��˹ͼģ�͵Ļ����������Ľ���IPSP�㷨

The IPSP algorithm is an efficient algorithm for computing maximum likelihood estimation of Gaussian graphical models. It first divides clique marginals of graphical models into several groups, and then it adjusts clique marginals in each group locally. This paper uses the IIPS algorithm on junction tree to replace local adjustment on each group in the IPSP algorithm and propose a resulting algorithm called IPSP-JT to reduce the complexity of the IPSP algorithm. Moreover, we give a graph with minimum edges used by IIPS to adjust locally, and we prove its existence and uniqueness and construct a local junction tree. Numerical experiments show that the IPSP-JT algorithm runs faster than the IPSP algorithm for large Gaussian graphical models.     

有缺失数据的META-MARKOV模型的局部计算

根据meta Markov模型的特征,本文提出了有缺失数据的meta Markov模型的局部计算方法．由于最小可压缩集与局部计算关系密切,本文给出了一种搜索包含预先给定的子集的最小可压缩集的算法．     

A Decision Procedure for Nonperiodic Sequents of the First-Order Linear Temporal Logic

A deduction-based decision procedure is presented for the nonperiodic D-sequents of the first-order linear temporal logic. The D-sequents are obtained from D ₂-sequents [7], [8] by removing the periodicity condition. The deductive procedure proposed consists of decidable deductive procedures that replace infinitary and finitary induction rules for the temporal operator ``always'. The soundness and completeness of the deduction-based decision procedure proposed is proved.     

Iterative solution of the drift-diffusion equations

The drift-diffusion model can be described by a nonlinear Poisson equation for the electrostatic potential coupled with a system of convection-reaction-diffusion equations for the transport of charge. We use a Gummel-like process [10] to decouple this system. Each of the obtained equations is discretised with the finite element method. We use a local scaling method to avoid breakdown in the numerical algorithm introduced by the use of Slotboom variables. Solution of the discrete nonlinear Poisson equation is accomplished with quasi-Newton methods. The nonsymmetric discrete transport equations are solved using an incomplete LU factorization preconditioner in conjunction with some robust linear solvers, such as (CGS), (BI-CGSTAB) and (GMRES). We investigate the behaviour of these iterative methods to define the effective strategy for this class of problems. This revised version was published online in June 2006 with corrections to the Cover Date.     

比例风险模型下参数估计的两种MM算法的一些应用

对于带有删失机制的生存数据的研究,比例风险模型是应用最为广泛的统计模型之一。实际中,为得到其参数的极大似然估计需要采用数值方法计算得分方程的解。MinorizationMaximization算法(以下简称"MM算法")将求解复杂的目标函数的极值问题转化为求解简单的代理函数的极值问题。本文主要探讨,在比例风险模型下通过两种不同的思想为偏似然函数构造代理函数,从而得到的两种MM算法。通过数值模拟和实际数据分析实现这两种MM算法在比例风险模型下的一些应用。     

A Theoretically Consistent Version of the Nelson and Siegel Class of Yield Curve Models

A popular class of yield curve models is based on the Nelson and Siegel approach of ‘fitting’ yield curve data with simple functions of maturity. However, such models cannot be consistent across time. This article addresses that deficiency by deriving an intertemporally consistent and arbitrage‐free version of the Nelson and Siegel model. Adding this theoretical consistency expands the potential applications of the Nelson and Siegel approach to exercises involving a time‐series context, such as forecasting the yield curve and pricing interest rate derivatives. As a practical example, the intertemporal consistency of the model is exploited to derive a theoretical framework for forecasting the yield curve. The empirical application of that framework to United States data results in out‐of‐sample forecasts that outperform the random walk over the sample period of almost 50 years, for forecast horizons ranging from six months to three years.     

A Parallel Preconditioned Iterative Realization of the Panel Method in 3D

The parallel version of precondition iterative techniques is developed for matrices arising from the panel boundary element method for three-dimensional simple connected domains with Dirichlet boundary conditions. Results were obtained on an nCube-2 parallel computer showing that preconditioned iterative methods are very well suited also in three-dimensional cases for implementation on an MIMD computer and that they are much more efficient than usual direct solution techniques.     

