Nonparametric inference for local extrema with application to oligonucleotide microarray data in yeast genome

Identifying local extrema of expression profiles is one primary objective in some cDNA microarray experiments. To study the replication dynamics of the yeast genome, for example, local peaks of hybridization intensity profiles correspond to putative replication origins. We propose a nonparametric kernel smoothing (NKS) technique to detect local hybridization intensity extrema across chromosomes. The novelty of our approach is that we base our inference procedures on equilibrium points, namely those locations at which the first derivative of the intensity curve is zero. The proposed smoothing technique provides both point and interval estimation for the location of local extrema. Also, this technique can be used to test for the hypothesis of either one or multiple suspected locations being the true equilibrium points. We illustrate the proposed method on a microarray data set from an experiment designed to study the replication origins in the yeast genome, in that the locations of autonomous replication sequence (ARS) elements are identified through the equilibrium points of the smoothed intensity profile curve. Our method found a few ARS elements that were not detected by the current smoothing methods such as the Fourier convolution smoothing.     

Beals smoothing revisited

Beals smoothing is a multivariate transformation specially designed for species presence/absence community data containing noise and/or a lot of zeros. This transformation replaces the observed values of the target species by predictions of occurrence on the basis of its co-occurrences with the remaining species. In many applications, the transformed values are used as input for multivariate analyses. As Beals smoothing values provide a sense of “probability of occurrence”, they have also been used for inference. However, this transformation can produce spurious results, and it must be used with caution. Here we study the statistical and ecological bases underlying the Beals smoothing function, and the factors that may affect the reliability of transformed values are explored using simulated data sets. Our simulations demonstrate that Beals predictions are unreliable for target species that are not related to the overall ecological structure. Furthermore, the presence of these “random” species may diminish the quality of Beals smoothing values for the remaining species. A statistical test is proposed to determine when observed values can be replaced with Beals smoothing predictions. Two real-data example applications are presented to illustrate the potentially false predictions of Beals smoothing and the necessary checking step performed by the new test. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Using local correlation in kernel-based smoothers for dependent data

We consider the general problem of smoothing correlated data to estimate the nonparametric mean function when a random, but bounded, number of measurements is available for each independent subject. We propose a simple extension to the local polynomial regression smoother that retains the asymptotic properties of the working independence estimator, while typically reducing both the conditional bias and variance for practical sample sizes, as demonstrated by exact calculations for some particular models. We illustrate our method by smoothing longitudinal functional decline data for 100 patients with Huntington's disease. The class of local polynomial kernel-based estimating equations previously considered in the literature is shown to use the global correlation structure in an apparently detrimental way, which explains why some previous attempts to incorporate correlation were found to be asymptotically inferior to the working independence estimator.     

Mapping Cancer Risk in Southwestern Ontario with Changing Census Boundaries

Summary Mapping disease risk often involves working with data that have been spatially aggregated to census regions or postal regions, either for administrative reasons or confidentiality. When studying rare diseases, data must be collected over a long time period in order to accumulate a meaningful number of cases. These long time periods can result in spatial boundaries of the census regions changing over time, as is the case with the motivating example of exploring the spatial structure of mesothelioma lung cancer risk in Lambton County and Middlesex County of southwestern Ontario, Canada. This article presents a local‐EM kernel smoothing algorithm that allows for the combining of data from different spatial maps, being capable of modeling risk for spatially aggregated data with time‐varying boundaries. Inference and uncertainty estimates are carried out with parametric bootstrap procedures, and cross‐validation is used for bandwidth selection. Results for the lung cancer study are shown and discussed.     

分子对接与全局极小化方法

全局极小化方法及其在结构生物学中的应用近年来取得了显著的进展.适当简化的分子对接问题是全局极小化方法的一个很好目标,并且是当前一个相当活跃的研究领域.对接可分为两类：主要用于从头配体设计的细致对接和用于已知化合物数据库筛选以发现药物的粗略对接,它们对全局极小化算法的要求是不同的.简要评述了新出现的适合于对接问题的随机和确定性全局极小化算法,其中势能平滑算法看来很有希望,值得密切关注.     

