Combinatorial reasoning to solve problems
Coenen, Tom; Hof, Frits; Verhoef, Nellie
2016-01-01
This study reports combinatorial reasoning to solve problems. We observed the mathematical thinking of students aged 14-16. We study the variation of the students’ solution strategies in the context of emergent modelling. The results show that the students are tempted to begin the problem solving pr
Combinatorial problems and exercises
Lovász, László
2007-01-01
The main purpose of this book is to provide help in learning existing techniques in combinatorics. The most effective way of learning such techniques is to solve exercises and problems. This book presents all the material in the form of problems and series of problems (apart from some general comments at the beginning of each chapter). In the second part, a hint is given for each exercise, which contains the main idea necessary for the solution, but allows the reader to practice the techniques by completing the proof. In the third part, a full solution is provided for each problem. This book w
Combinatorial algorithms for the seriation problem
Seminaroti, Matteo
2016-01-01
In this thesis we study the seriation problem, a combinatorial problem arising in data analysis, which asks to sequence a set of objects in such a way that similar objects are ordered close to each other. We focus on the combinatorial structure and properties of Robinsonian matrices, a special class
Advances in bio-inspired computing for combinatorial optimization problems
Pintea, Camelia-Mihaela
2013-01-01
Advances in Bio-inspired Combinatorial Optimization Problems' illustrates several recent bio-inspired efficient algorithms for solving NP-hard problems.Theoretical bio-inspired concepts and models, in particular for agents, ants and virtual robots are described. Large-scale optimization problems, for example: the Generalized Traveling Salesman Problem and the Railway Traveling Salesman Problem, are solved and their results are discussed.Some of the main concepts and models described in this book are: inner rule to guide ant search - a recent model in ant optimization, heterogeneous sensitive a
Grobner Basis Approach to Some Combinatorial Problems
Victor Ufnarovski
2012-10-01
Full Text Available We consider several simple combinatorial problems and discuss different ways to express them using polynomial equations and try to describe the \\GB of the corresponding ideals. The main instruments are complete symmetric polynomials that help to express different conditions in rather compact way.
Grobner Basis Approach to Some Combinatorial Problems
2012-01-01
We consider several simple combinatorial problems and discuss different ways to express them using polynomial equations and try to describe the \\GB of the corresponding ideals. The main instruments are complete symmetric polynomials that help to express different conditions in rather compact way.
Hybrid Genetic Algorithm with PSO Effect for Combinatorial Optimisation Problems
M. H. Mehta
2012-12-01
Full Text Available In engineering field, many problems are hard to solve in some definite interval of time. These problems known as “combinatorial optimisation problems” are of the category NP. These problems are easy to solve in some polynomial time when input size is small but as input size grows problems become toughest to solve in some definite interval of time. Long known conventional methods are not able to solve the problems and thus proper heuristics is necessary. Evolutionary algorithms based on behaviours of different animals and species have been invented and studied for this purpose. Genetic Algorithm is considered a powerful algorithm for solving combinatorial optimisation problems. Genetic algorithms work on these problems mimicking the human genetics. It follows principle of “survival of the fittest” kind of strategy. Particle swarm optimisation is a new evolutionary approach that copies behaviour of swarm in nature. However, neither traditional genetic algorithms nor particle swarm optimisation alone has been completely successful for solving combinatorial optimisation problems. Here a hybrid algorithm is proposed in which strengths of both algorithms are merged and performance of proposed algorithm is compared with simple genetic algorithm. Results show that proposed algorithm works definitely better than the simple genetic algorithm.
Binary Cockroach Swarm Optimization for Combinatorial Optimization Problem
Ibidun Christiana Obagbuwa
2016-09-01
Full Text Available The Cockroach Swarm Optimization (CSO algorithm is inspired by cockroach social behavior. It is a simple and efficient meta-heuristic algorithm and has been applied to solve global optimization problems successfully. The original CSO algorithm and its variants operate mainly in continuous search space and cannot solve binary-coded optimization problems directly. Many optimization problems have their decision variables in binary. Binary Cockroach Swarm Optimization (BCSO is proposed in this paper to tackle such problems and was evaluated on the popular Traveling Salesman Problem (TSP, which is considered to be an NP-hard Combinatorial Optimization Problem (COP. A transfer function was employed to map a continuous search space CSO to binary search space. The performance of the proposed algorithm was tested firstly on benchmark functions through simulation studies and compared with the performance of existing binary particle swarm optimization and continuous space versions of CSO. The proposed BCSO was adapted to TSP and applied to a set of benchmark instances of symmetric TSP from the TSP library. The results of the proposed Binary Cockroach Swarm Optimization (BCSO algorithm on TSP were compared to other meta-heuristic algorithms.
Analysis and design of algorithms for combinatorial problems
Ausiello, G
1985-01-01
Combinatorial problems have been from the very beginning part of the history of mathematics. By the Sixties, the main classes of combinatorial problems had been defined. During that decade, a great number of research contributions in graph theory had been produced, which laid the foundations for most of the research in graph optimization in the following years. During the Seventies, a large number of special purpose models were developed. The impressive growth of this field since has been strongly determined by the demand of applications and influenced by the technological increases in computing power and the availability of data and software. The availability of such basic tools has led to the feasibility of the exact or well approximate solution of large scale realistic combinatorial optimization problems and has created a number of new combinatorial problems.
Spreadsheet modelling for solving combinatorial problems: The vendor selection problem
Ipsilandis, Pandelis G
2008-01-01
Spreadsheets have grown up and became very powerful and easy to use tools in applying analytical techniques for solving business problems. Operations managers, production managers, planners and schedulers can work with them in developing solid and practical Do-It-Yourself Decision Support Systems. Small and Medium size organizations, can apply OR methodologies without the presence of specialized software and trained personnel, which in many cases cannot afford anyway. This paper examines an efficient approach in solving combinatorial programming problems with the use of spreadsheets. A practical application, which demonstrates the approach, concerns the development of a spreadsheet-based DSS for the Multi Item Procurement Problem with Fixed Vendor Cost. The DSS has been build using exclusively standard spreadsheet feature and can solve real problems of substantial size. The benefits and limitations of the approach are also discussed.
Juan, Angel A.; Javier Faulin; Scott E. Grasman; Markus Rabe; Gonçalo Figueira
2015-01-01
Many combinatorial optimization problems (COPs) encountered in real-world logistics, transportation, production, healthcare, financial, telecommunication, and computing applications are NP-hard in nature. These real-life COPs are frequently characterized by their large-scale sizes and the need for obtaining high-quality solutions in short computing times, thus requiring the use of metaheuristic algorithms. Metaheuristics benefit from different random-search and parallelization paradigms, but ...
Fast Combinatorial Algorithm for the Solution of Linearly Constrained Least Squares Problems
Van Benthem, Mark H.; Keenan, Michael R.
2008-11-11
A fast combinatorial algorithm can significantly reduce the computational burden when solving general equality and inequality constrained least squares problems with large numbers of observation vectors. The combinatorial algorithm provides a mathematically rigorous solution and operates at great speed by reorganizing the calculations to take advantage of the combinatorial nature of the problems to be solved. The combinatorial algorithm exploits the structure that exists in large-scale problems in order to minimize the number of arithmetic operations required to obtain a solution.
Neurogenetic Algorithm for Solving Combinatorial Engineering Problems
M. Jalali Varnamkhasti
2012-01-01
Full Text Available Diversity of the population in a genetic algorithm plays an important role in impeding premature convergence. This paper proposes an adaptive neurofuzzy inference system genetic algorithm based on sexual selection. In this technique, for choosing the female chromosome during sexual selection, a bilinear allocation lifetime approach is used to label the chromosomes based on their fitness value which will then be used to characterize the diversity of the population. The motivation of this algorithm is to maintain the population diversity throughout the search procedure. To promote diversity, the proposed algorithm combines the concept of gender and age of individuals and the fuzzy logic during the selection of parents. In order to appraise the performance of the techniques used in this study, one of the chemistry problems and some nonlinear functions available in literature is used.
Space-efficient parallel algorithms for combinatorial search problems
Pietrcaprina, Andrea; Pucci, Geppino; Silvestri, Francesco;
2015-01-01
We present space-efficient parallel strategies for two fundamental combinatorial search problems, namely, backtrack search and branch-and-bound , both involving the visit of an n-node tree of height h under the assumption that a node can be accessed only through its father or its children. For both...... problems we propose efficient algorithms that run on a p-processor distributed-memory machine. For backtrack search, we give a deterministic algorithm running in O(n/p+hlogp) time, and a Las Vegas algorithm requiring optimal O(n/p+h) time, with high probability. Building on the backtrack search algorithm...
Combinatorial particle swarm optimization for solving blocking flowshop scheduling problem
Mansour Eddaly
2016-10-01
Full Text Available This paper addresses to the flowshop scheduling problem with blocking constraints. The objective is to minimize the makespan criterion. We propose a hybrid combinatorial particle swarm optimization algorithm (HCPSO as a resolution technique for solving this problem. At the initialization, different priority rules are exploited. Experimental study and statistical analysis were performed to select the most adapted one for this problem. Then, the swarm behavior is tested for solving a combinatorial optimization problem such as a sequencing problem under constraints. Finally, an iterated local search algorithm based on probabilistic perturbation is sequentially introduced to the particle swarm optimization algorithm for improving the quality of solution. The computational results show that our approach is able to improve several best known solutions of the literature. In fact, 76 solutions among 120 were improved. Moreover, HCPSO outperforms the compared methods in terms of quality of solutions in short time requirements. Also, the performance of the proposed approach is evaluated according to a real-world industrial problem.
Estimating meme fitness in adaptive memetic algorithms for combinatorial problems.
Smith, J E
2012-01-01
Among the most promising and active research areas in heuristic optimisation is the field of adaptive memetic algorithms (AMAs). These gain much of their reported robustness by adapting the probability with which each of a set of local improvement operators is applied, according to an estimate of their current value to the search process. This paper addresses the issue of how the current value should be estimated. Assuming the estimate occurs over several applications of a meme, we consider whether the extreme or mean improvements should be used, and whether this aggregation should be global, or local to some part of the solution space. To investigate these issues, we use the well-established COMA framework that coevolves the specification of a population of memes (representing different local search algorithms) alongside a population of candidate solutions to the problem at hand. Two very different memetic algorithms are considered: the first using adaptive operator pursuit to adjust the probabilities of applying a fixed set of memes, and a second which applies genetic operators to dynamically adapt and create memes and their functional definitions. For the latter, especially on combinatorial problems, credit assignment mechanisms based on historical records, or on notions of landscape locality, will have limited application, and it is necessary to estimate the value of a meme via some form of sampling. The results on a set of binary encoded combinatorial problems show that both methods are very effective, and that for some problems it is necessary to use thousands of variables in order to tease apart the differences between different reward schemes. However, for both memetic algorithms, a significant pattern emerges that reward based on mean improvement is better than that based on extreme improvement. This contradicts recent findings from adapting the parameters of operators involved in global evolutionary search. The results also show that local reward schemes
The hard problem of cooperation.
Kimmo Eriksson
Full Text Available Based on individual variation in cooperative inclinations, we define the "hard problem of cooperation" as that of achieving high levels of cooperation in a group of non-cooperative types. Can the hard problem be solved by institutions with monitoring and sanctions? In a laboratory experiment we find that the answer is affirmative if the institution is imposed on the group but negative if development of the institution is left to the group to vote on. In the experiment, participants were divided into groups of either cooperative types or non-cooperative types depending on their behavior in a public goods game. In these homogeneous groups they repeatedly played a public goods game regulated by an institution that incorporated several of the key properties identified by Ostrom: operational rules, monitoring, rewards, punishments, and (in one condition change of rules. When change of rules was not possible and punishments were set to be high, groups of both types generally abided by operational rules demanding high contributions to the common good, and thereby achieved high levels of payoffs. Under less severe rules, both types of groups did worse but non-cooperative types did worst. Thus, non-cooperative groups profited the most from being governed by an institution demanding high contributions and employing high punishments. Nevertheless, in a condition where change of rules through voting was made possible, development of the institution in this direction was more often voted down in groups of non-cooperative types. We discuss the relevance of the hard problem and fit our results into a bigger picture of institutional and individual determinants of cooperative behavior.
Combinatorial optimization problem solution based on improved genetic algorithm
Zhang, Peng
2017-08-01
Traveling salesman problem (TSP) is a classic combinatorial optimization problem. It is a simplified form of many complex problems. In the process of study and research, it is understood that the parameters that affect the performance of genetic algorithm mainly include the quality of initial population, the population size, and crossover probability and mutation probability values. As a result, an improved genetic algorithm for solving TSP problems is put forward. The population is graded according to individual similarity, and different operations are performed to different levels of individuals. In addition, elitist retention strategy is adopted at each level, and the crossover operator and mutation operator are improved. Several experiments are designed to verify the feasibility of the algorithm. Through the experimental results analysis, it is proved that the improved algorithm can improve the accuracy and efficiency of the solution.
Polyhedral Techniques in Combinatorial Optimization
Aardal, K.I.; van Hoesel, S.
1995-01-01
Combinatorial optimization problems arise in several areas ranging from management to mathematics and graph theory. Most combinatorial optimization problems are compu- tationally hard due to the restriction that a subset of the variables have to take integral values. During the last two decades
Warners, J.P.
1997-01-01
We show how a large class of combinatorial optimization problems can be reformulated as a nonconvex minimization problem over the unit hyper cube with continuous variables. No additional constraints are required; all constraints are incorporated in the n onconvex objective function, which is a polyn
Trajectory and Population Metaheuristics applied to Combinatorial Optimization Problems
Natalia Alancay
2016-04-01
Full Text Available In the world there are a multitude of everyday problems that require a solution that meets a set of requirements in the most appropriate way maximizing or minimizing a certain value. However, finding an optimal solution for certain optimization problems can be an incredibly difficult or an impossible task. This is because when a problem becomes large enough, we have to look through a huge number of possible solutions, the most efficient solution, that is, the one that has the lower cost. The ways to treat feasible solutions for their practical application are varied. One of the strategy that has gained a great acceptance and that has been getting an important formal body are the metaheuristics since it is established strategies to cross and explore the space of solutions of the problem usually generated in a random and iterative way. The main advantage of this technique is their flexibility and robustness, which allows them to be applied to a wide range of problems. In this work we focus on a metaheuristic based on Simulated Annealing trajectory and a population - based Cellular Genetic Algorithm with the objective of carrying out a study and comparison of the results obtained in its application for the resolution of a set of academic problems of combinatorial optimization.
Algorithms and theoretical topics on selected combinatorial optimization problems
Kaveh, Arman
2010-01-01
We study the Quadratic Assignment Problem (QAP), Three Dimensional Assignment Problem (3AP) and Quadratic Three Dimensional Assignment Problem (Q3AP), which combines aspects of both QAP and 3AP. The three problems are known to be NP-hard. We propose new algorithms for obtaining near optimal solutions of QAP and 3AP and present computational results. Our algorithms obtain improved solutions in some benchmark instances of QAP and 3AP. We also discuss theoretical results on 3AP and Q3AP such as ...
AN ADAPTIVE MEMBRANE ALGORITHM FOR SOLVING COMBINATORIAL OPTIMIZATION PROBLEMS
Juanjuan HE; Jianhua XIAO; Zehui SHAO
2014-01-01
Membrane algorithms (MAs), which inherit from P systems, constitute a new parallel and distribute framework for approximate computation. In the paper, a membrane algorithm is proposed with the improvement that the involved parameters can be adaptively chosen. In the algorithm, some membranes can evolve dynamically during the computing process to specify the values of the requested parameters. The new algorithm is tested on a well-known combinatorial optimization problem, the travelling salesman problem. The em-pirical evidence suggests that the proposed approach is efficient and reliable when dealing with 11 benchmark instances, particularly obtaining the best of the known solutions in eight instances. Compared with the genetic algorithm, simulated annealing algorithm, neural net-work and a fine-tuned non-adaptive membrane algorithm, our algorithm performs better than them. In practice, to design the airline network that minimize the total routing cost on the CAB data with twenty-five US cities, we can quickly obtain high quality solutions using our algorithm.
Combinatorial approach to generalized Bell and Stirling numbers and boson normal ordering problem
Mendez, M A; Penson, K A
2005-01-01
We consider the numbers arising in the problem of normal ordering of expressions in canonical boson creation and annihilation operators. We treat a general form of a boson string which is shown to be associated with generalizations of Stirling and Bell numbers. The recurrence relations and closed-form expressions (Dobiski-type formulas) are obtained for these quantities by both algebraic and combinatorial methods. By extensive use of methods of combinatorial analysis we prove the equivalence of the aforementioned problem to the enumeration of special families of graphs. This link provides a combinatorial interpretation of the numbers arising in this normal ordering problem.
Hartmann, Alexander K
2005-01-01
A concise, comprehensive introduction to the topic of statistical physics of combinatorial optimization, bringing together theoretical concepts and algorithms from computer science with analytical methods from physics. The result bridges the gap between statistical physics and combinatorial optimization, investigating problems taken from theoretical computing, such as the vertex-cover problem, with the concepts and methods of theoretical physics. The authors cover rapid developments and analytical methods that are both extremely complex and spread by word-of-mouth, providing all the necessary
New Meta-Heuristic for Combinatorial Optimization Problems:Intersection Based Scaling
Peng Zou; Zhi Zhou; Ying-Yu Wan; Guo-Liang Chen; Jun Gu
2004-01-01
Combinatorial optimization problems are found in many application fields such as computer science, engineering and economy. In this paper, a new efficient meta-heuristic, Intersection-Based Scaling (IBS for abbreviation),is proposed and it can be applied to the combinatorial optimization problems. The main idea of IBS is to scale the size of the instance based on the intersection of some local optima, and to simplify the search space by extracting the intersection from the instance, which makes the search more efficient. The combination of IBS with some local search heuristics of different combinatorial optimization problems such as Traveling Salesman Problem (TSP) and Graph Partitioning Problem (GPP) is studied, and comparisons are made with some of the best heuristic algorithms and meta-heuristic algorithms. It is found that it has significantly improved the performance of existing local search heuristics and significantly outperforms the known best algorithms.
Angel A. Juan
2015-12-01
Full Text Available Many combinatorial optimization problems (COPs encountered in real-world logistics, transportation, production, healthcare, financial, telecommunication, and computing applications are NP-hard in nature. These real-life COPs are frequently characterized by their large-scale sizes and the need for obtaining high-quality solutions in short computing times, thus requiring the use of metaheuristic algorithms. Metaheuristics benefit from different random-search and parallelization paradigms, but they frequently assume that the problem inputs, the underlying objective function, and the set of optimization constraints are deterministic. However, uncertainty is all around us, which often makes deterministic models oversimplified versions of real-life systems. After completing an extensive review of related work, this paper describes a general methodology that allows for extending metaheuristics through simulation to solve stochastic COPs. ‘Simheuristics’ allow modelers for dealing with real-life uncertainty in a natural way by integrating simulation (in any of its variants into a metaheuristic-driven framework. These optimization-driven algorithms rely on the fact that efficient metaheuristics already exist for the deterministic version of the corresponding COP. Simheuristics also facilitate the introduction of risk and/or reliability analysis criteria during the assessment of alternative high-quality solutions to stochastic COPs. Several examples of applications in different fields illustrate the potential of the proposed methodology.
Locating phase transitions in computationally hard problems
B Ashok; T K Patra
2010-09-01
We discuss how phase-transitions may be detected in computationally hard problems in the context of anytime algorithms. Treating the computational time, value and utility functions involved in the search results in analogy with quantities in statistical physics, we indicate how the onset of a computationally hard regime can be detected and the transit to higher quality solutions be quantified by an appropriate response function. The existence of a dynamical critical exponent is shown, enabling one to predict the onset of critical slowing down, rather than finding it after the event, in the specific case of a travelling salesman problem (TSP). This can be used as a means of improving efficiency and speed in searches, and avoiding needless computations.
Using Neighborhood Diversity to Solve Hard Problems
Ganian, Robert
2012-01-01
Parameterized algorithms are a very useful tool for dealing with NP-hard problems on graphs. Yet, to properly utilize parameterized algorithms it is necessary to choose the right parameter based on the type of problem and properties of the target graph class. Tree-width is an example of a very successful graph parameter, however it cannot be used on dense graph classes and there also exist problems which are hard even on graphs of bounded tree-width. Such problems can be tackled by using vertex cover as a parameter, however this places severe restrictions on admissible graph classes. Michael Lampis has recently introduced neighborhood diversity, a new graph parameter which generalizes vertex cover to dense graphs. Among other results, he has shown that simple parameterized algorithms exist for a few problems on graphs of bounded neighborhood diversity. Our article further studies this area and provides new algorithms parameterized by neighborhood diversity for the p-Vertex-Disjoint Paths, Graph Motif and Prec...
An Onto-Semiotic Analysis of Combinatorial Problems and the Solving Processes by University Students
Godino, Juan D.; Batanero, Carmen; Roa, Rafael
2005-01-01
In this paper we describe an ontological and semiotic model for mathematical knowledge, using elementary combinatorics as an example. We then apply this model to analyze the solving process of some combinatorial problems by students with high mathematical training, and show its utility in providing a semiotic explanation for the difficulty of…
A methodology to find the elementary landscape decomposition of combinatorial optimization problems.
Chicano, Francisco; Whitley, L Darrell; Alba, Enrique
2011-01-01
A small number of combinatorial optimization problems have search spaces that correspond to elementary landscapes, where the objective function f is an eigenfunction of the Laplacian that describes the neighborhood structure of the search space. Many problems are not elementary; however, the objective function of a combinatorial optimization problem can always be expressed as a superposition of multiple elementary landscapes if the underlying neighborhood used is symmetric. This paper presents theoretical results that provide the foundation for algebraic methods that can be used to decompose the objective function of an arbitrary combinatorial optimization problem into a sum of subfunctions, where each subfunction is an elementary landscape. Many steps of this process can be automated, and indeed a software tool could be developed that assists the researcher in finding a landscape decomposition. This methodology is then used to show that the subset sum problem is a superposition of two elementary landscapes, and to show that the quadratic assignment problem is a superposition of three elementary landscapes.
Scheduling Internal Audit Activities: A Stochastic Combinatorial Optimization Problem
Rossi, R.; Tarim, S.A.; Hnich, B.; Prestwich, S.; Karacaer, S.
2010-01-01
The problem of finding the optimal timing of audit activities within an organisation has been addressed by many researchers. We propose a stochastic programming formulation with Mixed Integer Linear Programming (MILP) and Constraint Programming (CP) certainty-equivalent models. In experiments neithe
Scheduling Internal Audit Activities: A Stochastic Combinatorial Optimization Problem
Rossi, R.; Tarim, S.A.; Hnich, B.; Prestwich, S.; Karacaer, S.
2010-01-01
The problem of finding the optimal timing of audit activities within an organisation has been addressed by many researchers. We propose a stochastic programming formulation with Mixed Integer Linear Programming (MILP) and Constraint Programming (CP) certainty-equivalent models. In experiments
Concrete Physics Method for Solving NP hard Problem
无
2001-01-01
With a NP hard problem given, we may find a equivalent physicalworld. The rule of the changing of the physical states is simply the algorithm for sol ving the original NP hard problem .It is the most natural algorithm for solving NP hard problems. In this paper we deal with a famous example , the well known NP hard problem--Circles Packing. It shows that our algorithm is dramatically very efficient. We are inspired that, the concrete physics algorithm will alway s be very efficient for NP hard problem.
A Combinatorial Benders’ Cuts Algorithm for the Local Container Drayage Problem
Zhaojie Xue
2015-01-01
Full Text Available This paper examines the local container drayage problem under a special operation mode in which tractors and trailers can be separated; that is, tractors can be assigned to a new task at another location while trailers with containers are waiting for packing or unpacking. Meanwhile, the strategy of sharing empty containers between different customers is also considered to improve the efficiency and lower the operation cost. The problem is formulated as a vehicle routing and scheduling problem with temporal constraints. We adopt combinatorial benders’ cuts algorithm to solve this problem. Numerical experiments are performed on a group of randomly generated instances to test the performance of the proposed algorithm.
Adaptive Uncertainty Resolution in Bayesian Combinatorial Optimization Problems
Guha, Sudipto
2008-01-01
In several applications such as databases, planning, and sensor networks, parameters such as selectivity, load, or sensed values are known only with some associated uncertainty. The performance of such a system (as captured by some objective function over the parameters) is significantly improved if some of these parameters can be probed or observed. In a resource constrained situation, deciding which parameters to observe in order to optimize system performance itself becomes an interesting and important optimization problem. This general problem is the focus of this paper. One of the most important considerations in this framework is whether adaptivity is required for the observations. Adaptive observations introduce blocking or sequential operations in the system whereas non-adaptive observations can be performed in parallel. One of the important questions in this regard is to characterize the benefit of adaptivity for probes and observation. We present general techniques for designing constant factor appr...
Wanneng Shu
2009-01-01
Quantum-inspired genetic algorithm (QGA) is applied to simulated annealing (SA) to develop a class of quantum-inspired simulated annealing genetic algorithm (QSAGA) for combinatorial optimization. With the condition of preserving QGA advantages, QSAGA takes advantage of the SA algorithm so as to avoid premature convergence. To demonstrate its effectiveness and applicability, experiments are carried out on the knapsack problem. The results show that QSAGA performs well, without premature conve...
Some applications of W. Rudin's inequality to problems of combinatorial number theory
Shkredov, I D
2010-01-01
In the paper we obtain some new applications of well--known W. Rudin's theorem concerning lacunary series to problems of combinatorial number theory. We generalize a result of M.-C. Chang on L_2 (L)-norm of Fourier coefficients of a set (here L is a dissociated set), and prove a dual version of the theorem. Our main instrument is computing of eigenvalues of some operators.
On Some Numbers Related to Extremal Combinatorial Sum Problems
D. Petrassi
2014-01-01
Full Text Available Let n, d, and r be three integers such that 1≤r, d≤n. Chiaselotti (2002 defined γn,d,r as the minimum number of the nonnegative partial sums with d summands of a sum ∑1=1nai≥0, where a1,…,an are n real numbers arbitrarily chosen in such a way that r of them are nonnegative and the remaining n-r are negative. Chiaselotti (2002 and Chiaselotti et al. (2008 determine the values of γn,d,r for particular infinite ranges of the integer parameters n, d, and r. In this paper we continue their approach on this problem and we prove the following results: (i γ(n,d,r≤(rd+(rd-1 for all values of n, d, and r such that (d-1/dn-1≤r≤(d-1/dn; (ii γd+2,d,d=d+1.
Fushing Hsieh
2016-11-01
Full Text Available Discrete combinatorial optimization problems in real world are typically defined via an ensemble of potentially high dimensional measurements pertaining to all subjects of a system under study. We point out that such a data ensemble in fact embeds with system's information content that is not directly used in defining the combinatorial optimization problems. Can machine learning algorithms extract such information content and make combinatorial optimizing tasks more efficient? Would such algorithmic computations bring new perspectives into this classic topic of Applied Mathematics and Theoretical Computer Science? We show that answers to both questions are positive. One key reason is due to permutation invariance. That is, the data ensemble of subjects' measurement vectors is permutation invariant when it is represented through a subject-vs-measurement matrix. An unsupervised machine learning algorithm, called Data Mechanics (DM, is applied to find optimal permutations on row and column axes such that the permuted matrix reveals coupled deterministic and stochastic structures as the system's information content. The deterministic structures are shown to facilitate geometry-based divide-and-conquer scheme that helps optimizing task, while stochastic structures are used to generate an ensemble of mimicries retaining the deterministic structures, and then reveal the robustness pertaining to the original version of optimal solution. Two simulated systems, Assignment problem and Traveling Salesman problem, are considered. Beyond demonstrating computational advantages and intrinsic robustness in the two systems, we propose brand new robust optimal solutions. We believe such robust versions of optimal solutions are potentially more realistic and practical in real world settings.
A review of three decades of research on some combinatorial optimization problems
Horacio Hideki Yanasse
2013-04-01
Full Text Available This paper presents an overview of our research in combinatorial optimization problems. Over the last three decades, our team has been studying mostly optimization problems that arise in industrial environments through the elaboration and solution of mathematical decision models. In addition to elaborating innovative models, we have improved upon existing solutions to complex problems, helping decision makers and researchers to better understand complex industrial systems. Our work has focused on the development of computationally more efficient algorithms that improve on existing methods by improving the solution quality or reducing the computation effort to obtain good solutions. While some of our earlier work became less necessary with the speed up of the computational facilities, the search for improved solution quality and reduced computational effort continues. After reviewing our findings on lot sizing, production scheduling, cutting problems, pattern sequencing, tool switches in flexible manufacturing machines and integrated cutting and sequencing problems, we propose topics for future study.
Igeta, Hideki; Hasegawa, Mikio
Chaotic dynamics have been effectively applied to improve various heuristic algorithms for combinatorial optimization problems in many studies. Currently, the most used chaotic optimization scheme is to drive heuristic solution search algorithms applicable to large-scale problems by chaotic neurodynamics including the tabu effect of the tabu search. Alternatively, meta-heuristic algorithms are used for combinatorial optimization by combining a neighboring solution search algorithm, such as tabu, gradient, or other search method, with a global search algorithm, such as genetic algorithms (GA), ant colony optimization (ACO), or others. In these hybrid approaches, the ACO has effectively optimized the solution of many benchmark problems in the quadratic assignment problem library. In this paper, we propose a novel hybrid method that combines the effective chaotic search algorithm that has better performance than the tabu search and global search algorithms such as ACO and GA. Our results show that the proposed chaotic hybrid algorithm has better performance than the conventional chaotic search and conventional hybrid algorithms. In addition, we show that chaotic search algorithm combined with ACO has better performance than when combined with GA.
Zhang, Gexiang; Rong, Haina; Neri, Ferrante; Pérez-Jiménez, Mario J
2014-08-01
Membrane systems (also called P systems) refer to the computing models abstracted from the structure and the functioning of the living cell as well as from the cooperation of cells in tissues, organs, and other populations of cells. Spiking neural P systems (SNPS) are a class of distributed and parallel computing models that incorporate the idea of spiking neurons into P systems. To attain the solution of optimization problems, P systems are used to properly organize evolutionary operators of heuristic approaches, which are named as membrane-inspired evolutionary algorithms (MIEAs). This paper proposes a novel way to design a P system for directly obtaining the approximate solutions of combinatorial optimization problems without the aid of evolutionary operators like in the case of MIEAs. To this aim, an extended spiking neural P system (ESNPS) has been proposed by introducing the probabilistic selection of evolution rules and multi-neurons output and a family of ESNPS, called optimization spiking neural P system (OSNPS), are further designed through introducing a guider to adaptively adjust rule probabilities to approximately solve combinatorial optimization problems. Extensive experiments on knapsack problems have been reported to experimentally prove the viability and effectiveness of the proposed neural system.
Biased Random-Key Genetic Algorithms for the Winner Determination Problem in Combinatorial Auctions.
de Andrade, Carlos Eduardo; Toso, Rodrigo Franco; Resende, Mauricio G C; Miyazawa, Flávio Keidi
2015-01-01
In this paper we address the problem of picking a subset of bids in a general combinatorial auction so as to maximize the overall profit using the first-price model. This winner determination problem assumes that a single bidding round is held to determine both the winners and prices to be paid. We introduce six variants of biased random-key genetic algorithms for this problem. Three of them use a novel initialization technique that makes use of solutions of intermediate linear programming relaxations of an exact mixed integer linear programming model as initial chromosomes of the population. An experimental evaluation compares the effectiveness of the proposed algorithms with the standard mixed linear integer programming formulation, a specialized exact algorithm, and the best-performing heuristics proposed for this problem. The proposed algorithms are competitive and offer strong results, mainly for large-scale auctions.
Polyhredral techniques in combinatorial optimization I: theory
Aardal, K.; Hoesel, S. van
2001-01-01
Combinatorial optimization problems appear in many disciplines ranging from management and logistics to mathematics, physics, and chemistry. These problems are usually relatively easy to formulate mathematically, but most of them are computationally hard due to the restriction that a subset of the v
Tsuchiya, Kazuo; Nishiyama, Takehiro; Tsujita, Katsuyoshi
2001-02-01
We have proposed an optimization method for a combinatorial optimization problem using replicator equations. To improve the solution further, a deterministic annealing algorithm may be applied. During the annealing process, bifurcations of equilibrium solutions will occur and affect the performance of the deterministic annealing algorithm. In this paper, the bifurcation structure of the proposed model is analyzed in detail. It is shown that only pitchfork bifurcations occur in the annealing process, and the solution obtained by the annealing is the branch uniquely connected with the uniform solution. It is also shown experimentally that in many cases, this solution corresponds to a good approximate solution of the optimization problem. Based on the results, a deterministic annealing algorithm is proposed and applied to the quadratic assignment problem to verify its performance.
Kamioka, Shuhei; Takagaki, Tomoaki
2013-09-01
Combinatorial expressions are presented of the solutions to initial value problems of the discrete and ultradiscrete Toda molecules. For the discrete Toda molecule, a subtraction-free expression of the solution is derived in terms of non-intersecting paths, for which two results in combinatorics, Flajolet’s interpretation of continued fractions and Gessel-Viennot’s lemma on determinants, are applied. By ultradiscretizing the subtraction-free expression, the solution to the ultradiscrete Toda molecule is obtained. It is finally shown that the initial value problem of the ultradiscrete Toda molecule is exactly solved in terms of shortest paths on a specific graph. The behavior of the solution is also investigated in comparison with the box-ball system.
Hard graphs for the maximum clique problem
Hoede, Cornelis
1988-01-01
The maximum clique problem is one of the NP-complete problems. There are graphs for which a reduction technique exists that transforms the problem for these graphs into one for graphs with specific properties in polynomial time. The resulting graphs do not grow exponentially in order and number. Gra
Optimal recombination in genetic algorithms for combinatorial optimization problems: Part II
Eremeev Anton V.
2014-01-01
Full Text Available This paper surveys results on complexity of the optimal recombination problem (ORP, which consists in finding the best possible offspring as a result of a recombination operator in a genetic algorithm, given two parent solutions. In Part II, we consider the computational complexity of ORPs arising in genetic algorithms for problems on permutations: the Travelling Salesman Problem, the Shortest Hamilton Path Problem and the Makespan Minimization on Single Machine and some other related problems. The analysis indicates that the corresponding ORPs are NP-hard, but solvable by faster algorithms, compared to the problems they are derived from.
A COMBINATORIAL PROPERTY OF PALLET-CONSTRAINED TWO MACHINE FLOW SHOP PROBLEM IN MINIMIZING MAKESPAN
HOU Sixiang; Han Hoogeveen; Petra Schuurman
2002-01-01
We consider the problem of scheduling n jobs in a pallet-constrained flowshop so as to minimize the makespan. In such a flow shop environment, each job needs apallet the entire time, from the start of its first operation until the completion of the lastoperation, and the number of pallets in the shop at any given time is limited by a positiveinteger K ≤ n. Generally speaking, the optimal schedules may be passing schedules. In thispaper, we present a combinatorial property which shows that for two machines, K(K ≥ 3)pallets, there exists a no-passing schedule which is an optimal schedule for n ≤ 2K - 1 and2K - 1 is tight.
On a combinatorial problem of Erd\\H{o}s, Kleitman and Lemke
Girard, Benjamin
2010-01-01
In this paper, we study a combinatorial problem originating in the following conjecture of Erd{o}s and Lemke: out of n divisors of n, repetitions being allowed, one can always find some of them whose sum is n. Even though Kleitman and Lemke could prove this conjecture, they also noticed that more general results of this form could be derived from the investigation of a certain zero-sum invariant, in the context of finite Abelian groups. Building among others on earlier works by Alon and Dubiner and by the author, our main theorem gives a new upper bound for this invariant in the general case, and provides its right order of magnitude.
The Combinatorial Multi-Mode Resource Constrained Multi-Project Scheduling Problem
Denis Pinha
2016-11-01
Full Text Available This paper presents the formulation and solution of the Combinatorial Multi-Mode Resource Constrained Multi-Project Scheduling Problem. The focus of the proposed method is not on finding a single optimal solution, instead on presenting multiple feasible solutions, with cost and duration information to the project manager. The motivation for developing such an approach is due in part to practical situations where the definition of optimal changes on a regular basis. The proposed approach empowers the project manager to determine what is optimal, on a given day, under the current constraints, such as, change of priorities, lack of skilled worker. The proposed method utilizes a simulation approach to determine feasible solutions, under the current constraints. Resources can be non-consumable, consumable, or doubly constrained. The paper also presents a real-life case study dealing with scheduling of ship repair activities.
The "hard" problem of strong of interactions
Neuberger, Herbert
2010-01-01
This is a write-up of a lecture at the level of a physics colloquium. There exists an idealized mathematical formulation of strong interactions which has no free parameters but is known to describe the real world quite accurately. Over the last three decades the problem has been managed with increasing success. An overview of some facts and a little fiction will be presented, but the question whether the problem can now be considered "easy" will be left unanswered.
Clustering of solutions in hard satisfiability problems
Ardelius, John; Aurell, Erik; Krishnamurthy, Supriya
2007-10-01
We study numerically the solution space structure of random 3-SAT problems close to the SAT/UNSAT transition. This is done by considering chains of satisfiability problems, where clauses are added sequentially to a problem instance. Using the overlap measure of similarity between different solutions found on the same problem instance, we examine geometrical changes as a function of α. In each chain, the overlap distribution is first smooth, but then develops a tiered structure, indicating that the solutions are found in well separated clusters. On chains of not too large instances, all remaining solutions are eventually observed to be found in only one small cluster before vanishing. This condensation transition point is estimated by finite size scaling to be αc = 4.26 with an apparent critical exponent of about 1.7. The average overlap value is also observed to increase with α up to the transition, indicating a reduction in solutions space size, in accordance with theoretical predictions. The solutions are generated by a local heuristic, ASAT, and compared to those found by the Survey Propagation algorithm up to αc.
Combinatorial Algorithms for Portfolio Optimization Problems - Case of Risk Moderate Investor
Juarna, A.
2017-03-01
Portfolio optimization problem is a problem of finding optimal combination of n stocks from N ≥ n available stocks that gives maximal aggregate return and minimal aggregate risk. In this paper given N = 43 from the IDX (Indonesia Stock Exchange) group of the 45 most-traded stocks, known as the LQ45, with p = 24 data of monthly returns for each stock, spanned over interval 2013-2014. This problem actually is a combinatorial one where its algorithm is constructed based on two considerations: risk moderate type of investor and maximum allowed correlation coefficient between every two eligible stocks. The main outputs resulted from implementation of the algorithms is a multiple curve of three portfolio’s attributes, e.g. the size, the ratio of return to risk, and the percentage of negative correlation coefficient for every two chosen stocks, as function of maximum allowed correlation coefficient between each two stocks. The output curve shows that the portfolio contains three stocks with ratio of return to risk at 14.57 if the maximum allowed correlation coefficient between every two eligible stocks is negative and contains 19 stocks with maximum allowed correlation coefficient 0.17 to get maximum ratio of return to risk at 25.48.
Sabar, Nasser R; Ayob, Masri; Kendall, Graham; Qu, Rong
2015-02-01
Hyper-heuristics are search methodologies that aim to provide high-quality solutions across a wide variety of problem domains, rather than developing tailor-made methodologies for each problem instance/domain. A traditional hyper-heuristic framework has two levels, namely, the high level strategy (heuristic selection mechanism and the acceptance criterion) and low level heuristics (a set of problem specific heuristics). Due to the different landscape structures of different problem instances, the high level strategy plays an important role in the design of a hyper-heuristic framework. In this paper, we propose a new high level strategy for a hyper-heuristic framework. The proposed high-level strategy utilizes a dynamic multiarmed bandit-extreme value-based reward as an online heuristic selection mechanism to select the appropriate heuristic to be applied at each iteration. In addition, we propose a gene expression programming framework to automatically generate the acceptance criterion for each problem instance, instead of using human-designed criteria. Two well-known, and very different, combinatorial optimization problems, one static (exam timetabling) and one dynamic (dynamic vehicle routing) are used to demonstrate the generality of the proposed framework. Compared with state-of-the-art hyper-heuristics and other bespoke methods, empirical results demonstrate that the proposed framework is able to generalize well across both domains. We obtain competitive, if not better results, when compared to the best known results obtained from other methods that have been presented in the scientific literature. We also compare our approach against the recently released hyper-heuristic competition test suite. We again demonstrate the generality of our approach when we compare against other methods that have utilized the same six benchmark datasets from this test suite.