用于求根问题的一个基于Thiele连分式的四阶收敛的迭代方法

利用截断的Thiele连分式,本文给出了一个求解非线性单变量方程的单步迭代方法,并证明了所提出的迭代方法具有四阶收敛性.最后,本文通过一些数值例子说明了所提出的方法的有效性和表现.     

The Mixturegram: A Visualization Tool for Assessing the Number of Components in Finite Mixture Models

Certain practical and theoretical challenges surround the estimation of finite mixture models. One such challenge is how to determine the number of components when this is not assumed a priori. Available methods in the literature are primarily numerical and lack any substantial visualization component. Traditional numerical methods include the calculation of information criteria and bootstrapping approaches; however, such methods have known technical issues regarding the necessary regularity conditions for testing the number of components. The ability to visualize an appropriate number of components for a finite mixture model could serve to supplement the results from traditional methods or provide visual evidence when results from such methods are inconclusive. Our research fills this gap through development of a visualization tool, which we call a mixturegram. This tool is easy to implement and provides a quick way for researchers to assess the number of components for their hypothesized mixture model. Mixtures of univariate or multivariate data can be assessed. We validate our visualization assessments by comparing with results from information criteria and an ad hoc selection criterion based on calculations used for the mixturegram. We also construct the mixturegram for two datasets.     

Sylvester矩阵方程极小范数最小二乘解的迭代解法

研究了Sylvester矩阵方程最小二乘解以及极小范数最小二乘解的迭代解法,首先利用递阶辨识原理,得到了求解矩阵方程AX+YB=C的极小范数最小二乘解的一种迭代算法,进而,将这种算法推广到一般线性矩阵方程A_iX_iB_i=C的情形,最后,数值例子验证了算法的有效性.     

A Note on Mascarenhas' Counterexample about Global Convergence of the Affine Scaling Algorithm

Mascarenhas gave an instance of linear programming problems to show that the long-step affine scaling algorithm can fail to converge to an optimal solution with the step-size λ=0.999 . In this note, we give a simple and clear geometrical explanation for this phenomenon in terms of the Newton barrier flow induced by projecting the homogeneous affine scaling vector field conically onto a hyperplane where the objective function is constant. Based on this interpretation, we show that the algorithm can fail for "any" λ greater than about 0.91 (a more precise value is 0.91071), which is considerably shorter than λ = 0.95 and 0.99 recommended for efficient implementations. Accepted 17 February 1998     

A Central Limit Theorem for a Localized Version of the SK Model

In this note, we consider a SK (Sherrington–Kirkpatrick)-type model on ℤ ^d for d≥1, weighted by a function allowing to any single spin to interact with a small proportion of the other ones. In the thermodynamical limit, we investigate the equivalence of this model with the usual SK spin system, through the study of the fluctuations of the free energy. This author’s research partially supported by CAPES.     

A characterization of Kruskal sharing rules for minimum cost spanning tree problems

In Tijs et al. (Eur J Oper Res 175:121–134, 2006) a new family of cost allocation rules is introduced in the context of cost spanning tree problems. In this paper we provide the first characterization of this family by means of population monotonicity and a property of additivity.     

AHP中判断矩阵一致性改进的迭代算法

本文研究了扰动矩阵与判断矩阵的不一致性的关系 ,提出了一种新的改进判断矩阵一致性的迭代算法 .     

A Geometric Approach to Maximum Likelihood Estimation of the Functional Principal Components From Sparse Longitudinal Data

In this article, we consider the problem of estimating the eigenvalues and eigenfunctions of the covariance kernel (i.e., the functional principal components) from sparse and irregularly observed longitudinal data. We exploit the smoothness of the eigenfunctions to reduce dimensionality by restricting them to a lower dimensional space of smooth functions. We then approach this problem through a restricted maximum likelihood method. The estimation scheme is based on a Newton–Raphson procedure on the Stiefel manifold using the fact that the basis coefficient matrix for representing the eigenfunctions has orthonormal columns. We also address the selection of the number of basis functions, as well as that of the dimension of the covariance kernel by a second-order approximation to the leave-one-curve-out cross-validation score that is computationally very efficient. The effectiveness of our procedure is demonstrated by simulation studies and an application to a CD4+ counts dataset. In the simulation studies, our method performs well on both estimation and model selection. It also outperforms two existing approaches: one based on a local polynomial smoothing, and another using an EM algorithm. Supplementary materials including technical details, the R package fpca, and data analyzed by this article are available online.     