Application Fields of the Empirical Regression - A Case Study

Empirical regression is defined as conditional expected value based on an estimation of a twodimensional density. It is a modelfree mathematical means for a first evaluation of measured data of an unknown stochastical relation between two quantities. The numerical procedures may be applied for calculation of the mean course of an unknown relation hidden in the measured data. Disregarding the statistical background an other aspect of application is the analyzing of time series, especially smoothing of time series and modelfree recording of the trend component in non-stationary time series. The calculated regression curve provides an objective basis for comparing of different measured courses as well as for a further evaluation, e. g. in respect of a suitable choice of an analytical expression. The possibility of interpolation and the smoothing properties of empirical regression give essential advantages for internal regression as one step in the process of model construction.     

An adaptive bivariate kernel smoothing method for determining instars of Austrosimulium tillyardianum (Diptera: Simuliidae) larvae

1. In insects, instar determination is generally based on the frequency distribution of sclerotised body part measurements. Commonly used univariate methods, such as histograms and univariate kernel smoothing, are not sufficient to reflect the distribution of the measurements, because development of sclerotised body parts is multidimensional. 2. This study used an adaptive bivariate kernel smoothing method, based on 10 pairs of separating variables, to differentiate instars of Austrosimulium tillyardianum (Diptera: Simuliidae) larvae in two‐dimensional space. A variable bandwidth matrix was used and separation lines between instars were defined. Using the Crosby growth ratio, Brooks' rule and the new standard recently proposed, larvae were separated into nine instars. It was found that, using the bivariate kernel smoothing method, the clustering accuracy and determination of separation lines as instar class limits were higher than those associated with the univariate kernel smoothing method. With the exceptions of the paired separating variables, head capsule length and antennal segment 3 length (AS3L), the mean probabilities of correct classifications was > 85%. The pair of separating variables that yielded the greatest classification accuracy comprised mandible length (ML) and AS3L, which had mean probabilities of 0.8984. The clustering accuracy was higher for early‐ and late‐instar larvae, but lower for instars 6 and 7. The adaptive bivariate kernel smoothing method was better than univariate methods for instar determination, especially in the detection of divisions between instars and identification of a larval instar.     

Size-asymmetric competition and size-asymmetric growth in a spatially explicit zone-of-influence model of plant competition

Size-asymmetric competition among plants is usually defined as resource pre-emption by larger individuals, but it is usually observed and measured as a disproportionate size advantage in the growth of larger individuals in crowded populations (“size-asymmetric growth”). We investigated the relationship between size-asymmetric competition and size-asymmetric growth in a spatially explicit, individual-based plant competition model based on overlapping zones of influence (ZOI). The ZOI of each plant is modeled as a circle, growing in two dimensions. The size asymmetry of competition is reflected in the rules for dividing up the overlapping areas. We grew simulated populations with different degrees of size-asymmetric competition and at different densities and analyzed the size dependency of individual growth by fitting coupled growth functions to individuals. The relationship between size and growth within the populations was summarized with a parameter that measures the size asymmetry of growth. Complete competitive symmetry (equal division of contested resources) at the local level results in a very slight size asymmetry in growth. This slight size asymmetry of growth did not increase with increasing density. Increased density resulted in increased growth asymmetry when resource competition at the local level was size asymmetric to any degree. Size-asymmetric growth can be strong evidence that competitive mechanisms are at least partially size asymmetric, but the degree of size-asymmetric growth is influenced by the intensity as well as the mode of competition. Intuitive concepts of size-asymmetric competition among individuals in spatial and nonspatial contexts are very different.     

On the role of synchrony for neuron–astrocyte interactions and perceptual conscious processing

Recent research on brain correlates of cognitive processes revealed the occurrence of global synchronization during conscious processing of sensory stimuli. In spite of technological progress in brain imaging, an explanation of the computational role of synchrony is still a highly controversial issue. In this study, we depart from an analysis of the usage of blood-oxygen-level-dependent functional magnetic resonance imaging for the study of cognitive processing, leading to the identification of evoked local field potentials as the vehicle for sensory patterns that compose conscious episodes. Assuming the “astrocentric hypothesis” formulated by James M. Robertson (astrocytes being the final stage of conscious processing), we propose that the role of global synchrony in perceptual conscious processing is to induce the transfer of information patterns embodied in local field potentials to astrocytic calcium waves, further suggesting that these waves are responsible for the “binding” of spatially distributed patterns into unitary conscious episodes.     

