基于Voronoi图的林分空间模型及分布格局研究

以南洞庭湖龙虎山次生林为研究对象,建立林分Voronoi图模型,通过该模型表示林分空间结构特征,提取林木空间量化信息。在此基础上,引入变异系数量化Voronoi多边形面积的变化率,将林木空间格局分析转化为计算Voronoi图变异系数,并将计算结果与角尺度作相关性比较。结果表明:林分Voronoi图模型能准确表达林木邻接关系、相邻木距离及角度、空间密度等重要空间信息;大尺度取样时(76m以上),变异系数趋于稳定,林分整体空间格局呈接近随机分布的轻度聚集;Voronoi图变异系数和角尺度存在显著的正相关关系,进一步说明本研究格局分析方法的可行性和有效性;受多种因素影响,乔木层主要树种在不同发育阶段的空间格局表现出强烈的时间和空间动态特性,且小径木多为聚集分布,大径木呈轻度聚集或随机分布。基于Voronoi图的林分空间模型及格局分析方法,从空间上表征林木的生长繁育特性、种内种间关系、资源及环境分布特征,为计算几何方法应用于林分空间经营提供了新的思路。     

BetaVoid: Molecular voids via beta‐complexes and Voronoi diagrams

Molecular external structure is important for molecular function, with voids on the surface and interior being one of the most important features. Hence, recognition of molecular voids and accurate computation of their geometrical properties, such as volume, area and topology, are crucial, yet most popular algorithms are based on the crude use of sampling points and thus are approximations even with a significant amount of computation. In this article, we propose an analytic approach to the problem using the Voronoi diagram of atoms and the beta‐complex. The correctness and efficiency of the proposed algorithm is mathematically proved and experimentally verified. The benchmark test clearly shows the superiority of BetaVoid to two popular programs: VOIDOO and CASTp. The proposed algorithm is implemented in the BetaVoid program which is freely available at the Voronoi Diagram Research Center ( http://voronoi.hanyang.ac.kr ). Proteins 2014; 82:1829–1849. © 2014 Wiley Periodicals, Inc.     

Revisiting the Voronoi description of protein-protein interfaces

We developed a model of macromolecular interfaces based on the Voronoi diagram and the related alpha-complex, and we tested its properties on a set of 96 protein-protein complexes taken from the Protein Data Bank. The Voronoi model provides a natural definition of the interfaces, and it yields values of the number of interface atoms and of the interface area that have excellent correlation coefficients with those of the classical model based on solvent accessibility. Nevertheless, some atoms that do not lose solvent accessibility are part of the interface defined by the Voronoi model. The Voronoi model provides robust definitions of the curvature and of the connectivity of the interfaces, and leads to estimates of these features that generally agree with other approaches. Our implementation of the model allows an analysis of protein-water contacts that highlights the role of structural water molecules at protein-protein interfaces.     

Spatial Point Pattern Analysis by using Voronoi Diagrams and Delaunay Tessellations – A Comparative Study

Given a spatial point pattern, we use various characteristics of its Voronoi diagram and Delaunay tessellation to extract information of the dependence between points. In particular, we use the characteristics to construct statistics for testing complete spatial randomness. It is shown that the minimum angle of a typical Delaunay triangle is sensitive to both regularity and clustering alternatives, whilst the triangle's area or perimeter is more sensitive to clustering than regularity. These statistics are also sensitive to the Baddeley‐Silverman cell process.     

Steady-state solutions in mathematical models of atrial cell electrophysiology and their stability

The steady states of the Fenton-Karma, the Courtemanche and the Nygren cell models were studied by determining the fixed points of the dynamical system describing their cell kinetics. The linear stability of the fixed points was investigated, as well as their response to external stimuli. Symbolic calculations were carried out as far as possible in order to prove the existence of these fixed points. In the Fenton-Karma model, a unique stable fixed point was found, namely the resting state. In contrast, the Courtemanche model had an infinite number of fixed points. A bifurcation diagram was constructed by classifying these fixed points according to a conservation law. Initial conditions were identified, for which the dynamical behavior of the cell was auto-oscillatory. In its original formulation, the Nygren model had no fixed point. After having restored charge conservation, the system was found to have an infinite number of fixed points, resulting in a bifurcation diagram similar to that of the Courtemanche model. The approach proposed in this paper assists in the exploration of the high-dimensional parameter space of the cell models and the identification of the conditions leading to spontaneous pacemaker activity.     

