For instance, colonial bird populations could be described, from large to small scale, as scattered clumps of otherwise regularly distributed breeding pairs. We analysed the distribution of nests of a large colonial population of white storks (Ciconia ciconia) and found a fractal pattern in each of the 4 study years. Moreover, we found that the often-observed, long-tailed frequency distribution of colony sizes was well described by a power law, regardless of the cut-off used to define colonies (from 16 to 1024 m). Thus, although storks were locally highly clumped even with tens of nests in a single tree, the population was not structured in colonies (a simple clustered distribution) as previously thought. Rather, they were distributed in a continuous hierarchical set of clusters within clusters across scales, clusters lacking the commonly assumed characteristic mean size. These quantitative solutions to previously perceived scaling problems will potentially improve our understanding of the ecology and evolution of bird coloniality and animal spacing patterns and group living in general.     

中国翼手目地理分布的环境因子影响分析

利用地理信息系统提取了中国翼手目90个物种已知地理分布点的环境因子数据,并利用主成分分析和逐步回归分析研究了这些环境因子对中国翼手目动物地理分布和种数密度分布的影响程度。结果表明,按其影响程度大小,影响中国翼手目动物地理分布的连续型环境因子依次为年平均气温、大于零度日数、一月份平均气温、无霜期日数、年降雨量、年平均相对湿度、七月份平均气温、海拔高度和年日照时数,其中年日照时数和海拔高度为负影响;影响翼手目种数密度分布的决定环境因子是年降雨量,但年平均气温也有明显作用。作者认为,气候因子影响翼手目动物地理分布的机制是限制性因子的作用,主要受冬眠和活动及摄食时间长短的限制,而种数密度分布则决定于环境资源的丰富度,即主要受到由降雨量决定的食物种类多少的影响。另外,对类别环境因子的研究表明：植被类型对翼手目的种数分布没有明显影响;具有多洞穴特点的喀斯特和火山熔岩地貌具有较多的翼手目种类,但红层地貌由于分布于南方和分散分布的特点而具有最高的翼手目种数密度[动物学报51(3)：413—422,2005]。     

Deep analysis of perception through dynamic structures that emerge in cortical activity from self-regulated noise

The statistical properties of the spontaneous background electrocorticogram (ECoG) were modeled, starting with random numbers, constraining the distributions, and identifying characteristic deviations from randomness in ECoG from subjects at rest and during intentional behaviors. The ECoG had been recorded through 8 × 8 arrays of 64 electrodes, from the surfaces of auditory, visual, or somatic cortices of 9 rabbits, and from the inferotemporal cortex of a human subject. Power spectral densities (PSD) in coordinates of log₁₀ power versus log₁₀ frequency of ECoG from subjects at rest usually conformed to noise in power-law distributions in a continuum. PSD of ECoG from active subjects usually deviated from noise in having peaks in log₁₀ power above the power-law line in various frequency bands. The analytic signals from the Hilbert transform after band pass filtering in the beta and gamma ranges revealed beats from interference among distributed frequencies in band pass filtered noise called Rayleigh noise. The beats were displayed as repetitive down spikes in log₁₀ analytic power. Repetition rates were proportional to filter bandwidths for all center frequencies. Resting ECoG often gave histograms of the magnitudes and intervals of down spikes that conformed to noise. Histograms from active ECoG often deviated from noise in Rayleigh distributions of down spike intervals by giving what are called Rice (Mathematical analysis of random noise—and appendixes—technical publications monograph B-1589. Bell Telephone Labs Inc., New York, 1950) distributions. Adding power to noise as signals at single frequencies simulated those deviations. The beats in dynamic theory are deemed essential for perception, by gating beta and gamma bursts at theta rates through enhancement of the cortical signal-to-noise ratio in exceptionally deep down spikes called null spikes.     

The effect of the propagation coefficient on size distribution in micellar systems

In this study the effect of the propagation coefficient on the molar distribution function in a modified shell model for micellar systems was examined. The sharpness of the micelle size distribution boundary was found to depend less on the degree of polymerization, n, than on the propagation coefficient, P. Although Kegeles (J. Phys. Chem. 83 (1979) 1728) has reported a marked sharpening of the distribution boundary when P = 2.0. we found the boundary to be fairly broad at this point. However, as values of the propagation coefficient were increased from 3 to 10, the micelle distribution boundary became increasingly sharp. The possibility of such a change in the reaction boundary arising from a structural transition, accompanied by a change in the rate of dissociation of monomer from the shell, is also discussed.     

