Construction of Selection Indexes with Restrictions

In this paper the problem of unistage selection with inequality constraints is formulated. If the predictor and criterion variables are all normally distributed, this problem can be written as a convex programming problem, with a linear objective function and with linear constraints and a quadratic constraint. Using the duality theory, for convex nonlinear programming it is proved, that its dual problem can be transformed into a convex minimization problem with non-negativity conditions. Good computational methods are known for solving this problem. By the help of the dual problem sufficient conditions for a solution of the original primal problem are derived and illustrated by an example of practical interest.     

The component retrieval problem in printed circuit board assembly

Minimization of the makespan of a printed circuit board assembly process is a complex problem. Decisions involved in this problem concern the specification of the order in which components are to be placed on the board and the assignment of component types to the feeder slots of the placement machine. If some component types are assigned to multiple feeder slots, an additional problem emerges: for each placement on the board, one must select the feeder slot from which the required component is to be retrieved. In this paper, we consider this component retrieval problem for placement machines of the Fuji CP type. We explain why simple forward dynamic programming schemes cannot provide a solution to this problem, invalidating the correctness of an algorithm proposed by Bard, Clayton, and Feo (1994). We then present a polynomial algorithm that solves the problem to optimality. The analysis of the component retrieval problem is facilitated by its reformulation as a PERT/CPM problem with design aspects: finding the minimal makespan of the assembly process amounts to identifying a design for which the longest path in the induced PERT/CPM network is shortest. The complexity of this network problem is analyzed, and we prove that the polynomial solvability of the component retrieval problem is caused by the specific structure it inflicts on the arc lengths of the network: in the absence of this structure, the network problem is shown to be NP-hard.     

The Gene-Duplication Problem: Near-Linear Time Algorithms for NNI-Based Local Searches

The gene-duplication problem is to infer a species supertree from a collection of gene trees that are confounded by complex histories of gene-duplication events. This problem is NP-complete and thus requires efficient and effective heuristics. Existing heuristics perform a stepwise search of the tree space, where each step is guided by an exact solution to an instance of a local search problem. A classical local search problem is the {tt NNI} search problem, which is based on the nearest neighbor interchange operation. In this work, we 1) provide a novel near-linear time algorithm for the {tt NNI} search problem, 2) introduce extensions that significantly enlarge the search space of the {tt NNI} search problem, and 3) present algorithms for these extended versions that are asymptotically just as efficient as our algorithm for the {tt NNI} search problem. The exceptional speedup achieved in the extended {tt NNI} search problems makes the gene-duplication problem more tractable for large-scale phylogenetic analyses. We verify the performance of our algorithms in a comparison study using sets of large randomly generated gene trees.     

A special view on the nature of the allocation problem

One of the remaining important problems of life cycle inventory analysis is the allocation problem. A proper solution of this problem calls for a proper understanding of the nature of the problem itself. This paper argues that the established definition of the allocation problem as the fact that one unit process produces more than one function, is not appropriate. That definition points to an important reason of the occurrence of the problem, but the situation of internal (closed-loop) recycling already indicates that there may be product systems which contain multifunction processes, but which nevertheless need not exhibit an allocation problem. The paper proceeds by examining a number of simple hypothetical cases, and proposes a precise and operational definition of the allocation problem. This enables a systematic categorization of approaches for dealing with the allocation problem.     

Modelling the effect of immigration on drinking behaviour

A drinking model with immigration is constructed. For the model with problem drinking immigration, the model admits only one problem drinking equilibrium. For the model without problem drinking immigration, the model has two equilibria, one is problem drinking-free equilibrium and the other is problem drinking equilibrium. By employing the method of Lyapunov function, stability of all kinds of equilibria is obtained. Numerical simulations are also provided to illustrate our analytical results. Our results show that alcohol immigrants increase the difficulty of the temperance work of the region.     

Extensions and improvements to the chordal graph approach to the multistate perfect phylogeny problem

The multistate perfect phylogeny problem is a classic problem in computational biology. When no perfect phylogeny exists, it is of interest to find a set of characters to remove in order to obtain a perfect phylogeny in the remaining data. This is known as the character removal problem. We show how to use chordal graphs and triangulations to solve the character removal problem for an arbitrary number of states, which was previously unsolved. We outline a preprocessing technique that speeds up the computation of the minimal separators of a graph. Minimal separators are used in our solution to the missing data character removal problem and to Gusfield's solution of the perfect phylogeny problem with missing data.     