A Multiresolution Gaussian Process Model for the Analysis of Large Spatial Datasets

We develop a multiresolution model to predict two-dimensional spatial fields based on irregularly spaced observations. The radial basis functions at each level of resolution are constructed using a Wendland compactly supported correlation function with the nodes arranged on a rectangular grid. The grid at each finer level increases by a factor of two and the basis functions are scaled to have a constant overlap. The coefficients associated with the basis functions at each level of resolution are distributed according to a Gaussian Markov random field (GMRF) and take advantage of the fact that the basis is organized as a lattice. Several numerical examples and analytical results establish that this scheme gives a good approximation to standard covariance functions such as the Matérn and also has flexibility to fit more complicated shapes. The other important feature of this model is that it can be applied to statistical inference for large spatial datasets because key matrices in the computations are sparse. The computational efficiency applies to both the evaluation of the likelihood and spatial predictions.     

Two algorithms for generating and ranking the family of solutions of a finite irreflexive relation

The family of solutions, also known as 1-bases or kernels, of a finite irreflexive relation has a variety of many interesting applications. Furthermore, the decision as towhether the associated digraph posesses a solution belongs to the class of computationally intractable problems known as NP-complete. In this paper we present (a) a tree search algorithm to generate the family of solutions of a digraph and (b) a dynamic programming algorithm to generate the family of solutions ranked in increasing order of their cardinality. Extensive computational experience with the tree search algorithm on more than 1000 randomly generated digraphs ranging from 50 to 150 vertices and from 15% to 60% densities has shown that the proposed algorithm is effective.     

A Gaussian upper bound for the fundamental solutions of a class of ultraparabolic equations

We prove Gaussian estimates from above of the fundamental solutions to a class of ultraparabolic equations. These estimates are independent of the modulus of continuity of the coefficients and generalize the classical upper bounds by Aronson for uniformly parabolic equations.     

A note on the functional law of iterated logarithm for maxima of Gaussian sequences

Let {X_n, n ≥ 1} be a real-valued stationary Gaussian sequence with mean zero and variance one. Let M_n = max{X_t, i ≤ n} and H_n(t) = (M_[nt] ? b_n)a_n^?1 be the maximum resp. the properly normalised maximum process, where $\text{c}{}_{\mathrm{n}}\text{= (2}\text{log}\text{n)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$, $\text{a}{}_{\mathrm{n}}\text{=}\text{(}\text{log log}\text{n)}\text{c}{}_{\mathrm{n}}$ and $\text{b}{}_{\mathrm{n}}\text{= c}{}_{\mathrm{n}}\text{?}\text{1}\text{2}\text{(}\text{log}\text{(4π}\text{log}\text{n))}\text{c}{}_{\mathrm{n}}$. We characterize the almost sure limit functions of (H_n)_n≥3 in the set of non-negative, non-decreasing, right-continuous, real-valued functions on (0, ∞), if r(n) (log n)^3?Δ = O(1) for all Δ > 0 or if r(n) (log n)^2?Δ = O(1) for all Δ > 0 and r(n) convex and fulfills another regularity condition, where r(n) is the correlation function of the Gaussian sequence.     

A variable-metric variant of the Karmarkar algorithm for linear programming

The most time-consuming part of the Karmarkar algorithm for linear programming is the projection of a vector onto the nullspace of a matrix that changes at each iteration. We present a variant of the Karmarkar algorithm that uses standard variable-metric techniques in an innovative way to approximate this projection. In limited tests, this modification greatly reduces the number of matrix factorizations needed for the solution of linear programming problems. Research sponsored by DOE DE-AS05-82ER13016, ARO DAAG-29-83-K-0035, AFOSR 85-0243. Research sponsored by ARO DAAG-29-83-K-0035, AFOSR 85-0243, Shell Development Company.