Embedding optimisation algorithms with Mosel

Algebraic modelling languages allow models to be implemented in such a way that they can easily be understood and modified. They are therefore a working environment commonly used by practitioners in Operations Research. Having once developed models, they need to be integrated inside the company information system. This step often involves embedding a model into a programming language environment: many existing algebraic modelling languages make possible to run parameterised models and subsequently retrieve their results, but without any facility for interacting with the model during the model generation or solution process.In this paper we show how to use the Mosel environment to implement complex algorithms directly in the modelling language.The Office cleaning problem is solved by a branch-and-cut algorithm, implemented entirely in the modelling language (including the definition of the callback function for the solver). Secondly, a cutting stock problem is solved by column generation, also implemented in the modelling language.AMS classification: 90Cxx, 65K05, 68N15     

Structural and functional model of methane hydroxylase of membrane-bound methane monooxygenase from Methylococcus capsulatus (Bath)

Computer analysis of a wide range of primary sequences showed that -, -, and -peptides of membrane-bound methane hydroxylase contained 2, 7, and 6 transmembrane helices respectively. Conservative amino acid residues participating in complex formation were revealed. The - and -peptides are suggested to contain mononuclear copper ions with the ligand environment mainly consisting of His residues. The Cu sites are located in the hydrophilic region and are responsible for ESR signals. The active site of -peptide in which the activation of O₂ and oxidation of CH₄ occur is localized in the hydrophobic region close to the membrane surface. This site is formed by the amino acid residues of four transmembrane helices and one loop between them and is suggested to be a binuclear Cu—Fe or Fe—Fe center. The Cu site of -peptide transfers electrons to the active site of -peptide, and the Cu site of -peptide is either involved in this process or only stabilizes the protein structure.     

Ab initio Tertiary Structure Prediction of Proteins

A daunting challenge in the area of computational biology has been to develop a method to theoretically predict the correct three-dimensional structure of a protein given its linear amino acid sequence. The ability to surmount this challenge, which is known as the protein folding problem, has tremendous implications. We introduce a novel ab initio approach for the protein folding problem. The accurate prediction of the three-dimensional structure of a protein relies on both the mathematical model used to mimic the protein system and the technique used to identify the correct structure. The models employed are based solely on first principles, as opposed to the myriad of techniques relying on information from statistical databases. The framework integrates our recently proposed methods for the prediction of secondary structural features including helices and strands, as well as -sheet and disulfide bridge formation. The final stage of the approach, which culminates in the tertiary structure prediction of a protein, utilizes search techniques grounded on the foundations of deterministic global optimization, powerful methods which can potentially guarantee the correct identification of a protein's structure. The performance of the approach is illustrated with bovine pancreatic trypsin inhibitor protein and the immunoglobulin binding domain of protein G.     

Approximation and Prediction of the Numerical Solution of Some Burgers Problems

The Aitken's ²-prediction of Brezinski has already been used by Morandi Cecchi et al. in order to compute a numerical approximation of the solution of a parabolic initial-boundary value problem. This method consists in two consecutive steps: the first one is the approximation with a finite elements method, where the solution of the involved nonlinear system is computed by Gauss–Seidel method; the second one is a prediction of further terms with Aitken's ²-process. By comparison with this method, we use other methods of prediction in another way. First, we consider a generalization of ²-prediction, the so-called -prediction. In this paper, we only use vector prediction which is more stable than the scalar one. Then, the methods of prediction presented can be used in order to predict the starting vector of the Gauss–Seidel method.     

Refinement of modelled structures by knowledge-based energy profiles and secondary structure prediction: Application to the human procarboxypeptidase A2

Knowledge-based energy profiles combined with secondary structure prediction have been applied to molecular modelling refinement. To check the procedure, three different models of human procarboxypeptidase A2 (hPCPA2) have been built using the 3D structures of procarboxypeptidase A1 (pPCPA1) and bovine procarboxypeptidase A (bPCPA) as templates. The results of the refinement can be tested against the X-ray structure of hPCPA2 which has been recently determined. Regions miss-modelled in the activation segment of hPCPA2 were detected by means of pseudo-energies using Prosa II and modified afterwards according to the secondary structure prediction. Moreover, models obtained by automated methods as COMPOSER, MODELLER and distance restraints have also been compared, where it was found possible to find out the best model by means of pseudo-energies. Two general conclusions can be elicited from this work: (1) on a given set of putative models it is possible to distinguish among them the one closest to the crystallographic structure, and (2) within a given structure it is possible to find by means of pseudo-energies those regions that have been defectively modelled.     