Modeling survival of experimentally virus-infected laboratory animals--exploration of the survival diagram

In a recent paper (Sühnel & Veckenstedt, 1989, J. theor. Biol. 137, 27) we have proposed a new method of plotting survival data from experimentally virus-infected laboratory animals; the survival diagram. In this diagram two experiments, for which the mean number of virions inoculated is kept fixed but other parameters may vary, are compared. The variations in two basic quantities of survival analysis are simultaneously displayed: the standard mean survival time and the relative mean challenge virus dose, which is via a dose-response relation interrelated with the fraction of animals dying. It is analyzed in which manner variations in the kinetic parameters and the critical virus level necessary to produce a particular effect influence the location of the points of comparison in the survival diagram. The analysis presented is a prerequisite for further applications of this diagram and of the underlying mathematical model.     

A Fast Algorithm to Estimate the Deepest Points of Lakes for Regional Lake Registration

When conducting image registration in the U.S. state of Alaska, it is very difficult to locate satisfactory ground control points because ice, snow, and lakes cover much of the ground. However, GCPs can be located by seeking stable points from the extracted lake data. This paper defines a process to estimate the deepest points of lakes as the most stable ground control points for registration. We estimate the deepest point of a lake by computing the center point of the largest inner circle (LIC) of the polygon representing the lake. An LIC-seeking method based on Voronoi diagrams is proposed, and an algorithm based on medial axis simplification (MAS) is introduced. The proposed design also incorporates parallel data computing. A key issue of selecting a policy for partitioning vector data is carefully studied, the selected policy that equalize the algorithm complexity is proved the most optimized policy for vector parallel processing. Using several experimental applications, we conclude that the presented approach accurately estimates the deepest points in Alaskan lakes; furthermore, we gain perfect efficiency using MAS and a policy of algorithm complexity equalization.     

A new computational growth model for sea urchin skeletons

A new computational model has been developed to simulate growth of regular sea urchin skeletons. The model incorporates the processes of plate addition and individual plate growth into a composite model of whole-body (somatic) growth. A simple developmental model based on hypothetical morphogens underlies the assumptions used to define the simulated growth processes. The data model is based on a Delaunay triangulation of plate growth center points, using the dual Voronoi polygons to define plate topologies. A spherical frame of reference is used for growth calculations, with affine deformation of the sphere (based on a Young-Laplace membrane model) to result in an urchin-like three-dimensional form. The model verifies that the patterns of coronal plates in general meet the criteria of Voronoi polygonalization, that a morphogen/threshold inhibition model for plate addition results in the alternating plate addition pattern characteristic of sea urchins, and that application of the Bertalanffy growth model to individual plates results in simulated somatic growth that approximates that seen in living urchins. The model suggests avenues of research that could explain some of the distinctions between modern sea urchins and the much more disparate groups of forms that characterized the Paleozoic Era.     

Two-Dimensional Continuum Percolation Threshold for Diffusing Particles of Nonzero Radius

Lateral diffusion in the plasma membrane is obstructed by proteins bound to the cytoskeleton. The most important parameter describing obstructed diffusion is the percolation threshold. The thresholds are well known for point tracers, but for tracers of nonzero radius, the threshold depends on the excluded area, not just the obstacle concentration. Here thresholds are obtained for circular obstacles on the continuum. Random obstacle configurations are generated by Brownian dynamics or Monte Carlo methods, the obstacles are immobilized, and the percolation threshold is obtained by solving a bond percolation problem on the Voronoi diagram of the obstacles. The percolation threshold is expressed as the diameter of the largest tracer that can cross a set of immobile obstacles at a prescribed number density. For random overlapping obstacles, the results agree with the known analytical solution quantitatively. When the obstacles are soft disks with a 1/r¹² repulsion, the percolating diameter is ∼20% lower than for overlapping obstacles. A percolation model predicts that the threshold is highly sensitive to the tracer radius. To our knowledge, such a strong dependence has so far not been reported for the plasma membrane, suggesting that percolation is not the factor controlling lateral diffusion. A definitive experiment is proposed.     

