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.     

Detection of cardiac pathologies by dimensional characteristics of RR-intervals of the electrocardiograms

On the basis of the study of electrocardiograms by nonlinear dynamics methods, we consider the possibility to reveal pathologies of patients with different heart failures. Two parameters were analyzed: the correlation dimension and embedding dimension of RR-intervals of electrocardiorgams. Some restrictions of this method and the ways of their solutions are discussed. It was found that the proposed methods are suitable for the initial diagnosis.     

云贵鹅耳枥种群分布格局的分形特征

应用分形理论中的计盒维数和信息维数探讨了贵阳喀斯特山地贵鹅耳枥种群分布格局的分形特征。结果表明,贵鹅耳枥种群的分布格局具有分形特征,其计盒维数为1．1853－1．7419,信息维数为1．1961－1．7051。集群型的贵鹅耳枥种群的计盒维数和信息维数均比随机型的高。计盒维数定量地反映了贵鹅耳枥种群占据生态空间的能力,信息维数则揭示了该种群格局强度的尺度变化程度和表征了种群个体分布的非均匀性。这两种维数方法都适用于贵鹅耳枥种群分布格局分形特征的定量描述。     

基于流形学习的基因表达谱数据可视化

基因表达谱的可视化本质上是高维数据的降维问题。采用流形学习算法来解决基因表达谱的降维数据可视化,讨论了典型的流形学习算法（Isomap和LLE）在表达谱降维中的适用性。通过类内／类间距离定量评价数据降维的效果,对两个典型基因芯片数据集（结肠癌基因表达谱数据集和急性白血病基因表达谱数据集）进行降维分析,发现两个数据集的本征维数都低于3,因而可以用流形学习方法在低维投影空间中进行可视化。与传统的降维方法（如PCA和MDS）的投影结果作比较,显示Isomap流形学习方法有更好的可视化效果。     

Contraceptive choice of limiters ages 35-44 in the United States: an examination of selection of method from among a number of possible choices

A subsample from the 1970 National Fertility Survey and discriminant analysis were used in an effort to isolate, for the sample employed, those characteristics of contraceptive adopters which best differentiate among adopters of the various methods. The attempt was also made to isolate those contraceptive method characteristics which are most important to the potential adopter in determining method choice. Analysis of contraceptive choice initially included 7 choices -- rhythm, foam, condom, diaphragm, oral contraceptive (OC), IUD, and sterilization. There were 241 respondents in the sample. The analysis was divided into 2 parts: the choice from among the 6 methods usually thought of as contraceptives; and 2) the choice between sterilization and the 6 methods. 2 significant characteristic dimensions were isolated. The 1st dimension was interpreted as a distinction among methods from non-effective to less-effective and the 2nd as representing an aesthetics-health dimension, dividing methods between coitus-related versus non-coitus-related dimension. Income and number of births to be averted were found to play an important role in the choice of sterilization.     

Community scale 15N isoscapes: tracing the spatial impact of an exotic N2 -fixing invader

Plant-plant interactions are key processes shaping plant communities, but methods are lacking to accurately capture the spatial dimension of these processes. Isoscapes, i.e. spatially continuous observations of variations in stable isotope ratios, provide innovative methods to trace the spatial dimension of ecological processes at continental to global scales. Herein, we test the usefulness of nitrogen isoscapes (δ(15) N) for quantifying alterations in community functioning following exotic plant invasion. Nitrogen introduced by an exotic N(2) -fixing acacia could be accurately traced through the ecosystem and into the surrounding native vegetation by combining native species foliar δ(15) N with spatial information regarding plant location using geostatistical methods. The area impacted by N-addition was at least 3.5-fold greater than the physical area covered by the invader. Thus, downscaling isoscapes to the community level opens new frontiers in quantifying the spatial dimension of functional changes associated with invasion and in resolving the spatial component of within-community interactions.     

Sparse sufficient dimension reduction

Existing sufficient dimension reduction methods suffer fromthe fact that each dimension reduction component is a linearcombination of all the original predictors, so that it is difficultto interpret the resulting estimates. We propose a unified estimationstrategy, which combines a regression-type formulation of sufficientdimension reduction methods and shrinkage estimation, to producesparse and accurate solutions. The method can be applied tomost existing sufficient dimension reduction methods such assliced inverse regression, sliced average variance estimationand principal Hessian directions. We demonstrate the effectivenessof the proposed method by both simulations and real data analysis.     

