Robust DNA microarray image analysis

DNA microarrays are an increasingly important tool that allow biologists to gain insight into the function of thousands of genes in a single experiment. Common to all array-based approaches is the necessity to analyze digital images of the scanned DNA array. The ultimate image analysis goal is to automatically quantify every individual array element (spot), providing information about the amount of DNA bound to a spot. Irrespective of the quantification strategy, the preliminary information to extract about a spot includes the mapping between its location in the digital image and its possibly distorted position in the spot array (gridding). We present a gridding approach divided into a spot-amplification step (matched filter), a rotation estimation step (Radon transform), and a grid spanning step. Quantification of the spots is performed by robustly fitting of a parametric model to pixel intensities with the help of M-estimators. The main advantage of parametric spot fitting is its ability to cope with overlapping spots. If the goodness-of-fit is too bad, a semiparametric spot fitting is employed. We show that our approach is superior to simple quantification strategies such as averaging of the pixel intensities. The system was extensively tested on 1740 images resulting from two DNA libraries.Received: 15 June 2001, Accepted: 21 July 2002, Published online: 3 June 2003 Correspondence to: Norbert Brändle     

Modelling and effective modification of smooth boundary geometry in boundary problems using B-spline curves

To create curves in computer graphics, we use, among others, B-splines since they make it possible to effectively produce curves in a continuous way using a small number of de Boor’s control points. The properties of these curves have also been used to define and create boundary geometry in boundary problems solving using parametric integral equations system (PIES). PIES was applied for resolution 2D boundary-value problems described by Laplace’s equation. In this PIES, boundary geometry is theoretically defined in its mathematical formalism, hence the numerical solution of the PIES requires no boundary discretization (such as in BEM) and is simply reduced to the approximation of boundary functions. To solve this PIES a pseudospectral method has been proposed and the results obtained were compared with both exact and numerical solutions.     

Experimental study for the comparison of classifier combination methods

In this paper, we compare the performances of classifier combination methods (bagging, modified random subspace method, classifier selection, parametric fusion) to logistic regression in consideration of various characteristics of input data. Four factors used to simulate the logistic model are: (a) combination function among input variables, (b) correlation between input variables, (c) variance of observation, and (d) training data set size. In view of typically unknown combination function among input variables, we use a Taguchi design to improve the practicality of our study results by letting it as an uncontrollable factor. Our experimental study results indicate the following: when training set size is large, performances of logistic regression and bagging are not significantly different. However, when training set size is small, the performance of logistic regression is worse than bagging. When training data set size is small and correlation is strong, both modified random subspace method and bagging perform better than the other three methods. When correlation is weak and variance is small, both parametric fusion and classifier selection algorithm appear to be the worst at our disappointment.     

连续因果图的推理及参数学习

因果图理论是利用图形化和直接因果强度来表达知识和因果关系的一种基于概率论的推理方法，而对于连续的因果图连接事件的概率密度函数（或可能性密度函数）是连续因果图能进行推理的关键，一般都是假定它们可由领域专家给出。这在实际中很难办到。文章首先给出了连续因果图的推理过程，然后讨论了如何利用已知数据集。在因果图结构已知的条件下利用参数、非参数、半参数化方法估计出连接事件的概率密度函数的途径。     

Optimal sagittal gait with ZMP stability during complete walking cycle for humanoid robots

A parametric method to generate low energy gait for both single and double support phases with zero moment point（ZMP） stability is presented. The ZMP stability condition is expressed as a limit to the actuating torque of the support ankle, and the inverse dynamics of both walking phases is investigated. A parametric optimization method is implemented which approximates joint trajectories by cubic spline functions connected at uniformly distributed time knots and makes optimization parameters only involve finite discrete states describing key postures. Thus, the gait optimization is transformed into an ordinary constrained nonlinear programming problem. The effectiveness of the method is verified through numerical simulations conducted on the humanoid robot THBIP-I model.     

基于最小二乘支持向量机的函数拟合的研究

函数拟合通常要在有限的训练样本下对函数变量之间的关系做出预测,在实践中由于训练样本有限,并且训练样本本身存在噪音和孤立点,用传统的方法进行函数拟合的结果往往不能满足要求.本文主要利用最小二乘支持向量机对函数进行拟合.首先介绍了最小二乘支持向量机的工作原理,并对参数选择方法进行了研究,然后通过仿真实验对利用最小二乘支持向量机进行函数拟合的效果加以对比说明.     

Bayesian parametric inference in a nonparametric framework

This paper considers the problem of reporting a “posterior distribution” using a parametric family of distributions while working in a nonparametric framework. This “posterior” is obtained as the solution to a decision problem and can be found via a well-known optimization algorithm.      

Designing parametric linear quadratic regulators for parametric LTI systems via LMIs

This paper addresses the problem of determining parametric linear quadratic regulators (LQRs) for continuous-time linear-time invariant systems affected by parameters through rational functions. Three situations are considered, where the sought controller has to minimise the best cost, average cost, and worst cost, respectively, over the set of admissible parameters. It is shown that candidates for such controllers can be obtained by solving convex optimisation problems with linear matrix inequality (LMI) constraints. These candidates are guaranteed to approximate arbitrarily well the sought controllers by sufficiently increasing the size of the LMIs. In particular, the candidate that minimises the average cost approximates arbitrarily well the true LQR over the set of admissible parameters. Moreover, conditions for establishing the optimality of the found candidates are provided. Some numerical examples illustrate the proposed methodology.     

APPLYING MARGINAL VALUE ANALYSIS IN REFINERY PLANNING

Most research work and refinery decision makers mainly focus on direct planning results such as the optimal combination of raw materials, unit loads, and production rates. There exists much more useful hidden information from an LP model such as marginal values of the feed stocks, the intermediate products, and the final products than direct planning results. One of the limitations of using marginal values is that they are only applied for stream flows at the solution point. We have no idea how these marginal values are changed beyond the solution. To tackle this problem, two analytical methods, namely sensitivity analysis (SA) and parametric programming (PP), are proposed and applied in MVA (marginal value analysis). With these two analysis methods, MVA can be extended beyond the solution point and applied to process constraints. This article first uses a simple gasoline blending example to illustrate the required modeling techniques and procedures for performing these analyses. Then a multi-period refinery case study is presented to show how to interpret the results and apply the analyses to a real world refinery. The approach proposed here can be of great help for debottlenecking, retrofitting, pricing, and investment evaluation. The analytical methods proposed can also be generally applied to other chemical plants.     

Counting with rational generating functions

We examine two different ways of encoding a counting function: as a rational generating function and explicitly as a function (defined piecewise using the greatest integer function). We prove that, if the degree and number of input variables of the (quasi-polynomial) function are fixed, there is a polynomial time algorithm which converts between the two representations. Examples of such counting functions include Ehrhart quasi-polynomials, vector partition functions, integer points in parametric polytopes, and projections of the integer points in parametric polytopes. For this last example, this algorithm provides the first known way to compute the explicit function in polynomial time. We rely heavily on results by Barvinok and Pommersheim [Barvinok, A., Pommersheim, J., 1999. An algorithmic theory of lattice points in polyhedra. In: New Perspectives in Algebraic Combinatorics (Berkeley, CA, 1996–97). In: Math. Sci. Res. Inst. Publ., vol. 38. Cambridge Univ. Press, Cambridge, pp. 91–147], and also by Verdoolaege et al. [Verdoolaege, S., Seghir, R., Beyls, K., Loechner, V., Bruynooghe, M., 2007. Counting integer points in parametric polytopes using Barvinok’s rational functions, Algorithmica 48 (1), 37–66].