An Omega(n2/ log n) speed-up of TBR heuristics for the gene-duplication problem

The gene-duplication problem is to infer a species supertree from gene trees that are confounded by complex histories of gene duplications. This problem is NP-hard and thus requires efficient and effective heuristics. Existing heuristics perform a stepwise search of the tree space, where each step is guided by an exact solution to an instance of a local search problem. We improve on the time complexity of the local search problem by a factor of n2= log n, where n is the size of the resulting species supertree. Typically, several thousand instances of the local search problem are solved throughout a stepwise heuristic search. Hence, our improvement makes the gene-duplication problem much more tractable for large-scale phylogenetic analyses.     

Effective haplotype assembly via maximum Boolean satisfiability

The haplotype assembly problem seeks the haplotypes of an individual from which a set of aligned SNP fragments are available. The problem is important as the haplotypes contain all the SNP information, which is essential to such studies as the analysis of the association between specific diseases and their potential genetic causes. Using Minimum Error Correction as the objective function, the problem is NP-hard, which raises the demand for effective yet affordable solutions. In this paper, we propose a new method to solve the problem by providing a novel Max-2-SAT formulation for the problem. The proposed method is compared with several well-known algorithms proposed for the problem in the literature on a recent extensive benchmark, outperforming them all by achieving solutions of higher average quality.     

Analysis of mussel growth data*

This short paper considers the problem of estimating the year of birth of a mussel picked at an unknown time. This is an important problem not only for studying a certain mussel population but also for environmental monitoring. A mathematical formulation of the problem is presented, which leads to a combined delay estimation and constrained linear regression problem. A solution is developed and applied to the estimation problem. Examples with mussels picked from a river in Sweden are shown, which demonstrate that the proposed technique works well in practice.     

Reactive scheduling model for the operating theatre

This paper addresses the disruption management and rescheduling problem of the day-to-day running of a day surgery unit. The problem is modelled as a single machine scheduling problem with sequence dependent processing times and due dates. The proposed optimisation model sequences both elective and non-elective patients in the online environment. The weighted number of expected surgeries to complete on-time is maximised. We propose a branch and bound algorithm to solve the problem. Computational experiments are conducted illustrating its applicability to the problem of reactive scheduling in the operating theatre.     

The mind of the species problem

The species problem is the long-standing failure of biologists to agree on how we should identify species and how we should define the word 'species'. The innumerable attacks on the problem have turned the often-repeated question 'what are species?' into a philosophical conundrum. Today, the preferred form of attack is the well-crafted argument, and debaters seem to have stopped inquiring about what new information is needed to solve the problem. However, our knowledge is not complete and we have overlooked something. The species problem can be overcome if we understand our own role, as conflicted investigators, in causing the problem.     

蚂蚁群落优化算法在蛋白质折叠二维亲-疏水格点模型中的应用

氨基酸的亲疏水格点模型是研究蛋白质折叠的一种重要的简化模型,其优化问题是一个非确定型的多项式问题。采用蚂蚁群落优化算法对这一问题进行了研究,对测试数据的计算结果表明,在一定规模下,此算法能够有效地获得亲-疏水格点模型的最优解,其效率优于传统的Monte Carlo仿真等方法。     

Perfect phylogenetic networks with recombination.

The perfect phylogeny problem is a classical problem in evolutionary tree construction. In this paper, we propose a new model called phylogenetic network with recombination that takes recombination events into account. We show that the problem of finding a perfect phylogenetic network with the minimum number of recombination events is NP-hard; we also present an efficient polynomial time algorithm for an interesting restricted version of the problem.     

Fitting protein chains to cubic lattice is NP-complete

It is known that folding a protein chain into a cubic lattice is an NP-complete problem. We consider a seemingly easier problem: given a three-dimensional (3D) fold of a protein chain (coordinates of its C(alpha) atoms), we want to find the closest lattice approximation of this fold. This problem has been studied under names such as "lattice approximation of a protein chain", "the protein chain fitting problem", and "building of protein lattice models". We show that this problem is NP-complete for the cubic lattice with side close to 3.8 A and coordinate root mean square deviation.     

Transportation Optimization with Fuzzy Trapezoidal Numbers Based on Possibility Theory

In this paper, a parametric method is introduced to solve fuzzy transportation problem. Considering that parameters of transportation problem have uncertainties, this paper develops a generalized fuzzy transportation problem with fuzzy supply, demand and cost. For simplicity, these parameters are assumed to be fuzzy trapezoidal numbers. Based on possibility theory and consistent with decision-makers'' subjectiveness and practical requirements, the fuzzy transportation problem is transformed to a crisp linear transportation problem by defuzzifying fuzzy constraints and objectives with application of fractile and modality approach. Finally, a numerical example is provided to exemplify the application of fuzzy transportation programming and to verify the validity of the proposed methods.     