Concepts of combinatorial optimization
Paschos, Vangelis Th
2014-01-01
Combinatorial optimization is a multidisciplinary scientific area, lying in the interface of three major scientific domains: mathematics, theoretical computer science and management. The three volumes of the Combinatorial Optimization series aim to cover a wide range of topics in this area. These topics also deal with fundamental notions and approaches as with several classical applications of combinatorial optimization.Concepts of Combinatorial Optimization, is divided into three parts:- On the complexity of combinatorial optimization problems, presenting basics about worst-case and randomi
Kanazawa, Takahiko; Yasuda, Keiichiro
Metaheuristics is a new paradigm that aims to obtain an approximate solution within a feasible computation time. To design the effective metaheuristics, strategies of intensification and diversification are essential. This paper proposes an algorithm that has long term policy for realizing intensification and diversification based on higher level structure in solution space. In order to verify the performance, the proposed algorithm is applied to some traveling salesman problems which are typical combinatorial optimization problems.
Chefi Triki
2016-08-01
Full Text Available We address in this paper a periodic petroleum station replenishment problem (PPSRP that aims to plan the delivery of petroleum products to a set of geographically dispatched stations. It is assumed that each station is characterized by its weekly demand and by its frequency of service. The main objective of the delivery process is to minimize the total travelled distance by the vailable trucks over an extended planning horizon. The problem configuration is described through a set of trucks with several compartments each and a set of stations with demands and prefixed delivery frequencies. Given such input data, the minimization of the total distance is subject to assignment and routing constraints that express the capacity limitations of each truck's compartment in terms of the frequency and the pathways' restrictions. In this paper, we develop and solve the full space mathematical formulation for the PPSRP with application to the Omani context. Our ultimate aim is to include such a model into an integrated framework having the objective of advising petroleum distribution companies on how to prepare bids in case of participation in combinatorial auctions of the transportation procurement.
Spacetime Holism and the Hard Problem of Consciousness
Winkler, Franz-Günter
2006-06-01
We suppose that the reason for the obvious hardness of the so-called hard problem of consciousness lies in two implicit assumptions characteristic of western thinking. The assumption of the fundamental existence of the object and the assumption of the fundamental existence of the self cannot both be valid, if something like a psychophysical link is taken for granted. Other than monistic approaches that are incompatible with one of the two assumptions, we strictly reject both assumptions. Spacetime holism, which in the first place is a view of the material world, can be extended by an assumption on the nature of consciousness, thus providing the basis for a non-reductive solution to the hard problem of consciousness.
Vladimir A. Emelichev
2004-06-01
Full Text Available We consider one type of stability (quasistability of a vector combinatorial problem of finding the Pareto set. Under quasistability we understand a discrete analogue of lower semicontinuity by Hausdorff of the many-valued mapping, which defines the Pareto choice function. A vector problem on a system of subsets of a finite set (trajectorial problem with non-linear partial criteria is in focus. Two necessary and sufficient conditions for stability of this problem are proved. Mathematics Subject Classification: 2000, 90C10, 90C05, 90C29, 90C31
The Hard Truth: Problems and Issues in Urban School Reform
Yisrael, Sean
2012-01-01
"The Hard Truth" is a book written for principals and school administrators who want to implement effective change. The topics of the book candidly discuss the problems, people, and issues that get in the way of true school reform; and what building level principals can personally do attain the best possible outcomes.
The Hard Truth: Problems and Issues in Urban School Reform
Yisrael, Sean
2012-01-01
"The Hard Truth" is a book written for principals and school administrators who want to implement effective change. The topics of the book candidly discuss the problems, people, and issues that get in the way of true school reform; and what building level principals can personally do attain the best possible outcomes.
Replication-based Inference Algorithms for Hard Computational Problems
Alamino, Roberto C.; Neirotti, Juan P.; Saad, David
2013-01-01
Inference algorithms based on evolving interactions between replicated solutions are introduced and analyzed on a prototypical NP-hard problem - the capacity of the binary Ising perceptron. The efficiency of the algorithm is examined numerically against that of the parallel tempering algorithm, showing improved performance in terms of the results obtained, computing requirements and simplicity of implementation.
Hen, Itay; Rieffel, Eleanor G.; Do, Minh; Venturelli, Davide
2014-01-01
There are two common ways to evaluate algorithms: performance on benchmark problems derived from real applications and analysis of performance on parametrized families of problems. The two approaches complement each other, each having its advantages and disadvantages. The planning community has concentrated on the first approach, with few ways of generating parametrized families of hard problems known prior to this work. Our group's main interest is in comparing approaches to solving planning problems using a novel type of computational device - a quantum annealer - to existing state-of-the-art planning algorithms. Because only small-scale quantum annealers are available, we must compare on small problem sizes. Small problems are primarily useful for comparison only if they are instances of parametrized families of problems for which scaling analysis can be done. In this technical report, we discuss our approach to the generation of hard planning problems from classes of well-studied NP-complete problems that map naturally to planning problems or to aspects of planning problems that many practical planning problems share. These problem classes exhibit a phase transition between easy-to-solve and easy-to-show-unsolvable planning problems. The parametrized families of hard planning problems lie at the phase transition. The exponential scaling of hardness with problem size is apparent in these families even at very small problem sizes, thus enabling us to characterize even very small problems as hard. The families we developed will prove generally useful to the planning community in analyzing the performance of planning algorithms, providing a complementary approach to existing evaluation methods. We illustrate the hardness of these problems and their scaling with results on four state-of-the-art planners, observing significant differences between these planners on these problem families. Finally, we describe two general, and quite different, mappings of planning
José Antonio Martín H
Full Text Available Many practical problems in almost all scientific and technological disciplines have been classified as computationally hard (NP-hard or even NP-complete. In life sciences, combinatorial optimization problems frequently arise in molecular biology, e.g., genome sequencing; global alignment of multiple genomes; identifying siblings or discovery of dysregulated pathways. In almost all of these problems, there is the need for proving a hypothesis about certain property of an object that can be present if and only if it adopts some particular admissible structure (an NP-certificate or be absent (no admissible structure, however, none of the standard approaches can discard the hypothesis when no solution can be found, since none can provide a proof that there is no admissible structure. This article presents an algorithm that introduces a novel type of solution method to "efficiently" solve the graph 3-coloring problem; an NP-complete problem. The proposed method provides certificates (proofs in both cases: present or absent, so it is possible to accept or reject the hypothesis on the basis of a rigorous proof. It provides exact solutions and is polynomial-time (i.e., efficient however parametric. The only requirement is sufficient computational power, which is controlled by the parameter α∈N. Nevertheless, here it is proved that the probability of requiring a value of α>k to obtain a solution for a random graph decreases exponentially: P(α>k≤2(-(k+1, making tractable almost all problem instances. Thorough experimental analyses were performed. The algorithm was tested on random graphs, planar graphs and 4-regular planar graphs. The obtained experimental results are in accordance with the theoretical expected results.
Solving the hard problem of Bertrand's paradox
Aerts, Diederik, E-mail: diraerts@vub.ac.be [Center Leo Apostel for Interdisciplinary Studies and Department of Mathematics, Brussels Free University, Brussels (Belgium); Sassoli de Bianchi, Massimiliano, E-mail: autoricerca@gmail.com [Laboratorio di Autoricerca di Base, Lugano (Switzerland)
2014-08-15
Bertrand's paradox is a famous problem of probability theory, pointing to a possible inconsistency in Laplace's principle of insufficient reason. In this article, we show that Bertrand's paradox contains two different problems: an “easy” problem and a “hard” problem. The easy problem can be solved by formulating Bertrand's question in sufficiently precise terms, so allowing for a non-ambiguous modelization of the entity subjected to the randomization. We then show that once the easy problem is settled, also the hard problem becomes solvable, provided Laplace's principle of insufficient reason is applied not to the outcomes of the experiment, but to the different possible “ways of selecting” an interaction between the entity under investigation and that producing the randomization. This consists in evaluating a huge average over all possible “ways of selecting” an interaction, which we call a universal average. Following a strategy similar to that used in the definition of the Wiener measure, we calculate such universal average and therefore solve the hard problem of Bertrand's paradox. The link between Bertrand's problem of probability theory and the measurement problem of quantum mechanics is also briefly discussed.
E. Osaba
2014-01-01
Full Text Available Since their first formulation, genetic algorithms (GAs have been one of the most widely used techniques to solve combinatorial optimization problems. The basic structure of the GAs is known by the scientific community, and thanks to their easy application and good performance, GAs are the focus of a lot of research works annually. Although throughout history there have been many studies analyzing various concepts of GAs, in the literature there are few studies that analyze objectively the influence of using blind crossover operators for combinatorial optimization problems. For this reason, in this paper a deep study on the influence of using them is conducted. The study is based on a comparison of nine techniques applied to four well-known combinatorial optimization problems. Six of the techniques are GAs with different configurations, and the remaining three are evolutionary algorithms that focus exclusively on the mutation process. Finally, to perform a reliable comparison of these results, a statistical study of them is made, performing the normal distribution z-test.
Osaba, E; Carballedo, R; Diaz, F; Onieva, E; de la Iglesia, I; Perallos, A
2014-01-01
Since their first formulation, genetic algorithms (GAs) have been one of the most widely used techniques to solve combinatorial optimization problems. The basic structure of the GAs is known by the scientific community, and thanks to their easy application and good performance, GAs are the focus of a lot of research works annually. Although throughout history there have been many studies analyzing various concepts of GAs, in the literature there are few studies that analyze objectively the influence of using blind crossover operators for combinatorial optimization problems. For this reason, in this paper a deep study on the influence of using them is conducted. The study is based on a comparison of nine techniques applied to four well-known combinatorial optimization problems. Six of the techniques are GAs with different configurations, and the remaining three are evolutionary algorithms that focus exclusively on the mutation process. Finally, to perform a reliable comparison of these results, a statistical study of them is made, performing the normal distribution z-test.
Osaba, E.; Carballedo, R.; Diaz, F.; Onieva, E.; de la Iglesia, I.; Perallos, A.
2014-01-01
Since their first formulation, genetic algorithms (GAs) have been one of the most widely used techniques to solve combinatorial optimization problems. The basic structure of the GAs is known by the scientific community, and thanks to their easy application and good performance, GAs are the focus of a lot of research works annually. Although throughout history there have been many studies analyzing various concepts of GAs, in the literature there are few studies that analyze objectively the influence of using blind crossover operators for combinatorial optimization problems. For this reason, in this paper a deep study on the influence of using them is conducted. The study is based on a comparison of nine techniques applied to four well-known combinatorial optimization problems. Six of the techniques are GAs with different configurations, and the remaining three are evolutionary algorithms that focus exclusively on the mutation process. Finally, to perform a reliable comparison of these results, a statistical study of them is made, performing the normal distribution z-test. PMID:25165731
A COMBINATORIAL APPROACH TO THE OXIDATION RESISTANCE OF(Ti,Al)N AND Ti-Al-Si-N HARD COATINGS
R.Cremer; D.Neuschütz
2002-01-01
The increasing complexity of modern functional materials leads to the demand of acost efficient tool for the development of new products. One possible approach to thisquestion is the adaptation of combinatorial methods to the specific requirements of ma-terials industry. These methods, originally developed for the pharmaceutical industry,have recently been applied to the screening of superconductive, magnetoresistant andphotoluminescent materials. The principle of these combinatorial approaches is thedeposition of large materials libraries in one process combined with fast methods forthe determination of the resulting properties. In this paper, the deposition and charac-terization of laterally graded materials libraries (composition spread) is presented. Thefilms have been deposited by reactive magnetron sputtering, using two or three metallictargets at a low angle to the substrate surface as well as a system of apertures. Toillustrate the advantages of combinatorial approaches for the development of advancedmaterials, the multicomponent metastable hardcoatings (Ti, Al)N and Ti-Al-Si-N arediscussed with special emphasis on the relations between structure and composition onthe one hand and the oxidation resistance of these coatings on the other. The resultsillustrate that the composition spread approach is a powerful and cost efficient tool forthe development and optimization of new multicomponent functional materials.
Oscar Montiel
2015-01-01
Full Text Available Nowadays, solving optimally combinatorial problems is an open problem. Determining the best arrangement of elements proves being a very complex task that becomes critical when the problem size increases. Researchers have proposed various algorithms for solving Combinatorial Optimization Problems (COPs that take into account the scalability; however, issues are still presented with larger COPs concerning hardware limitations such as memory and CPU speed. It has been shown that the Reduce-Optimize-Expand (ROE method can solve COPs faster with the same resources; in this methodology, the reduction step is the most important procedure since inappropriate reductions, applied to the problem, will produce suboptimal results on the subsequent stages. In this work, an algorithm to improve the reduction step is proposed. It is based on a fuzzy inference system to classify portions of the problem and remove them, allowing COPs solving algorithms to utilize better the hardware resources by dealing with smaller problem sizes, and the use of metadata and adaptive heuristics. The Travelling Salesman Problem has been used as a case of study; instances that range from 343 to 3056 cities were used to prove that the fuzzy logic approach produces a higher percentage of successful reductions.
Structural qualia: a solution to the hard problem of consciousness
Kristjan eLoorits
2014-03-01
Full Text Available The hard problem of consciousness has been often claimed to be unsolvable by the methods of traditional empirical sciences. It has been argued that all the objects of empirical sciences can be fully analyzed in structural terms but that consciousness is (or has something over and above its structure. However, modern neuroscience has introduced a theoretical framework in which also the apparently non-structural aspects of consciousness, namely the so called qualia or qualitative properties, can be analyzed in structural terms. That framework allows us to see qualia as something compositional with internal structures that fully determine their qualitative nature. Moreover, those internal structures can be identified which certain neural patterns. Thus consciousness as a whole can be seen as a complex neural pattern that misperceives some of its own highly complex structural properties as monadic and qualitative. Such neural pattern is analyzable in fully structural terms and thereby the hard problem is solved.
Structural qualia: a solution to the hard problem of consciousness
Loorits, Kristjan
2014-01-01
The hard problem of consciousness has been often claimed to be unsolvable by the methods of traditional empirical sciences. It has been argued that all the objects of empirical sciences can be fully analyzed in structural terms but that consciousness is (or has) something over and above its structure. However, modern neuroscience has introduced a theoretical framework in which also the apparently non-structural aspects of consciousness, namely the so called qualia or qualitative properties, can be analyzed in structural terms. That framework allows us to see qualia as something compositional with internal structures that fully determine their qualitative nature. Moreover, those internal structures can be identified which certain neural patterns. Thus consciousness as a whole can be seen as a complex neural pattern that misperceives some of its own highly complex structural properties as monadic and qualitative. Such neural pattern is analyzable in fully structural terms and thereby the hard problem is solved. PMID:24672510
Nelson Maculan
2003-01-01
Full Text Available We present integer linear models with a polynomial number of variables and constraints for combinatorial optimization problems in graphs: optimum elementary cycles, optimum elementary paths and optimum tree problems.Apresentamos modelos lineares inteiros com um número polinomial de variáveis e restrições para problemas de otimização combinatória em grafos: ciclos elementares ótimos, caminhos elementares ótimos e problemas em árvores ótimas.
Sagnol, Guillaume
2010-01-01
The theory of "optimal experimental design" explains how to best select experiments in order to estimate a set of parameters. The quality of the estimation can be measured by the confidence ellipsoids of a certain estimator. This leads to concave maximization problems in which the objective function is nondecreasing with respect to the L\\"owner ordering of symmetric matrices, and is applied to the "information matrix" describing the structure of these confidence ellipsoids. In a number of real-world applications, the variables controlling the experimental design are discrete, or binary. This paper provides approximability bounds for this NP-hard problem. In particular, we establish a matrix inequality which shows that the objective function is submodular, from which it follows that the greedy approach, which has often been used for this problem, always gives a design within $1-1/e$ of the optimum. We next study the design found by rounding the solution of the continuous relaxed problem, an approach which has ...
Normal Order: Combinatorial Graphs
Solomon, A I; Blasiak, P; Horzela, A; Penson, K A; Solomon, Allan I.; Duchamp, Gerard; Blasiak, Pawel; Horzela, Andrzej; Penson, Karol A.
2004-01-01
A conventional context for supersymmetric problems arises when we consider systems containing both boson and fermion operators. In this note we consider the normal ordering problem for a string of such operators. In the general case, upon which we touch briefly, this problem leads to combinatorial numbers, the so-called Rook numbers. Since we assume that the two species, bosons and fermions, commute, we subsequently restrict ourselves to consideration of a single species, single-mode boson monomials. This problem leads to elegant generalisations of well-known combinatorial numbers, specifically Bell and Stirling numbers. We explicitly give the generating functions for some classes of these numbers. In this note we concentrate on the combinatorial graph approach, showing how some important classical results of graph theory lead to transparent representations of the combinatorial numbers associated with the boson normal ordering problem.
Nielsen, John
1994-01-01
An overview of combinatorial chemistry is presented. Combinatorial chemistry, sometimes referred to as `irrational drug design,' involves the generation of molecular diversity. The resulting chemical library is then screened for biologically active compounds.......An overview of combinatorial chemistry is presented. Combinatorial chemistry, sometimes referred to as `irrational drug design,' involves the generation of molecular diversity. The resulting chemical library is then screened for biologically active compounds....
Nielsen, John
1994-01-01
An overview of combinatorial chemistry is presented. Combinatorial chemistry, sometimes referred to as `irrational drug design,' involves the generation of molecular diversity. The resulting chemical library is then screened for biologically active compounds.......An overview of combinatorial chemistry is presented. Combinatorial chemistry, sometimes referred to as `irrational drug design,' involves the generation of molecular diversity. The resulting chemical library is then screened for biologically active compounds....
The Sorting Buffer Problem is NP-hard
Chan, Ho-Leung; van Stee, Rob; Sitters, Rene
2010-01-01
We consider the offline sorting buffer problem. The input is a sequence of items of different types. All items must be processed one by one by a server. The server is equipped with a random-access buffer of limited capacity which can be used to rearrange items. The problem is to design a scheduling strategy that decides upon the order in which items from the buffer are sent to the server. Each type change incurs unit cost, and thus, the cost minimizing objective is to minimize the total number of type changes for serving the entire sequence. This problem is motivated by various applications in manufacturing processes and computer science, and it has attracted significant attention in the last few years. The main focus has been on online competitive algorithms. Surprisingly little is known on the basic offline problem. In this paper, we show that the sorting buffer problem with uniform cost is NP-hard and, thus, close one of the most fundamental questions for the offline problem. On the positive side, we give ...
Machado, Marcelo Dornellas; Schirru, Roberto [Universidade Federal, Rio de Janeiro, RJ (Brazil). Coordenacao dos Programas de Pos-graduacao de Engenharia. Programa de Engenharia Nuclear
2000-07-01
Genetic algorithms are biologically motivated adaptive systems which have been used, with good results, for combinatorial problems optimization. In this work, a new learning mode, to be used by the population-based incremental learning algorithm, has the aim to build a new evolutionary algorithm to be used in optimization of numerical problems and combinatorial problems. This new learning mode uses a variable learning rate during the optimization process, constituting a process known as proportional reward. The development of this new algorithm aims its application in the optimization of reload problem of PWR nuclear reactors, in order to increase the useful life of the nuclear fuel. For the test, two classes of problems are used: numerical problems and combinatorial problems. Due to the fact that the reload problem is a combinatorial problem, the major interest relies on the last class. The results achieved with the tests indicate the applicability of the new learning mode, showing its potential as a developing tool in the solution of reload problem. (author)
Some combinatorial problems on binary rooted trees occurring in population genetics
Disanto, Filippo
2011-01-01
Models in evolutionary biology are intimately linked to the tree paradigm. Given a direction by time, ancestry relationship between species, individuals, alleles or cells can be depicted as a rooted tree. Of particular interest are binary rooted unordered trees. These can be further classified into shape trees, phylogenetic trees, ranked trees and labelled ranked trees. In this work we want to focus on several combinatorial aspects concerning these classes of trees. We consider numerations and probabilistic properties of these trees when generated under the random coalescent process. We derive several summary statistics which serve to characterize 'typical' trees.
Integer and combinatorial optimization
Nemhauser, George L
1999-01-01
Rave reviews for INTEGER AND COMBINATORIAL OPTIMIZATION ""This book provides an excellent introduction and survey of traditional fields of combinatorial optimization . . . It is indeed one of the best and most complete texts on combinatorial optimization . . . available. [And] with more than 700 entries, [it] has quite an exhaustive reference list.""-Optima ""A unifying approach to optimization problems is to formulate them like linear programming problems, while restricting some or all of the variables to the integers. This book is an encyclopedic resource for such f
钱巍; 冯玉强; 唐振宇
2012-01-01
迄今为止,组合拍卖竞胜标问题并不存在一个多项式时间复杂度的算法,其计算复杂性与拍卖效率之间的矛盾一直是影响组合拍卖广泛应用的主要障碍.它是一个NP难问题,也是组合拍卖机制设计中的难题之一.而有穷损害优先方法是纯粹递归论中的一个十分重要的现代方法,特别对NP难问题求解算法的设计,对研究依复杂度决定的偏序结构的构造是一个很基本的有用工具.因此,本文提出根据组合拍卖的内在特性,将各不同的拍卖商品按照拍卖机制的要求,并结合其自身的协同价值等因素,设定一个优先序,然后采用有穷损害优先法有效有序地解决.%So far, the winner determination problem in combinatorial auctions has not had a polynomial time complexity algorithm. It is an NP-hard problem. The finite injury priority method is one of the very important modern methods in recursion theory. In particular, it is a very useful tool or designing the NP-hard problem solving algorithm according to the complexity of the of the partial order structure. So, an approximate algorithm is proposed for solving the well-known NP hard problem-the winner determination problem in combinatorial auctions.
De Vincenzo, Ilario; Carbone, Giuseppe
2016-01-01
A large number of optimization algorithms have been developed by researchers to solve a variety of complex problems in operations management area. We present a novel optimization algorithm belonging to the class of swarm intelligence optimization methods. The algorithm mimics the decision making process of human groups and exploits the dynamics of this process as an optimization tool for combinatorial problems. In order to achieve this aim, a continuous-time Markov process is proposed to describe the behavior of a population of socially interacting agents, modelling how humans in a group modify their opinions driven by self-interest and consensus seeking. As in the case of a collection of spins, the dynamics of such a system is characterized by a phase transition from low to high values of the overall consenus (magnetization). We recognize this phase transition as being associated with the emergence of a collective superior intelligence of the population. While this state being active, a cooling schedule is a...
Digital Signature Scheme Based on a New Hard Problem
Nikolay A. Moldovyan
2008-07-01
Full Text Available Factorizing composite number n=qr, where q and r are two large primes, and finding discrete logarithm modulo large prime number p are two difficult computational problems which are usually put into the base of different digital signature schemes (DSSes. This paper introduces a new hard computational problem that consists in finding the k th roots modulo large prime p=Nk2+1 where N is an even number and k is a prime with the length |k|≥160. Difficulty of the last problem is estimated as O(√k. It is proposed a new DSS with the public key xkmodp, where x is the private key. The signature corresponding to some message M represents a pair of the |p|$-bit numbers S and R calculated as follows: R=tk mod p and S=txf(R,Mmodp, where f(R, M is a compression function. The verification equation is Sk mod p=yf(R, MRmodp. The DSS is used to implement an efficient protocol for generating collective digital signatures.
Communities of minima in local optima networks of combinatorial spaces
Daolio, Fabio; Tomassini, Marco; Vérel, Sébastien; Ochoa, Gabriela
2011-05-01
In this work, we present a new methodology to study the structure of the configuration spaces of hard combinatorial problems. It consists in building the network that has as nodes the locally optimal configurations and as edges the weighted oriented transitions between their basins of attraction. We apply the approach to the detection of communities in the optima networks produced by two different classes of instances of a hard combinatorial optimization problem: the quadratic assignment problem (QAP). We provide evidence indicating that the two problem instance classes give rise to very different configuration spaces. For the so-called real-like class, the networks possess a clear modular structure, while the optima networks belonging to the class of random uniform instances are less well partitionable into clusters. This is convincingly supported by using several statistical tests. Finally, we briefly discuss the consequences of the findings for heuristically searching the corresponding problem spaces.
高小平; 左爱军
2013-01-01
Combinatorial auctions winner determination problem is NP-hard. In order to solve this problem, a new algorithm named memetic algorithm (MA) was proposed. The results show that memetic algorithm in solving the problem with good stability, high quality solution, fast convergence and high computing efficiency, can improve efficiency of combinatorial auctions compare to genetic algorithm and simulated annealing algorithm.%针对组合拍卖竞胜标决定问题（WDP）这一NP难题，提出利用文化基因算法（Memetic Algorithm）对其进行求解。结果表明其在求解该问题上相比遗传算法、模拟退火算法具有稳定性好，求解质量高，收敛速度快，运算效率高的特点，能够提高组合拍卖的效率。
组合优化调度问题求解方法%The Approach to Solving Combinatorial Optimization Schedule Problems
张居阳; 孙吉贵
2003-01-01
Optimization schedule problem is this kind of problem that people often meet in the field of industrial manufacture,transportation and traffic. A good schedule scheme can improve the efficiency of production and reduce the cost of production. So scholars in all of the related fields have high regard for schedule problem at all times. This paper describes the method and technology about combinatorial optimization schedule problems. The research state and advances in this field are reviewed and surveyed. At the end of the paper an approach to solving Job Shop problem,a representative paradigm in schedule problem ,is introduced and discussed concretely.
Wos, L.; McCune, W.
1988-01-01
In this paper, we offer a set of problems for evaluating the power of automated theorem-proving programs and the potential of new ideas. Since the problems published in the proceedings of the first CADE conference proved to be so useful, and since researchers are now far more disposed to implementing and testing their ideas, a new set of problems to complement those that have been widely studied is in order. In general, the new problems provide a far greater challenge for an automated theorem-proving program than those in the first set do. Indeed, to our knowledge, five of the six problems we propose for study have never been proved with a theorem-proving program. For each problem, we give a set of statements that can easily be translated into a standard set of clauses. We also state each problem in its mathematical and logical form. In many cases, we also provide a proof of the theorem from which a problem is taken so that one can measure a program's progress in its attempt to solve the problem. Two of the theorems we discuss are of especial interest in that they answer questions that had been open concerning the constructibility of two types of combinator. We also include a brief description of a new strategy for restricting the application of paramodulation. All of the problems we propose for study emphasize the role of equality. This paper is tutorial in nature.
Buer, Tobias
2012-01-01
The bi-objective winner determination problem (2WDP-SC) of a combinatorial procurement auction for transport contracts comes up to a multi-criteria set covering problem. We are given a set B of bundle bids. A bundle bid b in B consists of a bidding carrier c_b, a bid price p_b, and a set tau_b of transport contracts which is a subset of the set T of tendered transport contracts. Additionally, the transport quality q_t,c_b is given which is expected to be realized when a transport contract t is executed by a carrier c_b. The task of the auctioneer is to find a set X of winning bids (X is subset of B), such that each transport contract is part of at least one winning bid, the total procurement costs are minimized, and the total transport quality is maximized. This article presents a metaheuristic approach for the 2WDP-SC which integrates the greedy randomized adaptive search procedure, large neighborhood search, and self-adaptive parameter setting in order to find a competitive set of non-dominated solutions. T...
A Comparison of Approaches for Solving Hard Graph-Theoretic Problems
2015-05-01
A Comparison of Approaches for Solving Hard Graph- Theoretic Problems Victoria Horan ∗ Air Force Research Laboratory Information Directorate Steve...Comparison of Approaches for Solving Hard Graph- Theoretic Problems 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) 5d...Minimizing the Size of an Identifying or Locating-Dominating Code in a Graph is NP- Hard ”, Theoret . Comput. Sci., 290 (2003) no. 3, 2109-2120. [4] M.G
Takabe, Satoshi; Hukushima, Koji
2016-05-01
Typical behavior of the linear programming (LP) problem is studied as a relaxation of the minimum vertex cover (min-VC), a type of integer programming (IP) problem. A lattice-gas model on the Erdös-Rényi random graphs of α -uniform hyperedges is proposed to express both the LP and IP problems of the min-VC in the common statistical mechanical model with a one-parameter family. Statistical mechanical analyses reveal for α =2 that the LP optimal solution is typically equal to that given by the IP below the critical average degree c =e in the thermodynamic limit. The critical threshold for good accuracy of the relaxation extends the mathematical result c =1 and coincides with the replica symmetry-breaking threshold of the IP. The LP relaxation for the minimum hitting sets with α ≥3 , minimum vertex covers on α -uniform random graphs, is also studied. Analytic and numerical results strongly suggest that the LP relaxation fails to estimate optimal values above the critical average degree c =e /(α -1 ) where the replica symmetry is broken.
Synchronization Patterns and Related Problems in Combinatorial Analysis and Graph Theory
1981-06-01
Costas type when n is 1 or 2 less than a power of a prime . It is still an open problem to prove that an nxn pattern with n dots exists for all n...nodeset - F, with an edge between nodes X and Y iff IX r) YI - 1. 54 For a proof of the above fact, please refer to P. Erdos and A. Hajnal, "On...whenever p is prime and m is any positive integer, and in certain other cases as well. On the other hand, we do not have any construction method
Allocation of advertising space by a web service provider using combinatorial auctions
Sandeep Dulluri; N R Srinivasa Raghavan
2005-04-01
Advertising is a critical process for promoting both products and services in global trade. Internet has emerged as a powerful medium for trade and commerce. Online advertising over the internet has increased more than hundredfold since 2001. In the present work, we address problems faced by online advertisement service providers. In this paper, we propose a multi-slot and multi-site combinatorial auction for allocating scarce advertisement slots available on multiple sites. We observe that combinatorial auctions serve as effective mechanisms for allocating advertising slots over the internet. We resort to “ant” systems (ant – social insect/intelligent agent) to solve the above $\\mathcal{NP}$-hard combinatorial optimization problem which involves winner-determination in multi-item and multi-unit combinatorial auctions.
Novel combinatorial algorithm for the problems of fuzzy grey multi-attribute group decision making
Rao Congjun; Xiao Xinping; Peng Jin
2007-01-01
To study the fuzzy and grey information in the problems of multi-attribute group decision making, the basic concepts of both fuzzy grey numbers and grey interval numbers are given firstly, then a new model of fuzzy grey multi-attribute group decision making based on the theories of fuzzy mathematics and grey system is presented. Furthermore, the grey interval relative degree and deviation degree is defined, and both the optimistic algorithm of the grey interval relational degree and the algorithm of deviation degree minimization for solving this new model are also given. Finally, a decision making example to demonstrate the feasibility and rationality of this new method is given, and the results by using these two algorithms are uniform.
1997-01-01
The invention provides a method for the production of a combinatorial library of compound of general formula (I) using solid phase methodologies. The cleavage of the array of immobilised compounds of the phthalimido type from the solid support matrix is accomplished by using an array of dinucleop......The invention provides a method for the production of a combinatorial library of compound of general formula (I) using solid phase methodologies. The cleavage of the array of immobilised compounds of the phthalimido type from the solid support matrix is accomplished by using an array...... of dinucleophiles, e.g. hydrazines (hydrazinolysis) or N-hydroxylamines, whereby a combinatorial dimension is introduced in the cleavage step. The invention also provides a compound library....
Chvátal, V
2011-01-01
This book is a collection of six articles arising from the meeting of the NATO Advanced Study Institute (ASI) "Combinatorial Optimization: Methods and Applications," which was held at the University of Montreal in June 2006. This ASI consisted of seven series of five one-hour lectures and one series of four one-hour lectures. It was attended by some sixty students of graduate or postdoctoral level from fifteen countries worldwide. It includes topics such as: integer and mixed integer programming, facility location, branching on split disjunctions, convexity in combinatorial optimizat
Combinatorial instruments in the design of a heuristic for the quadratic assignment problem
Paulo Oswaldo Boaventura-Netto
2003-12-01
Full Text Available This work discusses the use of a neighbouring structure in the design of specific heuristics for the Quadratic Assignment Problem (QAP. This structure is formed by the 4- and 6-cycles adjacent to a vertex in the Hasse diagram of the permutation lattice and it can be adequately partitioned in subsets of linear and quadratic cardinalities, a characteristics which frequently allows an economy in the processing time. We propose also a restart strategy and a mechanism for generating initial solutions which constitute, together with the neighbouring structure, a possible QAP-specific heuristic proposal. For the construction of these instruments we used the relaxed ordered set of QAP solutions.Este trabalho discute o uso de uma estrutura de vizinhança em heurísticas específicas para o Problema Quadrático de Alocação (PQA. Esta estrutura envolve os ciclos de comprimento 4 e 6 adjacentes a um vértice do diagrama de Hasse do reticulado das permutações e pode ser particionada em subconjuntos de cardinalidade linear e quadrática em relação à ordem da instância, o que permite frequentemente uma economia de tempo de processamento. Propõem-se ainda uma estratégia de repartida e um mecanismo de geração de soluções iniciais, que constituem, ao lado da estrutura de vizinhança, uma proposta de heurística específica para o PQA. Na construção desses instrumentos foi utilizada a noção de conjunto relaxado ordenado das soluções do PQA.
Hybrid IP/CP Methods for Solving Sports Scheduling Problems
Rasmussen, Rasmus Vinther
2006-01-01
The field of sports scheduling comprises a challenging research areawith a great variety of hard combinatorial optimization problems andchallenging practical applications. This dissertation gives acomprehensive survey of the area and a number of new contributionsare presented. First a general sol...
The hardness of the functional orientation 2-color problem
Stöckel, Morten; Vildhøj, Hjalte Wedel; Bøg, Søren
2013-01-01
We consider the Functional Orientation 2-Color problem, which was introduced by Valiant in his seminal paper on holographic algorithms [SIAM J. Comput. 37(5) (2008), 1565-1594]. For this decision problem, Valiant gave a polynomial time holographic algorithm for planar graphs of maximum degree 3, ...
New Unconditional Hardness Results for Dynamic and Online Problems
Clifford, Raphaël; Jørgensen, Allan Grønlund; Larsen, Kasper Green
2015-01-01
Data summarization is an effective approach to dealing with the 'big data' problem. While data summarization problems traditionally have been studied is the streaming model, the focus is starting to shift to distributed models, as distributed/parallel computation seems to be the only viable way...... to handle today's massive data sets. In this paper, we study ε-approximations, a classical data summary that, intuitively speaking, preserves approximately the density of the underlying data set over a certain range space. We consider the problem of computing ε-approximations for a data set which is held...
New Unconditional Hardness Results for Dynamic and Online Problems
Clifford, Raphaël; Jørgensen, Allan Grønlund; Larsen, Kasper Green
2015-01-01
to handle today's massive data sets. In this paper, we study ε-approximations, a classical data summary that, intuitively speaking, preserves approximately the density of the underlying data set over a certain range space. We consider the problem of computing ε-approximations for a data set which is held...
Dieleman, Peter; Waitukaitis, Scott; van Hecke, Martin
To design rigidly foldable quadrilateral meshes one generally needs to solve a complicated set of constraints. Here we present a systematic, combinatorial approach to create rigidly foldable quadrilateral meshes with a limited number of different vertices. The number of discrete, 1 degree-of-freedom folding branches for some of these meshes scales exponentially with the number of vertices on the edge, whilst other meshes generated this way only have two discrete folding branches, regardless of mesh size. We show how these two different behaviours both emerge from the two folding branches present in a single generic 4-vertex. Furthermore, we model generic 4-vertices as a spherical linkage and exploit a previously overlooked symmetry to create non-developable origami patterns using the same combinatorial framework.
Algorithmic Strategies in Combinatorial Chemistry
GOLDMAN,DEBORAH; ISTRAIL,SORIN; LANCIA,GIUSEPPE; PICCOLBONI,ANTONIO; WALENZ,BRIAN
2000-08-01
Combinatorial Chemistry is a powerful new technology in drug design and molecular recognition. It is a wet-laboratory methodology aimed at ``massively parallel'' screening of chemical compounds for the discovery of compounds that have a certain biological activity. The power of the method comes from the interaction between experimental design and computational modeling. Principles of ``rational'' drug design are used in the construction of combinatorial libraries to speed up the discovery of lead compounds with the desired biological activity. This paper presents algorithms, software development and computational complexity analysis for problems arising in the design of combinatorial libraries for drug discovery. The authors provide exact polynomial time algorithms and intractability results for several Inverse Problems-formulated as (chemical) graph reconstruction problems-related to the design of combinatorial libraries. These are the first rigorous algorithmic results in the literature. The authors also present results provided by the combinatorial chemistry software package OCOTILLO for combinatorial peptide design using real data libraries. The package provides exact solutions for general inverse problems based on shortest-path topological indices. The results are superior both in accuracy and computing time to the best software reports published in the literature. For 5-peptoid design, the computation is rigorously reduced to an exhaustive search of about 2% of the search space; the exact solutions are found in a few minutes.
The "Hard Problem" and the Quantum Physicists. Part 1: The First Generation
Smith, C. U. M.
2006-01-01
All four of the most important figures in the early twentieth-century development of quantum physics--Niels Bohr, Erwin Schroedinger, Werner Heisenberg and Wolfgang Pauli--had strong interests in the traditional mind--brain, or "hard," problem. This paper reviews their approach to this problem, showing the influence of Bohr's complementarity…
Some polyhedral results in combinatorial optimization
Xiao, Han; 肖汉
2016-01-01
Many combinatorial optimization problems can be conceived of as optimizing a linear function over a polyhedron. Investigating properties of the associated polyhedron has been evidenced to be a powerful schema for solving combinatorial optimization problems, especially for characterizing min-max relations. Three different topics in combinatorial optimization are explored in this thesis, which fall within a unified characterization: integrality of polyhedra. Various min-max relations in com...
A Near-Term Quantum Computing Approach for Hard Computational Problems in Space Exploration
Smelyanskiy, Vadim N; Knysh, Sergey I; Williams, Colin P; Johnson, Mark W; Thom, Murray C; Macready, William G; Pudenz, Kristen L
2012-01-01
In this article, we show how to map a sampling of the hardest artificial intelligence problems in space exploration onto equivalent Ising models that then can be attacked using quantum annealing implemented in D-Wave machine. We overview the existing results as well as propose new Ising model implementations for quantum annealing. We review supervised and unsupervised learning algorithms for classification and clustering with applications to feature identification and anomaly detection. We introduce algorithms for data fusion and image matching for remote sensing applications. We overview planning problems for space exploration mission applications and algorithms for diagnostics and recovery with applications to deep space missions. We describe combinatorial optimization algorithms for task assignment in the context of autonomous unmanned exploration. Finally, we discuss the ways to circumvent the limitation of the Ising mapping using a "blackbox" approach based on ideas from probabilistic computing. In this ...
Optimal Rapid Restart of Heuristic Methods of NP Hard Problems
侯越先; 王芳
2004-01-01
Many heuristic search methods exhibit a remarkable variability in the time required to solve some particular problem instances. Their cost distributions are often heavy-tailed. It has been demonstrated that, in most cases, rapid restart (RR) method can prominently suppress the heavy-tailed nature of the instances and improve computation efficiency. However, it is usually time-consuming to check whether an algorithm on a specific instance is heavy-tailed or not. Moreover, if the heavy-tailed distribution is confirmed and the RR method is relevant, an optimal RR threshold should be chosen to facilitate the RR mechanism. In this paper, an approximate approach is proposed to quickly check whether an algorithm on a specific instance is heavy-tailed or not.The method is realized by means of calculating the maximal Lyapunov exponent of its generic running trace.Then a statistical formula to estimate the optimal RR threshold is educed. The method is based on common nonparametric estimation, e. g. , Kernel estimation. Two heuristic methods are selected to verify our method. The experimental results are consistent with the theoretical consideration perfectly.