The assembly of ionic currents in a thalamic neuron. I. The three-dimensional model

We have previously discussed qualitative models for bursting and thalamic neurons that were obtained by modifying a simple two-dimensional model for repetitive firing. In this paper we report the results of making a similar sequence of modifications to a more elaborate six-dimensional model of repetitive firing which is based on the Hodgkin-Huxley equations. To do this we first reduce the six-dimensional model to a two-dimensional model that resembles our original two-dimensional qualitative model. This is achieved by defining a new variable, which we call q. We then add a subthreshold inward current and a subthreshold outward current having a variable, z, that changes slowly. This gives a three-dimensional (v,q,z) model of the Hodgkin-Huxley type, which we refer to as the z-model. Depending on the choice of parameter values this model resembles our previous models of bursting and thalamic neurons. At each stage in the development of these models we return to the corresponding seven-dimensional model to confirm that we can obtain similar solutions by using the complete system of equations. The analysis of the three-dimensional model involves a state diagram and a stability diagram. The state diagram shows the projection of the phase path from v,q,z space into the v,z plane, together with the projections of the curves z = 0 and v = q = 0. The stability of the points on the curve v = q = 0, which we call the v, q nullcurve, is determined by the stability diagram. Taken together the state and stability diagrams show how to assemble the ionic currents to produce a given firing pattern.     

A Kalman-Filter Based Approach to Identification of Time-Varying Gene Regulatory Networks

Motivation

Conventional identification methods for gene regulatory networks (GRNs) have overwhelmingly adopted static topology models, which remains unchanged over time to represent the underlying molecular interactions of a biological system. However, GRNs are dynamic in response to physiological and environmental changes. Although there is a rich literature in modeling static or temporally invariant networks, how to systematically recover these temporally changing networks remains a major and significant pressing challenge. The purpose of this study is to suggest a two-step strategy that recovers time-varying GRNs.

Results

It is suggested in this paper to utilize a switching auto-regressive model to describe the dynamics of time-varying GRNs, and a two-step strategy is proposed to recover the structure of time-varying GRNs. In the first step, the change points are detected by a Kalman-filter based method. The observed time series are divided into several segments using these detection results; and each time series segment belonging to two successive demarcating change points is associated with an individual static regulatory network. In the second step, conditional network structure identification methods are used to reconstruct the topology for each time interval. This two-step strategy efficiently decouples the change point detection problem and the topology inference problem. Simulation results show that the proposed strategy can detect the change points precisely and recover each individual topology structure effectively. Moreover, computation results with the developmental data of Drosophila Melanogaster show that the proposed change point detection procedure is also able to work effectively in real world applications and the change point estimation accuracy exceeds other existing approaches, which means the suggested strategy may also be helpful in solving actual GRN reconstruction problem.     

Voroprot: an interactive tool for the analysis and visualization of complex geometric features of protein structure

We present Voroprot, an interactive cross-platform software tool that provides a unique set of capabilities for exploring geometric features of protein structure. Voroprot allows the construction and visualization of the Apollonius diagram (also known as the additively weighted Voronoi diagram), the Apollonius graph, protein alpha shapes, interatomic contact surfaces, solvent accessible surfaces, pockets and cavities inside protein structure. AVAILABILITY: Voroprot is available for Windows, Linux and Mac OS X operating systems and can be downloaded from http://www.ibt.lt/bioinformatics/voroprot/.     

A model of cell sorting

Voronoi polygons are introduced as a suitable representation for a two-dimensional cell sheet. These polygons are defined in terms of a finite number of points, making numerical simulations tractable and yet allowing cells to change neighbors and their shape in response to deforming forces without leaving gaps in the tissue. Using this geometry and an extension of the equilibrium theory proposed by Steinberg to drive the motion, simulations of rounding of uneven tissue and engulfment of two intact tissues are carried out.     