A unified framework for pull control mechanisms in multi‐stage manufacturing systems

This paper presents a unified framework for pull production control mechanisms in multistage manufacturing systems. A pull production control mechanism in a multistage manufacturing system is a mechanism that coordinates the release of parts into each stage of the system with the arrival of customer demands for final products. Four basic pull production control mechanisms are presented: Base Stock, Kanban, Generalized Kanban, and Extended Kanban. It is argued that on top of any of these basic coordination mechanisms, a local mechanism to control the workinprocess in each stage may be superimposed. Several cases of basic stage coordination mechanisms with stage workinprocess control are presented, and several production control systems that have appeared in the literature are shown to be equivalent to some of these cases.     

Bayesian networks applied to credit scoring

Email: kchang{at}gmu.eduEmail: RobertFung{at}Fairlsaac.comEmail: alan.lucas{at}hotmail.com^¶Email: BobOliver{at}Fairlsaac.com^||Email: NShikaloff{at}Fairlsaac.com The objectives of this paper are to apply the theory and numericalalgorithms of Bayesian networks to risk scoring, and comparethe results with traditional methods for computing scores andposterior predictions of performance variables. Model identification,inference, and prediction of random variables using Bayesiannetworks have been successfully applied in a number of areas,including medical diagnosis, equipment failure, informationretrieval, rare-event prediction, and pattern recognition. Theability to graphically represent conditional dependencies andindependencies among random variables may also be useful incredit scoring. Although several papers have already appearedin the literature which use graphical models for model identification,as far as we know there have been no explicit experimental resultsthat compare a traditionally computed risk score with predictionsbased on Bayesian learning algorithms. In this paper, we examine a database of credit-card applicantsand attempt to ‘learn’ the graphical structure ofthe characteristics or variables that make up the database.We identify representative Bayesian networks in a developmentsample as well as the associated Markov blankets and cliquestructures within the Markov blanket. Once we obtain the structureof the underlying conditional independencies, we are able toestimate the probabilities of each node conditional on its directpredecessor node(s). We then calculate the posterior probabilitiesand scores of a performance variable for the development sample.Finally, we calculate the receiver operating characteristic(ROC) curves and relative profitability of scorecards basedon these identifications. The results of the different modelsand methods are compared with both development and validationsamples. Finally, we report on a statistical entropy calculationthat measures the degree to which cliques identified in theBayesian network are independent of one another.     

基于搜索平均法的气象观测数据的非线性去噪

介绍了一种新型基于相空间重构和返回图法的非线性降噪方法——搜索平均法，首先将该方法应用于被高斯白噪声所污染的Henon映射时间序列，说明根据降噪理论所编写的计算程序的正确性；然后应用于中国气象局公布全国435站1960—2000年的逐日气温观测时间序列，并利用非线性预报方法衡量降噪的效果，验证了该方法的有效性.     

Theoretical analysis of the onset of liquid entrainment for slots of finite width

The onset of liquid entrainment during discharge from large reservoirs containing a stratified mixture of two immiscible fluids through a side slot of a finite width is considered theoretically. A previously reported analysis in which the slot was approximated as a two-dimensional line sink has been extended to account for the finite width of the slot. The model resulting from the present analysis is expressed in terms of two simple algebraic equations suitable for hand calculations. According to the present results, the ratio of the critical height to the slot width is dependent only on the Froude number. Numerical results show that the present model approaches the correct physical limits at low Froude numbers and it converges to the predictions of the previously reported simple model at high Froude numbers.     

基于改进的语音参数提取的线性预测

根据语音发生基本原理和线性预测编码原理，针对自相关法需要加窗从而降低了解的精度，而协方差法不能保证保证解所重构出系统的稳定性的特点，提出了一种改进的Cholesky分解的方法求解协方差方程组以产生声道模型参数的方法，实践证明，这种方法既保证了系统的稳定性，又提高了解的精度。