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     

丙酮酸脱氢酶分形性质的光散射研究

生物大分子的分形性质与其三维结构,柔性,疏水性,进而与活性有重要关系。本文采用动态与静态光散射技术测量了丙酮酸脱氢酶的分维ｄｆ,讨论了上述两种光散方法测量分维各自适用的范围。     

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.     

Equivalence of two Fourier methods for biological sequences

 Two methods for defining Fourier power spectra for DNA sequences or other biological sequences are compared. The first method uses indicator sequences for each letter. The second method by Silverman and Linsker assigns to each letter a vertex of a regular tetrahedron in space, and this can be generalized to any dimension. While giving different Fourier transforms, it is shown that the power spectra of the two methods are essentially the same. This is also true if one replaces the Fourier transform in both methods with another linear transform, such as the Walsh transform. Received 4 December 1995     

Nonlinear analysis of continuous ECG during sleep I. Reconstruction

In recent years evidence has accumulated that ECG signals are of a nonlinear nature. It has been recognized that strictly periodic cardiac rhythms are not accompanied by healthy conditions but, on the contrary, by pathological states. Therefore, the application of methods from nonlinear system theory for the analysis of ECG signals has gained increasing interest. Crucial for the application of nonlinear methods is the reconstruction (embedding) of the time series in a phase space with appropriate dimension. In this study continuous ECG signals of 12 healthy subjects recorded during different sleep stages were analysed. Proper embedding dimension was determined by application of two techniques – the false nearest neighbours method and the saturation of the correlation dimension. Results for the ECG signals were compared with findings for simulated data (quasiperiodic dynamics, Lorenz data, white noise) and for phase randomized surrogates. Findings obtained with the two approaches suggest that embedding dimensions from 6 to 8 may be regarded as suitable for the topologically proper reconstruction of ECG signals. Received: 7 June 1999 / Accepted in revised form: 10 December 1999     

Graphical methods for class prediction using dimension reduction techniques on DNA microarray data

MOTIVATION: We introduce simple graphical classification and prediction tools for tumor status using gene-expression profiles. They are based on two dimension estimation techniques sliced average variance estimation (SAVE) and sliced inverse regression (SIR). Both SAVE and SIR are used to infer on the dimension of the classification problem and obtain linear combinations of genes that contain sufficient information to predict class membership, such as tumor type. Plots of the estimated directions as well as numerical thresholds estimated from the plots are used to predict tumor classes in cDNA microarrays and the performance of the class predictors is assessed by cross-validation. A microarray simulation study is carried out to compare the power and predictive accuracy of the two methods. RESULTS: The methods are applied to cDNA microarray data on BRCA1 and BRCA2 mutation carriers as well as sporadic tumors from Hedenfalk et al. (2001). All samples are correctly classified.     

Contraceptive choice of limiters ages 35–44 in the United States: An examination of selection of method from among a number of possible choices

Abstract

Utilizing a subsample of the 1970 National Fertility Survey and discriminant analysis, the choice of contraceptive method was examined. First, choice from among rhythm, chemicals, condoms, oral pill, and IUD was examined. Two significant characteristic dimensions were isolated. The first dimension was interpreted as a distinction among methods from more‐effective to less‐effective. The second dimension was concluded to represent an aesthetics‐health dimension, dividing methods between coitus‐related versus not‐coitus‐related. Second, the choice between these methods and sterilization was examined. The results indicated that income and the number of births to be averted play an important role in the choice of sterilization.     