Introduction: International conference on forest ecosystems: Ecology,conservation and sustainable management

Abstract

A pollen diagram from a small lake, Kutulahdenlampi, in northern Finland is interpreted in terms of the development of forest vegetation during the Holocene. The abundance of each of the forest taxa is considered independently by means of pollen accumulation rates (PARs), using as the reference material, long term average pollen deposition values monitored by a network of pollen traps. Particular attention is paid to the arrival of spruce and to the species in the original forests that this newcomer replaces. A model of pollen dispersal and deposition developed by Sugita is used to estimate the area around the lake that the pollen assemblage is most clearly reflecting. This relevant source area of pollen (RSAP), for the present day situations is c. 1,500 m. Pollen loadings calculated for a simulated landscape that mimics (i) that of the present day and (ii) for the situation at 8,000 BP (as deduced from the PARs) are compared with the pollen assemblages from the diagram at those points in time, and are seen to be compatible. The advantages of combining PAR and modelling to look at the spatial scale of vegetation reconstructions are discussed.     

面向区域土壤碳通量估算的多向插值空间采样策略

区域土壤碳通量的准确测量对陆地生态系统碳循环过程分析具有十分重要的作用。由于土壤碳通量空间异质性强,采用随机抽样的方法无法对区域土壤碳通量进行准确估算,而大范围的多点采样则需要大量的人力及设备成本。基于一种自制的仪器,提出了一种递增式采样的多向插值采样策略(MDI Multiple Directional Interpolation):在设定初始采样点的基础上,通过对已有采样点的测量,通过径向插值的方法计算采样点连线交点,将不同径向计算值差异最大的点作为新增采样点,以此逐步增加。通过对20幅的50×50网格区域仿真,结果表明(1)MDI布局策略能够针对土壤碳通量的变化情况而反馈采样点的疏密。(2)误差分析得出采样点数量(n=10)较少,MDI布局策略对碳通量的估算误差比随机布局策略低,比平均布局策略稍高;随采样点增多,3种布局策略误差均降低;采样点数量n=40,MDI布局策略对碳通量的估算误差(0.028)比平均布局策略的误差(0.32)降低了12.5%,比随机布局策略的误差(0.04)降低了30.0%。MDI布局策略根据土壤碳通量的变化梯度合理分配采样点,降低区域土壤碳通量监测误差。     

Optimization of biochemical systems by linear programming and general mass action model representations

A new method is proposed for the optimization of biochemical systems. The method, based on the separation of the stoichiometric and kinetic aspects of the system, follows the general approach used in the previously presented indirect optimization method (IOM) developed within biochemical systems theory. It is called GMA-IOM because it makes use of the generalized mass action (GMA) as the model system representation form. The GMA representation avoids flux aggregation and thus prevents possible stoichiometric errors. The optimization of a system is used to illustrate and compare the features, advantages and shortcomings of both versions of the IOM method as a general strategy for designing improved microbial strains of biotechnological interest. Special attention has been paid to practical problems for the actual implementation of the new proposed strategy, such as the total protein content of the engineered strain or the deviation from the original steady state and its influence on cell viability.     

A mixture model approach to the mapping of QTL controlling endosperm traits with bulked samples

Endosperm traits are of triploid inheritance and have become a focus of breeding effort for their close relations with the grain quality. Current methods for mapping quantitative trait loci (QTL) underlying endosperm traits are restricted to the use of the phenotypes of single grain samples as input data set, which are often not available in practice due to the small size of the cereal seeds. This paper proposed a statistical model for one specially tailored mapping strategy, where the marker genotypes are obtained from the maternal plants in the segregation population and the phenotypic responses are replaced by the trait means of composite endosperm samples pooled from each plant. It should therefore be more practical and have wide applicability in mapping endosperm traits. The method was implemented by fitting the phenotypic means of endosperms into a Gaussian mixture model. Both the exact and approximate Expectation-Maximization algorithms were proposed to estimate the model parameters. The presence of the QTL was determined by likelihood ratio test statistics. Statistical power and other properties of the new method were investigated and compared to the current single-seed method under a variety of scenarios through simulation studies. The simulations suggest a reasonable sample size should be used to ensure reliable results. The proposed method was also applied to a simulated genome data for further evaluation. As an illustration, a real data of maize was analyzed to find the loci responsible for the popping expansion volume.     

