Parameter inference in small world network disease models with approximate Bayesian Computational methods

Small world network models have been effective in capturing the variable behaviour of reported case data of the SARS coronavirus outbreak in Hong Kong during 2003. Simulations of these models have previously been realized using informed “guesses” of the proposed model parameters and tested for consistency with the reported data by surrogate analysis. In this paper we attempt to provide statistically rigorous parameter distributions using Approximate Bayesian Computation sampling methods. We find that such sampling schemes are a useful framework for fitting parameters of stochastic small world network models where simulation of the system is straightforward but expressing a likelihood is cumbersome.     

溶剂效应计算中两种积分方法的比较研究

采用多面体表面模拟溶质空腔, 讨论了溶剂效应计算中近似积分方法和解析积分方法的平行性和收敛性. 我们发现: 对所研究的40个中性分子, 近似方法和解析方法之间的平行性较好; 但是, 对于20个正离子和27个负离子, 当溶质空腔分别为0.002和0.001 a.u.的等电荷密度面时, 近似方法和解析方法之间的平行性较差, 因此, 近似方法的可靠性不一定有保证. 我们还发现当多面体的表面无限趋近空腔的表面时, 不管采用何种多面体序列, 近似方法和解析方法的基态总能量都基本趋向同一极限值.     

Tests of Parameters of Several Gamma Distributions with Inequality Restrictions

Gamma distribution is one of the most used methods of modeling lifetime data. However, testing homogeneity of parameters of m 3 gamma distributions against order restrictions is almost non-existent in the current literature. We propose two methods to this end: one uses quadratic forms involving ratios of cumulants as test statistic and the other is a stepwise procedure which uses Fisher's method of combining p-values when shape parameters are equal but unknown. Both procedures allow use of arbitrary sample sizes of m populations. Test of the inequality restrictions as a null hypothesis against unrestricted alternatives is also considered. A Monte Carlo study of power at various alternatives shows that both methods are competitive when they are applicable.     

非牛顿粘性不可压流方程的近似惯性流形

本文利用对非牛顿粘性不可压缩流方程对时间 t的解析性和长时间渐近性估计 ,具体构造了它的近似惯性流形 ,并得出收敛阶估计 .     

Large gaps in one-dimensional cutting stock problems

Its linear relaxation is often solved instead of the one-dimensional cutting stock problem (1CSP). This causes a difference between the optimal objective function values of the original problem and its relaxation, called a gap. The size of this gap is considered in this paper with the aim to formulate principles for the construction of instances of the 1CSP with large gaps. These principles are complemented by examples for such instances.     

Tradeoff-based decomposition and decision-making in multiobjective programming

To facilitate the evaluation of tradeoffs and the articulation of preferences in multiple criteria decision-making, a multiobjective decomposition scheme is proposed that restructures the original problem as a collection of smaller-sized subproblems with only subsets of the original criteria. A priori preferences on objective tradeoffs are integrated into this process by modifying the ordinary Pareto order by more general domination cones, and decision makers are supported by an interactive decision-making procedure to coordinate any remaining tradeoffs using concepts of approximate efficiency. A theoretical foundation for this method is provided, and an illustrative application to multiobjective portfolio optimization is described in detail.     

Approximate controllability for semilinear retarded systems

This paper deals with the approximate controllability for the semilinear retarded control system. We will also derive the equivalent relation between controllability and stabilizability of the solution for the corresponding linear control system.     

Global Classification of Two-Component Approximately Integrable Evolution Equations

We globally classify two-component evolution equations, with homogeneous diagonal linear part, admitting infinitely many approximate symmetries. Important ingredients are the symbolic calculus of Gel’fand and Dikiĭ, the Skolem–Mahler–Lech theorem, an algorithm of Smyth, and results on diophantine equations in roots of unity obtained by Beukers.      

Identification of Parameters through the Approximate Periodic Solutions of a Parabolic System

This work is concerned with the identification problem for the perturbation term or error term in a parabolic partial differential equation through its approximate periodic solutions. The observation is made over a subregion of the physical domain. The existence and uniqueness problem of the approximate periodic solutions is studied in the first part of the paper. A solution to the identification problem is given in the second part of the paper. The main ingredients to be used include the classical Galerkin method and the unique continuation property for a parabolic system. This work was supported by the National Natural Science Foundation of China Grant 10571161.     

On the generalized Hyers-Ulam stability of module left derivations

Let A be a unital normed algebra and let M be a unitary Banach left A-module. If f:A→M is an approximate module left derivation, then f:A→M is a module left derivation. Moreover, if M=A is a semiprime unital Banach algebra and f(tx) is continuous in t∈R for each fixed x in A, then every approximately linear left derivation f:A→A is a linear derivation which maps A into the intersection of its center Z(A) and its Jacobson radical rad(A). In particular, if A is semisimple, then f is identically zero.