A Modification of the Edgeworth Approximation in the AR (1) Model

This paper considers the sampling distribution problem of the least squares estimator for the parameter of some special autoregressive models. The Edgeworth approximation has been derived and a modification is proposed to improve its accuracy. Comparisons with the exact distribution and the so called Edgeworth-B approximation have been discussed. The results show that the proposed approximation performs more accurately than the Edgeworth-B approximation, especially, when models are close to the non-stationary boundary.     

生境破坏的空间结构对集合种群续存的影响

生境破坏及其影响是生态学亟待解决的问题之一,目前的研究主要集中在破坏数量,即遭破坏生境的比例,对物种续存的影响方面;其中最主要的结论是Levins原理和适合生境斑块最小数量(MASH),而关于生境破坏的空间结构的研究却比较稀少,在本文中,我们首先将偶对近似引入到集合种群的研究当中,并替代原有的均匀场假设.然后我们对生境破坏导致的集合种群大小、空间结构以及分布等做了全面讨论.结果显示:随破坏比例的增加,集合种群大小将下降并且其分布将远离破坏生境.进一步聚集式分布结构将瓦解.随着破坏规则化的下降,集合种群将萎缩并使其聚集结构崩溃,在破坏生境周围集合种群起初将增加然后迅速消失.根据这些结果,我们可以对边界效应进行分析:不能用破坏比例描述生境破坏的程度和影响,而只能用破坏区域边界的长短来描述.根据边界效应,我们可以得出在一连通生境上物种保护的条件是生境破坏后剩余的适合生境比例应该大于破坏前原始生境的一半.居住在斑块环境中的物种比连续生境中生存的物种可以更好地抵抗生境破坏带来的影响.     

空间异质性对植物种群动态的影响:三种模拟方法的比较

为了讨论单一物种在异质性景观中的空间传播,将平均场近似模型和偶对近似模型的结果进行对比研究.本研究选择了有代表性的四邻域和八邻域时物种的传播情况,首先运用细胞自动机建立了理想模型,对偶对近似模型和平均场近似模型在全局密度和局域密度固定时随着出生率与死亡率比值变化的结果比较,以细胞自动机模型结果为依据,判断偶对近似与平均场近似哪个结果更加接近细胞自动机模型的结果.通过分析得到四邻域时在近似细胞自动机模型结果时偶对近似的结果优于平均场近似的结果,但是在八邻域时三个模型之间的差异性不再那么明显,偶对近似依然能够很好的预测细胞自动机模型的结果.     

An approach to inverse scattering problems

There are several reasons for investigating the inverse scattering problem in medical image processing. A typical case, that of ultrasonic fields, is considered. Assuming that a plane wave illuminates a weakly inhomogeneous two-dimensional object, the fundamental equation is derived for the scattered waves in integral as well as in differential forms. It is shown that the scattered waves observed on a circle surrounding the object is sufficient to specify the structure of the object. This information is summarized in a single term, which is a function of the wavenumber as well as the angles of incidence and observation. A successive approximation is applied to reconstruct the image of the object from this function. Since no analytic solution is available, several methods of approximations are proposed, and examples of computations are shown for the case of a cylindrical object.     

The total quasi-steady-state approximation is valid for reversible enzyme kinetics

The Briggs-Haldane approximation of the irreversible Michaelis-Menten scheme of enzyme kinetics is cited in virtually every biochemistry textbook and is widely considered the classic example of a quasi-steady-state approximation. Though of similar importance, the reversible Michaelis-Menten scheme is not as well characterized. This is a serious limitation since even enzymatic reactions that go to completion may be reversible. The current work derives a total quasi-steady-state approximation (tQSSA) for the reversible Michaelis-Menten and delineates its validity domain. The tQSSA allows the derivation of uniformly valid approximations for the limit of low enzyme concentrations, ET相似文献   

Further approximations for selection intensity

Three new approximations are suggested for the standardized selection intensity, i. Two are simple functions of powers of b, the fraction selected. These improve on previous approximations by covering a broader range of selection intensities. A third approximation is developed using a rational polynomial. This gave accurate approximation, but simplicity was lost.Communicated by E. J. Eisen     

Analytical methods for predicting the behaviour of population models with general spatial interactions

Many biologists use population models that are spatial, stochastic and individual based. Analytical methods that describe the behaviour of these models approximately are attracting increasing interest as an alternative to expensive computer simulation. The methods can be employed for both prediction and fitting models to data. Recent work has extended existing (mean field) methods with the aim of accounting for the development of spatial correlations. A common feature is the use of closure approximations for truncating the set of evolution equations for summary statistics. We investigate an analytical approach for spatial and stochastic models where individuals interact according to a generic function of their distance; this extends previous methods for lattice models with interactions between close neighbours, such as the pair approximation. Our study also complements work by Bolker and Pacala (BP) [Theor. Pop. Biol. 52 (1997) 179; Am. Naturalist 153 (1999) 575]: it treats individuals as being spatially discrete (defined on a lattice) rather than as a continuous mass distribution; it tests the accuracy of different closure approximations over parameter space, including the additive moment closure (MC) used by BP and the Kirkwood approximation. The study is done in the context of an susceptible-infected-susceptible epidemic model with primary infection and with secondary infection represented by power-law interactions. MC is numerically unstable or inaccurate in parameter regions with low primary infection (or density-independent birth rates). A modified Kirkwood approximation gives stable and generally accurate transient and long-term solutions; we argue it can be applied to lattice and to continuous-space models as a substitute for MC. We derive a generalisation of the basic reproduction ratio, R(0), for spatial models.     