Optimal resource allocation to seeds and vegetative propagules under density-dependent regulation in Syneilesis palmata (Compositae)

Syneilesis palmata reproduces by both seeds and vegetative propagules (short rhizomes). The latter result in the production of new plants that are larger in size and hence have a higher survival probability and a higher growth rate than seeds. A previous study predicted that the optimal reproductive strategy, in terms of maximizing population growth rate (a fitness measure under no density regulations), was pure vegetative reproduction. However, high resource investment to vegetative propagules can cause local crowding resulting in reduced demographic performances of the plants, because the vegetative propagules of Syneilesis are produced close to one another. We examined, in this situation, the impact of allocating a certain proportion of reproductive resource to seeds with relatively greater capacity for dispersal. We simulated dynamics of hypothetical Syneilesis populations with various reproductive resource allocation balances (from pure seed to pure vegetative reproduction), using a density-dependent matrix model. In the model, it was assumed that plants from vegetative propagules experienced density-dependent reduction in their survival probabilities, but this was not the case for plants originating from seeds. Each allocation strategy was evaluated based on an equilibrium population density, a fitness measure under density-dependent regulations. The optimal reproductive strategy predicted was pure vegetative reproduction. Unrealistic conditions were required for seed reproduction to be favoured, such as the production of seeds one hundred times the normal number per unit resource investment. However, the conditions were fairly relaxed compared with those required in the model where no density effects were incorporated. This indicates that escape from local crowding is likely to be one of the roles of seed production in Syneilesis.     

Adaptive compressive learning for prediction of protein-protein interactions from primary sequence

Protein-protein interactions (PPIs) play an important role in biological processes. Although much effort has been devoted to the identification of novel PPIs by integrating experimental biological knowledge, there are still many difficulties because of lacking enough protein structural and functional information. It is highly desired to develop methods based only on amino acid sequences for predicting PPIs. However, sequence-based predictors are often struggling with the high-dimensionality causing over-fitting and high computational complexity problems, as well as the redundancy of sequential feature vectors. In this paper, a novel computational approach based on compressed sensing theory is proposed to predict yeast Saccharomyces cerevisiae PPIs from primary sequence and has achieved promising results. The key advantage of the proposed compressed sensing algorithm is that it can compress the original high-dimensional protein sequential feature vector into a much lower but more condensed space taking the sparsity property of the original signal into account. What makes compressed sensing much more attractive in protein sequence analysis is its compressed signal can be reconstructed from far fewer measurements than what is usually considered necessary in traditional Nyquist sampling theory. Experimental results demonstrate that proposed compressed sensing method is powerful for analyzing noisy biological data and reducing redundancy in feature vectors. The proposed method represents a new strategy of dealing with high-dimensional protein discrete model and has great potentiality to be extended to deal with many other complicated biological systems.     

Bayesian inference for stationary points in Gaussian process regression models for event-related potentials analysis

Stationary points embedded in the derivatives are often critical for a model to be interpretable and may be considered as key features of interest in many applications. We propose a semiparametric Bayesian model to efficiently infer the locations of stationary points of a nonparametric function, which also produces an estimate of the function. We use Gaussian processes as a flexible prior for the underlying function and impose derivative constraints to control the function's shape via conditioning. We develop an inferential strategy that intentionally restricts estimation to the case of at least one stationary point, bypassing possible mis-specifications in the number of stationary points and avoiding the varying dimension problem that often brings in computational complexity. We illustrate the proposed methods using simulations and then apply the method to the estimation of event-related potentials derived from electroencephalography (EEG) signals. We show how the proposed method automatically identifies characteristic components and their latencies at the individual level, which avoids the excessive averaging across subjects that is routinely done in the field to obtain smooth curves. By applying this approach to EEG data collected from younger and older adults during a speech perception task, we are able to demonstrate how the time course of speech perception processes changes with age.