Pseudorandomness and Combinatorial Constructions
2006-01-01
In combinatorics, the probabilistic method is a very powerful tool to prove the existence of combinatorial objects with interesting and useful properties. Explicit constructions of objects with such properties are often very difficult, or unknown. In computer science, probabilistic algorithms are sometimes simpler and more efficient than the best known deterministic algorithms for the same problem. Despite this evidence for the power of random choices, the computational theory of pseudorandom...
Problems in education, employment and social integration of hard of hearing artists
Radić-Šestić Marina
2013-01-01
Full Text Available The aim of this research was to determine the problems in education (primary, secondary and undergraduate academic studies, employment and social integration of hard of hearing artists based on a multiple case study. The sample consisted of 4 examinees of both genders, aged between 29 and 54, from the field of visual arts (a painter, a sculptor, a graphic designer, and an interior designer. The structured interview consisted of 30 questions testing three areas: the first area involved family, primary and secondary education; the second area was about the length of studying and socio-emotional problems of the examinees; the third area dealt with problems in employment and job satisfaction of our examinees. Research results indicate the existence of several problems which more or less reflect the success in education, employment and social integration of hard of hearing artists. One of the problems which can influence the development of language abilities, socioemotional maturity, and better educational achievement of hard of hearing artists in general, is prolongation in diagnosing hearing impairments, amplification and auditory rehabilitation. Furthermore, parents of hard of hearing artists have difficulties in adjusting to their children's hearing impairments and ignore the language and culture of the Deaf, i.e. they tend to identify their children with typically developing population. Another problem are negative attitudes of teachers/professors/employers and typically developing peers/ colleagues towards the inclusion of hard of hearing people into the regular education/employment system. Apart from that, unmodified instruction, course books, information, school and working area further complicate the acquisition of knowledge, information, and the progress of hard of hearing people in education and profession.
Solution of the NP-hard total tardiness minimization problem in scheduling theory
Lazarev, A. A.
2007-06-01
The classical NP-hard (in the ordinary sense) problem of scheduling jobs in order to minimize the total tardiness for a single machine 1‖Σ T j is considered. An NP-hard instance of the problem is completely analyzed. A procedure for partitioning the initial set of jobs into subsets is proposed. Algorithms are constructed for finding an optimal schedule depending on the number of subsets. The complexity of the algorithms is O( n 2Σ p j ), where n is the number of jobs and p j is the processing time of the jth job ( j = 1, 2, …, n).
Combinatorial fractal Brownian motion model
朱炬波; 梁甸农
2000-01-01
To solve the problem of how to determine the non-scaled interval when processing radar clutter using fractal Brownian motion (FBM) model, a concept of combinatorial FBM model is presented. Since the earth (or sea) surface varies diversely with space, a radar clutter contains several fractal structures, which coexist on all scales. Taking the combination of two FBMs into account, via theoretical derivation we establish a combinatorial FBM model and present a method to estimate its fractal parameters. The correctness of the model and the method is proved by simulation experiments and computation of practial data. Furthermore, we obtain the relationship between fractal parameters when processing combinatorial model with a single FBM model. Meanwhile, by theoretical analysis it is concluded that when combinatorial model is observed on different scales, one of the fractal structures is more obvious.
Fast solution of NP-hard coloring problems on large random graphs
Bedini, Andrea
2010-01-01
Combining tree decomposition and transfer matrix techniques provides a highly efficient and very general algorithm for computing exact partition functions of statistical models defined on large graphs. We illustrate this by considering the hard problem of computing the exact number of vertex colorings for randomly generated planar graphs with up to N = 100 vertices.
Cryptographic Combinatorial Clock-Proxy Auctions
Parkes, David C.; Rabin, Michael O.; Thorpe, Christopher
We present a cryptographic protocol for conducting efficient, provably correct and secrecy-preserving combinatorial clock-proxy auctions. The “clock phase” functions as a trusted auction despite price discovery: bidders submit encrypted bids, and prove for themselves that they meet activity rules, and can compute total demand and thus verify price increases without revealing any information about individual demands. In the sealed-bid “proxy phase”, all bids are revealed the auctioneer via time-lapse cryptography and a branch-and-bound algorithm is used to solve the winner-determination problem. Homomorphic encryption is used to prove the correctness of the solution, and establishes the correctness of the solution to any interested party. Still an NP-hard optimization problem, the use of homomorphic encryption imposes additional computational time on winner-determination that is linear in the size of the branch-and-bound search tree, and thus roughly linear in the original (search-based) computational time. The result is a solution that avoids, in the usual case, the exponential complexity of previous cryptographically-secure combinatorial auctions.
Combinatorial optimization networks and matroids
Lawler, Eugene
2011-01-01
Perceptively written text examines optimization problems that can be formulated in terms of networks and algebraic structures called matroids. Chapters cover shortest paths, network flows, bipartite matching, nonbipartite matching, matroids and the greedy algorithm, matroid intersections, and the matroid parity problems. A suitable text or reference for courses in combinatorial computing and concrete computational complexity in departments of computer science and mathematics.
Applications of combinatorial optimization
Paschos, Vangelis Th
2013-01-01
Combinatorial optimization is a multidisciplinary scientific area, lying in the interface of three major scientific domains: mathematics, theoretical computer science and management. The three volumes of the Combinatorial Optimization series aims to cover a wide range of topics in this area. These topics also deal with fundamental notions and approaches as with several classical applications of combinatorial optimization. "Applications of Combinatorial Optimization" is presenting a certain number among the most common and well-known applications of Combinatorial Optimization.
Combinatorial algebra syntax and semantics
Sapir, Mark V
2014-01-01
Combinatorial Algebra: Syntax and Semantics provides a comprehensive account of many areas of combinatorial algebra. It contains self-contained proofs of more than 20 fundamental results, both classical and modern. This includes Golod–Shafarevich and Olshanskii's solutions of Burnside problems, Shirshov's solution of Kurosh's problem for PI rings, Belov's solution of Specht's problem for varieties of rings, Grigorchuk's solution of Milnor's problem, Bass–Guivarc'h theorem about the growth of nilpotent groups, Kleiman's solution of Hanna Neumann's problem for varieties of groups, Adian's solution of von Neumann-Day's problem, Trahtman's solution of the road coloring problem of Adler, Goodwyn and Weiss. The book emphasize several ``universal" tools, such as trees, subshifts, uniformly recurrent words, diagrams and automata. With over 350 exercises at various levels of difficulty and with hints for the more difficult problems, this book can be used as a textbook, and aims to reach a wide and diversified...
Statistical mechanics of combinatorial auctions
Galla, Tobias; Leone, Michele; Marsili, Matteo; Sellitto, Mauro; Weigt, Martin; Zecchina, Riccardo
2006-05-01
Combinatorial auctions are formulated as frustrated lattice gases on sparse random graphs, allowing the determination of the optimal revenue by methods of statistical physics. Transitions between computationally easy and hard regimes are found and interpreted in terms of the geometric structure of the space of solutions. We introduce an iterative algorithm to solve intermediate and large instances, and discuss competing states of optimal revenue and maximal number of satisfied bidders. The algorithm can be generalized to the hard phase and to more sophisticated auction protocols.
Order-to-chaos transition in the hardness of random Boolean satisfiability problems
Varga, Melinda; Sumi, Róbert; Toroczkai, Zoltán; Ercsey-Ravasz, Mária
2016-05-01
Transient chaos is a ubiquitous phenomenon characterizing the dynamics of phase-space trajectories evolving towards a steady-state attractor in physical systems as diverse as fluids, chemical reactions, and condensed matter systems. Here we show that transient chaos also appears in the dynamics of certain efficient algorithms searching for solutions of constraint satisfaction problems that include scheduling, circuit design, routing, database problems, and even Sudoku. In particular, we present a study of the emergence of hardness in Boolean satisfiability (k -SAT), a canonical class of constraint satisfaction problems, by using an analog deterministic algorithm based on a system of ordinary differential equations. Problem hardness is defined through the escape rate κ , an invariant measure of transient chaos of the dynamical system corresponding to the analog algorithm, and it expresses the rate at which the trajectory approaches a solution. We show that for a given density of constraints and fixed number of Boolean variables N , the hardness of formulas in random k -SAT ensembles has a wide variation, approximable by a lognormal distribution. We also show that when increasing the density of constraints α , hardness appears through a second-order phase transition at αχ in the random 3-SAT ensemble where dynamical trajectories become transiently chaotic. A similar behavior is found in 4-SAT as well, however, such a transition does not occur for 2-SAT. This behavior also implies a novel type of transient chaos in which the escape rate has an exponential-algebraic dependence on the critical parameter κ ˜NB |α - αχ|1-γ with 0 <γ <1 . We demonstrate that the transition is generated by the appearance of metastable basins in the solution space as the density of constraints α is increased.
Takahashi, Jun; Takabe, Satoshi; Hukushima, Koji
2017-07-01
A recently proposed exact algorithm for the maximum independent set problem is analyzed. The typical running time is improved exponentially in some parameter regions compared to simple binary search. Furthermore, the algorithm overcomes the core transition point, where the conventional leaf removal algorithm fails, and works up to the replica symmetry breaking (RSB) transition point. This suggests that a leaf removal core itself is not enough for typical hardness in the random maximum independent set problem, providing further evidence for RSB being the obstacle for algorithms in general.
The 'hard problem' and the quantum physicists. Part 1: the first generation.
Smith, C U M
2006-07-01
All four of the most important figures in the early twentieth-century development of quantum physics-Niels Bohr, Erwin Schroedinger, Werner Heisenberg and Wolfgang Pauli-had strong interests in the traditional mind-brain, or 'hard,' problem. This paper reviews their approach to this problem, showing the influence of Bohr's complementarity thesis, the significance of Schroedinger's small book, 'What is life?,' the updated Platonism of Heisenberg and, perhaps most interesting of all, the interaction of Carl Jung and Wolfgang Pauli in the latter's search for a unification of mind and matter.
C. J. F. Ter Braak
2011-12-01
Full Text Available Formal and informal Bayesian approaches have found widespread implementation and use in environmental modeling to summarize parameter and predictive uncertainty. Successful implementation of these methods relies heavily on the availability of efficient sampling methods that approximate, as closely and consistently as possible the (evolving posterior target distribution. Much of this work has focused on continuous variables that can take on any value within their prior defined ranges. Here, we introduce theory and concepts of a discrete sampling method that resolves the parameter space at fixed points. This new code, entitled DREAM(D uses the recently developed DREAM algorithm (Vrugt et al., 2008, 2009a, b as its main building block but implements two novel proposal distributions to help solve discrete and combinatorial optimization problems. This novel MCMC sampler maintains detailed balance and ergodicity, and is especially designed to resolve the emerging class of optimal experimental design problems. Three different case studies involving a Sudoku puzzle, soil water retention curve, and rainfall – runoff model calibration problem are used to benchmark the performance of DREAM(D. The theory and concepts developed herein can be easily integrated into other (adaptive MCMC algorithms.
Hall, Marshall
2011-01-01
Includes proof of van der Waerden's 1926 conjecture on permanents, Wilson's theorem on asymptotic existence, and other developments in combinatorics since 1967. Also covers coding theory and its important connection with designs, problems of enumeration, and partition. Presents fundamentals in addition to latest advances, with illustrative problems at the end of each chapter. Enlarged appendixes include a longer list of block designs.
Guturu, Parthasarathy; Dantu, Ram
2008-06-01
Many graph- and set-theoretic problems, because of their tremendous application potential and theoretical appeal, have been well investigated by the researchers in complexity theory and were found to be NP-hard. Since the combinatorial complexity of these problems does not permit exhaustive searches for optimal solutions, only near-optimal solutions can be explored using either various problem-specific heuristic strategies or metaheuristic global-optimization methods, such as simulated annealing, genetic algorithms, etc. In this paper, we propose a unified evolutionary algorithm (EA) to the problems of maximum clique finding, maximum independent set, minimum vertex cover, subgraph and double subgraph isomorphism, set packing, set partitioning, and set cover. In the proposed approach, we first map these problems onto the maximum clique-finding problem (MCP), which is later solved using an evolutionary strategy. The proposed impatient EA with probabilistic tabu search (IEA-PTS) for the MCP integrates the best features of earlier successful approaches with a number of new heuristics that we developed to yield a performance that advances the state of the art in EAs for the exploration of the maximum cliques in a graph. Results of experimentation with the 37 DIMACS benchmark graphs and comparative analyses with six state-of-the-art algorithms, including two from the smaller EA community and four from the larger metaheuristics community, indicate that the IEA-PTS outperforms the EAs with respect to a Pareto-lexicographic ranking criterion and offers competitive performance on some graph instances when individually compared to the other heuristic algorithms. It has also successfully set a new benchmark on one graph instance. On another benchmark suite called Benchmarks with Hidden Optimal Solutions, IEA-PTS ranks second, after a very recent algorithm called COVER, among its peers that have experimented with this suite.
Hu, T C
2002-01-01
Newly enlarged, updated second edition of a valuable text presents algorithms for shortest paths, maximum flows, dynamic programming and backtracking. Also discusses binary trees, heuristic and near optimums, matrix multiplication, and NP-complete problems. 153 black-and-white illus. 23 tables.Newly enlarged, updated second edition of a valuable, widely used text presents algorithms for shortest paths, maximum flows, dynamic programming and backtracking. Also discussed are binary trees, heuristic and near optimums, matrix multiplication, and NP-complete problems. New to this edition: Chapter 9
A Novel Metaheuristic for Travelling Salesman Problem
Vahid Zharfi
2013-01-01
Full Text Available One of the well-known combinatorial optimization problems is travelling salesman problem (TSP. This problem is in the fields of logistics, transportation, and distribution. TSP is among the NP-hard problems, and many different metaheuristics are used to solve this problem in an acceptable time especially when the number of cities is high. In this paper, a new meta-heuristic is proposed to solve TSP which is based on new insight into network routing problems.
Neural Meta-Memes Framework for Combinatorial Optimization
Song, Li Qin; Lim, Meng Hiot; Ong, Yew Soon
In this paper, we present a Neural Meta-Memes Framework (NMMF) for combinatorial optimization. NMMF is a framework which models basic optimization algorithms as memes and manages them dynamically when solving combinatorial problems. NMMF encompasses neural networks which serve as the overall planner/coordinator to balance the workload between memes. We show the efficacy of the proposed NMMF through empirical study on a class of combinatorial problem, the quadratic assignment problem (QAP).
Variable and Value Ordering When Solving Balanced Academic Curriculum Problems
Castro, Carlos; Manzano, Sebastian
2001-01-01
In this paper we present the use of Constraint Programming for solving balanced academic curriculum problems. We discuss the important role that heuristics play when solving a problem using a constraint-based approach. We also show how constraint solving techniques allow to very efficiently solve combinatorial optimization problems that are too hard for integer programming techniques.
Krumke, S.O.; Rambau, J. [Zuse-Institut Berlin, Berlin (Germany)
2002-07-01
The automation of in-house logistic systems requires - beyond the physical control of the machinery - an efficient organization of transport requests: a field of combinatorial optimization. With the help of three concrete applications, this article illustrates the online-issues (incomplete knowledge) and the real-time issues (short time frame for computations) frequently occuring in logistic systems. We give an overview over general purpose methods to construct online-algorithms and over analysis methods which help to decide which algorithms are suitable for a particular problem setting. (orig.) [German] Die Automatisierung von innerbetrieblicher Logistik erfordert - ueber die physikalische Steuerung von Geraeten hinaus - auch eine effiziente Organisation der Transporte: ein Aufgabenfeld der kombinatorischen Optimierung. Dieser Artikel illustriert anhand von konkreten Aufgabenstellungen die Online-Problematik (unvollstaendiges Wissen) sowie die Echtzeit-Problematik (beschraenkte Rechenzeit), auf die man in der innerbetrieblichen Logistik trifft. Der Text gibt einen Ueberblick ueber allgemeine Konstruktionsprinzipien fuer Online-Algorithmen und Bewertungsmethoden, die bei der Entscheidung helfen, welche Algorithmen fuer eine vorliegende Problemstellung geeignet sind. (orig.)
Penalty Formulations and Trap-Avoidance Strategies for Solving Hard Satisfiability Problems
Benjamin W. Wah; Zhe Wu
2005-01-01
In this paper we study the solution of SAT problems formulated as discrete decision and discrete constrained optimization problems. Constrained formulations are better than traditional unconstrained formulations because violated constraints may provide additional forces to lead a search towards a satisfiable assignment. We summarize the theory of extended saddle points in penalty formulations for solving discrete constrained optimization problems and the associated discrete penalty method (DPM). We then examine various formulations of the objective function, choices of neighborhood in DPM, strategies for updating penalties, and heuristics for avoiding traps. Experimental evaluations on hard benchmark instances pinpoint that traps contribute significantly to the inefficiency of DPM and force a trajectory to repeatedly visit the same set of or nearby points in the original variable space. To address this issue, we propose and study two trap-avoidance strategies. The first strategy adds extra penalties on unsatisfied clauses inside a trap, leading to very large penalties for unsatisfied clauses that are trapped more often and making these clauses more likely to be satisfied in the future. The second strategy stores information on points visited before, whether inside traps or not, and avoids visiting points that are close to points visited before. It can be implemented by modifying the penalty function in such a way that, if a trajectory gets close to points visited before, an extra penalty will take effect and force the trajectory to a new region. It specializes to the first strategy because traps are special cases of points visited before. Finally, we show experimental results on evaluating benchmarks in the DIMACS and SATLIB archives and compare our results with existing results on GSAT, WalkSAT, LSDL, and Grasp. The results demonstrate that DPM with trap avoidance is robust as well as effective for solving hard SAT problems.
Jorge Perdomo
2013-12-01
Full Text Available The sports scheduling problem has been center of attention in the Operational Research community due to their variety of models, and computational complexity of solutions (see for example Ribeiro (2010. In a Round Robin tournament, the schedule is proposed by assigning a “home" or “away" labels to a preestablished itinerary, in a such way that the total distance traveled by the teams during the tournament is minimized. In terms of operation research, the problem is modeled as a binary quadratic programming problem with linear constraints. In Suzuka y cols. (2005 the problem is treated as a MIN-RES-CUT. In this work we study the structure of the home-away assignment problem, and propose a simplification of the combinatorial formulation. We solve exactly small instances of the problem with an exhaustive search, and also approximately solve larger instances with a random search. // RESUMEN El problema de elaboración de calendarios deportivos ha centrado la atención de la comunidad de investigación de operaciones por la variedad de modelos y la complejidad computacional de las soluciones (ver por ejemplo Ribeiro (2010. En torneos tipo Round Robin de ida y vuelta el calendario se propone asignando la etiqueta de local o visitante a cada equipo, en un itinerario preestablecido de manera que se minimice el recorrido total de los equipos durante el torneo. En términos de investigación de operaciones lo modelamos como un problema de optimización cuadrática binaria con restricciones lineales. Suzuka, Miyashiro, Yoshise, y Matsui (2005 lo tratan como uno de encontrar el corte mínimo con restricciones (Min-Res-Cut en un grafo no dirigido, proporcionando una formulación de optimización combinatoria. En el presente trabajo estudiamos la estructura del problema de asignación local-visitante, y proponemos una simplificación de la formulación de optimización combinatoria. Resolvemos de forma exacta con una búsqueda exhaustiva instancias peque
Lourdes Figueiras
2010-01-01
Full Text Available Describimos el proceso seguido por estudiantes de 11 y 12 años para descubrir patrones de conteo en un problema básico de combinatoria. Hacemos énfasis en la transición de las estrategias manipulativas para el conteo directo a la generalización. En esta transición hubo estudiantes que utilizaron, de forma espontánea, diagramas de árbol; y otros estudiantes que recurrieron a estrategias comunes en pensamiento numérico. Resaltamos el interés de resolver problemas de combinatoria sin haber aprendido fórmulas previas para que los estudiantes den significado a la regla del producto y relacionamos los resultados obtenidos con aspectos didácticos de la multiplicación en educación primaria. Reasoning and Strategies in the Transition to Generalization in a Combinatorial Problem We describe the procedure used by 11-12 years old students to discover counting patterns in basic combinatory problems. We emphasize the transition from manipulative strategies for direct counting to generalization. In this transition, there were students who spontaneously used tree diagrams of mathematical ideas and some students used numerical thinking strategies. We highlight the interest of solving combinatory problems in order to let the students make sense of the multiplication rule. We relate the results to the teaching of multiplication in primary school.
Conferences on Combinatorial and Additive Number Theory
2014-01-01
This proceedings volume is based on papers presented at the Workshops on Combinatorial and Additive Number Theory (CANT), which were held at the Graduate Center of the City University of New York in 2011 and 2012. The goal of the workshops is to survey recent progress in combinatorial number theory and related parts of mathematics. The workshop attracts researchers and students who discuss the state-of-the-art, open problems, and future challenges in number theory.
A product formula and combinatorial field theory
Horzela, A; Duchamp, G H E; Penson, K A; Solomon, A I
2004-01-01
We treat the problem of normally ordering expressions involving the standard boson operators a, a* where [a,a*]=1. We show that a simple product formula for formal power series - essentially an extension of the Taylor expansion - leads to a double exponential formula which enables a powerful graphical description of the generating functions of the combinatorial sequences associated with such functions - in essence, a combinatorial field theory. We apply these techniques to some examples related to specific physical Hamiltonians.
Accessing Specific Peptide Recognition by Combinatorial Chemistry
Li, Ming
Peptide Recognition by Combinatorial Chemistry”. Molecular recognition is a specific interaction between two or more molecules through noncovalent bonding, such as hydrogen bonding, metal coordination, van der Waals forces, π−π, hydrophobic, or electrostatic interactions. The association involves kinetic....... Combinatorial chemistry was invented in 1980s based on observation of functional aspects of the adaptive immune system. It was employed for drug development and optimization in conjunction with high-throughput synthesis and screening. (chapter 2) Combinatorial chemistry is able to rapidly produce many thousands...... was studied with this hook peptide library via the beadbead adhesion screening approach. The recognition pairs interlocked and formed a complex. (chapter 8) During accessing peptide molecular recognition by combinatorial chemistry, we faced several problems, which were solved by a range of analytical...
Phase Transitions and Backbones of the Asymmetric Traveling Salesman Problem
Zhang, W
2011-01-01
In recent years, there has been much interest in phase transitions of combinatorial problems. Phase transitions have been successfully used to analyze combinatorial optimization problems, characterize their typical-case features and locate the hardest problem instances. In this paper, we study phase transitions of the asymmetric Traveling Salesman Problem (ATSP), an NP-hard combinatorial optimization problem that has many real-world applications. Using random instances of up to 1,500 cities in which intercity distances are uniformly distributed, we empirically show that many properties of the problem, including the optimal tour cost and backbone size, experience sharp transitions as the precision of intercity distances increases across a critical value. Our experimental results on the costs of the ATSP tours and assignment problem agree with the theoretical result that the asymptotic cost of assignment problem is pi ^2 /6 the number of cities goes to infinity. In addition, we show that the average computation...
Cubature formulas on combinatorial graphs
Pesenson, Isaac Z
2011-01-01
Many contemporary applications, for example, cataloging of galaxies, document analysis, face recognition, learning theory, image processing, operate with a large amount of data which is often represented as a graph embedded into a high dimensional Euclidean space. The variety of problems arising in contemporary data processing requires development on graphs such topics of the classical harmonic analysis as Shannon sampling, splines, wavelets, cubature formulas. The goal of the paper is to establish cubature formulas on finite combinatorial graphs. The results have direct applications to problems that arise in connection with data filtering, data denoising and data dimension reduction.
A hybrid metaheuristic for the time-dependent vehicle routing problem with hard time windows
N. Rincon-Garcia
2017-01-01
Full Text Available This article paper presents a hybrid metaheuristic algorithm to solve the time-dependent vehicle routing problem with hard time windows. Time-dependent travel times are influenced by different congestion levels experienced throughout the day. Vehicle scheduling without consideration of congestion might lead to underestimation of travel times and consequently missed deliveries. The algorithm presented in this paper makes use of Large Neighbourhood Search approaches and Variable Neighbourhood Search techniques to guide the search. A first stage is specifically designed to reduce the number of vehicles required in a search space by the reduction of penalties generated by time-window violations with Large Neighbourhood Search procedures. A second stage minimises the travel distance and travel time in an ‘always feasible’ search space. Comparison of results with available test instances shows that the proposed algorithm is capable of obtaining a reduction in the number of vehicles (4.15%, travel distance (10.88% and travel time (12.00% compared to previous implementations in reasonable time.
Metaheuristic ILS with path relinking for the number partitioning problem
Cesar Augusto Souza de Oliveira
2017-07-01
Full Text Available This study brings an implementation of a metaheuristic procedure to solve the Number Partitioning Problem (NPP, which is a classic NP-hard combinatorial optimization problem. The presented problem has applications in different areas, such as: logistics, production and operations management, besides important relationships with other combinatorial problems. This paper aims to perform a comparative analysis between the proposed algorithm with others metaheuristics using a group of instances available on the literature. Implementations of constructive heuristics, local search and metaheuristics ILS with path relinking as mechanism of intensification and diversification were made in order to improve solutions, surpassing the others algorithms.
Marshall, Matthew M.; Carrano, Andres L.; Dannels, Wendy A.
2016-01-01
Individuals who are deaf and hard-of-hearing (DHH) are underrepresented in science, technology, engineering, and mathematics (STEM) professions, and this may be due in part to their level of preparation in the development and retention of mathematical and problem-solving skills. An approach was developed that incorporates experiential learning and…
Wilhelm F. Maier
2004-10-01
Full Text Available Two recently published books examine combinatorial materials synthesis, high-throughput screening of libraries, and the design of successful experiments. Both are a must for those interested in materials development and discovery, says Wilhelm F. Maier
de Silva, Vin; Salamon, Dietmar
2012-01-01
We define combinatorial Floer homology of a transverse pair of noncontractibe nonisotopic embedded loops in an oriented 2-manifold without boundary, prove that it is invariant under isotopy, and prove that it is isomorphic to the original Lagrangian Floer homology.
Ant Colony Optimization and Hypergraph Covering Problems
Pat, Ankit
2011-01-01
Ant Colony Optimization (ACO) is a very popular metaheuristic for solving computationally hard combinatorial optimization problems. Runtime analysis of ACO with respect to various pseudo-boolean functions and different graph based combinatorial optimization problems has been taken up in recent years. In this paper, we investigate the runtime behavior of an MMAS*(Max-Min Ant System) ACO algorithm on some well known hypergraph covering problems that are NP-Hard. In particular, we have addressed the Minimum Edge Cover problem, the Minimum Vertex Cover problem and the Maximum Weak- Independent Set problem. The influence of pheromone values and heuristic information on the running time is analysed. The results indicate that the heuristic information has greater impact towards improving the expected optimization time as compared to pheromone values. For certain instances of hypergraphs, we show that the MMAS* algorithm gives a constant order expected optimization time when the dominance of heuristic information is ...
Music algorithm for imaging of a sound-hard arc in limited-view inverse scattering problem
Park, Won-Kwang
2017-07-01
MUltiple SIgnal Classification (MUSIC) algorithm for a non-iterative imaging of sound-hard arc in limited-view inverse scattering problem is considered. In order to discover mathematical structure of MUSIC, we derive a relationship between MUSIC and an infinite series of Bessel functions of integer order. This structure enables us to examine some properties of MUSIC in limited-view problem. Numerical simulations are performed to support the identified structure of MUSIC.
Elementary Components of the Quadratic Assignment Problem
Chicano, Francisco; Alba, Enrique
2011-01-01
The Quadratic Assignment Problem (QAP) is a well-known NP-hard combinatorial optimization problem that is at the core of many real-world optimization problems. We prove that QAP can be written as the sum of three elementary landscapes when the swap neighborhood is used. We present a closed formula for each of the three elementary components and we compute bounds for the autocorrelation coefficient.
Partition functions and graphs: A combinatorial approach
Solomon, A I; Duchamp, G; Horzela, A; Penson, K A; Solomon, Allan I.; Blasiak, Pawel; Duchamp, Gerard; Horzela, Andrzej; Penson, Karol A.
2004-01-01
Although symmetry methods and analysis are a necessary ingredient in every physicist's toolkit, rather less use has been made of combinatorial methods. One exception is in the realm of Statistical Physics, where the calculation of the partition function, for example, is essentially a combinatorial problem. In this talk we shall show that one approach is via the normal ordering of the second quantized operators appearing in the partition function. This in turn leads to a combinatorial graphical description, giving essentially Feynman-type graphs associated with the theory. We illustrate this methodology by the explicit calculation of two model examples, the free boson gas and a superfluid boson model. We show how the calculation of partition functions can be facilitated by knowledge of the combinatorics of the boson normal ordering problem; this naturally gives rise to the Bell numbers of combinatorics. The associated graphical representation of these numbers gives a perturbation expansion in terms of a sequen...
Mental health problems among the survivors in the hard-hit areas of the Yushu earthquake.
Zhen Zhang
Full Text Available BACKGROUND: On April 14, 2010, an earthquake registering 7.1 on the Richter scale shook Qinghai Province in southwest China. The earthquake caused numerous casualties and much damage. The epicenter, Yushu County, suffered the most severe damage. As a part of the psychological relief work, the present study evaluated the mental health statuses of the people affected and identified the mental disorder risk factors related to earthquakes. METHODS: Five hundred and five earthquake survivors living in Yushu County were investigated 3-4 months after the earthquake. Participant demographic data including gender, age, marital status, ethnicity, educational level, and religious beliefs were collected. The Earthquake-Specific Trauma Exposure Indicators assessed the intensity of exposure to trauma during the earthquake. The PTSD Checklist-Civilian version (PCL-C and the Hopkins Symptoms Checklist-25 (HSCL-25 assessed the symptoms and prevalence rates of probable Posttraumatic Stress Disorder (PTSD as well as anxiety and depression, respectively. The Perceived Social Support Scale (PSSS evaluated subjective social support. RESULTS: The prevalence rates of probable PTSD, anxiety, and depression were 33.7%, 43.8% and 38.6%, respectively. Approximately one fifth of participants suffered from all three conditions. Individuals who were female, felt initial fear during the earthquake, and had less social support were the most likely to have poor mental health. CONCLUSIONS: The present study revealed that there are serious mental problems among the hard-hit survivors of the Yushu earthquake. Survivors at high risk for mental disorders should be specifically considered. The present study provides useful information for rebuilding and relief work.
Hard Data Analytics Problems Make for Better Data Analysis Algorithms: Bioinformatics as an Example.
Bacardit, Jaume; Widera, Paweł; Lazzarini, Nicola; Krasnogor, Natalio
2014-09-01
Data mining and knowledge discovery techniques have greatly progressed in the last decade. They are now able to handle larger and larger datasets, process heterogeneous information, integrate complex metadata, and extract and visualize new knowledge. Often these advances were driven by new challenges arising from real-world domains, with biology and biotechnology a prime source of diverse and hard (e.g., high volume, high throughput, high variety, and high noise) data analytics problems. The aim of this article is to show the broad spectrum of data mining tasks and challenges present in biological data, and how these challenges have driven us over the years to design new data mining and knowledge discovery procedures for biodata. This is illustrated with the help of two kinds of case studies. The first kind is focused on the field of protein structure prediction, where we have contributed in several areas: by designing, through regression, functions that can distinguish between good and bad models of a protein's predicted structure; by creating new measures to characterize aspects of a protein's structure associated with individual positions in a protein's sequence, measures containing information that might be useful for protein structure prediction; and by creating accurate estimators of these structural aspects. The second kind of case study is focused on omics data analytics, a class of biological data characterized for having extremely high dimensionalities. Our methods were able not only to generate very accurate classification models, but also to discover new biological knowledge that was later ratified by experimentalists. Finally, we describe several strategies to tightly integrate knowledge extraction and data mining in order to create a new class of biodata mining algorithms that can natively embrace the complexity of biological data, efficiently generate accurate information in the form of classification/regression models, and extract valuable new
ALE-PSO: An Adaptive Swarm Algorithm to Solve Design Problems of Laminates
Paolo Vannucci
2009-04-01
Full Text Available This paper presents an adaptive PSO algorithm whose numerical parameters can be updated following a scheduled protocol respecting some known criteria of convergence in order to enhance the chances to reach the global optimum of a hard combinatorial optimization problem, such those encountered in global optimization problems of composite laminates. Some examples concerning hard design problems are provided, showing the effectiveness of the approach.
Probabilistic methods in combinatorial analysis
Sachkov, Vladimir N
2014-01-01
This 1997 work explores the role of probabilistic methods for solving combinatorial problems. These methods not only provide the means of efficiently using such notions as characteristic and generating functions, the moment method and so on but also let us use the powerful technique of limit theorems. The basic objects under investigation are nonnegative matrices, partitions and mappings of finite sets, with special emphasis on permutations and graphs, and equivalence classes specified on sequences of finite length consisting of elements of partially ordered sets; these specify the probabilist
A NEW APPROACH FOR VARIANT MULTI ASSIGNMENT PROBLEM
SOBHAN BABU.K,
2010-08-01
Full Text Available A large number of real-world planning problems called Combinatorial Optimization Problems share the following properties: They are Optimization Problems, are easy to state, and have a finite but usually very large number of feasible solutions. Lexi-Search is by far the mostly used tool for solving large scale NP-hard Combinatorial Optimization problems. Lexi-Search is, however, an algorithm paradigm, which has to be filled out for each specific problem type, and numerous choices for each of the components exist. Even then, principles for the design of efficient Lexi-Search algorithms have emerged over the years. Although Lexi-Search methods are among the most widely used techniques for solving hard problems,it is still a challenge to make these methods smarter. The motivation of the calculation of the lower bounds is based on ideas frequently used in solving problems. Computationally, the algorithm extended the size of problem and find better solution.
An Efficient Algorithm For Variant Bulk Transportation Problem
Sobhan Babu.K
2010-07-01
Full Text Available A large number of real-world planning problems called Combinatorial Optimization Problems share the following properties: They are Optimization Problems, are easy to state, and have a finite but usually very large number of feasible solutions. Lexi-Search is by far the mostly used tool for solving large scale NP-hard Combinatorial Optimization problems. Lexi-Search is, however, an algorithm paradigm, which has to be filled out for each specific problem type, and numerous choices for each of the components exist. Even then, principles for the design of efficient Lexi-Search algorithms have emerged over the years. Although Lexi-Search methods are among the most widely used techniques for solving hard problems, it is still a challenge to make these methods smarter. The motivation of the calculation of the lower bounds is based on ideas frequently used in solving problems. Computationally, the algorithm extended the size of problem and find better solution.
Boldachev Alexander
2015-01-01
Full Text Available Any low-level processes, the sequence of chemical interactions in a living cell, muscle cellular activity, processor commands or neuron interaction, is possible only if there is a downward causality, only due to uniting and controlling power of the highest level. Therefore, there is no special “hard problem of consciousness”, i.e. the problem of relation of ostensibly purely biological materiality and non-causal mentality - we have only the single philosophical problem of relation between the upward and downward causalities, the problem of interrelation between hierarchic levels of existence. It is necessary to conclude that the problem of determinacy of chemical processes by the biological ones and the problem of neuron interactions caused by consciousness are of one nature and must have one solution.
Stochastic Combinatorial Optimization under Probabilistic Constraints
Agrawal, Shipra; Ye, Yinyu
2008-01-01
In this paper, we present approximation algorithms for combinatorial optimization problems under probabilistic constraints. Specifically, we focus on stochastic variants of two important combinatorial optimization problems: the k-center problem and the set cover problem, with uncertainty characterized by a probability distribution over set of points or elements to be covered. We consider these problems under adaptive and non-adaptive settings, and present efficient approximation algorithms for the case when underlying distribution is a product distribution. In contrast to the expected cost model prevalent in stochastic optimization literature, our problem definitions support restrictions on the probability distributions of the total costs, via incorporating constraints that bound the probability with which the incurred costs may exceed a given threshold.
Larsen, Jesper Abildgaard; Wisniewski, Rafal; Grunnet, Jacob Deleuran
2008-01-01
As initially suggested by E. Sontag, it is possible to approximate an arbitrary nonlinear system by a set of piecewise linear systems. In this work we concentrate on how to control a system given by a set of piecewise linear systems defined on simplices. By using the results of L. Habets and J. van...... Schuppen, it is possible to find a controller for the system on each of the simplices thus guaranteeing that the system flow on the simplex only will leave the simplex through a subset of its faces. Motivated by R. Forman, on the triangulated state space we define a combinatorial vector field, which...... indicates for a given face the future simplex. In the suggested definition we allow nondeterminacy in form of splitting and merging of solution trajectories. The combinatorial vector field gives rise to combinatorial counterparts of most concepts from dynamical systems, such as duals to vector fields, flow...
Combinatorial designs a tribute to Haim Hanani
Hartman, A
1989-01-01
Haim Hanani pioneered the techniques for constructing designs and the theory of pairwise balanced designs, leading directly to Wilson''s Existence Theorem. He also led the way in the study of resolvable designs, covering and packing problems, latin squares, 3-designs and other combinatorial configurations.The Hanani volume is a collection of research and survey papers at the forefront of research in combinatorial design theory, including Professor Hanani''s own latest work on Balanced Incomplete Block Designs. Other areas covered include Steiner systems, finite geometries, quasigroups, and t-designs.
Combinatorial optimization tolerances calculated in linear time
Goldengorin, Boris; Sierksma, Gerard
2003-01-01
For a given optimal solution to a combinatorial optimization problem, we show, under very natural conditions, the equality of the minimal values of upper and lower tolerances, where the upper tolerances are calculated for the given optimal solution and the lower tolerances outside the optimal
A Model of Students' Combinatorial Thinking
Lockwood, Elise
2013-01-01
Combinatorial topics have become increasingly prevalent in K-12 and undergraduate curricula, yet research on combinatorics education indicates that students face difficulties when solving counting problems. The research community has not yet addressed students' ways of thinking at a level that facilitates deeper understanding of how students…
A Model of Students' Combinatorial Thinking
Lockwood, Elise
2013-01-01
Combinatorial topics have become increasingly prevalent in K-12 and undergraduate curricula, yet research on combinatorics education indicates that students face difficulties when solving counting problems. The research community has not yet addressed students' ways of thinking at a level that facilitates deeper understanding of how students…
Combinatorial optimization tolerances calculated in linear time
Goldengorin, Boris; Sierksma, Gerard
2003-01-01
For a given optimal solution to a combinatorial optimization problem, we show, under very natural conditions, the equality of the minimal values of upper and lower tolerances, where the upper tolerances are calculated for the given optimal solution and the lower tolerances outside the optimal soluti
Switched Systems and Motion Coordination: Combinatorial Challenges
Sadovsky, Alexander V.
2016-01-01
Problems of routing commercial air traffic in a terminal airspace encounter different constraints: separation assurance, aircraft performance limitations, regulations. The general setting of these problems is that of a switched control system. Such a system combines the differentiable motion of the aircraft with the combinatorial choices of choosing precedence when traffic routes merge and choosing branches when the routes diverge. This presentation gives an overview of the problem, the ATM context, related literature, and directions for future research.
Pan, Feng [Los Alamos National Laboratory; Kasiviswanathan, Shiva [Los Alamos National Laboratory
2010-01-01
In the matrix interdiction problem, a real-valued matrix and an integer k is given. The objective is to remove k columns such that the sum over all rows of the maximum entry in each row is minimized. This combinatorial problem is closely related to bipartite network interdiction problem which can be applied to prioritize the border checkpoints in order to minimize the probability that an adversary can successfully cross the border. After introducing the matrix interdiction problem, we will prove the problem is NP-hard, and even NP-hard to approximate with an additive n{gamma} factor for a fixed constant {gamma}. We also present an algorithm for this problem that achieves a factor of (n-k) mUltiplicative approximation ratio.
