Fast detection of common sequence structure patterns in RNAs

We developed a dynamic programming approach for computing common exact sequential and structural patterns between two RNAs, given their sequences and their secondary structures. An RNA consists of a sequence of nucleotides and a secondary structure defined via bonds linking together complementary nucleotides. It is known that secondary structures are more preserved than sequences in the evolution of RNAs.We are able to compute all patterns between two RNAs in time O(nm) and space O(nm), where n and m are the lengths of the RNAs. Our method is useful for describing and detecting local motifs. It is especially suitable for finding similar regions of large RNAs that do not share global similarities. An implementation is available in C++ and can be obtained by contacting one of the authors.     

一种基于能量的RNA二级结构预测的动态划分算法

预测单链RNA分子序列的二级结构是计算生物学中的一个重要内容.本文基于RNA分子结构的稳定性原理.提出了一种预测RNA二级结构的新算法——基于能量的动态划分算法.该算法的空间复杂度仅为O(n),时间复杂度近似为O(n2·logn),且预测结构有较好的精度.     

RNA secondary structure, permutations, and statistics

We construct a permutation representation for RNA secondary structure. We also introduce some basic combinatorial statistics for RNA secondary structure and relate them to permutation statistics when appropriate. These statistics allow us to quantify some structural phenomena in RNA secondary structure.     

A new constrained edit distance between quotiented ordered trees

In this paper we propose a dynamic programming algorithm to compare two quotiented ordered trees using a constrained edit distance. An ordered tree is a tree in which the left-to-right order among siblings is significant. A quotiented ordered tree is an ordered tree T with an equivalence relation on vertices and such that, when the equivalence classes are collapsed to super-nodes, the graph so obtained is an ordered tree as well. Based on an algorithm proposed by Zhang and Shasha [K. Zhang, D. Shasha, Simple fast algorithms for the editing distance between trees and related problems, SIAM Journal on Computing 18 (6) (1989) 1245–1262] and introducing new notations, we describe a tree edit distance between quotiented ordered trees preserving equivalence relations on vertices during computation which works in polynomial time. Its application to RNA secondary structures comparison is finally presented.     

Optimization in Multiple-objective Linear Programming Problems with Pre-emptive Priorities

A decision-maker, using mathematical programming optimization models, is often faced with a choice of many alternative solutions optimizing the objective function. The decision may be based on secondary, tertiary or higher-order objectives. Such problems are usually handled using goal programming (GP) with pre-emptive priorities. Pre-emptive prioritization is discussed in the literature in the context of GP. This paper suggests that the two are separable, and presents algorithms to accomplish this. It argues that in a truly pre-emptive situation, direct lexicographical optimization of the objectives, without introduction of goals, has a number of advantages. In addition, when applied to special structure models such as transportation or assignment, this approach enables one to maintain the structure and hence the efficiency of those algorithms.     

一类RNA二级结构的计数

多核苷酸的二级结构可视为一类顶点标号平面图，通常通过枚举每类RNA二级结构图的各种子图来计算其递推公式。本文作者给出了限制端环长度的RNA二级结构的递推公式，并运用隐式估计法计算它的渐近值。     

Dynamical community structure of populations evolving on genotype networks

Neutral evolutionary dynamics of replicators occurs on large and heterogeneous networks of genotypes. These networks, formed by all genotypes that yield the same phenotype, have a complex architecture that conditions the molecular composition of populations and their movements on genome spaces. Here we consider as an example the case of populations evolving on RNA secondary structure neutral networks and study the community structure of the network revealed through dynamical properties of the population at equilibrium and during adaptive transients. We unveil a rich hierarchical community structure that, eventually, can be traced back to the non-trivial relationship between RNA secondary structure and sequence composition. We demonstrate that usual measures of modularity that only take into account the static, topological structure of networks, cannot identify the community structure disclosed by population dynamics.     

Linear programming in tector criterion markov and semi-Markov decision processes

Optimality problems in infinite horizon, discrete time, vector criterion Markov and semi-Markov decision processes are expressed as standard problems of multiobjective linear programming. Processes with discounting, absorbing processes and completely ergodie processes without discounting are investigated. The common properties and special structure of derived multiobjective linear programming problems are overviewed. Computational simplicities associated with these problems in comparison with general multiobjective linear programming problems are discussed. Methods for solving these problems are overviewed and simple numerical examples are given.     