Coherent patterns of abundance and size of a tropical snapper in dynamic estuary systems

Although tropical estuaries are important juvenile habitats for the snapper, Lutjanus russelli, the extent of this utilisation, and relationships to physical variation are unknown. We used fish trapsto investigate spatial and temporal patterns of distribution, abundance and size of L. russelli within and between three tropical estuaries (Cattle, Barramundi and Alligator Creeks) over a two year period. L. russelli showed no indication of spatial segregation by size along the lengths of the estauries. The probability of capturing L. russelli was similar throughout Barramundi Creek and the seaward parts of Cattle Creek. However, the probability of capture fell markedly in upstream regions of Cattle Creek. These areas where characterised by depressed salinity levels due to seasonal flooding. High probabilities of capture of L. russelli during the wet and post-wet seasons in the whole of Barramundi Creek correlated with the time of smallest modal sizes. Thisreflected the entry of large numbers of small recruits into the trappable population. Temporal patterns in mean length were consistent for both years. The major feature of the size data was a clear pattern of seasonal change in the mean fork length of L. russelli, with largest mean sizes occurring in the pre-wet and the smallest mean sizes in the wet and post-wet seasons. This pattern probably reflected the interaction of four processes; the entry of new recruits into the trappable population, growth and mortality during residence in the estuarine nursery habitats, and migration of large fish away from the estuaries. The three creeks studied provided L. russelli with a harsh and extremely variable environment. Over the three creeks, salinities ranged from extremely hyposaline (0) to very hypersaline (55.5) and varied up to 39 within a location. However, despite the substantial physical differences and the spatial separation of the three estuaries, the patterns of temporal change were clear and consistent. Overall, the annual pattern of change insize seemed to relate more to biological processes of recruitment, mortality and migration than to responses to physical variability.     

A survey of the distribution and density of the primates of Guyana

In January through February 1994, we conducted the first broad-scale survey of Guyanese primates since 1975. Our goals were (1) to follow up questions raised in the earlier survey, (2) to compare population densities, and (3) to locate potential sites for future long-term research. We used distributional survey methods along trails and rivers and interviewed local inhabitants in each region. We surveyed five general areas, two of which had been studied in 1975. The distribution reported in 1975 for five monkey species—Alouatta seniculus, Cebus olivaceus, Pithecia pithecia, Chiropotes satanas,and Saimiri sciureus—was confirmed. However, questions were raised concerning the western extent of the range of three species: Ateles paniscus, Cebus apella,and Saguinus midas.In comparing densities between 1994 and 1975, we found a significant drop in group densities over the past 20 years and a shift in relative proportions of individual primate species over time. For example, although the total number of kilometers surveyed was identical, group densities were three times higher in 1975 than in 1994. Further, group densities of Ateles, Alouatta,and Pitheciawere much lower, while those of Saguinuswere similar in both years. These findings strongly suggest that habitat destruction and continued hunting pressure are affecting the primate populations.     

Habitat distribution of the mallard in relation to vegetation structure,food, and population density

The mallard (Anas platyrhynchos Linnaeus) is a generalist feeder, breeding in a wide range of habitats, yet showing considerable between site differences in density. Variations in density and habitat use may result from inter- and intea-specific competition, habitat structure or food.We studied habitat selection of the mallard in four regions of Finland and Sweden. In each region, ten lakes were chosen ranging from oligotrophic to eutrophic. Habitat distribution of the mallard did not differ between regions despite variation in the density of the species and congenerics. Mallard density did not correlate with vegetation structure, but increased with food abundance and the number and density of congenerics although there were regional differences in mallard response.     

安徽省家畜分布与土地利用类型关系的研究

本文采用灰色系统理论与方法,研究了安徽省及其各畜牧区的家畜(禽)分布随土地利用类型及人口密度的变化规律,建立了家畜(禽)分布密度的灰色静动态模型。结果表明,安徽省由北向南旱地面积从54％下降到2％;林地则由5.5％上升到62％;水田和水面主要分布在江淮丘陵和沿江平原区。人口密度对各类畜禽的分布密度有较大的影响,关联度为0.65—0.83;旱地比率是影响草食动物分布密度的最主要因素,并联度高达0.9以上;水面的比重对家禽密度的影响高于其它因子。用土地利用类型因子及人口密度所建立的模型,对家畜的实际分布密度及其变化规律的拟合误差在2％左右。     

Seasonal and spatial distribution pattern of nitrogen fixing bacteria in fish ponds under different management systems

Enumeration of nitrogen fixing bacterial population in water and sediment samples of six fish farming ponds (polyculture, monoculture and traditional systems) over a period of two and a half years revealed significant differences between the culture systems with maximal and lowest counts in the monoculture and traditional systems, respectively. Polynomial equations of the 2nd to 4th degree were used to represent the observed seasonal data in these ponds. The bacterial populations peaked in summer, while the lowest count was observed in winter. The environmental factors such as pH, different species of nitrogen, dissolved organic carbon were responsible for the seasonal changes in nitrogen fixing bacteria.