Introduction to combinatorial designs
Wallis, WD
2007-01-01
Combinatorial theory is one of the fastest growing areas of modern mathematics. Focusing on a major part of this subject, Introduction to Combinatorial Designs, Second Edition provides a solid foundation in the classical areas of design theory as well as in more contemporary designs based on applications in a variety of fields. After an overview of basic concepts, the text introduces balanced designs and finite geometries. The author then delves into balanced incomplete block designs, covering difference methods, residual and derived designs, and resolvability. Following a chapter on the e
A two phase algorithm for solving a class of hard satissfiability problems
J.P. Warners; H. van Maaren
1998-01-01
textabstractThe DIMACS suite of satisfiability (SAT) benchmarks contains a set of instances that are very hard for existing algorithms. These instances arise from learning the parity function on 32 bits. In this paper we develop a two phase algorithm that is capable of solving these instances. In
Manipulating Combinatorial Structures.
Labelle, Gilbert
This set of transparencies shows how the manipulation of combinatorial structures in the context of modern combinatorics can easily lead to interesting teaching and learning activities at every level of education from elementary school to university. The transparencies describe: (1) the importance and relations of combinatorics to science and…
Bioinspired computation in combinatorial optimization: algorithms and their computational complexity
Neumann, Frank; Witt, Carsten
2012-01-01
Bioinspired computation methods, such as evolutionary algorithms and ant colony optimization, are being applied successfully to complex engineering and combinatorial optimization problems, and it is very important that we understand the computational complexity of these algorithms. This tutorials...
The backtracking survey propagation algorithm for solving random K-SAT problems
Marino, Raffaele; Parisi, Giorgio; Ricci-Tersenghi, Federico
2016-10-01
Discrete combinatorial optimization has a central role in many scientific disciplines, however, for hard problems we lack linear time algorithms that would allow us to solve very large instances. Moreover, it is still unclear what are the key features that make a discrete combinatorial optimization problem hard to solve. Here we study random K-satisfiability problems with K=3,4, which are known to be very hard close to the SAT-UNSAT threshold, where problems stop having solutions. We show that the backtracking survey propagation algorithm, in a time practically linear in the problem size, is able to find solutions very close to the threshold, in a region unreachable by any other algorithm. All solutions found have no frozen variables, thus supporting the conjecture that only unfrozen solutions can be found in linear time, and that a problem becomes impossible to solve in linear time when all solutions contain frozen variables.
Memetic firefly algorithm for combinatorial optimization
Fister, Iztok; Fister, Iztok; Brest, Janez
2012-01-01
Firefly algorithms belong to modern meta-heuristic algorithms inspired by nature that can be successfully applied to continuous optimization problems. In this paper, we have been applied the firefly algorithm, hybridized with local search heuristic, to combinatorial optimization problems, where we use graph 3-coloring problems as test benchmarks. The results of the proposed memetic firefly algorithm (MFFA) were compared with the results of the Hybrid Evolutionary Algorithm (HEA), Tabucol, and the evolutionary algorithm with SAW method (EA-SAW) by coloring the suite of medium-scaled random graphs (graphs with 500 vertices) generated using the Culberson random graph generator. The results of firefly algorithm were very promising and showed a potential that this algorithm could successfully be applied in near future to the other combinatorial optimization problems as well.
Research on universal combinatorial coding.
Lu, Jun; Zhang, Zhuo; Mo, Juan
2014-01-01
The conception of universal combinatorial coding is proposed. Relations exist more or less in many coding methods. It means that a kind of universal coding method is objectively existent. It can be a bridge connecting many coding methods. Universal combinatorial coding is lossless and it is based on the combinatorics theory. The combinational and exhaustive property make it closely related with the existing code methods. Universal combinatorial coding does not depend on the probability statistic characteristic of information source, and it has the characteristics across three coding branches. It has analyzed the relationship between the universal combinatorial coding and the variety of coding method and has researched many applications technologies of this coding method. In addition, the efficiency of universal combinatorial coding is analyzed theoretically. The multicharacteristic and multiapplication of universal combinatorial coding are unique in the existing coding methods. Universal combinatorial coding has theoretical research and practical application value.
Combinatorial materials synthesis
Ichiro Takeuchi
2005-10-01
Full Text Available The pace at which major technological changes take place is often dictated by the rate at which new materials are discovered, and the timely arrival of new materials has always played a key role in bringing advances to our society. It is no wonder then that the so-called combinatorial or high-throughput strategy has been embraced by practitioners of materials science in virtually every field. High-throughput experimentation allows simultaneous synthesis and screening of large arrays of different materials. Pioneered by the pharmaceutical industry, the combinatorial method is now widely considered to be a watershed in accelerating the discovery and optimization of new materials1–5.
Combinatorial Reciprocity Theorems
Beck, Matthias
2012-01-01
A common theme of enumerative combinatorics is formed by counting functions that are polynomials evaluated at positive integers. In this expository paper, we focus on four families of such counting functions connected to hyperplane arrangements, lattice points in polyhedra, proper colorings of graphs, and $P$-partitions. We will see that in each instance we get interesting information out of a counting function when we evaluate it at a \\emph{negative} integer (and so, a priori the counting function does not make sense at this number). Our goals are to convey some of the charm these "alternative" evaluations of counting functions exhibit, and to weave a unifying thread through various combinatorial reciprocity theorems by looking at them through the lens of geometry, which will include some scenic detours through other combinatorial concepts.
Gevorkyan, A. S., E-mail: g-ashot@sci.am; Sahakyan, V. V. [National Academy of Sciences of the Republic of Armenia, Institute for Informatics and Automation Problems (Armenia)
2017-03-15
We study the classical 1D Heisenberg spin glasses in the framework of nearest-neighboring model. Based on the Hamilton equations we obtained the system of recurrence equations which allows to perform node-by-node calculations of a spin-chain. It is shown that calculations from the first principles of classical mechanics lead to ℕℙ hard problem, that however in the limit of the statistical equilibrium can be calculated by ℙ algorithm. For the partition function of the ensemble a new representation is offered in the form of one-dimensional integral of spin-chains’ energy distribution.
Lyndon, Roger C
2001-01-01
From the reviews: "This book (...) defines the boundaries of the subject now called combinatorial group theory. (...)it is a considerable achievement to have concentrated a survey of the subject into 339 pages. This includes a substantial and useful bibliography; (over 1100 ÄitemsÜ). ...the book is a valuable and welcome addition to the literature, containing many results not previously available in a book. It will undoubtedly become a standard reference." Mathematical Reviews, AMS, 1979.
Trugenberger, Carlo A
2016-01-01
In a recently developed approach, geometry is modelled as an emergent property of random networks. Here I show that one of these models I proposed is exactly quantum gravity defined in terms of the combinatorial Ricci curvature recently derived by Ollivier. Geometry in the weak (classical) gravity regime arises in a phase transition driven by the condensation of short graph cycles. The strong (quantum) gravity regime corresponds to "small world" random graphs with logarithmic distance scaling.
An Augmented Lagrangian Approach for Scheduling Problems
Nishi, Tatsushi; Konishi, Masami
The paper describes an augmented Lagrangian decomposition and coordination approach for solving single machine scheduling problems to minimize the total weighted tardiness. The problem belongs to the class of NP-hard combinatorial optimization problem. We propose an augmented Lagrangian decomposition and coordination approach, which is commonly used for continuous optimization problems, for solving scheduling problems despite the fact that the problem is nonconvex and non-differentiable. The proposed method shows a good convergence to a feasible solution without heuristically constructing a feasible solution. The performance of the proposed method is compared with that of an ordinary Lagrangian relaxation.
Genetic algorithms for the vehicle routing problem
Volna, Eva
2016-06-01
The Vehicle Routing Problem (VRP) is one of the most challenging combinatorial optimization tasks. This problem consists in designing the optimal set of routes for fleet of vehicles in order to serve a given set of customers. Evolutionary algorithms are general iterative algorithms for combinatorial optimization. These algorithms have been found to be very effective and robust in solving numerous problems from a wide range of application domains. This problem is known to be NP-hard; hence many heuristic procedures for its solution have been suggested. For such problems it is often desirable to obtain approximate solutions, so they can be found fast enough and are sufficiently accurate for the purpose. In this paper we have performed an experimental study that indicates the suitable use of genetic algorithms for the vehicle routing problem.
Theoretical analysis of two ACO approaches for the traveling salesman problem
Kötzing, Timo; Neumann, Frank; Röglin, Heiko
2012-01-01
Bioinspired algorithms, such as evolutionary algorithms and ant colony optimization, are widely used for different combinatorial optimization problems. These algorithms rely heavily on the use of randomness and are hard to understand from a theoretical point of view. This paper contributes...... to the theoretical analysis of ant colony optimization and studies this type of algorithm on one of the most prominent combinatorial optimization problems, namely the traveling salesperson problem (TSP). We present a new construction graph and show that it has a stronger local property than one commonly used...
Marshall, Matthew M; Carrano, Andres L; Dannels, Wendy A
2016-10-01
Individuals who are deaf and hard-of-hearing (DHH) are underrepresented in science, technology, engineering, and mathematics (STEM) professions, and this may be due in part to their level of preparation in the development and retention of mathematical and problem-solving skills. An approach was developed that incorporates experiential learning and best practices of STEM instruction to give first-year DHH students enrolled in a postsecondary STEM program the opportunity to develop problem-solving skills in real-world scenarios. Using an industrial engineering laboratory that provides manufacturing and warehousing environments, students were immersed in real-world scenarios in which they worked on teams to address prescribed problems encountered during the activities. The highly structured, Plan-Do-Check-Act approach commonly used in industry was adapted for the DHH student participants to document and communicate the problem-solving steps. Students who experienced the intervention realized a 14.6% improvement in problem-solving proficiency compared with a control group, and this gain was retained at 6 and 12 months, post-intervention. © The Author 2016. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oup.com.
Combinatorial auctions for electronic business
Y Narahari; Pankaj Dayama
2005-04-01
Combinatorial auctions (CAs) have recently generated signiﬁcant interest as an automated mechanism for buying and selling bundles of goods. They are proving to be extremely useful in numerous e-business applications such as eselling, e-procurement, e-logistics, and B2B exchanges. In this article, we introduce combinatorial auctions and bring out important issues in the design of combinatorial auctions. We also highlight important contributions in current research in this area. This survey emphasizes combinatorial auctions as applied to electronic business situations.
The Yoccoz Combinatorial Analytic Invariant
Petersen, Carsten Lunde; Roesch, Pascale
2008-01-01
In this paper we develop a combinatorial analytic encoding of the Mandelbrot set M. The encoding is implicit in Yoccoz' proof of local connectivity of M at any Yoccoz parameter, i.e. any at most finitely renormalizable parameter for which all periodic orbits are repelling. Using this encoding we...... define an explicit combinatorial analytic modelspace, which is sufficiently abstract that it can serve as a go-between for proving that other sets such as the parabolic Mandelbrot set M1 has the same combinatorial structure as M. As an immediate application we use here the combinatorial-analytic model...
Dynamical System Approaches to Combinatorial Optimization
Starke, Jens
2013-01-01
Several dynamical system approaches to combinatorial optimization problems are described and compared. These include dynamical systems derived from penalty methods; the approach of Hopfield and Tank; self-organizing maps, that is, Kohonen networks; coupled selection equations; and hybrid methods....... Many of them are investigated analytically, and the costs of the solutions are compared numerically with those of solutions obtained by simulated annealing and the costs of a global optimal solution. Using dynamical systems, a solution to the combinatorial optimization problem emerges in the limit...... of large times as an asymptotically stable point of the dynamics. The obtained solutions are often not globally optimal but good approximations of it. Dynamical system and neural network approaches are appropriate methods for distributed and parallel processing. Because of the parallelization...
TARCMO: Theory and Algorithms for Robust, Combinatorial, Multicriteria Optimization
2016-11-28
magnitude in computational experiments on portfolio optimization problems. The research on this topic has been published as [CG15a], where details can...AFRL-AFOSR-UK-TR-2017-0001 TARCMO: Theory and Algorithms for Robust, Combinatorial, Multicriteria Optimization Horst Hamacher Technische Universität...To) 15 May 2013 to 12 May 2016 4. TITLE AND SUBTITLE TARCMO: Theory and Algorithms for Robust, Combinatorial, Multicriteria Optimization 5a. CONTRACT
Exact and Metaheuristic Approaches for a Bi-Objective School Bus Scheduling Problem
2015-01-01
As a class of hard combinatorial optimization problems, the school bus routing problem has received considerable attention in the last decades. For a multi-school system, given the bus trips for each school, the school bus scheduling problem aims at optimizing bus schedules to serve all the trips within the school time windows. In this paper, we propose two approaches for solving the bi-objective school bus scheduling problem: an exact method of mixed integer programming (MIP) and a metaheuri...
Introduction to combinatorial analysis
Riordan, John
2002-01-01
This introduction to combinatorial analysis defines the subject as ""the number of ways there are of doing some well-defined operation."" Chapter 1 surveys that part of the theory of permutations and combinations that finds a place in books on elementary algebra, which leads to the extended treatment of generation functions in Chapter 2, where an important result is the introduction of a set of multivariable polynomials.Chapter 3 contains an extended treatment of the principle of inclusion and exclusion which is indispensable to the enumeration of permutations with restricted position given
Infinitary Combinatory Reduction Systems
Ketema, Jeroen; Simonsen, Jakob Grue
2011-01-01
We define infinitary Combinatory Reduction Systems (iCRSs), thus providing the first notion of infinitary higher-order rewriting. The systems defined are sufficiently general that ordinary infinitary term rewriting and infinitary ¿-calculus are special cases. Furthermore,we generalise a number...... of knownresults fromfirst-order infinitary rewriting and infinitary ¿-calculus to iCRSs. In particular, for fully-extended, left-linear iCRSs we prove the well-known compression property, and for orthogonal iCRSs we prove that (1) if a set of redexes U has a complete development, then all complete developments...
Dynamic Combinatorial Chemistry
Lisbjerg, Micke
This thesis is divided into seven chapters, which can all be read individually. The first chapter, however, contains a general introduction to the chemistry used in the remaining six chapters, and it is therefore recommended to read chapter one before reading the other chapters. Chapter 1...... is a general introductory chapter for the whole thesis. The history and concepts of dynamic combinatorial chemistry are described, as are some of the new and intriguing results recently obtained. Finally, the properties of a broad range of hexameric macrocycles are described in detail. Chapter 2 gives...
Dynamic Combinatorial Chemistry
Lisbjerg, Micke
This thesis is divided into seven chapters, which can all be read individually. The first chapter, however, contains a general introduction to the chemistry used in the remaining six chapters, and it is therefore recommended to read chapter one before reading the other chapters. Chapter 1...... is a general introductory chapter for the whole thesis. The history and concepts of dynamic combinatorial chemistry are described, as are some of the new and intriguing results recently obtained. Finally, the properties of a broad range of hexameric macrocycles are described in detail. Chapter 2 gives...
Semenov, Alexander; Zaikin, Oleg
2016-01-01
In this paper we propose an approach for constructing partitionings of hard variants of the Boolean satisfiability problem (SAT). Such partitionings can be used for solving corresponding SAT instances in parallel. For the same SAT instance one can construct different partitionings, each of them is a set of simplified versions of the original SAT instance. The effectiveness of an arbitrary partitioning is determined by the total time of solving of all SAT instances from it. We suggest the approach, based on the Monte Carlo method, for estimating time of processing of an arbitrary partitioning. With each partitioning we associate a point in the special finite search space. The estimation of effectiveness of the particular partitioning is the value of predictive function in the corresponding point of this space. The problem of search for an effective partitioning can be formulated as a problem of optimization of the predictive function. We use metaheuristic algorithms (simulated annealing and tabu search) to move from point to point in the search space. In our computational experiments we found partitionings for SAT instances encoding problems of inversion of some cryptographic functions. Several of these SAT instances with realistic predicted solving time were successfully solved on a computing cluster and in the volunteer computing project SAT@home. The solving time agrees well with estimations obtained by the proposed method.
Hintermair, Manfred
2013-01-01
In this study, behavioral problems of deaf and hard-of-hearing (D/HH) school-aged children are discussed in the context of executive functioning and communicative competence. Teachers assessed the executive functions of a sample of 214 D/HH students from general schools and schools for the deaf, using a German version of the Behavior Rating Inventory of Executive Functions (BRIEF-D). This was complemented by a questionnaire that measured communicative competence and behavioral problems (German version of the Strengths and Difficulties Questionnaire; SDQ-D). The results in nearly all the scales show a significantly higher problem rate for executive functions in the group of D/HH students compared with a normative sample of hearing children. In the D/HH group, students at general schools had better scores on most scales than students at schools for the deaf. Regression analysis reveals the importance of executive functions and communicative competence for behavioral problems. The relevance of the findings for pedagogical work is discussed. A specific focus on competencies such as self-efficacy or self-control in educational concepts for D/HH students seems to be necessary in addition to extending language competencies.
A Heuristic Design Information Sharing Framework for Hard Discrete Optimization Problems
2007-03-01
and Solow 1993). In addition, if local search is applied and the local optimum obtained is a global optimum, then the problem is solved, though this...Jacobson and Solow (1993) and Armstrong and Jacobson (2005) investigate the complexity of finding polynomial time improvement algorithms for discrete...Applications. Robert E. Krieger Publishing Co., Inc., Malabar, FL. S.H. Jacobson, S.N. Hall, L.A. McLay, J.E. Orosz, 2005a, "Performance Analysis of
Neural blackboard architectures of combinatorial structures in cognition.
van der Velde, Frank; de Kamps, Marc
2006-02-01
Human cognition is unique in the way in which it relies on combinatorial (or compositional) structures. Language provides ample evidence for the existence of combinatorial structures, but they can also be found in visual cognition. To understand the neural basis of human cognition, it is therefore essential to understand how combinatorial structures can be instantiated in neural terms. In his recent book on the foundations of language, Jackendoff described four fundamental problems for a neural instantiation of combinatorial structures: the massiveness of the binding problem, the problem of 2, the problem of variables, and the transformation of combinatorial structures from working memory to long-term memory. This paper aims to show that these problems can be solved by means of neural "blackboard" architectures. For this purpose, a neural blackboard architecture for sentence structure is presented. In this architecture, neural structures that encode for words are temporarily bound in a manner that preserves the structure of the sentence. It is shown that the architecture solves the four problems presented by Jackendoff. The ability of the architecture to instantiate sentence structures is illustrated with examples of sentence complexity observed in human language performance. Similarities exist between the architecture for sentence structure and blackboard architectures for combinatorial structures in visual cognition, derived from the structure of the visual cortex. These architectures are briefly discussed, together with an example of a combinatorial structure in which the blackboard architectures for language and vision are combined. In this way, the architecture for language is grounded in perception. Perspectives and potential developments of the architectures are discussed.
Simple Combinatorial Optimisation Cost Games
van Velzen, S.
2005-01-01
In this paper we introduce the class of simple combinatorial optimisation cost games, which are games associated to {0, 1}-matrices.A coalitional value of a combinatorial optimisation game is determined by solving an integer program associated with this matrix and the characteristic vector of the
Gent, Tiejo van
2012-01-01
The aim of this thesis is to expand the knowledge of mental health problems with deaf and severely hard of hearing children and adolescents in the following domains: 1. The prevalence of mental health problems; 2. Specific intra- and interpersonal aspects of pathogenesis; 3. characteristics of the
Gent, Tiejo van
2012-01-01
The aim of this thesis is to expand the knowledge of mental health problems with deaf and severely hard of hearing children and adolescents in the following domains: 1. The prevalence of mental health problems; 2. Specific intra- and interpersonal aspects of pathogenesis; 3. characteristics of the h
Gems of combinatorial optimization and graph algorithms
Skutella, Martin; Stiller, Sebastian; Wagner, Dorothea
2015-01-01
Are you looking for new lectures for your course on algorithms, combinatorial optimization, or algorithmic game theory? Maybe you need a convenient source of relevant, current topics for a graduate student or advanced undergraduate student seminar? Or perhaps you just want an enjoyable look at some beautiful mathematical and algorithmic results, ideas, proofs, concepts, and techniques in discrete mathematics and theoretical computer science? Gems of Combinatorial Optimization and Graph Algorithms is a handpicked collection of up-to-date articles, carefully prepared by a select group of international experts, who have contributed some of their most mathematically or algorithmically elegant ideas. Topics include longest tours and Steiner trees in geometric spaces, cartograms, resource buying games, congestion games, selfish routing, revenue equivalence and shortest paths, scheduling, linear structures in graphs, contraction hierarchies, budgeted matching problems, and motifs in networks. This ...
Combinatorial Evolution and Forecasting of Communication Protocol ZigBee
Levin, Mark Sh; Kistler, Rolf; Klapproth, Alexander
2012-01-01
The article addresses combinatorial evolution and forecasting of communication protocol for wireless sensor networks (ZigBee). Morphological tree structure (a version of and-or tree) is used as a hierarchical model for the protocol. Three generations of ZigBee protocol are examined. A set of protocol change operations is generated and described. The change operations are used as items for forecasting based on combinatorial problems (e.g., clustering, knapsack problem, multiple choice knapsack problem). Two kinds of preliminary forecasts for the examined communication protocol are considered: (i) direct expert (expert judgment) based forecast, (ii) computation of the forecast(s) (usage of multicriteria decision making and combinatorial optimization problems). Finally, aggregation of the obtained preliminary forecasts is considered (two aggregation strategies are used).
Approximation Algorithms and Hardness of the k-Route Cut Problem
Chuzhoy, Julia; Zhou, Yuan; Vijayaraghavan, Aravindan
2011-01-01
We study the k-route cut problem: given an undirected edge-weighted graph G=(V,E), a collection {(s_1,t_1),(s_2,t_2),...,(s_r,t_r)} of source-sink pairs, and an integer connectivity requirement k, the goal is to find a minimum-weight subset E' of edges to remove, such that the connectivity of every pair (s_i, t_i) falls below k. Specifically, in the edge-connectivity version, EC-kRC, the requirement is that there are at most (k-1) edge-disjoint paths connecting s_i to t_i in G \\ E', while in the vertex-connectivity version, NC-kRC, the same requirement is for vertex-disjoint paths. Prior to our work, poly-logarithmic approximation algorithms have been known for the special case where k >= 3, but no non-trivial approximation algorithms were known for any value k>3, except in the single-source setting. We show an O(k log^{3/2}r)-approximation algorithm for EC-kRC with uniform edge weights, and several polylogarithmic bi-criteria approximation algorithms for EC-kRC and NC-kRC, where the connectivity requirement ...
Measuring systems of hard to get objects: problems with analysis of measurement results
Gilewska, Grazyna
2005-02-01
The problem accessibility of metrological parameters features of objects appeared in many measurements. Especially if it is biological object which parameters very often determined on the basis of indirect research. Accidental component predominate in forming of measurement results with very limited access to measurement objects. Every measuring process has a lot of conditions limiting its abilities to any way processing (e.g. increase number of measurement repetition to decrease random limiting error). It may be temporal, financial limitations, or in case of biological object, small volume of sample, influence measuring tool and observers on object, or whether fatigue effects e.g. at patient. It's taken listing difficulties into consideration author worked out and checked practical application of methods outlying observation reduction and next innovative methods of elimination measured data with excess variance to decrease of mean standard deviation of measured data, with limited aomunt of data and accepted level of confidence. Elaborated methods wee verified on the basis of measurement results of knee-joint width space got from radiographs. Measurements were carried out by indirectly method on the digital images of radiographs. Results of examination confirmed legitimacy to using of elaborated methodology and measurement procedures. Such methodology has special importance when standard scientific ways didn't bring expectations effects.
An explicit combinatorial design
Ma, Xiongfeng
2011-01-01
A combinatorial design is a family of sets that are almost disjoint, which is applied in pseudo random number generations and randomness extractions. The parameter, $\\rho$, quantifying the overlap between the sets within the family, is directly related to the length of a random seed needed and the efficiency of an extractor. Nisan and Wigderson proposed an explicit construction of designs in 1994. Later in 2003, Hartman and Raz proved a bound of $\\rho\\le e^2$ for the Nisan-Wigderson construction. In this work, we prove a tighter bound of $\\rho
Hardness amplification in nondeterministic logspace
Gupta, Sushmita
2007-01-01
A hard problem is one which cannot be easily computed by efficient algorithms. Hardness amplification is a procedure which takes as input a problem of mild hardness and returns a problem of higher hardness. This is closely related to the task of decoding certain error-correcting codes. We show amplification from mild average case hardness to higher average case hardness for nondeterministic logspace and worst-to-average amplification for nondeterministic linspace. Finally we explore possible ...
Criticality and parallelism in combinatorial optimization
Macready, W.G.; Kauffman, S.A. [Santa Fe Institute, NM (United States); Siapas, A.G. [Massachusetts Institute of Technology, Cambridge, MA (United States)
1996-01-05
Local search methods constitute one of the most successful approaches to solving large-scale combinatorial optimization problems. As these methods are increasingly parallelized, optimization performance initially improves, but then abruptly degrades to no matter than that of random search beyond a certain point. The existence of this transition is demonstrated for a family of generalized spin-glass models and the traveling salesman problem. Finite-size scaling is used to characterize size-dependent effects near the transition, and analytical insight is obtained through a mean-field approximation. 17 refs., 5 figs.
Combinatorial Maps with Normalized Knot
Zeps, Dainis
2010-01-01
We consider combinatorial maps with fixed combinatorial knot numbered with augmenting numeration called normalized knot. We show that knot's normalization doesn't affect combinatorial map what concerns its generality. Knot's normalization leads to more concise numeration of corners in maps, e.g., odd or even corners allow easy to follow distinguished cycles in map caused by the fixation of the knot. Knot's normalization may be applied to edge structuring knot too. If both are normalized then one is fully and other partially normalized mutually.
Combinatorial designs constructions and analysis
Stinson, Douglas R
2004-01-01
Created to teach students many of the most important techniques used for constructing combinatorial designs, this is an ideal textbook for advanced undergraduate and graduate courses in combinatorial design theory. The text features clear explanations of basic designs, such as Steiner and Kirkman triple systems, mutual orthogonal Latin squares, finite projective and affine planes, and Steiner quadruple systems. In these settings, the student will master various construction techniques, both classic and modern, and will be well-prepared to construct a vast array of combinatorial designs. Design theory offers a progressive approach to the subject, with carefully ordered results. It begins with simple constructions that gradually increase in complexity. Each design has a construction that contains new ideas or that reinforces and builds upon similar ideas previously introduced. A new text/reference covering all apsects of modern combinatorial design theory. Graduates and professionals in computer science, applie...
Stochastic integrals: a combinatorial approach
Rota, Gian-Carlo; Wallstrom, Timothy C.
1997-01-01
A combinatorial definition of multiple stochastic integrals is given in the setting of random measures. It is shown that some properties of such stochastic integrals, formerly known to hold in special cases, are instances of combinatorial identities on the lattice of partitions of a set. The notion of stochastic sequences of binomial type is introduced as a generalization of special polynomial sequences occuring in stochastic integration, such as Hermite, Poisson–Charlier an...
Combinatorial methods with computer applications
Gross, Jonathan L
2007-01-01
Combinatorial Methods with Computer Applications provides in-depth coverage of recurrences, generating functions, partitions, and permutations, along with some of the most interesting graph and network topics, design constructions, and finite geometries. Requiring only a foundation in discrete mathematics, it can serve as the textbook in a combinatorial methods course or in a combined graph theory and combinatorics course.After an introduction to combinatorics, the book explores six systematic approaches within a comprehensive framework: sequences, solving recurrences, evaluating summation exp
Combinatorial chemistry in the agrosciences.
Lindell, Stephen D; Pattenden, Lisa C; Shannon, Jonathan
2009-06-15
Combinatorial chemistry and high throughput screening have had a profound effect upon the way in which agrochemical companies conduct their lead discovery research. The article reviews recent applications of combinatorial synthesis in the lead discovery process for new fungicides, herbicides and insecticides. The role and importance of bioavailability guidelines, natural products, privileged structures, virtual screening and X-ray crystallographic protein structures on the design of solid- and solution-phase compound libraries is discussed and illustrated.
Relativity in Combinatorial Gravitational Fields
Mao Linfan
2010-04-01
Full Text Available A combinatorial spacetime $(mathscr{C}_G| uboverline{t}$ is a smoothly combinatorial manifold $mathscr{C}$ underlying a graph $G$ evolving on a time vector $overline{t}$. As we known, Einstein's general relativity is suitable for use only in one spacetime. What is its disguise in a combinatorial spacetime? Applying combinatorial Riemannian geometry enables us to present a combinatorial spacetime model for the Universe and suggest a generalized Einstein gravitational equation in such model. Forfinding its solutions, a generalized relativity principle, called projective principle is proposed, i.e., a physics law ina combinatorial spacetime is invariant under a projection on its a subspace and then a spherically symmetric multi-solutions ofgeneralized Einstein gravitational equations in vacuum or charged body are found. We also consider the geometrical structure in such solutions with physical formations, and conclude that an ultimate theory for the Universe maybe established if all such spacetimes in ${f R}^3$. Otherwise, our theory is only an approximate theory and endless forever.
Combinatorial reasoning an introduction to the art of counting
DeTemple, Duane
2014-01-01
Written by well-known scholars in the field, this book introduces combinatorics alongside modern techniques, showcases the interdisciplinary aspects of the topic, and illustrates how to problem solve with a multitude of exercises throughout. The authors' approach is very reader-friendly and avoids the ""scholarly tone"" found in many books on this topic. Combinatorial Reasoning: An Introduction to the Art of Counting: Focuses on enumeration and combinatorial thinking as a way to develop a variety of effective approaches to solving counting problemsIncludes brief summaries of basic concepts f
Approximating the Tutte polynomial of a binary matroid and other related combinatorial polynomials
Goldberg, Leslie Ann
2010-01-01
We consider the problem of approximating certain combinatorial polynomials. First, we consider the problem of approximating the Tutte polynomial of a binary matroid with parameters q>=2 and gamma. (Relative to the classical (x,y) parameterisation, q=(x-1)(y-1) and gamma=y-1.) A graph is a special case of a binary matroid, so earlier work by the authors shows that for q>2 and gamma 2 and gamma>0, the approximation problem is hard for the complexity class #RHPi_1 under approximation-preserving (AP) reducibility. The case gamma=0 corresponds to the infinite-temperature limit of the Potts model, and is computationally trivial. The situation for q=2 is different. For graphic matroids, the region gamma0. It is known that there is no FPRAS unless NP=RP in the in-between region -20 the approximation problem is hard for the complexity class#RHPi_1 under approximation-preserving (AP) reducibility. Thus, unless there is an FPRAS for all of #RHPi_1, the graphic case differs in approximat ion complexity from the binary ma...
A Comparative Study of Meta-heuristic Algorithms for Solving Quadratic Assignment Problem
Gamal Abd El-Nasser A. Said; Mahmoud, Abeer M.; El-Horbaty, El-Sayed M.
2014-01-01
Quadratic Assignment Problem (QAP) is an NP-hard combinatorial optimization problem, therefore, solving the QAP requires applying one or more of the meta-heuristic algorithms. This paper presents a comparative study between Meta-heuristic algorithms: Genetic Algorithm, Tabu Search, and Simulated annealing for solving a real-life (QAP) and analyze their performance in terms of both runtime efficiency and solution quality. The results show that Genetic Algorithm has a better solution quality wh...
Universally Balanced Combinatorial Optimization Games
Xiaotie Deng
2010-09-01
Full Text Available This article surveys studies on universally balanced properties of cooperative games defined in a succinct form. In particular, we focus on combinatorial optimization games in which the values to coalitions are defined through linear optimization programs, possibly combinatorial, that is subject to integer constraints. In economic settings, the integer requirement reflects some forms of indivisibility. We are interested in the classes of games that guarantee a non-empty core no matter what are the admissible values assigned to the parameters defining these programs. We call such classes universally balanced. We present characterization and complexity results on the universally balancedness property for some classes of interesting combinatorial optimization games. In particular, we focus on the algorithmic properties for identifying universally balancedness for the games under discussion.
On some interconnections between combinatorial optimization and extremal graph theory
Cvetković Dragoš M.
2004-01-01
Full Text Available The uniting feature of combinatorial optimization and extremal graph theory is that in both areas one should find extrema of a function defined in most cases on a finite set. While in combinatorial optimization the point is in developing efficient algorithms and heuristics for solving specified types of problems, the extremal graph theory deals with finding bounds for various graph invariants under some constraints and with constructing extremal graphs. We analyze by examples some interconnections and interactions of the two theories and propose some conclusions.
Identities for Generalized Fibonacci Numbers: A Combinatorial Approach
Plaza, A.; Falcon, S.
2008-01-01
This note shows a combinatorial approach to some identities for generalized Fibonacci numbers. While it is a straightforward task to prove these identities with induction, and also by arithmetical manipulations such as rearrangements, the approach used here is quite simple to follow and eventually reduces the proof to a counting problem. (Contains…
Combinatorial Problems of Applied Discrete Mathematics.
1979-12-01
Attenuated Spaces, Utilitas Mathematica, 15(1979) , 3—29. 6. Characterization of Projective Incidence Structures, Geometria Dedicata, 5 (1976), 361—376. 7...Pj rtia l geometries, generalized quadrang les and strong/v regular graf t/ us , • Att i dcl Convegno di Geometria Combinatoria e sue app
From combinatorial optimization to real algebraic geometry and back
Janez Povh
2014-12-01
Full Text Available In this paper, we explain the relations between combinatorial optimization and real algebraic geometry with a special focus to the quadratic assignment problem. We demonstrate how to write a quadratic optimization problem over discrete feasible set as a linear optimization problem over the cone of completely positive matrices. The latter formulation enables a hierarchy of approximations which rely on results from polynomial optimization, a sub-eld of real algebraic geometry.
Combinatorial optimization theory and algorithms
Korte, Bernhard
2002-01-01
Combinatorial optimization is one of the youngest and most active areas of discrete mathematics, and is probably its driving force today. This book describes the most important ideas, theoretical results, and algorithms of this field. It is conceived as an advanced graduate text, and it can also be used as an up-to-date reference work for current research. The book includes the essential fundamentals of graph theory, linear and integer programming, and complexity theory. It covers classical topics in combinatorial optimization as well as very recent ones. The emphasis is on theoretical results and algorithms with provably good performance. Some applications and heuristics are mentioned, too.
Combinatorial synthesis of natural products
Nielsen, John
2002-01-01
for preparation of combinatorial libraries. In other examples, natural products or intermediates have served as building blocks or scaffolds in the synthesis of complex natural products, bioactive analogues or designed hybrid molecules. Finally, structural motifs from the biologically active parent molecule have......Combinatorial syntheses allow production of compound libraries in an expeditious and organized manner immediately applicable for high-throughput screening. Natural products possess a pedigree to justify quality and appreciation in drug discovery and development. Currently, we are seeing a rapid...
Hard electronics; Hard electronics
NONE
1997-03-01
Hard material technologies were surveyed to establish the hard electronic technology which offers superior characteristics under hard operational or environmental conditions as compared with conventional Si devices. The following technologies were separately surveyed: (1) The device and integration technologies of wide gap hard semiconductors such as SiC, diamond and nitride, (2) The technology of hard semiconductor devices for vacuum micro- electronics technology, and (3) The technology of hard new material devices for oxides. The formation technology of oxide thin films made remarkable progress after discovery of oxide superconductor materials, resulting in development of an atomic layer growth method and mist deposition method. This leading research is expected to solve such issues difficult to be easily realized by current Si technology as high-power, high-frequency and low-loss devices in power electronics, high temperature-proof and radiation-proof devices in ultimate electronics, and high-speed and dense- integrated devices in information electronics. 432 refs., 136 figs., 15 tabs.
Integrating packing and distribution problems and optimization through mathematical programming
Fabio Miguel
2016-06-01
Full Text Available This paper analyzes the integration of two combinatorial problems that frequently arise in production and distribution systems. One is the Bin Packing Problem (BPP problem, which involves finding an ordering of some objects of different volumes to be packed into the minimal number of containers of the same or different size. An optimal solution to this NP-Hard problem can be approximated by means of meta-heuristic methods. On the other hand, we consider the Capacitated Vehicle Routing Problem with Time Windows (CVRPTW, which is a variant of the Travelling Salesman Problem (again a NP-Hard problem with extra constraints. Here we model those two problems in a single framework and use an evolutionary meta-heuristics to solve them jointly. Furthermore, we use data from a real world company as a test-bed for the method introduced here.
On an Extension of a Combinatorial Identity
M Rana; A K Agarwal
2009-02-01
Using Frobenius partitions we extend the main results of [4]. This leads to an infinite family of 4-way combinatorial identities. In some particular cases we get even 5-way combinatorial identities which give us four new combinatorial versions of Göllnitz–Gordon identities.
Algorithms in combinatorial design theory
Colbourn, CJ
1985-01-01
The scope of the volume includes all algorithmic and computational aspects of research on combinatorial designs. Algorithmic aspects include generation, isomorphism and analysis techniques - both heuristic methods used in practice, and the computational complexity of these operations. The scope within design theory includes all aspects of block designs, Latin squares and their variants, pairwise balanced designs and projective planes and related geometries.
The evolution of combinatorial phonology
Zuidema, Willem; de Boer, Bart
2009-01-01
A fundamental, universal property of human language is that its phonology is combinatorial. That is, one can identify a set of basic, distinct units (phonemes, syllables) that can be productively combined in many different ways. In this paper, we develop a methodological framework based on evolution
Combinatorial synthesis of natural products
Nielsen, John
2002-01-01
Combinatorial syntheses allow production of compound libraries in an expeditious and organized manner immediately applicable for high-throughput screening. Natural products possess a pedigree to justify quality and appreciation in drug discovery and development. Currently, we are seeing a rapid...
The Yoccoz Combinatorial Analytic Invariant
Petersen, Carsten Lunde; Roesch, Pascale
2008-01-01
In this paper we develop a combinatorial analytic encoding of the Mandelbrot set M. The encoding is implicit in Yoccoz' proof of local connectivity of M at any Yoccoz parameter, i.e. any at most finitely renormalizable parameter for which all periodic orbits are repelling. Using this encoding we ...
Theory of periodically specified problems: Complexity and approximability
Marathe, M.V. [Los Alamos National Lab., NM (United States); Hunt, H.B. III; Stearns, R.E.; Rosenkrantz, D.J. [Univ. at Albany - SUNY, NY (United States). Dept. of Computer Science
1997-12-05
We study the complexity and the efficient approximability of graph and satisfiability problems when specified using various kinds of periodic specifications studied. The general results obtained include the following: (1) We characterize the complexities of several basic generalized CNF satisfiability problems SAT(S) [Sc78], when instances are specified using various kinds of 1- and 2-dimensional periodic specifications. We outline how this characterization can be used to prove a number of new hardness results for the complexity classes DSPACE(n), NSPACE(n), DEXPTIME, NEXPTIME, EXPSPACE etc. These results can be used to prove in a unified way the hardness of a number of combinatorial problems when instances are specified succinctly using various succient specifications considered in the literature. As one corollary, we show that a number of basic NP-hard problems because EXPSPACE-hard when inputs are represented using 1-dimensional infinite periodic wide specifications. This answers a long standing open question posed by Orlin. (2) We outline a simple yet a general technique to devise approximation algorithms with provable worst case performance guarantees for a number of combinatorial problems specified periodically. Our efficient approximation algorithms and schemes are based on extensions of the ideas and represent the first non-trivial characterization of a class of problems having an {epsilon}-approximation (or PTAS) for periodically specified NEXPTIME-hard problems. Two of properties of our results are: (i) For the first time, efficient approximation algorithms and schemes have been developed for natural NEXPTIME-complete problems. (ii) Our results are the first polynomial time approximation algorithms with good performance guarantees for hard problems specified using various kinds of periodic specifications considered in this paper.
Solving the Generalized Vehicle Routing Problem with an ACS-based Algorithm
Pop, Petrica Claudiu; Pintea, Camelia; Zelina, Ioana; Dumitrescu, Dan
2009-04-01
Ant colony system is a metaheuristic algorithm inspired by the behavior of real ants and was proposed by Dorigo et al. as a method for solving hard combinatorial optimization problems. In this paper we show its successful application to solving a network design problem: Generalized Vehicle Routing Problem. The Generalized Vehicle Routing Problem (GVRP) is the problem of designing optimal delivery or collection routes, subject to capacity restrictions, from a given depot to a number of predefined, mutually exclusive and exhaustive clusters. Computational results for several benchmark problems are reported.