Complete analysis of cellular nucleotides by two-dimensional thin layer chromatography

We describe methods for the complete analysis of cellular nucleotides from as few as 10(6) 32Pi-labeled cells in a simple 2-day experiment. Nucleotides are extracted with acid, neutralized, and resolved by two-dimensional thin layer chromatography on polyethyleneimine cellulose. In the first dimension the nucleotides are separated based on the negative charge of their phosphate groups (i.e. cyclic, mono-, di, and triphosphates) and in the second dimension on their content of nucleobases (i.e. Ura, Cyt, Thy, Gua, and Ade). Because the separation is logical, one can predict the chromatographic migration of most nucleotides. By running standards we have determined the chromatographic location of over 90 biologically important nucleotides, nucleotide derivatives, and modified nucleotides from tRNA. We also developed a set of enzymatic and chemical methods to be used in conjunction with the chromatographic separations for verifying the identity of nucleotides and characterizing novel nucleotides. In this paper we use these methods to analyze and inventory the nucleotide content of Salmonella typhimurium in balanced log phase growth. Other potential uses of the method are also described.     

Sufficient dimension reduction for censored regressions

Methodology of sufficient dimension reduction (SDR) has offered an effective means to facilitate regression analysis of high-dimensional data. When the response is censored, however, most existing SDR estimators cannot be applied, or require some restrictive conditions. In this article, we propose a new class of inverse censoring probability weighted SDR estimators for censored regressions. Moreover, regularization is introduced to achieve simultaneous variable selection and dimension reduction. Asymptotic properties and empirical performance of the proposed methods are examined.     

Refuting phylogenetic relationships

Background  

Phylogenetic methods are philosophically grounded, and so can be philosophically biased in ways that limit explanatory power. This constitutes an important methodologic dimension not often taken into account. Here we address this dimension in the context of concatenation approaches to phylogeny.     

Coherence, species turnover, and boundary clumping: elements of meta-community structure

Ecologists have identified several kinds of pattern in the distribution of species among sites, including a) nested subsets, b) checkerboards, c) Clementsian gradients, d) Gleasonian gradients, and e) evenly spaced gradients. Most past efforts to diagnose such patterns have focused on only one at a time, often contrasted with a sixth type of pattern, f) "randomness". While there are statistical tests to distinguish each of the first five patterns from randomness, there are currently no established methods for discriminating among these first five patterns in a given data set. Here we propose a method that will identify which of these possibilities is most prevalent in a site-by-species incidence matrix based on three basic aspects of meta-community structure. Our method is based on first ordinating the incidence matrix to identify the dominant axis of variation and identifying three aspects variation along this dominant axis. The first aspect, "coherence", is the degree to which pattern can be collapsed into a single dimension. The second, "species turnover", describes the number of species replacements along this dimension. The third aspect, "boundary clumping", has to do with how the edges of species boundaries are distributed along this dimension. We present methods for analyzing these three aspects of meta-community structure, use them to identify the six different patterns, and illustrate them with a representative set of cases drawn from previously published data.     

Adding the third dimension to studies of parallel evolution of morphology and function: An exploration based on parapatric lake‐stream stickleback

Recent methodological advances have led to a rapid expansion of evolutionary studies employing three‐dimensional landmark‐based geometric morphometrics (GM). GM methods generally enable researchers to capture and compare complex shape phenotypes, and to quantify their relationship to environmental gradients. However, some recent studies have shown that the common, inexpensive, and relatively rapid two‐dimensional GM methods can distort important information and produce misleading results because they cannot capture variation in the depth (Z) dimension. We use micro‐CT scanned threespine stickleback (Gasterosteus aculeatus Linnaeus, 1758) from six parapatric lake‐stream populations on Vancouver Island, British Columbia, to test whether the loss of the depth dimension in 2D GM studies results in misleading interpretations of parallel evolution. Using joint locations described with 2D or 3D landmarks, we compare results from separate 2D and 3D shape spaces, from a combined 2D‐3D shape space, and from estimates of biomechanical function. We show that, although shape is distorted enough in 2D projections to strongly influence the interpretation of morphological parallelism, estimates of biomechanical function are relatively robust to the loss of the Z dimension.

The use of methods to acquire 3D morphological data is becoming increasingly widespread, but remains expensive and time consuming. We investigated whether 2D morphometric landmark data, which can be acquired much more quickly and with less expensive equipment, distorts interpretation of parallel evolution in threespine stickleback. Separately, we test whether morphological parallelism is distorted by 2D data, and whether calculations of biomechanical function derived from 2D data are affected by the loss of the width dimension.     

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.