<Emphasis Type="Italic">K</Emphasis>-Sum Linear Programming

In this note we introduce the k-sum linear programming problem (KLP) which subsumes the classical linear programming problem and the minmax linear programming problem. KLP can be transformed into a linear program with an exponential number of additional constraints and one additional variable. Exploiting the special structure of these additional constraints, we show that KLP can be solved in polynomial time. Two promising simplex-based algorithms are also suggested to solve KLP.     

Solving non-linear portfolio optimization problems with the primal-dual interior point method

Stochastic programming is recognized as a powerful tool to help decision making under uncertainty in financial planning. The deterministic equivalent formulations of these stochastic programs have huge dimensions even for moderate numbers of assets, time stages and scenarios per time stage. So far models treated by mathematical programming approaches have been limited to simple linear or quadratic models due to the inability of currently available solvers to solve NLP problems of typical sizes. However stochastic programming problems are highly structured. The key to the efficient solution of such problems is therefore the ability to exploit their structure. Interior point methods are well-suited to the solution of very large non-linear optimization problems. In this paper we exploit this feature and show how portfolio optimization problems with sizes measured in millions of constraints and decision variables, featuring constraints on semi-variance, skewness or non-linear utility functions in the objective, can be solved with the state-of-the-art solver.     

Goal Programming and Allocating Children to Secondary Schools in Reading

The secondary allocation scheme proposed for Reading by Berkshire County Council (B.C.C.) in 1978 has been investigated under the Race Relations Act. After reviewing previous programming studies of devising school catchment areas, this paper uses the technique of goal programming to analyze the problem of proposing catchment areas for the secondary schools in Greater Reading. Six goals are identified: distance, difficulty of journey, racial balance, reading-age retarded balance, sex balance and capacity utilization. The problem is solved for 10 alternative sets of goal weights, and it is shown that most of these dominate the B.C.C. solution.     

The prediction of a protein and nucleic acid structure: Problems and prospects

Recent advances in DNA and protein-sequencing technologies have made an increasing number of primary structures available for theoretical investigations. The prediction of a higher-order protein, and nucleic acid structure in particular, is an area where computational approaches will be able to complement the lack of experimental observations. We review some of the problems related to structure predictions: sequence homology searches, secondary structure prediction in RNAs, and regular structure prediction in proteins. The first two are mathematically well-defined problems, for it is not usually necessary to consider long-range interactions. The solution to a smaller segment is a part of the solution to the entire sequence. Thus, the problem can be solved by dynamic programming algorithms. The prediction of protein structures poses a more complex combinatorial problem, as illustrated in our statistical mechanical treatment. A promising approximation is to calculate locally optimal structures stabilized by relatively short-range interactions, and then to include longer-range effects as interactions between the locally optimal structures.     

Faster,but weaker,relaxations for quadratically constrained quadratic programs

We introduce a new relaxation framework for nonconvex quadratically constrained quadratic programs (QCQPs). In contrast to existing relaxations based on semidefinite programming (SDP), our relaxations incorporate features of both SDP and second order cone programming (SOCP) and, as a result, solve more quickly than SDP. A downside is that the calculated bounds are weaker than those gotten by SDP. The framework allows one to choose a block-diagonal structure for the mixed SOCP-SDP, which in turn allows one to control the speed and bound quality. For a fixed block-diagonal structure, we also introduce a procedure to improve the bound quality without increasing computation time significantly. The effectiveness of our framework is illustrated on a large sample of QCQPs from various sources.     

An integrated model for screening cargo containers

This paper focuses on detecting nuclear weapons on cargo containers using port security screening methods, where the nuclear weapons would presumably be used to attack a target within the United States. This paper provides a linear programming model that simultaneously identifies optimal primary and secondary screening policies in a prescreening-based paradigm, where incoming cargo containers are classified according to their perceived risk. The proposed linear programming model determines how to utilize primary and secondary screening resources in a cargo container screening system given a screening budget, prescreening classifications, and different device costs. Structural properties of the model are examined to shed light on the optimal screening policies. The model is illustrated with a computational example. Sensitivity analysis is performed on the ability of the prescreening in correctly identifying prescreening classifications and secondary screening costs. Results reveal that there are fewer practical differences between the screening policies of the prescreening groups when prescreening is inaccurate. Moreover, devices that can better detect shielded nuclear material have the potential to substantially improve the system’s detection capabilities.     