A combinatorial morphospace for angiosperm pollen
Mander, Luke
2016-04-01
The morphology of angiosperm (flowering plant) pollen is extraordinarily diverse. This diversity results from variations in the morphology of discrete anatomical components. These components include the overall shape of a pollen grain, the stratification of the exine, the number and form of any apertures, the type of dispersal unit, and the nature of any surface ornamentation. Different angiosperm pollen morphotypes reflect different combinations of these discrete components. In this talk, I ask the following question: given the anatomical components of angiosperm pollen that are known to exist in the plant kingdom, how many unique biologically plausible combinations of these components are there? I explore this question from the perspective of enumerative combinatorics using an algorithm I have written in the Python programming language. This algorithm (1) calculates the number of combinations of these components; (2) enumerates those combinations; and (3) graphically displays those combinations. The result is a combinatorial morphospace that reflects an underlying notion that the process of morphogenesis in angiosperm pollen can be thought of as an n choose k counting problem. I compare the morphology of extant and fossil angiosperm pollen grains to this morphospace, and suggest that from a combinatorial point of view angiosperm pollen is not as diverse as it could be, which may be a result of developmental constraints.
Combinatorial Multiobjective Optimization Using Genetic Algorithms
Crossley, William A.; Martin. Eric T.
2002-01-01
The research proposed in this document investigated multiobjective optimization approaches based upon the Genetic Algorithm (GA). Several versions of the GA have been adopted for multiobjective design, but, prior to this research, there had not been significant comparisons of the most popular strategies. The research effort first generalized the two-branch tournament genetic algorithm in to an N-branch genetic algorithm, then the N-branch GA was compared with a version of the popular Multi-Objective Genetic Algorithm (MOGA). Because the genetic algorithm is well suited to combinatorial (mixed discrete / continuous) optimization problems, the GA can be used in the conceptual phase of design to combine selection (discrete variable) and sizing (continuous variable) tasks. Using a multiobjective formulation for the design of a 50-passenger aircraft to meet the competing objectives of minimizing takeoff gross weight and minimizing trip time, the GA generated a range of tradeoff designs that illustrate which aircraft features change from a low-weight, slow trip-time aircraft design to a heavy-weight, short trip-time aircraft design. Given the objective formulation and analysis methods used, the results of this study identify where turboprop-powered aircraft and turbofan-powered aircraft become more desirable for the 50 seat passenger application. This aircraft design application also begins to suggest how a combinatorial multiobjective optimization technique could be used to assist in the design of morphing aircraft.
Hard electronics; Hard electronics
NONE
1998-03-01
In the fields of power conversion devices and broadcasting/communication amplifiers, high power, high frequency and low losses are desirable. Further, for electronic elements in aerospace/aeronautical/geothermal surveys, etc., heat resistance to 500degC is required. Devices which respond to such hard specifications are called hard electronic devices. However, with Si which is at the core of the present electronics, the specifications cannot fully be fulfilled because of the restrictions arising from physical values. Accordingly, taking up new device materials/structures necessary to construct hard electronics, technologies to develop these to a level of IC were examined and studied. They are a technology to make devices/IC of new semiconductors such as SiC, diamond, etc. which can handle higher temperature, higher power and higher frequency than Si and also is possible of reducing losses, a technology to make devices of hard semiconducter materials such as a vacuum microelectronics technology using ultra-micro/high-luminance electronic emitter using negative electron affinity which diamond, etc. have, a technology to make devices of oxides which have various electric properties, etc. 321 refs., 194 figs., 8 tabs.
K. Bristow
2011-01-01
Full Text Available Background. In the UK, most people with mental health problems are managed in primary care. However, many individuals in need of help are not able to access care, either because it is not available, or because the individual's interaction with care-givers deters or diverts help-seeking. Aims. To understand the experience of seeking care for distress from the perspective of potential patients from “hard-to-reach” groups. Methods. A qualitative study using semi-structured interviews, analysed using a thematic framework. Results. Access to primary care is problematic in four main areas: how distress is conceptualised by individuals, the decision to seek help, barriers to help-seeking, and navigating and negotiating services. Conclusion. There are complex reasons why people from “hard-to-reach” groups may not conceptualise their distress as a biomedical problem. In addition, there are particular barriers to accessing primary care when distress is recognised by the person and help-seeking is attempted. We suggest how primary care could be more accessible to people from “hard-to-reach” groups including the need to offer a flexible, non-biomedical response to distress.
Two Reformulations for the Dynamic Quadratic Assignment Problem
Sirirat Muenvanichakul
2010-01-01
Full Text Available Problem statement: The Dynamic Quadratic Assignment Problem (DQAP, an NP-hard problem, is outlined and reformulated in two alternative models: Linearized model and logic-based model. Approach: The solution methods for both models based on combinatorial methods (Benders Decomposition and Approximate Dynamic Programming and constraint logic programming, respectively, are proposed. Results: Proofs of model equivalence and solution methodology are presented. Conclusion: Both proposed models are more simplified leading to possible hybrid adaptations of existing techniques for more practical approaches.
Combinatorial Properties of Finite Models
Hubicka, Jan
2010-01-01
We study countable embedding-universal and homomorphism-universal structures and unify results related to both of these notions. We show that many universal and ultrahomogeneous structures allow a concise description (called here a finite presentation). Extending classical work of Rado (for the random graph), we find a finite presentation for each of the following classes: homogeneous undirected graphs, homogeneous tournaments and homogeneous partially ordered sets. We also give a finite presentation of the rational Urysohn metric space and some homogeneous directed graphs. We survey well known structures that are finitely presented. We focus on structures endowed with natural partial orders and prove their universality. These partial orders include partial orders on sets of words, partial orders formed by geometric objects, grammars, polynomials and homomorphism orders for various combinatorial objects. We give a new combinatorial proof of the existence of embedding-universal objects for homomorphism-defined...
Stem cells and combinatorial science.
Fang, Yue Qin; Wong, Wan Qing; Yap, Yan Wen; Orner, Brendan P
2007-09-01
Stem cell-based technologies have the potential to help cure a number of cell degenerative diseases. Combinatorial and high throughput screening techniques could provide tools to control and manipulate the self-renewal and differentiation of stem cells. This review chronicles historic and recent progress in the stem cell field involving both pluripotent and multipotent cells, and it highlights relevant cellular signal transduction pathways. This review further describes screens using libraries of soluble, small-molecule ligands, and arrays of molecules immobilized onto surfaces while proposing future trends in similar studies. It is hoped that by reviewing both the stem cell and the relevant high throughput screening literature, this paper can act as a resource to the combinatorial science community.
Combinatorial Approach of Associative Classification
P. R. Pal; R.C. Jain
2010-01-01
Association rule mining and classification are two important techniques of data mining in knowledge discovery process. Integration of these two has produced class association rule mining or associative classification techniques, which in many cases have shown better classification accuracy than conventional classifiers. Motivated by this study we have explored and applied the combinatorial mathematics in class association rule mining in this paper. Our algorithm is based on producing co...
Combinatorial aspects of covering arrays
Charles J. Colbourn
2004-11-01
Full Text Available Covering arrays generalize orthogonal arrays by requiring that t -tuples be covered, but not requiring that the appearance of t -tuples be balanced.Their uses in screening experiments has found application in software testing, hardware testing, and a variety of fields in which interactions among factors are to be identified. Here a combinatorial view of covering arrays is adopted, encompassing basic bounds, direct constructions, recursive constructions, algorithmic methods, and applications.
Combinatorics of bicubic maps with hard particles
Bouttier, J.; Di Francesco, P.; Guitter, E.
2005-05-01
We present a purely combinatorial solution of the problem of enumerating planar bicubic maps with hard particles. This is done by the use of a bijection with a particular class of blossom trees with particles, obtained by an appropriate cutting of the maps. Although these trees have no simple local characterization, we prove that their enumeration may be performed upon introducing a larger class of 'admissible' trees with possibly doubly occupied edges and summing them with appropriate signed weights. The proof relies on an extension of the cutting procedure allowing for the presence on the maps of special non-sectile edges. The admissible trees are characterized by simple local rules, allowing eventually for an exact enumeration of planar bicubic maps with hard particles. We also discuss generalizations for maps with particles subject to more general exclusion rules and show how to re-derive the enumeration of quartic maps with Ising spins in the present framework of admissible trees. We finally comment on a possible interpretation in terms of branching processes.
Genetic Algorithm Based Combinatorial Auction Method for Multi-Robot Task Allocation
GONG Jian-wei; HUANG Wan-ning; XIONG Guang-ming; MAN Yi-ming
2007-01-01
An improved genetic algorithm is proposed to solve the problem of bad real-time performance or inability to get a global optimal/better solution when applying single-item auction (SIA) method or combinatorial auction method to multi-robot task allocation.The genetic algorithm based combinatorial auction (GACA) method which combines the basic-genetic algorithm with a new concept of ringed chromosome is used to solve the winner determination problem (WDP) of combinatorial auction.The simulation experiments are conducted in OpenSim, a multi-robot simulator.The results show that GACA can get a satisfying solution in a reasonable shot time, and compared with SIA or parthenogenesis algorithm combinatorial auction (PGACA) method, it is the simplest and has higher search efficiency, also, GACA can get a global better/optimal solution and satisfy the high real-time requirement of multi-robot task allocation.
Some unsolved problems in discrete mathematics and mathematical cybernetics
Korshunov, Aleksei D.
2009-10-01
There are many unsolved problems in discrete mathematics and mathematical cybernetics. Writing a comprehensive survey of such problems involves great difficulties. First, such problems are rather numerous and varied. Second, they greatly differ from each other in degree of completeness of their solution. Therefore, even a comprehensive survey should not attempt to cover the whole variety of such problems; only the most important and significant problems should be reviewed. An impersonal choice of problems to include is quite hard. This paper includes 13 unsolved problems related to combinatorial mathematics and computational complexity theory. The problems selected give an indication of the author's studies for 50 years; for this reason, the choice of the problems reviewed here is, to some extent, subjective. At the same time, these problems are very difficult and quite important for discrete mathematics and mathematical cybernetics. Bibliography: 74 items.
Path following algorithm for the graph matching problem
Zaslavskiy, Mikhail; Vert, Jean-Philippe
2008-01-01
We propose a convex-concave programming approach for the labeled weighted graph matching problem. The convex-concave programming formulation is obtained by rewriting the graph matching problem as a least-square problem on the set of permutation matrices and relaxing it to two different optimization problems: a quadratic convex and a quadratic concave optimization problem on the set of doubly stochastic matrices. The concave relaxation has the same global minimum as the initial graph matching problem, but the search for its global minimum is also a hard combinatorial problem. We therefore construct an approximation of the concave problem solution by following a solution path of a convex-concave problem obtained by linear interpolation of the convex and concave formulations, starting from the convex relaxation. This method allows to easily integrate the information on graph label similarities into the optimization problem, and therefore to perform labeled graph matching. The algorithm is compared with some of t...
Some unsolved problems in discrete mathematics and mathematical cybernetics
Korshunov, Aleksei D [S.L. Sobolev Institute for Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk (Russian Federation)
2009-10-31
There are many unsolved problems in discrete mathematics and mathematical cybernetics. Writing a comprehensive survey of such problems involves great difficulties. First, such problems are rather numerous and varied. Second, they greatly differ from each other in degree of completeness of their solution. Therefore, even a comprehensive survey should not attempt to cover the whole variety of such problems; only the most important and significant problems should be reviewed. An impersonal choice of problems to include is quite hard. This paper includes 13 unsolved problems related to combinatorial mathematics and computational complexity theory. The problems selected give an indication of the author's studies for 50 years; for this reason, the choice of the problems reviewed here is, to some extent, subjective. At the same time, these problems are very difficult and quite important for discrete mathematics and mathematical cybernetics. Bibliography: 74 items.
Rich Vehicle Routing Problems and Applications
Wen, Min
The Vehicle Routing Problem (VRP) is one of the most important and challenging optimization problems in the field of Operations Research. It was introduced by Dantzig and Ramser (1959) and defined as the problem of designing the optimal set of routes for a fleet of vehicles in order to serve...... a given set of customers. The VRP is a computationally hard combinatorial problem and has been intensively studied by numerous researchers in the last fifty years. Due to the significant economic benefit that can be achieved by optimizing the routing problems in practice, more and more attention has been...... given to various extensions of the VRP that arise in real life. These extensions are often called Rich Vehicle Routing Problems (RVRPs). In contrast to the research of classical VRP that focuses on the idealized models with unrealistic assumptions, the research of RVRPs considers those complicated...
Dynamic Combinatorial Libraries : From Exploring Molecular Recognition to Systems Chemistry
Li, Jianwei; Nowak, Piotr; Otto, Sijbren
2013-01-01
Dynamic combinatorial chemistry (DCC) is a subset of combinatorial chemistry where the library members interconvert continuously by exchanging building blocks with each other. Dynamic combinatorial libraries (DCLs) are powerful tools for discovering the unexpected and have given rise to many
Fairness in Combinatorial Auctioning Systems
Saini, Megha
2008-01-01
One of the Multi-Agent Systems that is widely used by various government agencies, buyers and sellers in a market economy, in such a manner so as to attain optimized resource allocation, is the Combinatorial Auctioning System (CAS). We study another important aspect of resource allocations in CAS, namely fairness. We present two important notions of fairness in CAS, extended fairness and basic fairness. We give an algorithm that works by incorporating a metric to ensure fairness in a CAS that uses the Vickrey-Clark-Groves (VCG) mechanism, and uses an algorithm of Sandholm to achieve optimality. Mathematical formulations are given to represent measures of extended fairness and basic fairness.
Application of Viral Systems for Single-Machine Total Weighted Tardiness Problem
Santosa, Budi; Affandi, Umar
2013-06-01
In this paper, a relatively new algorithm inspired by the viral replication system called Viral Systems is used to solve the Single-Machine Total Weighted Tardiness (SMTWTP). SMTWTP is a job scheduling problem which is one of classical combinatorial problems known as np-hard problems. This algorithm makes the process of finding solutions through neighborhood and mutation mechanism. The experiment was conducted to evaluate its performance. There are seven parameters which are required to tune in to find best solution. The experiment was implemented on data sets of 40 jobs, 50 jobs, and 100 jobs. The results show that the algorithm can solve 235 optimally out of 275 problems.
Combinatorial Interpretation of General Eulerian Numbers
Tingyao Xiong
2014-01-01
Full Text Available Since the 1950s, mathematicians have successfully interpreted the traditional Eulerian numbers and q-Eulerian numbers combinatorially. In this paper, the authors give a combinatorial interpretation to the general Eulerian numbers defined on general arithmetic progressions a,a+d,a+2d,….
Combinatorial Solutions to Normal Ordering of Bosons
Blasiak, P; Horzela, A; Penson, K A; Solomon, A I
2005-01-01
We present a combinatorial method of constructing solutions to the normal ordering of boson operators. Generalizations of standard combinatorial notions - the Stirling and Bell numbers, Bell polynomials and Dobinski relations - lead to calculational tools which allow to find explicitly normally ordered forms for a large class of operator functions.
Combinatorial Properties of Finite Models
Hubicka, Jan
2010-09-01
We study countable embedding-universal and homomorphism-universal structures and unify results related to both of these notions. We show that many universal and ultrahomogeneous structures allow a concise description (called here a finite presentation). Extending classical work of Rado (for the random graph), we find a finite presentation for each of the following classes: homogeneous undirected graphs, homogeneous tournaments and homogeneous partially ordered sets. We also give a finite presentation of the rational Urysohn metric space and some homogeneous directed graphs. We survey well known structures that are finitely presented. We focus on structures endowed with natural partial orders and prove their universality. These partial orders include partial orders on sets of words, partial orders formed by geometric objects, grammars, polynomials and homomorphism orders for various combinatorial objects. We give a new combinatorial proof of the existence of embedding-universal objects for homomorphism-defined classes of structures. This relates countable embedding-universal structures to homomorphism dualities (finite homomorphism-universal structures) and Urysohn metric spaces. Our explicit construction also allows us to show several properties of these structures.
A Combinatorial Auction Based Algorithm for Flexible Seat Reservation Systems
Otomura, Kazutoshi; Tomii, Norio
We present algorithms for flexible seat distribution problems, which is defined as a problem to give an appropriate travel plan to each passenger after receiving their requests concerning their travel demands. Seat distribution problems occur when a flexible seat reservation system is implemented in which passengers are allowed to reserve seats by submitting their demands instead of specifying trains. To solve the seat distribution problem, we have formalized it as a winner determination problem of the combinatorial auction mechanism. It should be noted that difficulty of the seat distribution problem varies depending on instances of the problem, because the number of demands often varies and users' requests sometimes converge on particular trains. This suggests that in order to get solutions with high quality, algorithms that appropriately control the search space are indispensable. In this paper, we present three kinds of such algorithms for the seat distribution problem together with the results of several experiments.
Song, Bosheng; Pérez-Jiménez, Mario J; Pan, Linqiang
2015-04-01
P systems are computing models inspired by some basic features of biological membranes. In this work, membrane division, which provides a way to obtain an exponential workspace in linear time, is introduced into (cell-like) P systems with communication (symport/antiport) rules, where objects are never modified but they just change their places. The computational efficiency of this kind of P systems is studied. Specifically, we present a (uniform) linear time solution to the NP-complete problem, Subset Sum by using division rules for elementary membranes and communication rules of length at most 3. We further prove that such P system allowing division rules for non-elementary membranes can efficiently solve the PSPACE-complete problem, QSAT in a uniform way.
Parsing Combinatory Categorial Grammar with Answer Set Programming: Preliminary Report
Lierler, Yuliya
2011-01-01
Combinatory categorial grammar (CCG) is a grammar formalism used for natural language parsing. CCG assigns structured lexical categories to words and uses a small set of combinatory rules to combine these categories to parse a sentence. In this work we propose and implement a new approach to CCG parsing that relies on a prominent knowledge representation formalism, answer set programming (ASP) - a declarative programming paradigm. We formulate the task of CCG parsing as a planning problem and use an ASP computational tool to compute solutions that correspond to valid parses. Compared to other approaches, there is no need to implement a specific parsing algorithm using such a declarative method. Our approach aims at producing all semantically distinct parse trees for a given sentence. From this goal, normalization and efficiency issues arise, and we deal with them by combining and extending existing strategies. We have implemented a CCG parsing tool kit - AspCcgTk - that uses ASP as its main computational mean...
Quasi-combinatorial energy landscapes for nanoalloy structure optimisation.
Schebarchov, D; Wales, D J
2015-11-14
We formulate nanoalloy structure prediction as a mixed-variable optimisation problem, where the homotops can be associated with an effective, quasi-combinatorial energy landscape in permutation space. We survey this effective landscape for a representative set of binary systems modelled by the Gupta potential. In segregating systems with small lattice mismatch, we find that homotops have a relatively straightforward landscape with few local optima - a scenario well-suited for local (combinatorial) optimisation techniques that scale quadratically with system size. Combining these techniques with multiple local-neighbourhood structures yields a search for multiminima, and we demonstrate that generalised basin-hopping with a metropolis acceptance criterion in the space of multiminima can then be effective for global optimisation of binary and ternary nanoalloys.
Xie, Zongtang; Xu, Jiuping; Wu, Zhibin
2017-02-01
Earthquake exposure has often been associated with psychological distress. However, little is known about the cumulative effect of exposure to two earthquakes on psychological distress and in particular, the effect on the development of post-traumatic stress disorder (PTSD), anxiety and depression disorders. This study explored the effect of exposure on mental health outcomes after a first earthquake and again after a second earthquake. A population-based mental health survey using self-report questionnaires was conducted on 278 people in the hard-hit areas of Lushan and Baoxing Counties 13-16 months after the Wenchuan earthquake (Sample 1). 191 of these respondents were evaluated again 8-9 months after the Lushan earthquake (Sample 2), which struck almost 5 years after the Wenchuan earthquake. In Sample 1, the prevalence rates for PTSD, anxiety and depression disorders were 44.53, 54.25 and 51.82%, respectively, and in Sample 2 the corresponding rates were 27.27, 38.63 and 36.93%. Females, the middle-aged, those of Tibetan nationality, and people who reported fear during the earthquake were at an increased risk of experiencing post-traumatic symptoms. Although the incidence of PTSD, anxiety and depression disorders decreased from Sample 1 to Sample 2, the cumulative effect of exposure to two earthquakes on mental health problems was serious in the hard-hit areas. Therefore, it is important that psychological counseling be provided for earthquake victims, and especially those exposed to multiple earthquakes.
Petters, Dean; Hogg, David
2014-01-01
Cognitive Science is a discipline that brings together research in natural and artificial systems and this is clearly reflected in the diverse contributions to From Animals to Robots and Back: Reflections on Hard Problems in the Study of Cognition. In tribute to Aaron Sloman and his pioneering work in Cognitive Science and Artificial Intelligence, the editors have collected a unique collection of cross-disciplinary papers that include work on: · intelligent robotics; · philosophy of cognitive science; · emotional research · computational vision; · comparative psychology; and · human-computer interaction. Key themes such as the importance of taking an architectural view in approaching cognition, run through the text. Drawing on the expertize of leading international researchers, contemporary debates in the study of natural and artificial cognition are addressed from complementary and contrasting perspectives with key issues being outlined at various levels of abstraction. From Animals to Robots and Back:...
Combinatorial Chemistry for Optical Sensing Applications
Díaz-García, M. E.; Luis, G. Pina; Rivero-Espejel, I. A.
The recent interest in combinatorial chemistry for the synthesis of selective recognition materials for optical sensing applications is presented. The preparation, screening, and applications of libraries of ligands and chemosensors against molecular species and metal ions are first considered. Included in this chapter are also the developments involving applications of combinatorial approaches to the discovery of sol-gel and acrylic-based imprinted materials for optical sensing of antibiotics and pesticides, as well as libraries of doped sol-gels for high-throughput optical sensing of oxygen. The potential of combinatorial chemistry applied to the discovery of new sensing materials is highlighted.
Combinatorial Discovery and Optimization of New Materials
Gao Chen; Zhang Xinyi; Yan Dongsheng
2001-01-01
The concept of the combinatorial discovery and optimization of new materials, and its background,importance, and application, as well as its current status in the world, are briefly reviewed in this paper.
Cubical version of combinatorial differential forms
Kock, Anders
2010-01-01
The theory of combinatorial differential forms is usually presented in simplicial terms. We present here a cubical version; it depends on the possibility of forming affine combinations of mutual neighbour points in a manifold, in the context of synthetic differential geometry.......The theory of combinatorial differential forms is usually presented in simplicial terms. We present here a cubical version; it depends on the possibility of forming affine combinations of mutual neighbour points in a manifold, in the context of synthetic differential geometry....
Colored Traveling Salesman Problem.
Li, Jun; Zhou, MengChu; Sun, Qirui; Dai, Xianzhong; Yu, Xiaolong
2015-11-01
The multiple traveling salesman problem (MTSP) is an important combinatorial optimization problem. It has been widely and successfully applied to the practical cases in which multiple traveling individuals (salesmen) share the common workspace (city set). However, it cannot represent some application problems where multiple traveling individuals not only have their own exclusive tasks but also share a group of tasks with each other. This work proposes a new MTSP called colored traveling salesman problem (CTSP) for handling such cases. Two types of city groups are defined, i.e., each group of exclusive cities of a single color for a salesman to visit and a group of shared cities of multiple colors allowing all salesmen to visit. Evidences show that CTSP is NP-hard and a multidepot MTSP and multiple single traveling salesman problems are its special cases. We present a genetic algorithm (GA) with dual-chromosome coding for CTSP and analyze the corresponding solution space. Then, GA is improved by incorporating greedy, hill-climbing (HC), and simulated annealing (SA) operations to achieve better performance. By experiments, the limitation of the exact solution method is revealed and the performance of the presented GAs is compared. The results suggest that SAGA can achieve the best quality of solutions and HCGA should be the choice making good tradeoff between the solution quality and computing time.
Paweł Sitek
2016-01-01
Full Text Available This paper presents a hybrid method for modeling and solving supply chain optimization problems with soft, hard, and logical constraints. Ability to implement soft and logical constraints is a very important functionality for supply chain optimization models. Such constraints are particularly useful for modeling problems resulting from commercial agreements, contracts, competition, technology, safety, and environmental conditions. Two programming and solving environments, mathematical programming (MP and constraint logic programming (CLP, were combined in the hybrid method. This integration, hybridization, and the adequate multidimensional transformation of the problem (as a presolving method helped to substantially reduce the search space of combinatorial models for supply chain optimization problems. The operation research MP and declarative CLP, where constraints are modeled in different ways and different solving procedures are implemented, were linked together to use the strengths of both. This approach is particularly important for the decision and combinatorial optimization models with the objective function and constraints, there are many decision variables, and these are summed (common in manufacturing, supply chain management, project management, and logistic problems. The ECLiPSe system with Eplex library was proposed to implement a hybrid method. Additionally, the proposed hybrid transformed model is compared with the MILP-Mixed Integer Linear Programming model on the same data instances. For illustrative models, its use allowed finding optimal solutions eight to one hundred times faster and reducing the size of the combinatorial problem to a significant extent.
New Public Key Cryptosystems from Combinatorial Group Theory
TANG Xueming; WANG Xiaofei; HONG Fan; CUI Guohua
2006-01-01
External direct product of some low layer groups such as braid groups and general Artin groups, with a kind of special group action on it, provides a secure cryptographic computation platform, which can keep secure in the quantum computing epoch. Three hard problems on this new platform, Subgroup Root Problem, Multi-variant Subgroup Root Problem and Subgroup Action Problem are presented and well analyzed, which all have no relations with conjugacy. New secure public key encryption system and key agreement protocol are designed based on these hard problems. The new cryptosystems can be implemented in a general group environment other than in braid or Artin groups.
Solving the 0/1 Knapsack Problem by a Biomolecular DNA Computer
Hassan Taghipour
2013-01-01
Full Text Available Solving some mathematical problems such as NP-complete problems by conventional silicon-based computers is problematic and takes so long time. DNA computing is an alternative method of computing which uses DNA molecules for computing purposes. DNA computers have massive degrees of parallel processing capability. The massive parallel processing characteristic of DNA computers is of particular interest in solving NP-complete and hard combinatorial problems. NP-complete problems such as knapsack problem and other hard combinatorial problems can be easily solved by DNA computers in a very short period of time comparing to conventional silicon-based computers. Sticker-based DNA computing is one of the methods of DNA computing. In this paper, the sticker based DNA computing was used for solving the 0/1 knapsack problem. At first, a biomolecular solution space was constructed by using appropriate DNA memory complexes. Then, by the application of a sticker-based parallel algorithm using biological operations, knapsack problem was resolved in polynomial time.
Topics in combinatorial pattern matching
Vildhøj, Hjalte Wedel
Problem. Given m documents of total length n, we consider the problem of finding a longest string common to at least d ≥ 2 of the documents. This problem is known as the longest common substring (LCS) problem and has a classic O(n) space and O(n) time solution (Weiner [FOCS’73], Hui [CPM’92]). However...
Distributed Systems: The Hard Problems
CERN. Geneva
2015-01-01
**Nicholas Bellerophon** works as a client services engineer at Basho Technologies, helping customers setup and run distributed systems at scale in the wild. He has also worked in massively multiplayer games, and recently completed a live scalable simulation engine. He is an avid TED-watcher with interests in many areas of the arts, science, and engineering, including of course high-energy physics.
林培群; 徐建闽
2012-01-01
针对国内外许多城市的BRT专用道仅有1个车道、车辆进站排队容易造成通道阻塞的情况,首先以最小化排队概率为目标,推导出车站组的停靠线路组合优化模型,然后定义上游交叉口的累积效应系数以使模型适应车辆间歇性批量到站的情况,随后针对模型的求解,给出了一种n进制数编码的新的遗传算法.算例以广州市某典型BRT车站组为例进行停靠线路配置优化,并利用VISSIM软件对原始方案及优化方案进行多次仿真和对比,结果表明所提出的方法能有效地缓解公交车辆的进站排队现象,并降低泊位占有率,减少停车次数和行程时间.%Queuing in the bus station often causes traffic jam owing to the fact that BRT system in many cities contains only one lane. In order to relieve this crunch, firstly, a combinatorial optimization model of bus stop in BRT station group was put forward to minimize the queuing probability, then by defining the intersection vehicle cumulative effect coefficient, the optimization model was improved to adapt to intermittent bus batch arrivals caused by the upstream intersection. Furthermore, a genetic algorithm with n-based number encoding was put forward to solve the optimization model. Finally, several bus stop optimization programs of a typical station group in Guangzhou BRT system were obtained in the example, and the simulated results of the original and the new programs from VISSIM software showed that the proposed method could reduce the queuing situation effectively, and decrease the berth occupation rate, bus stop times and travel time simultaneously.
Single-Parameter Combinatorial Auctions with Partially Public Valuations
Goel, Gagan; Karande, Chinmay; Wang, Lei
We consider the problem of designing truthful auctions, when the bidders' valuations have a public and a private component. In particular, we consider combinatorial auctions where the valuation of an agent i for a set S of items can be expressed as v i f(S), where v i is a private single parameter of the agent, and the function f is publicly known. Our motivation behind studying this problem is two-fold: (a) Such valuation functions arise naturally in the case of ad-slots in broadcast media such as Television and Radio. For an ad shown in a set S of ad-slots, f(S) is, say, the number of unique viewers reached by the ad, and v i is the valuation per-unique-viewer. (b) From a theoretical point of view, this factorization of the valuation function simplifies the bidding language, and renders the combinatorial auction more amenable to better approximation factors. We present a general technique, based on maximal-in-range mechanisms, that converts any α-approximation non-truthful algorithm (α ≤ 1) for this problem into Ω(α/log{n}) and Ω(α)-approximate truthful mechanisms which run in polynomial time and quasi-polynomial time, respectively.
A Comparative Study of Meta-heuristic Algorithms for Solving Quadratic Assignment Problem
Gamal Abd El-Nasser A. Said
2014-01-01
Full Text Available Quadratic Assignment Problem (QAP is an NP-hard combinatorial optimization problem, therefore, solving the QAP requires applying one or more of the meta-heuristic algorithms. This paper presents a comparative study between Meta-heuristic algorithms: Genetic Algorithm, Tabu Search, and Simulated annealing for solving a real-life (QAP and analyze their performance in terms of both runtime efficiency and solution quality. The results show that Genetic Algorithm has a better solution quality while Tabu Search has a faster execution time in comparison with other Meta-heuristic algorithms for solving QAP.
Combinatorial stresses kill pathogenic Candida species.
Kaloriti, Despoina; Tillmann, Anna; Cook, Emily; Jacobsen, Mette; You, Tao; Lenardon, Megan; Ames, Lauren; Barahona, Mauricio; Chandrasekaran, Komelapriya; Coghill, George; Goodman, Daniel; Gow, Neil A R; Grebogi, Celso; Ho, Hsueh-Lui; Ingram, Piers; McDonagh, Andrew; de Moura, Alessandro P S; Pang, Wei; Puttnam, Melanie; Radmaneshfar, Elahe; Romano, Maria Carmen; Silk, Daniel; Stark, Jaroslav; Stumpf, Michael; Thiel, Marco; Thorne, Thomas; Usher, Jane; Yin, Zhikang; Haynes, Ken; Brown, Alistair J P
2012-10-01
Pathogenic microbes exist in dynamic niches and have evolved robust adaptive responses to promote survival in their hosts. The major fungal pathogens of humans, Candida albicans and Candida glabrata, are exposed to a range of environmental stresses in their hosts including osmotic, oxidative and nitrosative stresses. Significant efforts have been devoted to the characterization of the adaptive responses to each of these stresses. In the wild, cells are frequently exposed simultaneously to combinations of these stresses and yet the effects of such combinatorial stresses have not been explored. We have developed a common experimental platform to facilitate the comparison of combinatorial stress responses in C. glabrata and C. albicans. This platform is based on the growth of cells in buffered rich medium at 30°C, and was used to define relatively low, medium and high doses of osmotic (NaCl), oxidative (H(2)O(2)) and nitrosative stresses (e.g., dipropylenetriamine (DPTA)-NONOate). The effects of combinatorial stresses were compared with the corresponding individual stresses under these growth conditions. We show for the first time that certain combinations of combinatorial stress are especially potent in terms of their ability to kill C. albicans and C. glabrata and/or inhibit their growth. This was the case for combinations of osmotic plus oxidative stress and for oxidative plus nitrosative stress. We predict that combinatorial stresses may be highly significant in host defences against these pathogenic yeasts.
de Lara-Castells, M. P.; Villarreal, P.; Delgado-Barrio, G.; Mitrushchenkov, A. O.
2009-11-01
An efficient full-configuration-interaction nuclear orbital treatment has been recently developed as a benchmark quantum-chemistry-like method to calculate ground and excited "solvent" energies and wave functions in small doped ΔEest clusters (N ≤4) [M. P. de Lara-Castells, G. Delgado-Barrio, P. Villarreal, and A. O. Mitrushchenkov, J. Chem. Phys. 125, 221101 (2006)]. Additional methodological and computational details of the implementation, which uses an iterative Jacobi-Davidson diagonalization algorithm to properly address the inherent "hard-core" He-He interaction problem, are described here. The convergence of total energies, average pair He-He interaction energies, and relevant one- and two-body properties upon increasing the angular part of the one-particle basis set (expanded in spherical harmonics) has been analyzed, considering Cl2 as the dopant and a semiempirical model (T-shaped) He-Cl2(B) potential. Converged results are used to analyze global energetic and structural aspects as well as the configuration makeup of the wave functions, associated with the ground and low-lying "solvent" excited states. Our study reveals that besides the fermionic nature of H3e atoms, key roles in determining total binding energies and wave-function structures are played by the strong repulsive core of the He-He potential as well as its very weak attractive region, the most stable arrangement somehow departing from the one of N He atoms equally spaced on equatorial "ring" around the dopant. The present results for N =4 fermions indicates the structural "pairing" of two H3e atoms at opposite sides on a broad "belt" around the dopant, executing a sort of asymmetric umbrella motion. This pairing is a compromise between maximizing the H3e-H3e and the He-dopant attractions, and suppressing at the same time the "hard-core" repulsion. Although the He-He attractive interaction is rather weak, its contribution to the total energy is found to scale as a power of three and it thus
Particle Swarm Optimization with Genetic Operators for Vehicle Routing Problem
P. V. PURANIK
2012-07-01
Full Text Available Vehicle Routing Problem (VRP is to find shortest route thereby minimizing total cost. VRP is a NP-hard and Combinatorial optimization problem. Such problems increase exponentially with the problem size. Various derivative based optimization techniques are employed for optimization. Derivative based optimization techniques are difficult to evaluate. Therefore parallel search algorithm emerged to solve VRP. In this work, a particle swarm optimization (PSO algorithm and Genetic algorithm (GA with crossover and mutation operator are applied to two typical functions to deal with the problem of VRP efficiently using MATLAB software. Before solving VRP, optimization of functions using PSO and GA are checked. In this paper capacitate VRP with time window (CVRPTW is proposed. The computational result shows generation of input for VRP, optimization of Rastrigin function, Rosenbrock function using PSO and GA.
On the Border Length Minimization Problem (BLMP) on a Square Array
Kundeti, Vamsi; Dinh, Hieu
2010-01-01
Protein/Peptide microarrays are rapidly gaining momentum in the diagnosis of cancer. High-density and highthroughput peptide arrays are being extensively used to detect tumor biomarkers, examine kinase activity, identify antibodies having low serum titers and locate antibody signatures. Improving the yield of microarray fabrication involves solving a hard combinatorial optimization problem called the Border Length Minimization Problem (BLMP). An important question that remained open for the past seven years is if the BLMP is tractable or not. We settle this open problem by proving that the BLMP is NP-hard. We also present a hierarchical refinement algorithm which can refine any heuristic solution for the BLMP problem. We also prove that the TSP+1-threading heuristic is an O(N)- approximation. The hierarchical refinement solver is available as an opensource code at http://launchpad.net/blm-solve.
Accessing Specific Peptide Recognition by Combinatorial Chemistry
Li, Ming
Molecular recognition is at the basis of all processes for life, and plays a central role in many biological processes, such as protein folding, the structural organization of cells and organelles, signal transduction, and the immune response. Hence, my PhD project is entitled “Accessing Specific...... Peptide Recognition by Combinatorial Chemistry”. Molecular recognition is a specific interaction between two or more molecules through noncovalent bonding, such as hydrogen bonding, metal coordination, van der Waals forces, π−π, hydrophobic, or electrostatic interactions. The association involves kinetic....... Combinatorial chemistry was invented in 1980s based on observation of functional aspects of the adaptive immune system. It was employed for drug development and optimization in conjunction with high-throughput synthesis and screening. (chapter 2) Combinatorial chemistry is able to rapidly produce many thousands...
Solutions manual to accompany Combinatorial reasoning an introduction to the art of counting
DeTemple, Duane
2014-01-01
This is a solutions manual to accompany Combinatorial Reasoning: An Introduction to the Art of CountingWritten by well-known scholars in the field, Combinatorial Reasoning: An Introduction to the Art of Counting introduces combinatorics alongside modern techniques, showcases the interdisciplinary aspects of the topic, and illustrates how to problem solve with a multitude of exercises throughout. The authors'' approach is very reader-friendly and avoids the ""scholarly tone"" found in many books on this topic.
A Special Role of Boolean Quadratic Polytopes among Other Combinatorial Polytopes
A. N. Maksimenko
2016-01-01
Full Text Available We consider several families of combinatorial polytopes associated with the following NP-complete problems: maximum cut, Boolean quadratic programming, quadratic linear ordering, quadratic assignment, set partition, set packing, stable set, 3-assignment. For comparing two families of polytopes we use the following method. We say that a family
Combinatorial study of colored Hurwitz polyz\\^etas
Enjalbert, Jean-Yves; Minh, Hoang Ngoc
2012-01-01
A combinatorial study discloses two surjective morphisms between generalized shuffle algebras and algebras generated by the colored Hurwitz polyz\\^etas. The combinatorial aspects of the products and co-products involved in these algebras will be examined.
Development of Combinatorial Methods for Alloy Design and Optimization
Pharr, George M.; George, Easo P.; Santella, Michael L
2005-07-01
powerful technique for rapid structural and chemical characterization of alloy libraries was developed based on high intensity x-radiation available at synchrotron sources such as the Advanced Photon Source (APS) at Argonne National Laboratory (ANL). With the technique, structural and chemical characterization of up to 2500 discrete positions on a library can made in a period of less than 4 hours. Among the parameters that can be measured are the chemical composition, crystal structure, lattice parameters, texture, and grain size. From these, one can also deduce isothermal sections of ternary phase diagrams. The equipment and techniques needed to do this are now in place for use in future combinatorial studies at the ORNL beam line at the APS. In conjunction with the chemical and structural investigations, nanoindentation techniques were developed to investigate the mechanical properties of the combinatorial libraries. The two primary mechanical properties of interest were the elastic modulus, E, and hardness, H, both of which were measured on alloy library surfaces with spatial resolutions of better than 1 m. A nanoindentation testing system at ORNL was programmed to make a series of indentations at specified locations on the library surface and automatically collect and store all the data needed to obtain hardness and modulus as a function of position. Approximately 200 indentations can be made during an overnight run, which allows for mechanical property measurement over a wide range of chemical composition in a relatively short time. Since the materials based on the Fe-Ni-Cr system often find application in highly carburizing and harsh chemical environments, simple techniques were developed to assess the resistance of Fe-Ni-Cr alloy libraries to carburization and corrosion. Alloy libraries were carburized by standard techniques, and the effectiveness of the carburization at various points along the sample surface was assessed by nanoindentation hardness measurement
Non-orthodox combinatorial models based on discordant structures
Romanov, V F
2010-01-01
This paper introduces a novel method for compact representation of sets of n-dimensional binary sequences in a form of compact triplets structures (CTS), supposing both logic and arithmetic interpretations of data. Suitable illustration of CTS application is the unique graph-combinatorial model for the classic intractable 3-Satisfiability problem and a polynomial algorithm for the model synthesis. The method used for Boolean formulas analysis and classification by means of the model is defined as a bijective mapping principle for sets of components of discordant structures to a basic set. The statistic computer-aided experiment showed efficiency of the algorithm in a large scale of problem dimension parameters, including those that make enumeration procedures of no use. The formulated principle expands resources of constructive approach to investigation of intractable problems.