On the existence of limit cycles for the enzyme-catalyzed hydrolysis reaction in a zero-dimensional representation of a membrane

This article is a continuation of the work done by N. J. Zabusky and R. H. Hardin [2] on an enzyme-catalyzed unbuffered hydrolysis reaction in a one-dimensional membrane. We consider the zero-dimensional approximation to a membrane. The system is then governed by a pair of ordinary differential equations. We give a sufficient condition on the parameters of the system for the existence of a limit cycle and present numerical solutions for realistic parameter ranges. Furthermore, we also give a sketched proof of the existence of a pH front for the stationary solutions of the full system of partial differential equations.     

Statistical mechanics approach to inhomogeneous van der Waals fluids

A general methodology is proposed to formulate density functional approximation (DFA) for inhomogeneous van der Waals fluids. The present methodology needs as input only a hard sphere DFA, second order direct correlation function (DCF) and pressure of coexistence bulk fluid, and therefore can be applicable to both supercitical and subcritical temperature regions. As illustrating example, the present report combines a recently proposed hard sphere “Formally exact truncated non-uniform excess Helmholtz free energy density functional approximation” with the present methodology, and applies the resultant DFA to calculate density profile of the inhomogeneous Lennard-Jones (LJ) fluid in coexistence with a bulk LJ fluid being situated at “dangerous” regions, i.e. the coexistence bulk state is near the critical temperature or the gas-liquid coexistence line. The theoretical predictions are in very good agreement with the recent simulation results, it is concluded that the present DFA is a globally excellent one. A discussion is given why the present methodology can lead to so excellent DFA.     

Semiclassical approximations of stochastic epidemiological processes towards parameter estimation using as prime example the SIS system with import

In this paper we investigate several schemes to approximate the stationary distribution of the stochastic SIS system with import. We begin by presenting the model and analytically computing its stationary distribution. We then approximate this distribution using Kramers–Moyal approximation, van Kampen's system size expansion, and a semiclassical scheme, also called WKB or eikonal approximation depending on its different applications in physics. For the semiclassical scheme, done in the context of the Hamilton–Jacobi formalism, two approaches are taken. In the first approach we assume a semiclassical ansatz for the generating function, while in the second the solution of the master equation is approximated directly. The different schemes are compared and the semiclassical approximation, which performs better, is then used to analyse the time dependent solution of stochastic systems for which no analytical expression is known. Stochastic epidemiological models are studied in order to investigate how far such semiclassical approximations can be used for parameter estimation.     

Thermo-mechanical properties of cubic titanium nitride

The equilibrium structure, elastic constants C_ij and thermodynamic functions of cubic titanium nitride (TiN) were calculated within the temperature range of 0–3100 K and under a pressure range 0–60 GPa. Properties were computed using the generalised gradient approximations (GGA) exchange-correlation functional. Calculated mechanical properties (Elastic constants, Young’s modulus and shear modulus) and phonon spectra of TiN obtained via robust DFT-QHA algorithm, were generally in a good agreement with available experimental and theoretical analogous values. In particular, a well-examined quasi-harmonic approximation method implemented in the Gibbs2 code is utilised herein to provide accurate estimation of thermal expansion coefficients, entropies, heat capacity values (at different combinations of temperature/volume/pressure) and Debye’s temperature. Parameters calculated herein shall be useful to elucidate the superior performance of TiN at harsh operational conditions encompassing elevated temperatures and pressures pertinent to cutting machineries and surface coatings.     

Comments on the rank product method for analyzing replicated experiments

Breitling et al. [1] introduced a statistical technique, the rank product method, for detecting differentially regulated genes in replicated microarray experiments. The technique has achieved widespread acceptance and is now used more broadly, in such diverse fields as RNAi analysis, proteomics, and machine learning. In this note, we relate the rank product method to linear rank statistics and provide an alternative derivation of distribution theory attending the rank product method.     

Parameter estimation for discretely observed linear birth‐and‐death processes

Birth‐and‐death processes are widely used to model the development of biological populations. Although they are relatively simple models, their parameters can be challenging to estimate, as the likelihood can become numerically unstable when data arise from the most common sampling schemes, such as annual population censuses. A further difficulty arises when the discrete observations are not equi‐spaced, for example, when census data are unavailable for some years. We present two approaches to estimating the birth, death, and growth rates of a discretely observed linear birth‐and‐death process: via an embedded Galton‐Watson process and by maximizing a saddlepoint approximation to the likelihood. We study asymptotic properties of the estimators, compare them on numerical examples, and apply the methodology to data on monitored populations.     

Modelling disease spread through random and regular contacts in clustered populations

An epidemic spreading through a network of regular, repeated, contacts behaves differently from one that is spread by random interactions: regular contacts serve to reduce the speed and eventual size of an epidemic. This paper uses a mathematical model to explore the difference between regular and random contacts, considering particularly the effect of clustering within the contact network. In a clustered population random contacts have a much greater impact, allowing infection to reach parts of the network that would otherwise be inaccessible. When all contacts are regular, clustering greatly reduces the spread of infection; this effect is negated by a small number of random contacts.     

Simplified neuron model as a principal component analyzer

A simple linear neuron model with constrained Hebbian-type synaptic modification is analyzed and a new class of unconstrained learning rules is derived. It is shown that the model neuron tends to extract the principal component from a stationary input vector sequence.