Inference Based on Kernel Estimates of the Relative Risk Function in Geographical Epidemiology

Kernel smoothing is a popular approach to estimating relative risk surfaces from data on the locations of cases and controls in geographical epidemiology. The interpretation of such surfaces is facilitated by plotting of tolerance contours which highlight areas where the risk is sufficiently high to reject the null hypothesis of unit relative risk. Previously it has been recommended that these tolerance intervals be calculated using Monte Carlo randomization tests. We examine a computationally cheap alternative whereby the tolerance intervals are derived from asymptotic theory. We also examine the performance of global tests of hetereogeneous risk employing statistics based on kernel risk surfaces, paying particular attention to the choice of smoothing parameters on test power (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A Bayesian model for sparse functional data

Summary.   We propose a method for analyzing data which consist of curves on multiple individuals, i.e., longitudinal or functional data. We use a Bayesian model where curves are expressed as linear combinations of B-splines with random coefficients. The curves are estimated as posterior means obtained via Markov chain Monte Carlo (MCMC) methods, which automatically select the local level of smoothing. The method is applicable to situations where curves are sampled sparsely and/or at irregular time points. We construct posterior credible intervals for the mean curve and for the individual curves. This methodology provides unified, efficient, and flexible means for smoothing functional data.     

A Note on the Local Current Associated with the Rising Phase of a Propagating Impulse in Nonmyelinated Nerve Fibers

To extend our recent paper dealing with the cable properties and the conduction velocity of nonmyelinated nerve fibers (Bull. Math. Biol. 64, 1069; 2002), the behavior of the local current associated with the rising phase of a propagating action potential is discussed. It is shown that the process of charging the membrane capacity by means of the local current plays a crucial role in determining the velocity of nerve conduction. The symmetry of the local current with respect to the boundary between the resting and active regions of the nerve fiber is emphasized. It is noted that there are several simple quantitative rules governing the intensities of the capacitive, resistive and total membrane currents observed during the rising phase of an action potential.     

Use of local and global geometry from object arrays by adult humans

Disoriented men and women were trained to search for a goal hidden in front of one of four objects forming a rectangular-shaped array. The angular properties of these objects (either 50° or 75°) served as local geometric cues and the rectangular shape of the array served as global geometric cues. Upon successful completion of training, transformation tests were conducted during which either the local angle cues were removed and the global geometry was preserved (Global Cues test) or the local angles were preserved and the global geometry was removed (Local Cues test). A Cue Conflict test was also conducted which placed the local geometry in direct competition with the global geometry for control of search behavior. Results from testing showed that neither men nor women could successfully use only the global geometric cues provided by the shape of the array to reorient. Analyses of sex differences for the use of local cues revealed that men showed clear evidence that they had successfully encoded the local angular cues whereas women did not. Furthermore, the size of the training angle may have affected the encoding of local cues.     

Local–regional species richness relationships are linear at very small to large scales in west-central Pacific corals

If local communities are saturated with species, the relationship between local and regional species richness [the local species richness (LSR)–regional species richness (RSR) relationship] is predicted to become increasingly curvilinear at more local spatial scales. This study tested whether the LSR–RSR relationship for coral species was linear or curvilinear at three local scales across the west-central Pacific Ocean, along a regional biodiversity gradient that includes the world’s most diverse coral assemblages. The local scales comprised transects 10^0–2 m apart, sites 10^3–4 m apart and islands 10^4–6 m apart. The LSR–RSR relationship was never significantly different from linear at any scale. When the Chao1 estimator was used to predict true RSR and LSR, all relationships were also strongly linear. We conclude that local assemblages are open to regional influences even when the local scale is very small relative to the regional scale, and even in extraordinarily rich regions.     