Combinatorial set theory partition relations for cardinals
Erdös, P; Hajnal, A; Rado, P
2011-01-01
This work presents the most important combinatorial ideas in partition calculus and discusses ordinary partition relations for cardinals without the assumption of the generalized continuum hypothesis. A separate section of the book describes the main partition symbols scattered in the literature. A chapter on the applications of the combinatorial methods in partition calculus includes a section on topology with Arhangel''skii''s famous result that a first countable compact Hausdorff space has cardinality, at most continuum. Several sections on set mappings are included as well as an account of
Toward Chemical Implementation of Encoded Combinatorial Libraries
Nielsen, John; Janda, Kim D.
1994-01-01
by existing methodologies. Here we detail the synthesis of several matrices and the necessary chemistry to implement the conceptual scheme. In addition, we disclose how this novel technology permits a controlled ′dendritic" display of the chemical libraries. © 1994 Academic Press. All rights reserved.......The recent application of "combinatorial libraries" to supplement existing drug screening processes might simplify and accelerate the search for new lead compounds or drugs. Recently, a scheme for encoded combinatorial chemistry was put forward to surmount a number of the limitations possessed...
Combinatorial optimization with Boolean constraints
Hulme, B.L.; Worrell, R.B.
1983-02-01
This report shows how Boolean algebraic formula manipulation can be used to solve certain kinds of optimization problems. If the problem can be formulated in terms of 0 to 1 variables and if the feasible solutions can be described by a Boolean equation, then the method of this report can be used. The method generates feasible solutions algebraically as terms of a disjunctive normal form of a Boolean function. Many small sample problems are solved to illustrate the method and the practical situations in which these optimization problems arise.
Combinatorial Clustering Algorithm of Quantum-Behaved Particle Swarm Optimization and Cloud Model
Mi-Yuan Shan
2013-01-01
Full Text Available We propose a combinatorial clustering algorithm of cloud model and quantum-behaved particle swarm optimization (COCQPSO to solve the stochastic problem. The algorithm employs a novel probability model as well as a permutation-based local search method. We are setting the parameters of COCQPSO based on the design of experiment. In the comprehensive computational study, we scrutinize the performance of COCQPSO on a set of widely used benchmark instances. By benchmarking combinatorial clustering algorithm with state-of-the-art algorithms, we can show that its performance compares very favorably. The fuzzy combinatorial optimization algorithm of cloud model and quantum-behaved particle swarm optimization (FCOCQPSO in vague sets (IVSs is more expressive than the other fuzzy sets. Finally, numerical examples show the clustering effectiveness of COCQPSO and FCOCQPSO clustering algorithms which are extremely remarkable.
Models of optimum discrete signals on the vector combinatorial configurations
V. V. Riznyk
2016-06-01
Full Text Available Method for construction of optimum discrete signals, based on a new conceptual combinatorial model of the systems - Ideal Ring Vector sequences (clusters of the IRV is proposed. IRV clusters are cyclic ordered sequences of t- integer sub-sequences of sequence, which form perfect relationships of t-dimensional partitions over a virtual t-dimensional lattice covered surface of a finite space interval. The sums of connected sub-sequences of an IRV enumerate the set of t- coordinates specified with respect to cyclic frame reference exactly R-times. This property makes IRVs useful in applications, which need to partition multidimensional objects with the smallest possible number of intersections. There are discover a great class of new two- and multidimensional combinatorial constructions, which being in excess classic models of discrete systems with respect to number and combinatorial varieties with theoretically non-limited values of upper boundaries on order of dimensionality –IRV. It shows that remarkable properties of IRVs encoded in fine structure of torus circular symmetry. There are regarded basic properties these models and made shortest comparative analysis of the models with classical models. Indicate that the IRVs to be in exceed of difference sets multiply, and set of the classical difference sets is subset of the IRVs. Some of useful examples for constructing of the optimum discrete signals, error-correcting codes, and ring monolithic optimum vector codes using IRVs are considered. The problem statement involves development the regular method for construction of the optimum discrete signals using two- and multidimensional IRVs. The favorable technical merits of IRVs sets named “Gloria to Ukraine Stars”, which remarkable properties hold for the same set of the IRVs in varieties permutations of its terms is demonstrated, and method for design of two- or multidimensional vector signals coded based on the optimum binary monolithic
On Range Searching in the Group Model and Combinatorial Discrepancy
Larsen, Kasper Green
2011-01-01
In this paper we establish an intimate connection between dynamic range searching in the group model and combinatorial discrepancy. Our result states that, for a broad class of range searching data structures (including all known upper bounds), it must hold that $t_ut_q = Omega(disc^2/lg n)$ where...... $t_u$ is the worst case update time, $t_q$ the worst case query time and $disc$ is the combinatorial discrepancy of the range searching problem in question. This relation immediately implies a whole range of exceptionally high and near-tight lower bounds for all of the basic range searching problems....... We list a few of them in the following:begin{itemize}item For half space range searching in $d$-dimensional space, we get a lower bound of $t_u t_q = Omega(n^{1-1/d}/lg n)$. This comes within a $lg n lg lg n$ factor of the best known upper bound. item For orthogonal range searching in $d...
ON range searching in the group model and combinatorial discrepancy
Larsen, Kasper Green
2014-01-01
In this paper we establish an intimate connection between dynamic range searching in the group model and combinatorial discrepancy. Our result states that, for a broad class of range searching data structures (including all known upper bounds), it must hold that $t_u t_q=\\Omega(\\mbox{disc}^2......)$, where $t_u$ is the worst case update time, $t_q$ is the worst case query time, and disc is the combinatorial discrepancy of the range searching problem in question. This relation immediately implies a whole range of exceptionally high and near-tight lower bounds for all of the basic range searching...... problems. We list a few of them in the following: (1) For $d$-dimensional halfspace range searching, we get a lower bound of $t_u t_q=\\Omega(n^{1-1/d})$. This comes within an lg lg $n$ factor of the best known upper bound. (2) For orthogonal range searching, we get a lower bound of $t_u t...
Combinatorial solutions to integrable hierarchies
Kazarian, M.; Lando, S.
2015-01-01
We give a review of modern approaches to constructing formal solutions to integrable hierarchies of mathematical physics, whose coefficients are answers to various enumerative problems. The relationship between these approaches and combinatorics of symmetric groups and their representations is explained. Applications of the results to constructing efficient computations in problems related to models of quantum field theories are given.
A New Approach for Proving or Generating Combinatorial Identities
Gonzalez, Luis
2010-01-01
A new method for proving, in an immediate way, many combinatorial identities is presented. The method is based on a simple recursive combinatorial formula involving n + 1 arbitrary real parameters. Moreover, this formula enables one not only to prove, but also generate many different combinatorial identities (not being required to know them "a…
Geometric Generalisation of Surrogate Model-Based Optimisation to Combinatorial and Program Spaces
Yong-Hyuk Kim
2014-01-01
Full Text Available Surrogate models (SMs can profitably be employed, often in conjunction with evolutionary algorithms, in optimisation in which it is expensive to test candidate solutions. The spatial intuition behind SMs makes them naturally suited to continuous problems, and the only combinatorial problems that have been previously addressed are those with solutions that can be encoded as integer vectors. We show how radial basis functions can provide a generalised SM for combinatorial problems which have a geometric solution representation, through the conversion of that representation to a different metric space. This approach allows an SM to be cast in a natural way for the problem at hand, without ad hoc adaptation to a specific representation. We test this adaptation process on problems involving binary strings, permutations, and tree-based genetic programs.
Methods of using the quadratic assignment problem solution
Izabela Kudelska
2012-09-01
Full Text Available Background: Quadratic assignment problem (QAP is one of the most interesting of combinatorial optimization. Was presented by Koopman and Beckamanna in 1957, as a mathematical model of the location of indivisible tasks. This problem belongs to the class NP-hard issues. This forces the application to the solution already approximate methods for tasks with a small size (over 30. Even though it is much harder than other combinatorial optimization problems, it enjoys wide interest because it models the important class of decision problems. Material and methods: The discussion was an artificial intelligence tool that allowed to solve the problem QAP, among others are: genetic algorithms, Tabu Search, Branch and Bound. Results and conclusions: QAP did not arise directly as a model for certain actions, but he found its application in many areas. Examples of applications of the problem is: arrangement of buildings on the campus of the university, layout design of electronic components in systems with large scale integration (VLSI, design a hospital, arrangement of keys on the keyboard.
Melting of polydisperse hard disks
Pronk, S.; Frenkel, D.
2004-01-01
The melting of a polydisperse hard-disk system is investigated by Monte Carlo simulations in the semigrand canonical ensemble. This is done in the context of possible continuous melting by a dislocation-unbinding mechanism, as an extension of the two-dimensional hard-disk melting problem. We find
Melting of polydisperse hard disks
Pronk, S.; Frenkel, D.
2004-01-01
The melting of a polydisperse hard-disk system is investigated by Monte Carlo simulations in the semigrand canonical ensemble. This is done in the context of possible continuous melting by a dislocation-unbinding mechanism, as an extension of the two-dimensional hard-disk melting problem. We find th
Combinatorial biosynthesis of medicinal plant secondary metabolites
Julsing, Mattijs K.; Koulman, Albert; Woerdenbag, Herman J.; Quax, Wim J.; Kayser, Oliver
2006-01-01
Combinatorial biosynthesis is a new tool in the generation of novel natural products and for the production of rare and expensive natural products. The basic concept is combining metabolic pathways in different organisms on a genetic level. As a consequence heterologous organisms provide precursors
Infinitary Combinatory Reduction Systems: Normalising Reduction Strategies
Ketema, Jeroen; Simonsen, Jakob Grue
2010-01-01
We study normalising reduction strategies for infinitary Combinatory Reduction Systems (iCRSs). We prove that all fair, outermost-fair, and needed-fair strategies are normalising for orthogonal, fully-extended iCRSs. These facts properly generalise a number of results on normalising strategies in fi
Erratum to Ordered Partial Combinatory Algebras
Hofstra, P.; Oosten, J. van
2003-01-01
To our regret the paper Ordered Partial Combinatory Algebras contains a mistake which we correct here The flaw concerns the definition of compu tational density definition 3.5 which appeared in section 3.3 page 451 This definition is too rigid and as a consequence Lemma 3.6 on page 452
Recent developments in dynamic combinatorial chemistry
Otto, Sijbren; Furlan, Ricardo L.E.; Sanders, Jeremy K.M.
2002-01-01
Generating combinatorial libraries under equilibrium conditions has the important advantage that the libraries are adaptive (i.e. they can respond to exterior influences in the form of molecular recognition events). Thus, a ligand will direct and amplify the formation of its ideal receptor and vice
Boltzmann Samplers for Colored Combinatorial Objects
Bodini, Olivier
2009-01-01
In this paper, we give a general framework for the Boltzmann generation of colored objects belonging to combinatorial constructible classes. We propose an intuitive notion called profiled objects which allows the sampling of size-colored objects (and also of k-colored objects) although the corresponding class cannot be described by an analytic ordinary generating function.
Combinatorial biosynthesis of medicinal plant secondary metabolites
Julsing, Mattijs K.; Koulman, Albert; Woerdenbag, Herman J.; Quax, Wim J.; Kayser, Oliver
2006-01-01
Combinatorial biosynthesis is a new tool in the generation of novel natural products and for the production of rare and expensive natural products. The basic concept is combining metabolic pathways in different organisms on a genetic level. As a consequence heterologous organisms provide precursors
PIPERIDINE OLIGOMERS AND COMBINATORIAL LIBRARIES THEREOF
1999-01-01
The present invention relates to piperidine oligomers, methods for the preparation of piperidine oligomers and compound libraries thereof, and the use of piperidine oligomers as drug substances. The present invention also relates to the use of combinatorial libraries of piperidine oligomers...... in libraries (arrays) of compounds especially suitable for screening purposes....
Combinatorial solutions to integrable hierarchies
Kazarian, M. E.; Lando, S. K.
2015-06-01
This paper reviews modern approaches to the construction of formal solutions to integrable hierarchies of mathematical physics whose coefficients are answers to various enumerative problems. The relationship between these approaches and the combinatorics of symmetric groups and their representations is explained. Applications of the results to the construction of efficient computations in problems related to models of quantum field theories are described. Bibliography: 34 titles.
TSP based Evolutionary optimization approach for the Vehicle Routing Problem
Kouki, Zoulel; Chaar, Besma Fayech; Ksouri, Mekki
2009-03-01
Vehicle Routing and Flexible Job Shop Scheduling Problems (VRP and FJSSP) are two common hard combinatorial optimization problems that show many similarities in their conceptual level [2, 4]. It was proved for both problems that solving techniques like exact methods fail to provide good quality solutions in a reasonable amount of time when dealing with large scale instances [1, 5, 14]. In order to overcome this weakness, we decide in the favour of meta heuristics and we focalize on evolutionary algorithms that have been successfully used in scheduling problems [1, 5, 9]. In this paper we investigate the common properties of the VRP and the FJSSP in order to provide a new controlled evolutionary approach for the CVRP optimization inspired by the FJSSP evolutionary optimization algorithms introduced in [10].
Combinatorial structures to modeling simple games and applications
Molinero, Xavier
2017-09-01
We connect three different topics: combinatorial structures, game theory and chemistry. In particular, we establish the bases to represent some simple games, defined as influence games, and molecules, defined from atoms, by using combinatorial structures. First, we characterize simple games as influence games using influence graphs. It let us to modeling simple games as combinatorial structures (from the viewpoint of structures or graphs). Second, we formally define molecules as combinations of atoms. It let us to modeling molecules as combinatorial structures (from the viewpoint of combinations). It is open to generate such combinatorial structures using some specific techniques as genetic algorithms, (meta-)heuristics algorithms and parallel programming, among others.
Combinatorial Clustering and the Beta Negative Binomial Process.
Broderick, Tamara; Mackey, Lester; Paisley, John; Jordan, Michael I
2015-02-01
We develop a Bayesian nonparametric approach to a general family of latent class problems in which individuals can belong simultaneously to multiple classes and where each class can be exhibited multiple times by an individual. We introduce a combinatorial stochastic process known as the negative binomial process ( NBP ) as an infinite-dimensional prior appropriate for such problems. We show that the NBP is conjugate to the beta process, and we characterize the posterior distribution under the beta-negative binomial process ( BNBP) and hierarchical models based on the BNBP (the HBNBP). We study the asymptotic properties of the BNBP and develop a three-parameter extension of the BNBP that exhibits power-law behavior. We derive MCMC algorithms for posterior inference under the HBNBP , and we present experiments using these algorithms in the domains of image segmentation, object recognition, and document analysis.
American Society for Testing and Materials. Philadelphia
2007-01-01
1.1 Conversion Table 1 presents data in the Rockwell C hardness range on the relationship among Brinell hardness, Vickers hardness, Rockwell hardness, Rockwell superficial hardness, Knoop hardness, and Scleroscope hardness of non-austenitic steels including carbon, alloy, and tool steels in the as-forged, annealed, normalized, and quenched and tempered conditions provided that they are homogeneous. 1.2 Conversion Table 2 presents data in the Rockwell B hardness range on the relationship among Brinell hardness, Vickers hardness, Rockwell hardness, Rockwell superficial hardness, Knoop hardness, and Scleroscope hardness of non-austenitic steels including carbon, alloy, and tool steels in the as-forged, annealed, normalized, and quenched and tempered conditions provided that they are homogeneous. 1.3 Conversion Table 3 presents data on the relationship among Brinell hardness, Vickers hardness, Rockwell hardness, Rockwell superficial hardness, and Knoop hardness of nickel and high-nickel alloys (nickel content o...
Two-Phase Heuristic for the Vehicle Routing Problem with Time Windows
Sándor Csiszár
2007-08-01
Full Text Available The subject of the paper is a complete solution for the vehicle routing problemwith time windows, an industrial realization of an NP hard combinatorial optimizationproblem. The primary objective –the minimization of the number of routes- is aimed in thefirst phase, the secondary objective –the travel distance minimization- is going to berealized in the second phase by tabu search. The initial route construction applies aprobability density function for seed selection. Guided Route Elimination procedure wasalso developed. The solution was tested on the Solomon Problem Set and seems to be verycompeitive with the best heuristics published in the latest years (2003-2005.
Towards a 4/3 Approximation for the Asymmetric Traveling Salesman Problem
Carr, Robert; Vempala, Santosh
1999-06-10
A long-standing conjecture in combinatorial optimization says that the integrality gap of the famous Held-Karp relaxation of the symmetric TSP is precisely 4/3. In this paper, we show that a slight strengthening of this conjecture implies a tight 4/3 integrality gap for a linear programming relaxation of the asymmetric TSP. This is surprising since no constant-factor approximation is known for the latter problem. Our main tools are a new characterization of the integrality gap for linear objective functions over polyhedra, and the isolation of ''hard-to-round'' solutions of the relaxations.
Solving Stochastic Demand Inventory Routing Problem with Hard Time Windows%求解硬时间窗约束下随机需求库存-路径问题的优化算法
赵达; 李军; 马丹祥; 李妍峰
2014-01-01
The Stochastic Demand Inventory Routing Problem (SDIRP)is a kind of typical NP-hard problem.To consider the coordination and optimization problem of inventory and distribution in the supply chain is the key to implementing vendor managed inventory .This paper explores the stochastic demand IRP with hard time windows ( SDIRPHTW) , and decomposes SDIRPHTW into two sub-problems: stochastic inventory routing problem with direct distribution and vehicle routing problem with hard time windows .Then, with the objective to minimizing the system cost and the number of vehicles , we present a heuristic algorithm based on ( s,S) inventory policy and modified C-W saving algorithm , and analyses the efficiency of the algorithm through a numerical example .%随机需求库存-路径问题（ Stochastic Demand Inventory Routing Problem ， SDIRP）即考虑随机需求环境下供应链中库存与配送的协调优化问题，是实施供应商管理库存策略过程中的关键所在，也是典型的NP难题之一。文章以具有硬时间窗约束的随机需求库存-路径问题（ Stochastic Demand Inventory Routing Problem with Hard Time Windows ， SDIRPHTW）为研究对象，将SDIRPHTW分解为直接配送的随机库存-路径问题和具有硬时间窗约束的路径优化问题两个子问题，并以最小化系统运行成本和用车数量为目标，设计了一个基于（ s，S）库存策略和修正C-W节约法的启发式算法。最后，通过相应的数值算例验证了算法的有效性。
Three Syntactic Theories for Combinatory Graph Reduction
Danvy, Olivier; Zerny, Ian
2011-01-01
We present a purely syntactic theory of graph reduction for the canonical combinators S, K, and I, where graph vertices are represented with evaluation contexts and let expressions. We express this syntactic theory as a reduction semantics, which we refocus into the first storeless abstract machine...... for combinatory graph reduction, which we refunctionalize into the first storeless natural semantics for combinatory graph reduction.We then factor out the introduction of let expressions to denote as many graph vertices as possible upfront instead of on demand, resulting in a second syntactic theory, this one...... of term graphs in the sense of Barendregt et al. The corresponding storeless abstract machine and natural semantics follow mutatis mutandis. We then interpret let expressions as operations over a global store (thus shifting, in Strachey's words, from denotable entities to storable entities), resulting...
Three Syntactic Theories for Combinatory Graph Reduction
Danvy, Olivier; Zerny, Ian
2013-01-01
We present a purely syntactic theory of graph reduction for the canonical combinators S, K, and I, where graph vertices are represented with evaluation contexts and let expressions. We express this rst syntactic theory as a storeless reduction semantics of combinatory terms. We then factor out...... the introduction of let expressions to denote as many graph vertices as possible upfront instead of on demand . The factored terms can be interpreted as term graphs in the sense of Barendregt et al. We express this second syntactic theory, which we prove equivalent to the rst, as a storeless reduction semantics...... of combinatory term graphs. We then recast let bindings as bindings in a global store, thus shifting, in Strachey's words, from denotable entities to storable entities. The store-based terms can still be interpreted as term graphs. We express this third syntactic theory, which we prove equivalent to the second...
Dynamic combinatorial self-replicating systems.
Moulin, Emilie; Giuseppone, Nicolas
2012-01-01
Thanks to their intrinsic network topologies, dynamic combinatorial libraries (DCLs) represent new tools for investigating fundamental aspects related to self-organization and adaptation processes. Very recently the first examples integrating self-replication features within DCLs have pushed even further the idea of implementing dynamic combinatorial chemistry (DCC) towards minimal systems capable of self-construction and/or evolution. Indeed, feedback loop processes - in particular in the form of autocatalytic reactions - are keystones to build dynamic supersystems which could possibly approach the roots of "Darwinian" evolvability at mesoscale. This topic of current interest also shows significant potentialities beyond its fundamental character, because truly smart and autonomous materials for the future will have to respond to changes of their environment by selecting and by exponentially amplifying their fittest constituents.
Assessment of structural diversity in combinatorial synthesis.
Fergus, Suzanne; Bender, Andreas; Spring, David R
2005-06-01
This article covers the combinatorial synthesis of small molecules with maximal structural diversity to generate a collection of pure compounds that are attractive for lead generation in a phenotypic, high-throughput screening approach. Nature synthesises diverse small molecules, but there are disadvantages with using natural product sources. The efficient chemical synthesis of structural diversity (and complexity) is the aim of diversity-oriented synthesis, and recent progress is reviewed. Specific highlights include a discussion of strategies to obtain structural diversity and an analysis of molecular descriptors used to classify compounds. The assessment of how successful one synthesis is versus another is subjective, therefore we test-drive software to assess structural diversity in combinatorial synthesis, which is freely available via a web interface.
DNA-Encoded Dynamic Combinatorial Chemical Libraries.
Reddavide, Francesco V; Lin, Weilin; Lehnert, Sarah; Zhang, Yixin
2015-06-26
Dynamic combinatorial chemistry (DCC) explores the thermodynamic equilibrium of reversible reactions. Its application in the discovery of protein binders is largely limited by difficulties in the analysis of complex reaction mixtures. DNA-encoded chemical library (DECL) technology allows the selection of binders from a mixture of up to billions of different compounds; however, experimental results often show low a signal-to-noise ratio and poor correlation between enrichment factor and binding affinity. Herein we describe the design and application of DNA-encoded dynamic combinatorial chemical libraries (EDCCLs). Our experiments have shown that the EDCCL approach can be used not only to convert monovalent binders into high-affinity bivalent binders, but also to cause remarkably enhanced enrichment of potent bivalent binders by driving their in situ synthesis. We also demonstrate the application of EDCCLs in DNA-templated chemical reactions.
High throughput combinatorial screening of semiconductor materials
Mao, Samuel S.
2011-11-01
This article provides an overview of an advanced combinatorial material discovery platform developed recently for screening semiconductor materials with properties that may have applications ranging from radiation detectors to solar cells. Semiconductor thin-film libraries, each consisting of 256 materials of different composition arranged into a 16×16 matrix, were fabricated using laser-assisted evaporation process along with a combinatorial mechanism to achieve variations. The composition and microstructure of individual materials on each thin-film library were characterized with an integrated scanning micro-beam x-ray fluorescence and diffraction system, while the band gaps were determined by scanning optical reflection and transmission of the libraries. An ultrafast ultraviolet photon-induced charge probe was devised to measure the mobility and lifetime of individual thin-film materials on semiconductor libraries. Selected results on the discovery of semiconductors with desired band gaps and transport properties are illustrated.
COMBINATORIAL DESIGN APPROACHES FOR TEST GENERATION
Shi Liang; Xu Baowen; Nie Changhai
2005-01-01
The n-way combination testing is a specification-based testing criterion, which requires that for a system consisted of a few parameters, every combination of valid values of arbitrary n(n ≥ 2) parameters be covered by at least one test. This letter proposed two different test generation algorithms based on combinatorial design for the n-way coverage criterion. The automatic test generators are implemented and some valuable empirical results are obtained.
A combinatorial approach to metamaterials discovery
Plum, E; Chen, W T; Fedotov, V A; Tsai, D P; Zheludev, N I
2010-01-01
We report a high through-put combinatorial approach to photonic metamaterial optimization. The new approach is based on parallel synthesis and consecutive optical characterization of large numbers of spatially addressable nano-fabricated metamaterial samples (libraries) with quasi-continuous variation of design parameters under real manufacturing conditions. We illustrate this method for Fano-resonance plasmonic nanostructures arriving at explicit recipes for high quality factors needed for switching and sensing applications.
One-parameter groups and combinatorial physics
Duchamp, G; Solomon, A I; Horzela, A; Blasiak, P; Duchamp, Gerard; Penson, Karol A.; Solomon, Allan I.; Horzela, Andrej; Blasiak, Pawel
2004-01-01
In this communication, we consider the normal ordering of sums of elements of the form (a*^r a a*^s), where a* and a are boson creation and annihilation operators. We discuss the integration of the associated one-parameter groups and their combinatorial by-products. In particular, we show how these groups can be realized as groups of substitutions with prefunctions.
The Combinatorial Retention Auction Mechanism (CRAM)
Coughlan, Peter; Gates, William (Bill); Myung, Noah
2013-01-01
Approved for public release; distribution is unlimited. Revised version We propose a reverse uniform price auction called Combinatorial Retention Auction Mechanism (CRAM) that integrates both monetary and non-monetary incentives (NMIs). CRAM computes the cash bonus and NMIs to a single cost parameter, retains the lowest cost employees and provides them with compensation equal to the cost of the first excluded employee. CRAM is dominant strategy incentive compatible. We provide optimal b...
Combinatorial Cis-regulation in Saccharomyces Species
Aaron T. Spivak
2016-03-01
Full Text Available Transcriptional control of gene expression requires interactions between the cis-regulatory elements (CREs controlling gene promoters. We developed a sensitive computational method to identify CRE combinations with conserved spacing that does not require genome alignments. When applied to seven sensu stricto and sensu lato Saccharomyces species, 80% of the predicted interactions displayed some evidence of combinatorial transcriptional behavior in several existing datasets including: (1 chromatin immunoprecipitation data for colocalization of transcription factors, (2 gene expression data for coexpression of predicted regulatory targets, and (3 gene ontology databases for common pathway membership of predicted regulatory targets. We tested several predicted CRE interactions with chromatin immunoprecipitation experiments in a wild-type strain and strains in which a predicted cofactor was deleted. Our experiments confirmed that transcription factor (TF occupancy at the promoters of the CRE combination target genes depends on the predicted cofactor while occupancy of other promoters is independent of the predicted cofactor. Our method has the additional advantage of identifying regulatory differences between species. By analyzing the S. cerevisiae and S. bayanus genomes, we identified differences in combinatorial cis-regulation between the species and showed that the predicted changes in gene regulation explain several of the species-specific differences seen in gene expression datasets. In some instances, the same CRE combinations appear to regulate genes involved in distinct biological processes in the two different species. The results of this research demonstrate that (1 combinatorial cis-regulation can be inferred by multi-genome analysis and (2 combinatorial cis-regulation can explain differences in gene expression between species.
Potential health impacts of hard water
Sengupta, Pallav
2013-01-01
... the hardness of the drinking water. In addition, several epidemiological investigations have demonstrated the relation between risk for cardiovascular disease, growth retardation, reproductive failure, and other health problems...
Methods for combinatorial and parallel library design.
Schnur, Dora M; Beno, Brett R; Tebben, Andrew J; Cavallaro, Cullen
2011-01-01
Diversity has historically played a critical role in design of combinatorial libraries, screening sets and corporate collections for lead discovery. Large library design dominated the field in the 1990s with methods ranging anywhere from purely arbitrary through property based reagent selection to product based approaches. In recent years, however, there has been a downward trend in library size. This was due to increased information about the desirable targets gleaned from the genomics revolution and to the ever growing availability of target protein structures from crystallography and homology modeling. Creation of libraries directed toward families of receptors such as GPCRs, kinases, nuclear hormone receptors, proteases, etc., replaced the generation of libraries based primarily on diversity while single target focused library design has remained an important objective. Concurrently, computing grids and cpu clusters have facilitated the development of structure based tools that screen hundreds of thousands of molecules. Smaller "smarter" combinatorial and focused parallel libraries replaced those early un-focused large libraries in the twenty-first century drug design paradigm. While diversity still plays a role in lead discovery, the focus of current library design methods has shifted to receptor based methods, scaffold hopping/bio-isostere searching, and a much needed emphasis on synthetic feasibility. Methods such as "privileged substructures based design" and pharmacophore based design still are important methods for parallel and small combinatorial library design. This chapter discusses some of the possible design methods and presents examples where they are available.
Solving Optimization Problems by the Spatial Public Goods Game
Javarone, Marco Alberto
2016-01-01
We introduce a method based on the spatial Public Goods Game for solving optimization tasks. In particular, we focus on the Traveling Salesman Problem, i.e., a problem whose search space exponentially grows increasing the number of cities, then becoming NP-hard. The proposed method considers a population whose agents are provided with a random solution to the given problem. Then, agents interact by playing the Public Goods Game using the fitness of their solution as currency of the game. In doing so, agents with better solutions provide higher contributions, while agents with lower ones tend to imitate the solution of richer agents to increase their fitness. Numerical simulations show that the proposed method allows to compute exact solutions, and suboptimal ones, in the considered search spaces. As result, beyond to propose a new heuristic for combinatorial optimization tasks, our work aims to highlight the potentiality of evolutionary game theory outside its current horizons.
Parsimony score of phylogenetic networks: hardness results and a linear-time heuristic.
Jin, Guohua; Nakhleh, Luay; Snir, Sagi; Tuller, Tamir
2009-01-01
Phylogenies-the evolutionary histories of groups of organisms-play a major role in representing the interrelationships among biological entities. Many methods for reconstructing and studying such phylogenies have been proposed, almost all of which assume that the underlying history of a given set of species can be represented by a binary tree. Although many biological processes can be effectively modeled and summarized in this fashion, others cannot: recombination, hybrid speciation, and horizontal gene transfer result in networks of relationships rather than trees of relationships. In previous works, we formulated a maximum parsimony (MP) criterion for reconstructing and evaluating phylogenetic networks, and demonstrated its quality on biological as well as synthetic data sets. In this paper, we provide further theoretical results as well as a very fast heuristic algorithm for the MP criterion of phylogenetic networks. In particular, we provide a novel combinatorial definition of phylogenetic networks in terms of "forbidden cycles," and provide detailed hardness and hardness of approximation proofs for the "small" MP problem. We demonstrate the performance of our heuristic in terms of time and accuracy on both biological and synthetic data sets. Finally, we explain the difference between our model and a similar one formulated by Nguyen et al., and describe the implications of this difference on the hardness and approximation results.
PCB Drill Path Optimization by Combinatorial Cuckoo Search Algorithm
Wei Chen Esmonde Lim
2014-01-01
Full Text Available Optimization of drill path can lead to significant reduction in machining time which directly improves productivity of manufacturing systems. In a batch production of a large number of items to be drilled such as printed circuit boards (PCB, the travel time of the drilling device is a significant portion of the overall manufacturing process. To increase PCB manufacturing productivity and to reduce production costs, a good option is to minimize the drill path route using an optimization algorithm. This paper reports a combinatorial cuckoo search algorithm for solving drill path optimization problem. The performance of the proposed algorithm is tested and verified with three case studies from the literature. The computational experience conducted in this research indicates that the proposed algorithm is capable of efficiently finding the optimal path for PCB holes drilling process.
PCB drill path optimization by combinatorial cuckoo search algorithm.
Lim, Wei Chen Esmonde; Kanagaraj, G; Ponnambalam, S G
2014-01-01
Optimization of drill path can lead to significant reduction in machining time which directly improves productivity of manufacturing systems. In a batch production of a large number of items to be drilled such as printed circuit boards (PCB), the travel time of the drilling device is a significant portion of the overall manufacturing process. To increase PCB manufacturing productivity and to reduce production costs, a good option is to minimize the drill path route using an optimization algorithm. This paper reports a combinatorial cuckoo search algorithm for solving drill path optimization problem. The performance of the proposed algorithm is tested and verified with three case studies from the literature. The computational experience conducted in this research indicates that the proposed algorithm is capable of efficiently finding the optimal path for PCB holes drilling process.
Generalized topological spaces in evolutionary theory and combinatorial chemistry.
Stadler, Bärbel M R; Stadler, Peter F
2002-01-01
The search spaces in combinatorial chemistry as well as the sequence spaces underlying (molecular) evolution are conventionally thought of as graphs. Recombination, however, implies a nongraphical structure of the combinatorial search spaces. These structures, and their implications for search process itself, are heretofore not well understood in general. In this contribution we review a very general formalism from point set topology and discuss its application to combinatorial search spaces, fitness landscapes, evolutionary trajectories, and artificial chemistries.
Advanced Aqueous Phase Catalyst Development using Combinatorial Methods Project
National Aeronautics and Space Administration — Combinatorial methods are proposed to develop advanced Aqueous Oxidation Catalysts (AOCs) with the capability to mineralize organic contaminants present in effluents...
Mohammad Javad Namazifar
2015-09-01
Full Text Available The Freeze-Tag Problem (FTP arises in the study of swarm robotics. The FTP is a combinatorial optimization problem that starts by locating a set of robots in a Euclidean plane. Here, we are given a swarm of n asleep (frozen or inactive robots and a single awake (active robot. In order to activate an inactive robot in FTP, the active robot should either be in the physical proximity to the inactive robot or ``touch`` it. The new activated robot starts moving and can wake up other inactive robots. The goal is to ﬁnd an optimal activating schedule with the minimum time required for activating all robots. In general, FTP is an NP-Hard problem and in the Euclidean space is an open problem. In this paper, we present a recursive approximation algorithm with a constant approximation factor and a linear running time for the Euclidean Freeze-Tag Problem.
A set partitioning reformulation for the multiple-choice multidimensional knapsack problem
Voß, Stefan; Lalla-Ruiz, Eduardo
2016-05-01
The Multiple-choice Multidimensional Knapsack Problem (MMKP) is a well-known ?-hard combinatorial optimization problem that has received a lot of attention from the research community as it can be easily translated to several real-world problems arising in areas such as allocating resources, reliability engineering, cognitive radio networks, cloud computing, etc. In this regard, an exact model that is able to provide high-quality feasible solutions for solving it or being partially included in algorithmic schemes is desirable. The MMKP basically consists of finding a subset of objects that maximizes the total profit while observing some capacity restrictions. In this article a reformulation of the MMKP as a set partitioning problem is proposed to allow for new insights into modelling the MMKP. The computational experimentation provides new insights into the problem itself and shows that the new model is able to improve on the best of the known results for some of the most common benchmark instances.
Combinatorial problems arising from pooling designs for dna library screening
Masakazu Jimbo
2004-11-01
Full Text Available Colbourn (1999 developed some strategy for nonadaptive group testing when the items are linearly ordered and the positive items form a consecutive subset of all items.Müller and Jimbo (2004 improved his strategy by introducing the concept of 2-consecutive positive detectable matrices (2CPD-matrix requiring that all columns and bitwise OR-sum of each two consecutive columns are pairwise distinct. Such a matrix is called maximal if it has a maximal possible number of columns with respect to some obvious constraints. Using a recursive construction they proved the existence of maximal 2CPD-matrices for any column size m ∈ N except for the case m = 3. Moreover, maximal 2CPD-matrices such that each column is of some fixed constant weight areconstructed. This leads to pooling designs, where each item appears in the same number of pools and all pools are of the same size.Secondly, we investigate 2CPD-matrices of some constant column weight τ ∈ N. We give some recursive construction of such matrices having the maximal possible number of columns. Thirdly, error correction capability of group testing procedures is essential in view of applications such as DNA library screening. We consider a error correcting 2CPD-matrices.
Probabilistic Analysis of Combinatorial Optimization Problems on Hypergraph Matchings
2012-02-01
PfBng; (16) where Bn is the event that there are no empty boxes, for which it holds (see, e.g., Feller , 1968): PfBng D nX iD0 .1/i n i ! 1 i n...Combinatorics, Academic Press, New York. Feller , W. (1968) An Introduction to Probability Theory and Its Applications, volume I, John Wiley & Sons, New York, 3rd
Tree-tree matrices and other combinatorial problems from taxonomy
Hazewinkel, M.
1995-01-01
Let A be a bipartite graph between two sets D and T. Then A defines by Hamming distance, metrics on both T and D. The question is studied which pairs of metric spaces can arise this way. If both spaces are trivial the matrix A comes from a Hadamard matrix or is a BIBD. The second question studied i
Effects of Suboptimal Bidding in Combinatorial Auctions
Schneider, Stefan; Shabalin, Pasha; Bichler, Martin
Though the VCG auction assumes a central place in the mechanism design literature, there are a number of reasons for favoring iterative combinatorial auction designs. Several promising ascending auction formats have been developed throughout the past few years based on primal-dual and subgradient algorithms and linear programming theory. Prices are interpreted as a feasible dual solution and the provisional allocation is interpreted as a feasible primal solution. iBundle( 3) (Parkes and Ungar 2000), dVSV (de Vries et al. 2007) and the Ascending Proxy auction (Ausubel and Milgrom 2002) result in VCG payoffs when the coalitional value function satisfies the buyer submodularity condition and bidders bid straightforward, which is an expost Nash equilibrium in that case. iBEA and CreditDebit auctions (Mishra and Parkes 2007) do not even require the buyer submodularity condition and achieve the same properties for general valuations. In many situations, however, one cannot assume bidders to bid straightforward and it is not clear from the theory how these non-linear personalized price auctions (NLPPAs) perform in this case. Robustness of auctions with respect to different bidding behavior is therefore a critical issue for any application. We have conducted a large number of computational experiments to analyze the performance of NLPPA designs with respect to different bidding strategies and different valuation models. We compare the results of NLPPAs to those of the VCG auction and those of iterative combinatorial auctions with approximate linear prices, such as ALPS (Bichler et al. 2009) and the Combinatorial Clock auction (Porter et al. 2003).
Algebraic and combinatorial Brill-Noether theory
Caporaso, Lucia
2011-01-01
The interplay between algebro-geometric and combinatorial Brill-Noether theory is studied. The Brill-Noether variety of a graph shown to be non-empty if the Brill-Noether number is non-negative, as a consequence of the analogous fact for smooth projective curves. Similarly, the existence of a graph for which the Brill-Noether variety is empty implies the emptiness of the corresponding Brill-Noether variety for a general curve. The main tool is a refinement of Baker's Specialization Lemma.
Method and apparatus for combinatorial chemistry
Foote, Robert S.
2007-02-20
A method and apparatus are provided for performing light-directed reactions in spatially addressable channels within a plurality of channels. One aspect of the invention employs photoactivatable reagents in solutions disposed into spatially addressable flow streams to control the parallel synthesis of molecules immobilized within the channels. The reagents may be photoactivated within a subset of channels at the site of immobilized substrate molecules or at a light-addressable site upstream from the substrate molecules. The method and apparatus of the invention find particularly utility in the synthesis of biopolymer arrays, e.g., oligonucleotides, peptides and carbohydrates, and in the combinatorial synthesis of small molecule arrays for drug discovery.
Apparatus for combinatorial screening of electrochemical materials
A high throughput combinatorial screening method and apparatus for the evaluation of electrochemical materials using a single voltage source is disclosed wherein temperature changes arising from the application of an electrical load to a cell array are used to evaluate the relative electrochemical efficiency of the materials comprising the array. The apparatus may include an array of electrochemical cells that are connected to each other in parallel or in series, an electronic load for applying a voltage or current to the electrochemical cells , and a device , external to the cells, for monitoring the relative temperature of each cell when the load is applied.
2009-12-15
A high throughput combinatorial screening method and apparatus for the evaluation of electrochemical materials using a single voltage source (2) is disclosed wherein temperature changes arising from the application of an electrical load to a cell array (1) are used to evaluate the relative electrochemical efficiency of the materials comprising the array. The apparatus may include an array of electrochemical cells (1) that are connected to each other in parallel or in series, an electronic load (2) for applying a voltage or current to the electrochemical cells (1), and a device (3), external to the cells, for monitoring the relative temperature of each cell when the load is applied.