Efficient substructure RMSD query algorithms.

Protein structure analysis is a very important research topic in the molecular biology of the post-genomic era. The root mean square deviation (RMSD) is the most frequently used measure for comparing two protein three-dimensional (3-D) structures. In this paper, we deal with two fundamental problems related to the RMSD. We first deal with a problem called the "range RMSD query" problem. Given an aligned pair of structures, the problem is to compute the RMSD between two aligned substructures of them without gaps. This problem has many applications in protein structure analysis. We propose a linear-time preprocessing algorithm that enables constant-time RMSD computation. Next, we consider a problem called the "substructure RMSD query" problem, which is a generalization of the above range RMSD query problem. It is a problem to compute the RMSD between any substructures of two unaligned structures without gaps. Based on the algorithm for the range RMSD problem, we propose an O(nm) preprocessing algorithm that enables constant-time RMSD computation, where n and m are the lengths of the given structures. Moreover, we propose O(nm log r/r)-time and O(nm/r)-space preprocessing algorithm that enables O(r) query, where r is an arbitrary integer such that 1 < or = r < or = min(n, m). We also show that our strategy also works for another measure called the unit-vector root mean square deviation (URMSD), which is a variant of the RMSD.     

PCB assembly scheduling with alternative nozzle types for one component type

The placement machine is the bottleneck of a printed circuit board (PCB) assembly line. The type of machine considered in this paper is the beam-type placement machine that can simultaneously pick up several components from feeders. It is assumed that the number of nozzle types (NTs) is less than the number of heads on the beam. The objective of the PCB assembly scheduling for a single placement machine is to minimize the cycle time based on the average machine operation time instead of the travelling distance. To minimize the cycle time, the number of turns and the number of pickups should be minimized. The PCB assembly scheduling is hierarchically decomposed into four problems: the nozzle assignment problem, the head allocation problem, the component type (CT) grouping problem and the pickup clustering problem, which are optimized successively and iteratively. First, the nozzle assignment problem considering alternative NTs for one CT is dealt with by the proposed genetic algorithm. For a given nozzle assignment solution, the head allocation problem is solved by a previously greedy heuristic to minimize the number of turns.Then, the CT grouping problem and the pickup clustering problem are solved by a proposed greedy heuristic and a modified agglomerative hierarchical clustering approach, respectively, to minimize the number of pickups. Numerical experiments are carried out to examine the performances of these proposed heuristic approaches. The importance of considering alternative NTs for one CT for the cycle time is also confirmed.     

Reconstructing recombination network from sequence data: the small parsimony problem

The small parsimony problem is studied for reconstructing recombination networks from sequence data. The small parsimony problem is polynomial-time solvable for phylogenetic trees. However, the problem is proved NP-hard even for galled recombination networks. A dynamic programming algorithm is also developed to solve the small parsimony problem. It takes O(dn2(3h)) time on an input recombination network over length-d sequences in which there are h recombination and n - h tree nodes.     

基于Progressive多序列比对方法的求解多序列比对的启发式算法

在生物信息学研究中,生物序列比对问题占有重要的地位。多序列比对问题是一个NPC问题,由于时间和空间的限制不能够求出精确解。文中简要介绍了Feng和Doolittle提出的多序列比对算法的基本思想,并改进了该算法使之具有更好的比对精度。实验结果表明,新算法对解决一般的progressive多序列比对方法中遇到的局部最优问题有较好的效果。     

Scaffold filling under the breakpoint and related distances

Motivated by the trend of genome sequencing without completing the sequence of the whole genomes, a problem on filling an incomplete multichromosomal genome (or scaffold) I with respect to a complete target genome G was studied. The objective is to minimize the resulting genomic distance between I' and G, where I' is the corresponding filled scaffold. We call this problem the onesided scaffold filling problem. In this paper, we conduct a systematic study for the scaffold filling problem under the breakpoint distance and its variants, for both unichromosomal and multichromosomal genomes (with and without gene repetitions). When the input genome contains no gene repetition (i.e., is a fragment of a permutation), we show that the two-sided scaffold filling problem (i.e., G is also incomplete) is polynomially solvable for unichromosomal genomes under the breakpoint distance and for multichromosomal genomes under the genomic (or DCJ--Double-Cut-and-Join) distance. However, when the input genome contains some repeated genes, even the one-sided scaffold filling problem becomes NP-complete when the similarity measure is the maximum number of adjacencies between two sequences. For this problem, we also present efficient constant-factor approximation algorithms: factor-2 for the general case and factor 1.33 for the one-sided case.