Estimation of fish abundance indices based on scientific research trawl surveys

The fish abundance index over an ocean region is defined here to be the integral of expected catch per unit effort (CPUE), approximated by the sum of expected CPUE over grid squares. When trawl surveys are done within grid squares selected according to a probability sampling design, several other sources of variation such as the fish population dynamics and the catching process are also involved. In such situations model-assisted methods for estimating abundance, assessed under both design and model perspectives, have some advantages over purely design-based methods such as the Horvitz-Thompson (HT) estimator or purely model-based prediction approaches. This article develops model-assisted empirical likelihood (EL) methods via loglinear regression and nonparametric smoothing. The methods are applied to grid surveys of the Grand Bank region carried out annually by Fishery Products International from 1996 through 2002. The HT and EL methods produce similar point estimates of abundance indices. Simulation results, however, indicate that the EL estimator under local linear smoothing is associated with smaller standard errors.     

降水空间插值技术的研究进展

降水的空间分布信息在水资源管理、灾害预测预警和区域可持续发展研究等方面的地位已越来越重要。然而,空间降水插值却一直是个难题,影响降水的因素很多,如经度、纬度、高程、坡度、坡向、离水体的距离等,建立一个通用的降水插值模型几乎是不可能的。空间降水插值方法很多,优缺点和适用性不同。总体上,降水的空间插值方法有3类：整体插值法（趋势面法和多元回归法等）、局部插值法（泰森多边形法、反距离加权法、克里金插值法和样条法）和混合插值法（整体插值法和局部插值法的综合）。近年来,随着应用数学和人工神经网络技术的发展,很多新方法如BP网络、径向基函数网络等逐渐应用到降水插值中。另外,研究区域和时间尺度的不同决定了所选用的插值方法及模型不同;即使是同一种插值方法,应用于不同的研究区域,所取得的结果也不同。因此,应根据具体的研究区域的自然地理特征,选择不同的插值方法建立不同的插值模型。在各种插值方法中,兼具其它插值方法优点的混合插值法有利于提高降水插值的精度,是未来降水插值研究的一个发展方向。     

Dynamic logistic state space prediction model for clinical decision making

Prediction modeling for clinical decision making is of great importance and needed to be updated frequently with the changes of patient population and clinical practice. Existing methods are either done in an ad hoc fashion, such as model recalibration or focus on studying the relationship between predictors and outcome and less so for the purpose of prediction. In this article, we propose a dynamic logistic state space model to continuously update the parameters whenever new information becomes available. The proposed model allows for both time-varying and time-invariant coefficients. The varying coefficients are modeled using smoothing splines to account for their smooth trends over time. The smoothing parameters are objectively chosen by maximum likelihood. The model is updated using batch data accumulated at prespecified time intervals, which allows for better approximation of the underlying binomial density function. In the simulation, we show that the new model has significantly higher prediction accuracy compared to existing methods. We apply the method to predict 1 year survival after lung transplantation using the United Network for Organ Sharing data.     

The effect of end-point adjustments on smoothing splines used for tree-ring standardization

The cubic smoothing spline has been a popular method for detrending tree-ring data since the 1980s. The common implementation of this procedure (e.g., ARSTAN, dplR) uses a unique method for determining the smoothing parameter that is widely known as the %n criterion. However, this smoothing parameter selection method carries the assumption that end point effects are ignorable. In this paper, we complete the mathematical derivation and show how the original method differs from the complete version, both in the interpretation of the smoothing parameter and in the spline fit. Frequency response curves (FRC) demonstrate how the smoothing parameter is affected by the original assumption. For example, the FRC results indicate that a tree core of 250-year length has a 14% difference in the cut-off frequency when looking at the 67%n criterion. The FRC analysis shows that the existing approach produces a more flexible fit than anticipated, i.e., it is removing more variance than previously thought. For example, a 67%n spline under the existing approach corresponds to a 53%n spline fit. By using both simulated tree-core sequences and a dataset from a Midwest forest, we discuss which conditions result in greater differences between the spline fits and which conditions will have small differences. Tree-core sequences that have more curvature, such as a large-amplitude growth release, will lead to greater differences. Finally, we provide approximations to the end-point effect procedure. For example, using an 83%n criterion under the original approach produces a spline fit approximating the 67%n fit under the complete approach. These approximations could be easily implemented within existing programs like ARSTAN.