Combinatorial level densities for practical applications
Sin M.
2010-03-01
Full Text Available We review our calculated energy-, spin- and parity-dependent nuclear level densities based on the microscopic combinatorial model described in ref. [1]. We show that this model predicts the experimental sand p-wave neutron resonance spacings with a degree of accuracy comparable to that of the best global models available and also provides reasonable description of low energies cumulative number of levels as well as of the experimental data obtained by the Oslo group [2]. We also provide a renormalization recipe which enables to play with the tabulated results for practical applications. Finally, we study the impact of temperature dependent calculation on s-wave neutron resonance spacings.
Automatic generation of combinatorial test data
Zhang, Jian; Ma, Feifei
2014-01-01
This book reviews the state-of-the-art in combinatorial testing, with particular emphasis on the automatic generation of test data. It describes the most commonly used approaches in this area - including algebraic construction, greedy methods, evolutionary computation, constraint solving and optimization - and explains major algorithms with examples. In addition, the book lists a number of test generation tools, as well as benchmarks and applications. Addressing a multidisciplinary topic, it will be of particular interest to researchers and professionals in the areas of software testing, combi
Combinatorial nuclear level-density model
Moller, Peter [Los Alamos National Laboratory; Aberg, Sven [LUND SWEDEN; Uhrenhoit, Henrik [LUND SWEDEN; Ickhikawa, Takatoshi [RIKEN
2008-01-01
A microscopic nuclear level-density model is presented. The model is a completely combinatorial (micro-canonical) model based on the folded-Yukawa single-particle potential and includes explicit treatment of pairing, rotational and vibrational states. The microscopic character of all states enables extraction of level distribution functions with respect to pairing gaps, parity and angular momentum. The results of the model are compared to available experimental data: neutron separation energy level spacings, data on total level-density functions from the Oslo method and data on parity ratios.
Quantitative control of organ shape by combinatorial gene activity.
Min-Long Cui
Full Text Available The development of organs with particular shapes, like wings or flowers, depends on regional activity of transcription factors and signalling molecules. However, the mechanisms that link these molecular activities to the morphogenetic events underlying shape are poorly understood. Here we describe a combination of experimental and computational approaches that address this problem, applying them to a group of genes controlling flower shape in the Snapdragon (Antirrhinum. Four transcription factors are known to play a key role in the control of floral shape and asymmetry in Snapdragon. We use quantitative shape analysis of mutants for these factors to define principal components underlying flower shape variation. We show that each transcription factor has a specific effect on the shape and size of regions within the flower, shifting the position of the flower in shape space. These shifts are further analysed by generating double mutants and lines that express some of the genes ectopically. By integrating these observations with known gene expression patterns and interactions, we arrive at a combinatorial scheme for how regional effects on shape are genetically controlled. We evaluate our scheme by incorporating the proposed interactions into a generative model, where the developing flower is treated as a material sheet that grows according to how genes modify local polarities and growth rates. The petal shapes generated by the model show a good quantitative match with those observed experimentally for each petal in numerous genotypes, thus validating the hypothesised scheme. This article therefore shows how complex shapes can be accounted for by combinatorial effects of transcription factors on regional growth properties. This finding has implications not only for how shapes develop but also for how they may have evolved through tinkering with transcription factors and their targets.
Zhang, X.D. [School of Material Science and Engineering, Central South University, Changsha, Hunan, 410083 (China); Liu, L.B., E-mail: lbliu.csu@gmail.com [School of Material Science and Engineering, Central South University, Changsha, Hunan, 410083 (China); State Key Laboratory for Powder Metallurgy, Changsha, Hunan, 410083 (China); Zhao, J.-C. [State Key Laboratory for Powder Metallurgy, Changsha, Hunan, 410083 (China); Department of Materials Science and Engineering, The Ohio State University, 2041 College Road, Columbus, OH 43210 (United States); Wang, J.L.; Zheng, F.; Jin, Z.P. [School of Material Science and Engineering, Central South University, Changsha, Hunan, 410083 (China)
2014-06-01
A high-efficiency combinatorial approach has been applied to rapidly build the database of composition-dependent elastic modulus and hardness of the Ti–Ta and Ti–Zr–Ta systems. A diffusion multiple of the Ti–Zr–Ta system was manufactured, then annealed at 1173 K for 1800 h, and water quenched to room temperature. Extensive interdiffusion among Ti, Zr and Ta has taken place. Combining nanoindentation and electron probe micro-analysis (EPMA), the elastic modulus, hardness as well as composition across the diffusion multiple were determined. The composition/elastic modulus/hardness relationship of the Ti–Ta and Ti–Zr–Ta alloys has been obtained. It was found that the elastic modulus and hardness depend strongly on the Ta and Zr content. The result can be used to accelerate the discovery/development of bio-titanium alloys for different components in implant prosthesis. - Highlights: • High-efficiency diffusion multiple of Ti–Zr–Ta was manufactured. • Composition-dependent elastic modulus and hardness of the Ti–Ta and Ti–Zr–Ta systems have been obtained effectively, • The methodology and the information can be used to accelerate the discovery/development of bio-titanium alloys.
Yekini Shehu
2010-01-01
real Banach space which is also uniformly smooth using the properties of generalized f-projection operator. Using this result, we discuss strong convergence theorem concerning general H-monotone mappings and system of generalized mixed equilibrium problems in Banach spaces. Our results extend many known recent results in the literature.
Shim, Yong; Jaiswal, Akhilesh; Roy, Kaushik
2017-05-01
Ising spin model is considered as an efficient computing method to solve combinatorial optimization problems based on its natural tendency of convergence towards low energy state. The underlying basic functions facilitating the Ising model can be categorized into two parts, "Annealing and Majority vote." In this paper, we propose an Ising cell based on Spin Hall Effect (SHE) induced magnetization switching in a Magnetic Tunnel Junction (MTJ). The stochasticity of our proposed Ising cell based on SHE induced MTJ switching can implement the natural annealing process by preventing the system from being stuck in solutions with local minima. Further, by controlling the current through the Heavy-Metal (HM) underlying the MTJ, we can mimic the majority vote function which determines the next state of the individual spins. By solving coupled Landau-Lifshitz-Gilbert equations, we demonstrate that our Ising cell can be replicated to map certain combinatorial problems. We present results for two representative problems—Maximum-cut and Graph coloring—to illustrate the feasibility of the proposed device-circuit configuration in solving combinatorial problems. Our proposed solution using a HM based MTJ device can be exploited to implement compact, fast, and energy efficient Ising spin model.
Solving Set Cover with Pairs Problem using Quantum Annealing
Cao, Yudong; Jiang, Shuxian; Perouli, Debbie; Kais, Sabre
2016-09-01
Here we consider using quantum annealing to solve Set Cover with Pairs (SCP), an NP-hard combinatorial optimization problem that plays an important role in networking, computational biology, and biochemistry. We show an explicit construction of Ising Hamiltonians whose ground states encode the solution of SCP instances. We numerically simulate the time-dependent Schrödinger equation in order to test the performance of quantum annealing for random instances and compare with that of simulated annealing. We also discuss explicit embedding strategies for realizing our Hamiltonian construction on the D-wave type restricted Ising Hamiltonian based on Chimera graphs. Our embedding on the Chimera graph preserves the structure of the original SCP instance and in particular, the embedding for general complete bipartite graphs and logical disjunctions may be of broader use than that the specific problem we deal with.
Computational Study on a PTAS for Planar Dominating Set Problem
Qian-Ping Gu
2013-01-01
Full Text Available The dominating set problem is a core NP-hard problem in combinatorial optimization and graph theory, and has many important applications. Baker [JACM 41,1994] introduces a k-outer planar graph decomposition-based framework for designing polynomial time approximation scheme (PTAS for a class of NP-hard problems in planar graphs. It is mentioned that the framework can be applied to obtain an O(2ckn time, c is a constant, (1+1/k-approximation algorithm for the planar dominating set problem. We show that the approximation ratio achieved by the mentioned application of the framework is not bounded by any constant for the planar dominating set problem. We modify the application of the framework to give a PTAS for the planar dominating set problem. With k-outer planar graph decompositions, the modified PTAS has an approximation ratio (1 + 2/k. Using 2k-outer planar graph decompositions, the modified PTAS achieves the approximation ratio (1+1/k in O(22ckn time. We report a computational study on the modified PTAS. Our results show that the modified PTAS is practical.
On Definitions and Existence of Combinatorial Entropy of 2d Fields
Forchhammer, Søren Otto; Shtarkov, Yuri; Justesen, Jørn
1998-01-01
Different definitions of combinatorial entropy is presented and conditions for their existence examined.......Different definitions of combinatorial entropy is presented and conditions for their existence examined....
Self-encoding resin beads of combinatorial library screening
Lei, Du; Zhao, Yuandi; Cheng, Tongsheng; Zeng, Shaoqun; Luo, Qingming
2003-07-01
The latest self-encoding resin bead is a novel technology for solid phase synthesis combinatorial library screening. A new encode-positional deconvolution strategy which was based on that technology been illustrated compared with positional scanning and iterative strategies. The self-encoding resin beads technology provides an efficient method for improving the high-throughput screening of combinatorial library.
Combinatorial design of textured mechanical metamaterials.
Coulais, Corentin; Teomy, Eial; de Reus, Koen; Shokef, Yair; van Hecke, Martin
2016-07-28
The structural complexity of metamaterials is limitless, but, in practice, most designs comprise periodic architectures that lead to materials with spatially homogeneous features. More advanced applications in soft robotics, prosthetics and wearable technology involve spatially textured mechanical functionality, which requires aperiodic architectures. However, a naive implementation of such structural complexity invariably leads to geometrical frustration (whereby local constraints cannot be satisfied everywhere), which prevents coherent operation and impedes functionality. Here we introduce a combinatorial strategy for the design of aperiodic, yet frustration-free, mechanical metamaterials that exhibit spatially textured functionalities. We implement this strategy using cubic building blocks-voxels-that deform anisotropically, a local stacking rule that allows cooperative shape changes by guaranteeing that deformed building blocks fit together as in a three-dimensional jigsaw puzzle, and three-dimensional printing. These aperiodic metamaterials exhibit long-range holographic order, whereby the two-dimensional pixelated surface texture dictates the three-dimensional interior voxel arrangement. They also act as programmable shape-shifters, morphing into spatially complex, but predictable and designable, shapes when uniaxially compressed. Finally, their mechanical response to compression by a textured surface reveals their ability to perform sensing and pattern analysis. Combinatorial design thus opens up a new avenue towards mechanical metamaterials with unusual order and machine-like functionalities.
Combinatorial design of textured mechanical metamaterials
Coulais, Corentin; Teomy, Eial; de Reus, Koen; Shokef, Yair; van Hecke, Martin
2016-07-01
The structural complexity of metamaterials is limitless, but, in practice, most designs comprise periodic architectures that lead to materials with spatially homogeneous features. More advanced applications in soft robotics, prosthetics and wearable technology involve spatially textured mechanical functionality, which requires aperiodic architectures. However, a naive implementation of such structural complexity invariably leads to geometrical frustration (whereby local constraints cannot be satisfied everywhere), which prevents coherent operation and impedes functionality. Here we introduce a combinatorial strategy for the design of aperiodic, yet frustration-free, mechanical metamaterials that exhibit spatially textured functionalities. We implement this strategy using cubic building blocks—voxels—that deform anisotropically, a local stacking rule that allows cooperative shape changes by guaranteeing that deformed building blocks fit together as in a three-dimensional jigsaw puzzle, and three-dimensional printing. These aperiodic metamaterials exhibit long-range holographic order, whereby the two-dimensional pixelated surface texture dictates the three-dimensional interior voxel arrangement. They also act as programmable shape-shifters, morphing into spatially complex, but predictable and designable, shapes when uniaxially compressed. Finally, their mechanical response to compression by a textured surface reveals their ability to perform sensing and pattern analysis. Combinatorial design thus opens up a new avenue towards mechanical metamaterials with unusual order and machine-like functionalities.
Locating Minimal Fault Interaction in Combinatorial Testing
Wei Zheng
2016-01-01
Full Text Available Combinatorial testing (CT technique could significantly reduce testing cost and increase software system quality. By using the test suite generated by CT as input to conduct black-box testing towards a system, we are able to detect interactions that trigger the system’s faults. Given a test case, there may be only part of all its parameters relevant to the defects in system and the interaction constructed by those partial parameters is key factor of triggering fault. If we can locate those parameters accurately, this will facilitate the software diagnosing and testing process. This paper proposes a novel algorithm named complete Fault Interaction Location (comFIL to locate those interactions that cause system’s failures and meanwhile obtains the minimal set of target interactions in test suite produced by CT. By applying this method, testers can analyze and locate the factors relevant to defects of system more precisely, thus making the process of software testing and debugging easier and more efficient. The results of our empirical study indicate that comFIL performs better compared with known fault location techniques in combinatorial testing because of its improved effectiveness and precision.
Chang, Yi-Pin; Chu, Yen-Ho
2014-05-16
The design, synthesis and screening of diversity-oriented peptide libraries using a "libraries from libraries" strategy for the development of inhibitors of α1-antitrypsin deficiency are described. The major buttress of the biochemical approach presented here is the use of well-established solid-phase split-and-mix method for the generation of mixture-based libraries. The combinatorial technique iterative deconvolution was employed for library screening. While molecular diversity is the general consideration of combinatorial libraries, exquisite design through systematic screening of small individual libraries is a prerequisite for effective library screening and can avoid potential problems in some cases. This review will also illustrate how large peptide libraries were designed, as well as how a conformation-sensitive assay was developed based on the mechanism of the conformational disease. Finally, the combinatorially selected peptide inhibitor capable of blocking abnormal protein aggregation will be characterized by biophysical, cellular and computational methods.
Yi-Pin Chang
2014-05-01
Full Text Available The design, synthesis and screening of diversity-oriented peptide libraries using a “libraries from libraries” strategy for the development of inhibitors of α1-antitrypsin deficiency are described. The major buttress of the biochemical approach presented here is the use of well-established solid-phase split-and-mix method for the generation of mixture-based libraries. The combinatorial technique iterative deconvolution was employed for library screening. While molecular diversity is the general consideration of combinatorial libraries, exquisite design through systematic screening of small individual libraries is a prerequisite for effective library screening and can avoid potential problems in some cases. This review will also illustrate how large peptide libraries were designed, as well as how a conformation-sensitive assay was developed based on the mechanism of the conformational disease. Finally, the combinatorially selected peptide inhibitor capable of blocking abnormal protein aggregation will be characterized by biophysical, cellular and computational methods.
Systematic hardness studies on lithium niobate crystals
K G Subhadra; K Kishan Rao; D B Sirdeshmukh
2000-04-01
In view of discrepancies in the available information on the hardness of lithium niobate, a systematic study of the hardness has been carried out. Measurements have been made on two pure lithium niobate crystals with different growth origins, and a Fe-doped sample. The problem of load variation of hardness is examined in detail. The true hardness of LiNbO3 is found to be 630 ± 30 kg/mm2. The Fe-doped crystal has a larger hardness of 750 ± 50 kg/mm2.
Microbatteries for Combinatorial Studies of Conventional Lithium-Ion Batteries
West, William; Whitacre, Jay; Bugga, Ratnakumar
2003-01-01
Integrated arrays of microscopic solid-state batteries have been demonstrated in a continuing effort to develop microscopic sources of power and of voltage reference circuits to be incorporated into low-power integrated circuits. Perhaps even more importantly, arrays of microscopic batteries can be fabricated and tested in combinatorial experiments directed toward optimization and discovery of battery materials. The value of the combinatorial approach to optimization and discovery has been proven in the optoelectronic, pharmaceutical, and bioengineering industries. Depending on the specific application, the combinatorial approach can involve the investigation of hundreds or even thousands of different combinations; hence, it is time-consuming and expensive to attempt to implement the combinatorial approach by building and testing full-size, discrete cells and batteries. The conception of microbattery arrays makes it practical to bring the advantages of the combinatorial approach to the development of batteries.
Bruno Avila Leal de Meirelles Herrera
2015-12-01
Full Text Available ABSTRACT The Traveling Salesman Problem (TSP is one of the most well-known and studied problems of Operations Research field, more specifically, in the Combinatorial Optimization field. As the TSP is a NP (Non-Deterministic Polynomial time-hard problem, there are several heuristic methods which have been proposed for the past decades in the attempt to solve it the best possible way. The aim of this work is to introduce and to evaluate the performance of some approaches for achieving optimal solution considering some symmetrical and asymmetrical TSP instances, which were taken from the Traveling Salesman Problem Library (TSPLIB. The analyzed approaches were divided into three methods: (i Lin-Kernighan-Helsgaun (LKH algorithm; (ii LKH with initial tour based on uniform distribution; and (iii an hybrid proposal combining Particle Swarm Optimization (PSO with quantum inspired behavior and LKH for local search procedure. The tested algorithms presented promising results in terms of computational cost and solution quality.
Approximability of the d-dimensional Euclidean capacitated vehicle routing problem
Khachay, Michael; Dubinin, Roman
2016-10-01
Capacitated Vehicle Routing Problem (CVRP) is the well known intractable combinatorial optimization problem, which remains NP-hard even in the Euclidean plane. Since the introduction of this problem in the middle of the 20th century, many researchers were involved into the study of its approximability. Most of the results obtained in this field are based on the well known Iterated Tour Partition heuristic proposed by M. Haimovich and A. Rinnoy Kan in their celebrated paper, where they construct the first Polynomial Time Approximation Scheme (PTAS) for the single depot CVRP in ℝ2. For decades, this result was extended by many authors to numerous useful modifications of the problem taking into account multiple depots, pick up and delivery options, time window restrictions, etc. But, to the best of our knowledge, almost none of these results go beyond the Euclidean plane. In this paper, we try to bridge this gap and propose a EPTAS for the Euclidean CVRP for any fixed dimension.
A 16-bit Coherent Ising Machine for One-Dimensional Ring and Cubic Graph Problems
Takata, Kenta; Hamerly, Ryan; Haribara, Yoshitaka; Maruo, Daiki; Tamate, Shuhei; Sakaguchi, Hiromasa; Utsunomiya, Shoko; Yamamoto, Yoshihisa
2016-01-01
Many tasks in modern life, such as efficient traveling, image processing and integrated circuit optimization, are modeled as complex combinatorial optimization problems. Such problems can be mapped to finding a ground state of the Ising Hamiltonian, thus various physical systems have been studied to emulate and solve this Ising problem. Recently, networks of mutually injected optical oscillators, called coherent Ising machines, have been developed as promising solvers for the problem, benefiting from programmability, scalability and room temperature operation. Here, we report a 16-bit coherent Ising machine with a network of time-division-multiplexed femtosecond degenerate optical parametric oscillators. The system experimentally gives more than 99.6 % of success rates for one-dimensional Ising ring and nondeterministic polynomial-time (NP) hard instances. The experimental and numerical results indicate that gradual pumping of the network combined with multimode dynamics of femtosecond pulses can improve its ...
Combinatorial Algorithms to Enable Computational Science and Engineering: The CSCAPES Institute
Pothen, Alex [Purdue University
2015-01-16
This final progress report summarizes the work accomplished at the Combinatorial Scientific Computing and Petascale Simulations Institute. We developed Zoltan, a parallel mesh partitioning library that made use of accurate hyeprgraph models to provide load balancing in mesh-based computations. We developed several graph coloring algorithms for computing Jacobian and Hessian matrices and organized them into a software package called ColPack. We developed parallel algorithms for graph coloring and graph matching problems, and also designed multi-scale graph algorithms. Three PhD students graduated, six more are continuing their PhD studies, and four postdoctoral scholars were advised. Six of these students and Fellows have joined DOE Labs (Sandia, Berkeley, as staff scientists or as postdoctoral scientists. We also organized the SIAM Workshop on Combinatorial Scientific Computing (CSC) in 2007, 2009, and 2011 to continue to foster the CSC community.
Boman, Erik G. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States). Scalable Algorithms Dept.; Catalyurek, Umit V. [The Ohio State Univ., Columbus, OH (United States). Biomedical Informatics. Electrical and Computer Engineering; Chevalier, Cedric [Alternative Energies and Atomic Energy Commission (CEA), Cadarache (France); Devine, Karen D. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States). Scalable Algorithms Dept.; Gebremedhin, Assefaw H. [Purdue Univ., West Lafayette, IN (United States). Computer Science; Hovland, Paul D. [Argonne National Lab. (ANL), Argonne, IL (United States). Mathematics and Computer Science Division; Pothen, Alex [Purdue Univ., West Lafayette, IN (United States). Computer Science; Rajamanickam, Sivasankaran [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States). Scalable Algorithms Dept.; Safro, Ilya [Argonne National Lab. (ANL), Argonne, IL (United States). Mathematics and Computer Science Division; Wolf, Michael M. [Massachusetts Inst. of Technology (MIT), Lexington, MA (United States). Lincoln Lab.; Zhou, Min [Rensselaer Polytechnic Inst., Troy, NY (United States). Scientific Computation Research Center
2015-01-16
This final progress report summarizes the work accomplished at the Combinatorial Scientific Computing and Petascale Simulations Institute. We developed Zoltan, a parallel mesh partitioning library that made use of accurate hypergraph models to provide load balancing in mesh-based computations. We developed several graph coloring algorithms for computing Jacobian and Hessian matrices and organized them into a software package called ColPack. We developed parallel algorithms for graph coloring and graph matching problems, and also designed multi-scale graph algorithms. Three PhD students graduated, six more are continuing their PhD studies, and four postdoctoral scholars were advised. Six of these students and Fellows have joined DOE Labs (Sandia, Berkeley), as staff scientists or as postdoctoral scientists. We also organized the SIAM Workshop on Combinatorial Scientific Computing (CSC) in 2007, 2009, and 2011 to continue to foster the CSC community.
Research on Li Shanlan's Combinatorial Thought%李善兰组合思想研究
张必胜
2016-01-01
This paper reviews Li Shanlan traditional mathematics works on combinatorial problems of historical documents, obtained Li Shanlan combinatorial identities and Western mathematics is consistent. Li Shanlan in his book "DuoJiBiLei" got some mathematical expressions combination summation.%基于李善兰传统数学著作中关于组合问题历史文献的研究，得出李善兰组合恒等式与西方数学是保持一致的。李善兰在其著作《垛积比类》得到了一些组合求和的数学表达式。
Ant colony optimization for solving university facility layout problem
Mohd Jani, Nurul Hafiza; Mohd Radzi, Nor Haizan; Ngadiman, Mohd Salihin
2013-04-01
Quadratic Assignment Problems (QAP) is classified as the NP hard problem. It has been used to model a lot of problem in several areas such as operational research, combinatorial data analysis and also parallel and distributed computing, optimization problem such as graph portioning and Travel Salesman Problem (TSP). In the literature, researcher use exact algorithm, heuristics algorithm and metaheuristic approaches to solve QAP problem. QAP is largely applied in facility layout problem (FLP). In this paper we used QAP to model university facility layout problem. There are 8 facilities that need to be assigned to 8 locations. Hence we have modeled a QAP problem with n ≤ 10 and developed an Ant Colony Optimization (ACO) algorithm to solve the university facility layout problem. The objective is to assign n facilities to n locations such that the minimum product of flows and distances is obtained. Flow is the movement from one to another facility, whereas distance is the distance between one locations of a facility to other facilities locations. The objective of the QAP is to obtain minimum total walking (flow) of lecturers from one destination to another (distance).
Howe, A E; Whitley, L D; 10.1613/jair.1576
2011-01-01
Tabu search is one of the most effective heuristics for locating high-quality solutions to a diverse array of NP-hard combinatorial optimization problems. Despite the widespread success of tabu search, researchers have a poor understanding of many key theoretical aspects of this algorithm, including models of the high-level run-time dynamics and identification of those search space features that influence problem difficulty. We consider these questions in the context of the job-shop scheduling problem (JSP), a domain where tabu search algorithms have been shown to be remarkably effective. Previously, we demonstrated that the mean distance between random local optima and the nearest optimal solution is highly correlated with problem difficulty for a well-known tabu search algorithm for the JSP introduced by Taillard. In this paper, we discuss various shortcomings of this measure and develop a new model of problem difficulty that corrects these deficiencies. We show that Taillards algorithm can be modeled with ...
A Combinatorial Auction among Versatile Experts and Amateurs
Ito, Takayuki; Yokoo, Makoto; Matsubara, Shigeo
Auctions have become an integral part of electronic commerce and a promising field for applying multi-agent technologies. Correctly judging the quality of auctioned goods is often difficult for amateurs, in particular, in Internet auctions. However, experts can correctly judge the quality of goods. In this situation, it is difficult to make experts tell the truth and attain an efficient allocation, since experts have a clear advantage over amateurs and they would not reveal their valuable information without some reward. In our previous work, we have succeeded in developing such auction protocols under the following two cases: (1) the case of a single-unit auction among experts and amateurs, and (2) the case of a combinatorial auction among single-skilled experts and amateurs. In this paper, we focus on versatile experts. Versatile experts have an interest in, and expert knowledge on the qualities of several goods. In the case of versatile experts, there would be several problems, e.g., free riding problems, if we simply extended the previous VCG-style auction protocol. Thus, in this paper, we employ PORF (price-oriented, rationing-free) protocol for designing our new protocol to realize a strategy-proof auction protocol for experts. In the protocol, the dominant strategy for experts is truth-telling. Also, for amateurs, truth-telling is the best response when two or more experts select the dominant strategy. Furthermore, the protocol is false-name-proof.
Identification and Interrogation of Combinatorial Histone Modifications
Kelly R Karch
2013-12-01
Full Text Available Histone proteins are dynamically modified to mediate a variety of cellular processes including gene transcription, DNA damage repair, and apoptosis. Regulation of these processes occurs through the recruitment of non-histone proteins to chromatin by specific combinations of histone post-translational modifications (PTMs. Mass spectrometry has emerged as an essential tool to discover and quantify histone PTMs both within and between samples in an unbiased manner. Developments in mass spectrometry that allow for characterization of large histone peptides or intact protein has made it possible to determine which modifications occur simultaneously on a single histone polypeptide. A variety of techniques from biochemistry, biophysics, and chemical biology have been employed to determine the biological relevance of discovered combinatorial codes. This review first describes advancements in the field of mass spectrometry that have facilitated histone PTM analysis and then covers notable approaches to probe the biological relevance of these modifications in their nucleosomal context.
Human Performance on the Traveling Salesman and Related Problems: A Review
MacGregor, James N.; Chu, Yun
2011-01-01
The article provides a review of recent research on human performance on the traveling salesman problem (TSP) and related combinatorial optimization problems. We discuss what combinatorial optimization problems are, why they are important, and why they may be of interest to cognitive scientists. We next describe the main characteristics of human…
The balanced minimum evolution problem under uncertain data
Catanzaro, Daniele; Labbe, Martine; Pesenti, Raffaele
2013-01-01
We investigate the Robust Deviation Balanced Minimum Evolution Problem (RDBMEP), a combinatorial optimization problem that arises in computational biology when the evolutionary distances from taxa are uncertain and varying inside intervals. By exploiting some fundamental properties of the objective
Hintermair, Manfred; Korneffel, Désirée
2013-09-01
Fragestellung: Da im Zuge inklusiver Bestrebungen immer mehr hörgeschädigte Kinder eine allgemeine Schule besuchen werden, gilt es, relevante entwicklungspsychologische Voraussetzungen hierfür genauer zu betrachten. In einer Studie wurden deshalb sozial-emotionale Probleme hörgeschädigter Kinder an allgemeinen Schulen im Zusammenhang mit möglichen Problemen in der Entwicklung exekutiver Funktionen und der kommunikativen Kompetenz diskutiert. Methodik: Eine Stichprobe von 69 Schülern wurde mit einer deutschen Version des «Behavior Rating Inventory of Executive Functions (BRIEF)», einer Kurzskala zur Erfassung der kommunikativen Kompetenz sowie dem Strengths and Difficulties Questionnaire untersucht. Die Daten wurden mit einer Normierungsstichprobe verglichen, weiter wurden korrelative und regressionsanalytische Zusammenhänge der Variablen berechnet. Ebenso wurden Zusammenhänge der exekutiven Funktionen mit soziodemographischen Variablen analysiert. Ergebnisse: Die Ergebnisse zeigen, dass in fast allen Bereichen exekutiver Funktionen die hörgeschädigten Kinder mehr Probleme aufweisen als die Kinder der hörenden Normierungsstichprobe und die Prävalenzrate durchschnittlich ca. dreimal höher ist. Der Index für verhaltensregulierende exekutive Funktionen erweist sich neben dem Geschlecht am besten zur Vorhersage sozial-emotionaler Probleme. Schlussfolgerungen: Für die pädagogische Praxis ergibt sich, dass hörgeschädigte Schüler an allgemeinen Schulen in Bezug auf ihre psychosoziale Entwicklung von einem pädagogischen Konzept profitieren, das neben der Förderung sprachkommunikativer Kompetenzen auch auf die Stärkung von Selbstkontrolle und Selbstwirksamkeit der Kinder fokussiert.
The Directed Dominating Set Problem: Generalized Leaf Removal and Belief Propagation
Habibulla, Yusupjan; Zhou, Hai-Jun
2015-01-01
A minimum dominating set for a digraph (directed graph) is a smallest set of vertices such that each vertex either belongs to this set or has at least one parent vertex in this set. We solve this hard combinatorial optimization problem approximately by a local algorithm of generalized leaf removal and by a message-passing algorithm of belief propagation. These algorithms can construct near-optimal dominating sets or even exact minimum dominating sets for random digraphs and also for real-world digraph instances. We further develop a core percolation theory and a replica-symmetric spin glass theory for this problem. Our algorithmic and theoretical results may facilitate applications of dominating sets to various network problems involving directed interactions.
Chang, Yuchao; Tang, Hongying; Cheng, Yongbo; Zhao, Qin; Yuan, Baoqing Li andXiaobing
2017-07-19
Routing protocols based on topology control are significantly important for improving network longevity in wireless sensor networks (WSNs). Traditionally, some WSN routing protocols distribute uneven network traffic load to sensor nodes, which is not optimal for improving network longevity. Differently to conventional WSN routing protocols, we propose a dynamic hierarchical protocol based on combinatorial optimization (DHCO) to balance energy consumption of sensor nodes and to improve WSN longevity. For each sensor node, the DHCO algorithm obtains the optimal route by establishing a feasible routing set instead of selecting the cluster head or the next hop node. The process of obtaining the optimal route can be formulated as a combinatorial optimization problem. Specifically, the DHCO algorithm is carried out by the following procedures. It employs a hierarchy-based connection mechanism to construct a hierarchical network structure in which each sensor node is assigned to a special hierarchical subset; it utilizes the combinatorial optimization theory to establish the feasible routing set for each sensor node, and takes advantage of the maximum-minimum criterion to obtain their optimal routes to the base station. Various results of simulation experiments show effectiveness and superiority of the DHCO algorithm in comparison with state-of-the-art WSN routing algorithms, including low-energy adaptive clustering hierarchy (LEACH), hybrid energy-efficient distributed clustering (HEED), genetic protocol-based self-organizing network clustering (GASONeC), and double cost function-based routing (DCFR) algorithms.
Implementation of a combinatorial cleavage and deprotection scheme
Nielsen, John; Rasmussen, Palle H.
1996-01-01
Phthalhydrazide libraries are synthesized in solution from substituted hydrazines and phthalimides in several different library formats including single compounds, indexed sub-libraries and a full library. When carried out during solid-phase synthesis, this combinatorial cleavage and deprotection...
Combinatorial polynomials as moments, Hankel transforms and exponential Riordan arrays
Barry, Paul
2011-01-01
In the case of two combinatorial polynomials, we show that they can exhibited as moments of paramaterized families of orthogonal polynomials, and hence derive their Hankel transforms. Exponential Riordan arrays are the main vehicles used for this.
Advanced Aqueous Phase Catalyst Development using Combinatorial Methods Project
National Aeronautics and Space Administration — The use of combinatorial methods is proposed to rapidly screen catalyst formulations for the advanced development of aqueous phase oxidation catalysts with greater...
New opioid peptides, peptidomimetics, and heterocyclic compounds from combinatorial libraries.
Dooley, C T; Houghten, R A
1999-01-01
Here we review the use of combinatorial libraries in opioid receptor assays. Following a brief description of the history of the combinatorial field, methods for the generation of synthetic libraries and the deconvolution of mixture-based libraries are presented. Case studies involving opioid assays used to demonstrate the viability of combinatorial libraries are described. The identification of new opioid peptides from combinatorial libraries is reviewed. The peptides found are composed of L-amino acids, D-amino acids, or L-, D-, and unnatural amino acids, and range from tetrapeptides to decapeptides. Likewise, new opioid compounds identified from peptidomimetic libraries, such as peptoids and alkylated dipeptides, and those identified from acyclic (e.g., polyamine, urea) and heterocyclic (e.g., bicyclic guanidine) libraries, are reviewed.
Combinatorial Hopf Algebras in (Noncommutative) Quantum Field Theory
Tanasa, Adrian
2010-01-01
We briefly review the r\\^ole played by algebraic structures like combinatorial Hopf algebras in the renormalizability of (noncommutative) quantum field theory. After sketching the commutative case, we analyze the noncommutative Grosse-Wulkenhaar model.
Combinatorial and high-throughput screening approaches for strain engineering.
Liu, Wenshan; Jiang, Rongrong
2015-03-01
Microbes have long been used in the industry to produce valuable biochemicals. Combinatorial engineering approaches, new strain engineering tools derived from inverse metabolic engineering, have started to attract attention in recent years, including genome shuffling, error-prone DNA polymerase, global transcription machinery engineering (gTME), random knockout/overexpression libraries, ribosome engineering, multiplex automated genome engineering (MAGE), customized optimization of metabolic pathways by combinatorial transcriptional engineering (COMPACTER), and library construction of "tunable intergenic regions" (TIGR). Since combinatorial approaches and high-throughput screening methods are fundamentally interconnected, color/fluorescence-based, growth-based, and biosensor-based high-throughput screening methods have been reviewed. We believe that with the help of metabolic engineering tools and new combinatorial approaches, plus effective high-throughput screening methods, researchers will be able to achieve better results on improving microorganism performance under stress or enhancing biochemical yield.
Reinvigorating natural product combinatorial biosynthesis with synthetic biology.
Kim, Eunji; Moore, Bradley S; Yoon, Yeo Joon
2015-09-01
Natural products continue to play a pivotal role in drug-discovery efforts and in the understanding if human health. The ability to extend nature's chemistry through combinatorial biosynthesis--altering functional groups, regiochemistry and scaffold backbones through the manipulation of biosynthetic enzymes--offers unique opportunities to create natural product analogs. Incorporating emerging synthetic biology techniques has the potential to further accelerate the refinement of combinatorial biosynthesis as a robust platform for the diversification of natural chemical drug leads. Two decades after the field originated, we discuss the current limitations, the realities and the state of the art of combinatorial biosynthesis, including the engineering of substrate specificity of biosynthetic enzymes and the development of heterologous expression systems for biosynthetic pathways. We also propose a new perspective for the combinatorial biosynthesis of natural products that could reinvigorate drug discovery by using synthetic biology in combination with synthetic chemistry.
Dynamic Combinatorial Libraries of Disulfide Cages in Water
West, Kevin R.; Bake, Kyle D.; Otto, Sijbren
2005-01-01
Dynamic combinatorial libraries (DCLs) containing water-soluble disulfide-linked cages (alongside macrocyclic structures) have been generated and characterized. Unlike most other strategies for generating molecular cages, the structures are held together by covalent bonds, which are formed under
Syed Tauhid Zuhori
2012-02-01
Full Text Available The traveling salesman problem (TSP is one of the most widely studied NP hard combinatorial optimization problems and has already solved in the semi-optimal manners using numbers of different methods. Among them, Genetic Algorithms (GA are pre-dominating. In this paper I solve the problem with a new operator, Inver-over, for an evolutionary algorithm for the TSP. This operator outperforms all other 'genetic' operators, whether unary or binary, which was first introduced by Guo Tao and Zbigniew Michalewicz. I also propose a new algorithm for solving TSP. To get a comparative idea of the performance of these algorithms I solve same problems with the two algorithms. The performance analysis shows that my proposed algorithm produces relatively better solutions in the case of the tour length every time. But when we increase the cities it takes more time to solve than the Inver-Over operator for TSP.
Scanning SQUID microscopy of local superconductivity in inhomogeneous combinatorial ceramics.
Iranmanesh, Mitra; Stir, Manuela; Kirtley, John R; Hulliger, Jürg
2014-11-24
Although combinatorial solid-state chemistry promises to be an efficient way to search for new superconducting compounds, the problem of determining which compositions are strongly diamagnetic in a mixed-phase sample is challenging. By means of reactions in a system of randomly mixed starting components (Ca, Sr, Ba, La, Y, Pb, Bi, Tl, and Cu oxides), samples were produced that showed an onset of diamagnetic response above 115 K in bulk measurements. Imaging of this diamagnetic response in ceramic samples by scanning SQUID microscopy (SSM) revealed local superconducting areas with sizes down to as small as the spatial resolution of a few micrometers. In addition, locally formed superconducting matter was extracted from mixed-phase samples by magnetic separation. The analysis of single grains (d<80 μm) by X-ray diffraction, elemental analysis, and bulk SQUID measurements allowed Tl2Ca3Ba2Cu4O12, TlCaBaSrCu2O(7-δ), BaPb(0.5)Bi(0.25)Tl(0.25)O(3-δ), TlBa2Ca2Cu3O9, Tl2Ba2CaCu2O8, and YBa2Cu3O7 phases to be identified. SSM, in combination with other diagnostic techniques, is therefore shown to be a useful instrument to analyze inhomogeneous reaction products in the solid-state chemistry of materials showing magnetic properties.
An improved combinatorial geometry model for arbitrary geometry in DSMC
Kargaran, H.; Minuchehr, A.; Zolfaghari, A.
2017-03-01
This paper focuses on a new direct simulation Monte Carlo (DSMC) code based on combinatorial geometry (CG) for simulation of any rarefied gas flow. The developed code, called DgSMC-A, has been supplied with an improved CG modeling able to significantly optimize the particle-tracking process, resulting in a highly reduced runtime compared to the conventional codes. The improved algorithm inserts a grid over the geometry and saves those grid elements containing some part of the geometry border. Since only a small part of a grid is engaged with the geometry border, significant time can be saved using the proposed algorithm. Embedding the modified algorithm in the DgSMC-A resulted in a fast, robust and self-governing code needless to any mesh generator. The code completely handles complex geometries created with first-and second-order surfaces. In addition, we developed a new surface area calculator in the CG methodology for complex geometries based on the Monte Carlo method with acceptable accuracy. Several well-known test cases are examined to indicate the code ability to deal with a wide range of realistic problems. Results are also found to be in good agreement with references and experimental data.
Analysis of selection methodologies for combinatorial library design.
Pascual, Rosalia; Borrell, José I; Teixidó, Jordi
2003-01-01
We have implemented and adapted in Pralins (Program for Rational Analysis of Libraries in silico), the most popular sparse (cherry picking) and full array (sublibrary) selection algorithms: hierarchical clustering, k-means clustering, Optimum Binning, Jarvis Patrick, Pral-SE (partitioning techniques) and MaxSum, MaxMin, MaxMin averaged, DN2, CTD (distance-based methods). We have validated the program with an already synthesized three-component combinatorial library of FXR partial agonists characterized by standard computational chemistry descriptors as case study. This has let us analyze the goodness of both the partitioning techniques for space division and all the selection methodologies with respect to representativity in terms of population and space coverage for different selection sizes. Within the chemical space analyzed, both hierarchical clustering and Optimum Binning division strategies are found to be the most advantageous reference space divisions to be used in the subsequent population and space coverage studies. Complete hierarchical clustering appears also to be the preferred selection methodology for both sparse and full array problems. The full array restriction fulfillment can easily be overcome by convenient optimization algorithms that allow optimal reagent selection preserving > 90% of the population coverage.