Power generator scheduling by dynamic programming

Dynamic programming is applied to the problem of determining an optimal short-run schedule for a series of power generating units to meet a time varying system load. Typical scheduling procedures include a priority ordering constraint which requires that units be committed to or removed from power production in a fixed order. A dynamic programming model which relaxes this constraints yields a large combinatorial problem whose state space depends on the number of feasible combinations of generating units. Reduction of storage requirements is achieved through the implementation of data structure techniques. An example of the dynamic programming procedure with data from an actual system suggests significant coast reductions. A comparison with a case in the literature also results in significant savings. Perhaps more important, however, are the substantial energy savings, in light of the current emphasis on energy conservation.     

Optimal solutions for the economic lot-sizing problem with multiple suppliers and cost structures

This paper considers a multi-supplier economic lot-sizing problem in which the retailer replenishes his inventory from several suppliers. Each supplier is characterized by one of three types of order cost structures: incremental quantity discount cost structure, multiple set-ups cost structure and all-unit quantity discount cost structure. The problem is challenging due to the mix of different cost structures. For all cases of the problem where each supplier is characterized by one of the first two cost structures, some optimality properties are proposed and optimal algorithms based on dynamic programming are designed. For the case where all suppliers are characterized by all-unit quantity discount cost structures, it is hard to design a polynomial time algorithm by the analyzed optimal properties. However, it is proved that one of its special cases can be solved in polynomial time.     

Representation of time in mathematical programming modeling languages

Time-staged mathematical programming models have a planning horizon that is divided into a sequence of consecutive time periods. For the modeling of this sequence of time periods the use of calendars is proposed as an additional set concept for mathematical programming modeling languages. The definition of calendars is based on familiar notions such as set, ordering, interval length and functions. A calendar is an interval set and can be used to verify automatically the proper time referencing in stock balances. When a calendar is also a difference set, then backward and forward time referencing can be stated with the explicit use of time units. For models with a rolling horizon, concise and flexible ways to specify the structure of calendars are presented. The aggregation of raw data into model parameter values is supported by linking calendars that represent different time scales. The influence of the proposed calendar concept on the human ability to understand, maintain and verify models is analyzed throughout the paper on the basis of selected examples.     

First-order optimization algorithms via inertial systems with Hessian driven damping

For controlled discrete-time stochastic processes we introduce a new class of dynamic risk measures, which we call process-based. Their main feature is that they measure risk of processes that are functions of the history of a base process. We introduce a new concept of conditional stochastic time consistency and we derive the structure of process-based risk measures enjoying this property. We show that they can be equivalently represented by a collection of static law-invariant risk measures on the space of functions of the state of the base process. We apply this result to controlled Markov processes and we derive dynamic programming equations. We also derive dynamic programming equations for multistage stochastic programming with decision-dependent distributions.

     

Discrete time dynamic multi-leader–follower games with stage-depending leaders under feedback information

Discrete time dynamic Stackelberg games with alternating leaders are recently brought forward by and dynamic programming algorithms are extended to discrete time dynamic Stackelberg games of two players with alternating leaders under feedback information structure. In many practical problems, there are multiple leaders and multiple followers. Moreover, the positions of leaders and followers may change at some stages. We aim to extend the results of discrete time dynamic Stackelberg games with alternating leaders to multi-leader–follower games and to obtain a new type of game, dynamic multi-leader–follower game with stage-depending leaders. To simplify the problem, all players in the model are divided into two groups. At each stage, players in one group act as leaders and the players in other group are followers. In the subsequent stage, the positions may go to the contrary. Actually, whether the players in some group act as leaders or not at some stage, depends on the information at the previous stage(s). Furthermore, dynamic programming algorithms are extended to dynamic multi-leader–follower game with stage-depending leaders under feedback information structure in this paper.