Variational Splines and Paley--Wiener Spaces on Combinatorial Graphs
Pesenson, Isaac
2011-01-01
Notions of interpolating variational splines and Paley-Wiener spaces are introduced on a combinatorial graph G. Both of these definitions explore existence of a combinatorial Laplace operator onG. The existence and uniqueness of interpolating variational splines on a graph is shown. As an application of variational splines, the paper presents a reconstruction algorithm of Paley-Wiener functions on graphs from their uniqueness sets.
Variational Splines and Paley--Wiener Spaces on Combinatorial Graphs
Pesenson, Isaac
2011-01-01
Notions of interpolating variational splines and Paley-Wiener spaces are introduced on a combinatorial graph G. Both of these definitions explore existence of a combinatorial Laplace operator onG. The existence and uniqueness of interpolating variational splines on a graph is shown. As an application of variational splines, the paper presents a reconstruction algorithm of Paley-Wiener functions on graphs from their uniqueness sets.
Sampling, Filtering and Sparse Approximations on Combinatorial Graphs
Pesenson, Isaac Z
2011-01-01
In this paper we address sampling and approximation of functions on combinatorial graphs. We develop filtering on graphs by using Schr\\"odinger's group of operators generated by combinatorial Laplace operator. Then we construct a sampling theory by proving Poincare and Plancherel-Polya-type inequalities for functions on graphs. These results lead to a theory of sparse approximations on graphs and have potential applications to filtering, denoising, data dimension reduction, image processing, image compression, computer graphics, visualization and learning theory.
Combinatorial Dyson-Schwinger equations and inductive data types
Kock, Joachim
2016-06-01
The goal of this contribution is to explain the analogy between combinatorial Dyson-Schwinger equations and inductive data types to a readership of mathematical physicists. The connection relies on an interpretation of combinatorial Dyson-Schwinger equations as fixpoint equations for polynomial functors (established elsewhere by the author, and summarised here), combined with the now-classical fact that polynomial functors provide semantics for inductive types. The paper is expository, and comprises also a brief introduction to type theory.
Combinatorial Dyson-Schwinger equations and inductive data types
Kock, Joachim
2015-01-01
The goal of this contribution is to explain the analogy between combinatorial Dyson-Schwinger equations and inductive data types to a readership of mathematical physicists. The connection relies on an interpretation of combinatorial Dyson-Schwinger equations as fixpoint equations for polynomial functors (established elsewhere by the author, and summarised here), combined with the now-classical fact that polynomial functors provide semantics for inductive types. The paper is expository, and co...
The problem of compatible representatives
Knuth, Donald E
2008-01-01
The purpose of this note is to attach a name to a natural class of combinatorial problems and to point out that this class includes many important special cases. We also show that a simple problem of placing nonoverlapping labels on a rectangular map is NP-complete.
Geometric and Combinatorial Structure of Hypersurface Coamoebas
Nisse, Mounir
2009-01-01
Let $V$ be a complex algebraic hypersurface defined by a polynomial $f$ with Newton polytope $\\Delta$. It is well known that the spine of its amoeba has a structure of a tropical hypersurface. We prove in this paper that there exists a complex tropical hypersurface $V_{\\infty, f}$ such that its coamoeba is homeomorphic to the closure in the real torus of the coamoeba of $V$. Moreover, the coamoeba of $V_{\\infty, f}$ contains an arrangement of $(n-1)$-torus depending only on the geometry of $\\Delta$ and the coefficients of $f$. In addition, we can consider this arrangement, as a weighted codual hyperplanes arrangement in the universal covering of the real torus, and the balancing condition (the analogous to that of tropical hypersurfaces) is satisfied. This codual hyperplanes arrangement is called the {\\em shell} of the complex coamoeba (the cousin of the spine of the complex amoeba). %(or the {\\em average contour} of the complex coamoeba). Using this combinatorial coamoebas structure, we show that the amoebas...
Similarity searching in large combinatorial chemistry spaces
Rarey, Matthias; Stahl, Martin
2001-06-01
We present a novel algorithm, called Ftrees-FS, for similarity searching in large chemistry spaces based on dynamic programming. Given a query compound, the algorithm generates sets of compounds from a given chemistry space that are similar to the query. The similarity search is based on the feature tree similarity measure representing molecules by tree structures. This descriptor allows handling combinatorial chemistry spaces as a whole instead of looking at subsets of enumerated compounds. Within few minutes of computing time, the algorithm is able to find the most similar compound in very large spaces as well as sets of compounds at an arbitrary similarity level. In addition, the diversity among the generated compounds can be controlled. A set of 17 000 fragments of known drugs, generated by the RECAP procedure from the World Drug Index, was used as the search chemistry space. These fragments can be combined to more than 1018 compounds of reasonable size. For validation, known antagonists/inhibitors of several targets including dopamine D4, histamine H1, and COX2 are used as queries. Comparison of the compounds created by Ftrees-FS to other known actives demonstrates the ability of the method to jump between structurally unrelated molecule classes.
Scalable Combinatorial Tools for Health Disparities Research
Michael A. Langston
2014-10-01
Full Text Available Despite staggering investments made in unraveling the human genome, current estimates suggest that as much as 90% of the variance in cancer and chronic diseases can be attributed to factors outside an individual’s genetic endowment, particularly to environmental exposures experienced across his or her life course. New analytical approaches are clearly required as investigators turn to complicated systems theory and ecological, place-based and life-history perspectives in order to understand more clearly the relationships between social determinants, environmental exposures and health disparities. While traditional data analysis techniques remain foundational to health disparities research, they are easily overwhelmed by the ever-increasing size and heterogeneity of available data needed to illuminate latent gene x environment interactions. This has prompted the adaptation and application of scalable combinatorial methods, many from genome science research, to the study of population health. Most of these powerful tools are algorithmically sophisticated, highly automated and mathematically abstract. Their utility motivates the main theme of this paper, which is to describe real applications of innovative transdisciplinary models and analyses in an effort to help move the research community closer toward identifying the causal mechanisms and associated environmental contexts underlying health disparities. The public health exposome is used as a contemporary focus for addressing the complex nature of this subject.
Dynamic combinatorial libraries of artificial repeat proteins.
Eisenberg, Margarita; Shumacher, Inbal; Cohen-Luria, Rivka; Ashkenasy, Gonen
2013-06-15
Repeat proteins are found in almost all cellular systems, where they are involved in diverse molecular recognition processes. Recent studies have suggested that de novo designed repeat proteins may serve as universal binders, and might potentially be used as practical alternative to antibodies. We describe here a novel chemical methodology for producing small libraries of repeat proteins, and screening in parallel the ligand binding of library members. The first stage of this research involved the total synthesis of a consensus-based three-repeat tetratricopeptide (TPR) protein (~14 kDa), via sequential attachment of the respective peptides. Despite the effectiveness of the synthesis and ligation steps, this method was found to be too demanding for the production of proteins containing variable number of repeats. Additionally, the analysis of binding of the individual proteins was time consuming. Therefore, we designed and prepared novel dynamic combinatorial libraries (DCLs), and show that their equilibration can facilitate the formation of TPR proteins containing up to eight repeating units. Interestingly, equilibration of the library building blocks in the presence of the biologically relevant ligands, Hsp90 and Hsp70, induced their oligomerization into forming more of the proteins with large recognition surfaces. We suggest that this work presents a novel simple and rapid tool for the simultaneous screening of protein mixtures with variable binding surfaces, and for identifying new binders for ligands of interest.
潘立军; 符卓
2012-01-01
针对已有求解带硬时间窗车辆路径问题时插入启发式算法结构复杂、参数多、求解效率不高的缺点,提出了求解该问题的时差插入启发式算法.该算法引入时差的概念,将时差作为启发规则的评价指标.相比已有求解该问题的经典启发式算法,该算法有参数个数少、算法结构简单等特点.应用标准测试算例测试表明,所提算法的求解质量优于Solomon的插入启发式算法和Potvin的平行插入启发式算法.%The Vehicle Routing Problem with Hard Time Window ( VRPHTW) is a kind of Vehicle Routing Problem (VRP) which has a lot of applications. The existing heuristics of this problem hold shortcomings such as complex structure, lots of parameters and low efficiency. Therefore, Time Difference Insertion Heuristics (TDIH) for VRPHTW was proposed. The algorithm introduced the concept of Time Difference ( TD), and took TD as a heuristic rule evaluation indicator. Compared to other classic heuristics, the algorithm was characterized with fewer parameters and simpler structure. The computational results on the benchmark problems show that the algorithm is better than the Solomon's insertion heuristics and Potvin's parallel insertion heuristics.
Tuning the physical properties of amorphous In–Zn–Sn–O thin films using combinatorial sputtering
Ndione, P. F.; Zakutayev, A.; Kumar, M.; Packard, C. E.; Berry, J. J.; Perkins, J. D.; Ginley, D. S.
2016-12-01
Transparent conductive oxides and amorphous oxide semiconductors are important materials for many modern technologies. Here, we explore the ternary indium zinc tin oxide (IZTO) using combinatorial synthesis and spatially resolved characterization. The electrical conductivity, work function, absorption onset, mechanical hardness, and elastic modulus of the optically transparent (>85%) amorphous IZTO thin films were found to be in the range of 10–2415 S/cm, 4.6–5.3 eV, 3.20–3.34 eV, 9.0–10.8 GPa, and 111–132 GPa, respectively, depending on the cation composition and the deposition conditions. This study enables control of IZTO performance over a broad range of cation compositions.
Hardness and Methods to Solve CLIQUE
ZHU Daming; LUAN Junfeng; MA Shaohan
2001-01-01
The paper briefly reviews NP-hard optimization problems and their inapproximability. The hardness of solving CLIQUE problem is specifically discussed. A dynamic-programming algorithm and its improved version for CLIQUE are reviewed and some additional analysis is presented. The analysis implies that the improved algorithm, HEWN (hierarchical edge-weighted network), only provides a heuristic or useful method, but cannot be called a polynomial algorithm.
Thermodynamic hardness and the maximum hardness principle
Franco-Pérez, Marco; Gázquez, José L.; Ayers, Paul W.; Vela, Alberto
2017-08-01
An alternative definition of hardness (called the thermodynamic hardness) within the grand canonical ensemble formalism is proposed in terms of the partial derivative of the electronic chemical potential with respect to the thermodynamic chemical potential of the reservoir, keeping the temperature and the external potential constant. This temperature dependent definition may be interpreted as a measure of the propensity of a system to go through a charge transfer process when it interacts with other species, and thus it keeps the philosophy of the original definition. When the derivative is expressed in terms of the three-state ensemble model, in the regime of low temperatures and up to temperatures of chemical interest, one finds that for zero fractional charge, the thermodynamic hardness is proportional to T-1(I -A ) , where I is the first ionization potential, A is the electron affinity, and T is the temperature. However, the thermodynamic hardness is nearly zero when the fractional charge is different from zero. Thus, through the present definition, one avoids the presence of the Dirac delta function. We show that the chemical hardness defined in this way provides meaningful and discernible information about the hardness properties of a chemical species exhibiting integer or a fractional average number of electrons, and this analysis allowed us to establish a link between the maximum possible value of the hardness here defined, with the minimum softness principle, showing that both principles are related to minimum fractional charge and maximum stability conditions.
Wear of hard materials by hard particles
Hawk, Jeffrey A.
2003-10-01
Hard materials, such as WC-Co, boron carbide, titanium diboride and composite carbide made up of Mo2C and WC, have been tested in abrasion and erosion conditions. These hard materials showed negligible wear in abrasion against SiC particles and erosion using Al2O3 particles. The WC-Co materials have the highest wear rate of these hard materials and a very different material removal mechanism. Wear mechanisms for these materials were different for each material with the overall wear rate controlled by binder composition and content and material grain size.
Mapping the Materials Genome through Combinatorial Informatics
Rajan, Krishna
2012-02-01
The recently announced White House Materials Genome Initiative provides an exciting challenge to the materials science community. To meet that challenge one needs to address a critical question, namely what is the materials genome? Some guide on how to the answer this question can be gained by recognizing that a ``gene'' is a carrier of information. In the biological sciences, discovering how to manipulate these genes has generated exciting discoveries in fundamental molecular biology as well as significant advances in biotechnology. Scaling that up to molecular, cellular length scales and beyond, has spawned from genomics, fields such as proteomics, metabolomics and essentially systems biology. The ``omics'' approach requires that one needs to discover and track these ``carriers of information'' and then correlate that information to predict behavior. A similar challenge lies in materials science, where there is a diverse array of modalities of materials ``discovery'' ranging from new materials chemistries and molecular arrangements with novel properties, to the development and design of new micro- and mesoscale structures. Hence to meaningfully adapt the spirit of ``genomics'' style research in materials science, we need to first identify and map the ``genes'' across different materials science applications On the experimental side, combinatorial experiments have opened a new approach to generate data in a high throughput manner, but without a clear way to link that to models, the full value of that data is not realized. Hence along with experimental and computational materials science, we need to add a ``third leg'' to our toolkit to make the ``Materials Genome'' a reality, the science of Materials Informatics. In this presentation we provide an overview of how information science coupled to materials science can in fact achieve the goal of mapping the ``Materials Genome''.
Solid-Phase Synthesis of Small Molecule Libraries using Double Combinatorial Chemistry
Nielsen, John; Jensen, Flemming R.
1997-01-01
The first synthesis of a combinatorial library using double combinatorial chemistry is presented. Coupling of unprotected Fmoc-tyrosine to the solid support was followed by Mitsunobu O-alkylation. Introduction of a diacid linker yields a system in which the double combinatorial step can be demons......The first synthesis of a combinatorial library using double combinatorial chemistry is presented. Coupling of unprotected Fmoc-tyrosine to the solid support was followed by Mitsunobu O-alkylation. Introduction of a diacid linker yields a system in which the double combinatorial step can...... be demonstrated. The resulting library of model compounds was verified by LC-MS analysis. (C) 1997 Elsevier Science Ltd....
Shibata, Kazuaki; Horio, Yoshihiko; Aihara, Kazuyuki
The quadratic assignment problem (QAP) is one of the NP-hard combinatorial optimization problems. An exponential chaotic tabu search using a 2-opt algorithm driven by chaotic neuro-dynamics has been proposed as one heuristic method for solving QAPs. In this paper we first propose a new local search, the double-assignment method, suitable for the exponential chaotic tabu search, which adopts features of the Lin-Kernighan algorithm. We then introduce chaotic neuro-dynamics into the double-assignment method to propose a novel exponential chaotic tabu search. We further improve the proposed exponential chaotic tabu search with the double-assignment method by enhancing the effect of chaotic neuro-dynamics.
Hybrid Genetic Algorithm with Multiparents Crossover for Job Shop Scheduling Problems
Noor Hasnah Moin
2015-01-01
Full Text Available The job shop scheduling problem (JSSP is one of the well-known hard combinatorial scheduling problems. This paper proposes a hybrid genetic algorithm with multiparents crossover for JSSP. The multiparents crossover operator known as extended precedence preservative crossover (EPPX is able to recombine more than two parents to generate a single new offspring distinguished from common crossover operators that recombine only two parents. This algorithm also embeds a schedule generation procedure to generate full-active schedule that satisfies precedence constraints in order to reduce the search space. Once a schedule is obtained, a neighborhood search is applied to exploit the search space for better solutions and to enhance the GA. This hybrid genetic algorithm is simulated on a set of benchmarks from the literatures and the results are compared with other approaches to ensure the sustainability of this algorithm in solving JSSP. The results suggest that the implementation of multiparents crossover produces competitive results.
Combinatorial effects on clumped isotopes and their significance in biogeochemistry
Yeung, Laurence Y.
2016-01-01
The arrangement of isotopes within a collection of molecules records their physical and chemical histories. Clumped-isotope analysis interrogates these arrangements, i.e., how often rare isotopes are bound together, which in many cases can be explained by equilibrium and/or kinetic isotope fractionation. However, purely combinatorial effects, rooted in the statistics of pairing atoms in a closed system, are also relevant, and not well understood. Here, I show that combinatorial isotope effects are most important when two identical atoms are neighbors on the same molecule (e.g., O2, N2, and D-D clumping in CH4). When the two halves of an atom pair are either assembled with different isotopic preferences or drawn from different reservoirs, combinatorial effects cause depletions in clumped-isotope abundance that are most likely between zero and -1‰, although they could potentially be -10‰ or larger for D-D pairs. These depletions are of similar magnitude, but of opposite sign, to low-temperature equilibrium clumped-isotope effects for many small molecules. Enzymatic isotope-pairing reactions, which can have site-specific isotopic fractionation factors and atom reservoirs, should express this class of combinatorial isotope effect, although it is not limited to biological reactions. Chemical-kinetic isotope effects, which are related to a bond-forming transition state, arise independently and express second-order combinatorial effects related to the abundance of the rare isotope. Heteronuclear moeties (e.g., Csbnd O and Csbnd H), are insensitive to direct combinatorial influences, but secondary combinatorial influences are evident. In general, both combinatorial and chemical-kinetic factors are important for calculating and interpreting clumped-isotope signatures of kinetically controlled reactions. I apply this analytical framework to isotope-pairing reactions relevant to geochemical oxygen, carbon, and nitrogen cycling that may be influenced by combinatorial
The priming of basic combinatory responses in MEG.
Blanco-Elorrieta, Esti; Ferreira, Victor S; Del Prato, Paul; Pylkkänen, Liina
2017-09-21
Priming has been a powerful tool for the study of human memory and especially the memory representations relevant for language. However, although it is well established that lexical access can be primed, we do not know exactly what types of computations can be primed above the word level. This work took a neurobiological approach and assessed the ways in which the complex representation of a minimal combinatory phrase, such as red boat, can be primed, as evidenced by the spatiotemporal profiles of magnetoencephalography (MEG) signals. Specifically, we built upon recent progress on the neural signatures of phrasal composition and tested whether the brain activities implicated for the basic combination of two words could be primed. In two experiments, MEG was recorded during a picture naming task where the prime trials were designed to replicate previously reported combinatory effects and the target trials to test whether those combinatory effects could be primed. The manipulation of the primes was successful in eliciting larger activity for adjective-noun combinations than single nouns in left anterior temporal and ventromedial prefrontal cortices, replicating prior MEG studies on parallel contrasts. Priming of similarly timed activity was observed during target trials in anterior temporal cortex, but only when the prime and target shared an adjective. No priming in temporal cortex was observed for single word repetition and two control tasks showed that the priming effect was not elicited if the prime pictures were simply viewed but not named. In sum, this work provides evidence that very basic combinatory operations can be primed, with the necessity for some lexical overlap between prime and target suggesting combinatory conceptual, as opposed to syntactic processing. Both our combinatory and priming effects were early, onsetting between 100 and 150ms after picture onset and thus are likely to reflect the very earliest planning stages of a combinatory message
Erik G. Boman
2012-01-01
Full Text Available Partitioning and load balancing are important problems in scientific computing that can be modeled as combinatorial problems using graphs or hypergraphs. The Zoltan toolkit was developed primarily for partitioning and load balancing to support dynamic parallel applications, but has expanded to support other problems in combinatorial scientific computing, including matrix ordering and graph coloring. Zoltan is based on abstract user interfaces and uses callback functions. To simplify the use and integration of Zoltan with other matrix-based frameworks, such as the ones in Trilinos, we developed Isorropia as a Trilinos package, which supports most of Zoltan's features via a matrix-based interface. In addition to providing an easy-to-use matrix-based interface to Zoltan, Isorropia also serves as a platform for additional matrix algorithms. In this paper, we give an overview of the Zoltan and Isorropia toolkits, their design, capabilities and use. We also show how Zoltan and Isorropia enable large-scale, parallel scientific simulations, and describe current and future development in the next-generation package Zoltan2.
Improved genetic algorithm for vehicle routing problem with hard time windows%求解有硬时间窗车辆路径问题的改进遗传算法
吴天羿; 许继恒; 刘建永; 昝良
2014-01-01
针对军事运输中有硬时间窗的车辆路径问题（vehicle routing problem with hard time windows，VR-PHTW），结合混合交叉运算、改进变异运算和精英保留策略，以所有车辆的配送总时间最少为目标，设计了改进遗传算法。借鉴贪婪思想，提高了初始种群的优越性；构造了迭代种群的入口矩阵和出口矩阵，并以此为基础提出改进交叉算子，期间引入前向插入法设计了混合交叉运算，加快了种群的寻优速度；同时提出改进变异算子，增加了种群的多样性。实验结果表明，改进遗传算法较之基本算法有着更快的收敛速度和更优的收敛效果。%In view of the vehicle routing problem with hard time windows in military transportation,an im-proved genetic algorithm which aims to minimize the vehicles’total delivery time with the combination of hybrid crossover operation,improved mutation operation and an elite reserve strategy is put forward.First,it improves the initial population superiority by the greedy thought.Second,the entrance matrix and export matrix of the convergence population are constructed and the improved crossover operator based on the matrices is proposed. At the same time,the hybrid crossover operation is designed,which speeds up the population optimization through introducing the push forward insertion heuristic algorithm.At last,the population diversity is increased with the introduction of an improved mutation operator.The experimental results show that the improved ge-netic algorithm has a faster convergence speed and a better convergence effect than the basic algorithm.
Invention as a combinatorial process: evidence from US patents.
Youn, Hyejin; Strumsky, Deborah; Bettencourt, Luis M A; Lobo, José
2015-05-06
Invention has been commonly conceptualized as a search over a space of combinatorial possibilities. Despite the existence of a rich literature, spanning a variety of disciplines, elaborating on the recombinant nature of invention, we lack a formal and quantitative characterization of the combinatorial process underpinning inventive activity. Here, we use US patent records dating from 1790 to 2010 to formally characterize invention as a combinatorial process. To do this, we treat patented inventions as carriers of technologies and avail ourselves of the elaborate system of technology codes used by the United States Patent and Trademark Office to classify the technologies responsible for an invention's novelty. We find that the combinatorial inventive process exhibits an invariant rate of 'exploitation' (refinements of existing combinations of technologies) and 'exploration' (the development of new technological combinations). This combinatorial dynamic contrasts sharply with the creation of new technological capabilities-the building blocks to be combined-that has significantly slowed down. We also find that, notwithstanding the very reduced rate at which new technologies are introduced, the generation of novel technological combinations engenders a practically infinite space of technological configurations.
Combinatorial optimization using dynamical phase transitions in driven-dissipative systems
Leleu, Timothée; Yamamoto, Yoshihisa; Utsunomiya, Shoko; Aihara, Kazuyuki
2017-02-01
The dynamics of driven-dissipative systems is shown to be well-fitted for achieving efficient combinatorial optimization. The proposed method can be applied to solve any combinatorial optimization problem that is equivalent to minimizing an Ising Hamiltonian. Moreover, the dynamics considered can be implemented using various physical systems as it is based on generic dynamics—the normal form of the supercritical pitchfork bifurcation. The computational principle of the proposed method relies on an hybrid analog-digital representation of the binary Ising spins by considering the gradient descent of a Lyapunov function that is the sum of an analog Ising Hamiltonian and archetypal single or double-well potentials. By gradually changing the shape of the latter potentials from a single to double well shape, it can be shown that the first nonzero steady states to become stable are associated with global minima of the Ising Hamiltonian, under the approximation that all analog spins have the same amplitude. In the more general case, the heterogeneity in amplitude between analog spins induces the stabilization of local minima, which reduces the quality of solutions to combinatorial optimization problems. However, we show that the heterogeneity in amplitude can be reduced by setting the parameters of the driving signal near a regime, called the dynamic phase transition, where the analog spins' DC components map more accurately the global minima of the Ising Hamiltonian which, in turn, increases the quality of solutions found. Last, we discuss the possibility of a physical implementation of the proposed method using networks of degenerate optical parametric oscillators.
Science of consciousness and the hard problem
Stapp, H.P.
1996-05-22
Quantum theory is essentially a rationally coherent theory of the interaction of mind and matter, and it allows our conscious thoughts to play a causally efficacious and necessary role in brain dynamics. It therefore provides a natural basis, created by scientists, for the science of consciousness. As an illustration it is explained how the interaction of brain and consciousness can speed up brain processing, and thereby enhance the survival prospects of conscious organisms, as compared to similar organisms that lack consciousness. As a second illustration it is explained how, within the quantum framework, the consciously experienced {open_quotes}I{close_quotes} directs the actions of a human being. It is concluded that contemporary science already has an adequate framework for incorporating causally efficacious experimential events into the physical universe in a manner that: (1) puts the neural correlates of consciousness into the theory in a well defined way, (2) explains in principle how the effects of consciousness, per se, can enhance the survival prospects of organisms that possess it, (3) allows this survival effect to feed into phylogenetic development, and (4) explains how the consciously experienced {open_quotes}I{close_quotes} can direct human behaviour.
Easily Stated but Hard Statistical Problems
1986-05-01
o ^ H- K - o o Santa Maria K . ,- M H- o o isabela o - H- o o o Fernandina...o H- •- o o o Los Hermanos o *-•-►- o o pinzon O O i-1 o o o La...Fred Huff er, Duane Meeter, Edsel Pena and Arif Zaman for helpful discussions. i^ REFERENCES Abbott, I., Abbott, L. K ., and Grant, P. R. (1977
The hard problem a quantum approach
Stapp, Henry P
1995-01-01
Contents 1. Introduction: Philosophical Setting. 2. Quantum Model of the Mind/Brain. 3. Person and Self. 4. Meeting Baars's Criteria for Consciousness. 5. Qualia. 6. Free-Will. Prepared for a special issue of the Journal of Consciousness Studies.
Comprehensive Approach Workshop: Hard Problem First Steps
2011-10-01
T being done and to be done. It is important to have the right people involved in these initial steps included those performing and managing the...attend the workshop: those performing as well as managing the science. Another lesson learned was to seek early endorsement of the science activity...Interagency, Multinational, Public », un regard historique, et d’explorer d’agilité organisationnelle comme un facteur essential d’améliorer
Combinatorial vector fields and the valley structure of fitness landscapes.
Stadler, Bärbel M R; Stadler, Peter F
2010-12-01
Adaptive (downhill) walks are a computationally convenient way of analyzing the geometric structure of fitness landscapes. Their inherently stochastic nature has limited their mathematical analysis, however. Here we develop a framework that interprets adaptive walks as deterministic trajectories in combinatorial vector fields and in return associate these combinatorial vector fields with weights that measure their steepness across the landscape. We show that the combinatorial vector fields and their weights have a product structure that is governed by the neutrality of the landscape. This product structure makes practical computations feasible. The framework presented here also provides an alternative, and mathematically more convenient, way of defining notions of valleys, saddle points, and barriers in landscape. As an application, we propose a refined approximation for transition rates between macrostates that are associated with the valleys of the landscape.
Dynamic Combinatorial Chemistry with Diselenides, Disulfides, Imines and Metal Coordination
Sørensen, Anne
The design and preparation of strong and selective artificial receptors, especially biomi-metic receptors that function in aqueous solution, has proved truly challenging. In this thesis it will be described how the strengths of dynamic combinatorial chemistry can be used to great advantage...... in this field. The aim of this project has therefore been to develop new ways of using dynamic combinatorial libraries for molecular recognition in aqueous media. The focus has been on using what has been learned from the well-established di-sulfide exchange chemistry to incorporate a new reaction into dynamic...... combinatorial chemistry, namely the reversible diselenide exchange reaction. The first part of the thesis describes the development of a thermally induced OAr → SeAr migration reaction. Here, it was proven possible to rearrange a variety of substituted O-aryl selenocarbamates into the corresponding Se...
Combinatorial Constructions for Sifting Primes and Enumerating the Rationals
Gnang, Edinah K
2012-01-01
We describe a combinatorial approach for investigating properties of rational numbers. The overall approach rests on structural bijections between rational numbers and familiar combinatorial objects, namely rooted trees. We emphasize that such mappings achieve much more than enumeration of rooted trees. We discuss two related structural bijections. The first corresponds to a bijective map between integers and rooted trees. The first bijection also suggests a new algorithm for sifting primes. The second bijection extends the first one in order to map rational numbers to a family of rooted trees. The second bijection suggests a new combinatorial construction for generating reduced rational numbers, thereby producing refinements of the output of the Wilf-Calkin[1] Algorithm.
Combinatorial Selection and Least Absolute Shrinkage via the CLASH Algorithm
Kyrillidis, Anastasios
2012-01-01
The least absolute shrinkage and selection operator (LASSO) for linear regression exploits the geometric interplay of the $\\ell_2$-data error objective and the $\\ell_1$-norm constraint to arbitrarily select sparse models. Guiding this uninformed selection process with sparsity models has been precisely the center of attention over the last decade in order to improve learning performance. To this end, we alter the selection process of LASSO to explicitly leverage combinatorial sparsity models (CSMs) via the combinatorial selection and least absolute shrinkage (CLASH) operator. We provide concrete guidelines how to leverage combinatorial constraints within CLASH, and characterize CLASH's guarantees as a function of the set restricted isometry constants of the sensing matrix. Finally, our experimental results show that CLASH can outperform both LASSO and model-based compressive sensing in sparse estimation.
Key Updating Methods for Combinatorial Design Based Key Management Schemes
Chonghuan Xu
2014-01-01
Full Text Available Wireless sensor network (WSN has become one of the most promising network technologies for many useful applications. However, for the lack of resources, it is different but important to ensure the security of the WSNs. Key management is a corner stone on which to build secure WSNs for it has a fundamental role in confidentiality, authentication, and so on. Combinatorial design theory has been used to generate good-designed key rings for each sensor node in WSNs. A large number of combinatorial design based key management schemes have been proposed but none of them have taken key updating into consideration. In this paper, we point out the essence of key updating for the unital design based key management scheme and propose two key updating methods; then, we conduct performance analysis on the two methods from three aspects; at last, we generalize the two methods to other combinatorial design based key management schemes and enhance the second method.
Combinatorial realizations of crystals via torus actions on quiver varieties
Sam, Steven V
2012-01-01
Consider Kashiwara's crystal associated to a highest weight representation of a symmetric Kac--Moody algebra. There is a geometric realization of this object using Nakajima's quiver varieties. In many particular cases it can also be realized by elementary combinatorial methods. Here we propose a framework for extracting combinatorial realizations from the geometric picture: we construct certain torus actions on the quiver varieties and use Morse theory to index the irreducible components by connected components of the subvariety of torus fixed points. We then discuss the case of affine sl(n). There the fixed point components are just points, and are naturally indexed by multi-partitions. There is some choice in our construction, leading to a family of combinatorial realizations for each highest weight crystal. In the case of the crystal of the fundamental representation we recover a family of realizations which was recently constructed by Fayers. This gives a more conceptual proof of Fayers' result as well as...
On green routing and scheduling problem
Touati, Nora
2012-01-01
The vehicle routing and scheduling problem has been studied with much interest within the last four decades. In this paper, some of the existing literature dealing with routing and scheduling problems with environmental issues is reviewed, and a description is provided of the problems that have been investigated and how they are treated using combinatorial optimization tools.
On green routing and scheduling problem
Touati, Nora; Jost, Vincent
2011-01-01
The vehicle routing and scheduling problem has been studied with much interest within the last four decades. In this paper, some of the existing literature dealing with routing and scheduling problems with environmental issues is reviewed, and a description is provided of the problems that have been investigated and how they are treated using combinatorial optimization tools.
修桂华; 王俊鸿
2008-01-01
蚁群算法具有较强的鲁棒性和优良的分布式计算机制.研究重点是对现有的求解带硬时间窗的车辆路径问题VRP-H(Vehicle Routing Problem with Hard Time Windows)的蚁群算法作出更好的改进,使得算法的计算效率更高且得到的解更优,提出了蚁群算法的改进算法-改进的自适应蚁群算法.该算法先用自适应蚁群算法对VRP-H求得一个可行解,再利用多种改善方法对初始解进一步优化,从而得到最优解.测试时选用Solomon提出的题库,结果表明该算法能够有效地求解VRP-H.
Recent advances in combinatorial biosynthesis for drug discovery
Sun H
2015-02-01
Full Text Available Huihua Sun,1,* Zihe Liu,1,* Huimin Zhao,1,2 Ee Lui Ang1 1Metabolic Engineering Research Laboratory, Institute of Chemical and Engineering Sciences, Agency for Science, Technology and Research, Singapore; 2Department of Chemical and Biomolecular Engineering, University of Illinois at Urbana-Champaign, Urbana, IL, USA *These authors contributed equally to this work Abstract: Because of extraordinary structural diversity and broad biological activities, natural products have played a significant role in drug discovery. These therapeutically important secondary metabolites are assembled and modified by dedicated biosynthetic pathways in their host living organisms. Traditionally, chemists have attempted to synthesize natural product analogs that are important sources of new drugs. However, the extraordinary structural complexity of natural products sometimes makes it challenging for traditional chemical synthesis, which usually involves multiple steps, harsh conditions, toxic organic solvents, and byproduct wastes. In contrast, combinatorial biosynthesis exploits substrate promiscuity and employs engineered enzymes and pathways to produce novel “unnatural” natural products, substantially expanding the structural diversity of natural products with potential pharmaceutical value. Thus, combinatorial biosynthesis provides an environmentally friendly way to produce natural product analogs. Efficient expression of the combinatorial biosynthetic pathway in genetically tractable heterologous hosts can increase the titer of the compound, eventually resulting in less expensive drugs. In this review, we will discuss three major strategies for combinatorial biosynthesis: 1 precursor-directed biosynthesis; 2 enzyme-level modification, which includes swapping of the entire domains, modules and subunits, site-specific mutagenesis, and directed evolution; 3 pathway-level recombination. Recent examples of combinatorial biosynthesis employing these
Improving Combinatorial Ambiguities of ttbar Events Using Neural Networks
Shim, Ji Hyun
2014-01-01
We present a method for resolving the combinatorial issues in the \\ttbar lepton+jets events occurring at the Tevatron collider. By incorporating multiple information into an artificial neural network, we introduce a novel event reconstruction method for such events. We find that this method significantly reduces the number of combinatorial ambiguities. Compared to the classical reconstruction method, our method provides significantly higher purity with same efficiency. We illustrate the reconstructed observables for the realistic top-quark mass and the forward-backward asymmetry measurements. A Monte Carlo study shows that our method provides meaningful improvements in the top-quark measurements using same amount of data as other methods.
Revisiting Combinatorial Ambiguities at Hadron Colliders with MT2
Baringer, Philip; McCaskey, Mathew; Noonan, Daniel
2011-01-01
We present a method to resolve combinatorial issues in multi-particle final states at hadron colliders. The use of kinematic variables such as MT2 and invariant mass significantly reduces combinatorial ambiguities in the signal, but at a cost of losing statistics. We illustrate this idea with gluino pair production leading to 4 jets $+\\met$ in the final state as well as $t\\bar{t}$ production in the dilepton channel. Compared to results in recent studies, our method provides greater efficiency with similar purity
Combinatorial theory of Macdonald polynomials I: Proof of Haglund's formula
Haglund, J.; Haiman, M.; Loehr, N
2005-01-01
Haglund recently proposed a combinatorial interpretation of the modified Macdonald polynomials H̃μ. We give a combinatorial proof of this conjecture, which establishes the existence and integrality of H̃μ. As corollaries, we obtain the cocharge formula of Lascoux and Schützenberger for Hall–Littlewood polynomials, a formula of Sahi and Knop for Jack's symmetric functions, a generalization of this result to the integral Macdonald polynomials Jμ, a formula for H̃μ in terms of Lascoux–Leclerc–Th...
Hard sphere packings within cylinders.
Fu, Lin; Steinhardt, William; Zhao, Hao; Socolar, Joshua E S; Charbonneau, Patrick
2016-03-07
Arrangements of identical hard spheres confined to a cylinder with hard walls have been used to model experimental systems, such as fullerenes in nanotubes and colloidal wire assembly. Finding the densest configurations, called close packings, of hard spheres of diameter σ in a cylinder of diameter D is a purely geometric problem that grows increasingly complex as D/σ increases, and little is thus known about the regime for D > 2.873σ. In this work, we extend the identification of close packings up to D = 4.00σ by adapting Torquato-Jiao's adaptive-shrinking-cell formulation and sequential-linear-programming (SLP) technique. We identify 17 new structures, almost all of them chiral. Beyond D ≈ 2.85σ, most of the structures consist of an outer shell and an inner core that compete for being close packed. In some cases, the shell adopts its own maximum density configuration, and the stacking of core spheres within it is quasiperiodic. In other cases, an interplay between the two components is observed, which may result in simple periodic structures. In yet other cases, the very distinction between the core and shell vanishes, resulting in more exotic packing geometries, including some that are three-dimensional extensions of structures obtained from packing hard disks in a circle.
Directed Bee Colony Optimization Algorithm to Solve the Nurse Rostering Problem
Amudhavel, J.; Pothula, Sujatha; Dhavachelvan, P.
2017-01-01
The Nurse Rostering Problem is an NP-hard combinatorial optimization, scheduling problem for assigning a set of nurses to shifts per day by considering both hard and soft constraints. A novel metaheuristic technique is required for solving Nurse Rostering Problem (NRP). This work proposes a metaheuristic technique called Directed Bee Colony Optimization Algorithm using the Modified Nelder-Mead Method for solving the NRP. To solve the NRP, the authors used a multiobjective mathematical programming model and proposed a methodology for the adaptation of a Multiobjective Directed Bee Colony Optimization (MODBCO). MODBCO is used successfully for solving the multiobjective problem of optimizing the scheduling problems. This MODBCO is an integration of deterministic local search, multiagent particle system environment, and honey bee decision-making process. The performance of the algorithm is assessed using the standard dataset INRC2010, and it reflects many real-world cases which vary in size and complexity. The experimental analysis uses statistical tools to show the uniqueness of the algorithm on assessment criteria. PMID:28473849
Applying the INN model to the MaxClique problem
Grossman, T.
1993-09-01
Max-Clique is the problem of finding the largest clique in a given graph. It is not only NP-hard, but, as recent results suggest, even hard to approximate. Nevertheless it is still very important to develop and test practical algorithms that will find approximate solutions for the maximum clique problem on various graphs stemming from numerous applications. Indeed, many different types of algorithmic approaches are applied to that problem. Several neural networks and related algorithms were applied recently to combinatorial optimization problems in general and to the Max-Clique problem in particular. These neural nets are dynamical system which minimize a cost (or computational ``energy``) function that represents the optimization problem, the Max-Clique in our case. Therefore they all belong to the class of integer programming algorithms surveyed in the Pardalos and Xue review. The work presented here is a development and improvement of a neural network algorithm that was introduced recently. In the previous work, we have considered two Hopfield type neural networks, the INN and the HcN, and their application to the max-clique problem. In this paper, I concentrate on the INN network and present an improved version of the t-A algorithm that was introduced in. The rest of this paper is organized as follows: in section 2, I describe the INN model and how it implements a given graph. In section 3, it is characterized in terms of graph theory. In particular, the stable states of the network are mapped to the maximal cliques of its underling graph. In section 4, I present the t-Annealing algorithm and an improved version of it, the Adaptive t-Annealing. Several experiments done with these algorithms on benchmark graphs are reported in section 5, and the efficiency of the new algorithm is demonstrated. I conclude with a short discussion.
Solid-Phase Synthesis of Small Molecule Libraries using Double Combinatorial Chemistry
Nielsen, John; Jensen, Flemming R.
1997-01-01
The first synthesis of a combinatorial library using double combinatorial chemistry is presented. Coupling of unprotected Fmoc-tyrosine to the solid support was followed by Mitsunobu O-alkylation. Introduction of a diacid linker yields a system in which the double combinatorial step can...
Polyomino Problems to Confuse Computers
Coffin, Stewart
2009-01-01
Computers are very good at solving certain types combinatorial problems, such as fitting sets of polyomino pieces into square or rectangular trays of a given size. However, most puzzle-solving programs now in use assume orthogonal arrangements. When one departs from the usual square grid layout, complications arise. The author--using a computer,…
柴获; 何瑞春; 马昌喜; 代存杰
2016-01-01
This paper presents a univariate marginal distribution algorithm hybridized with insertion heuristics for the vehicle routing problem with hard time windows (VRPHTW). In the VRPHTW,a fleet of vehicles must deliver goods to a set of customers,time window constraints of the customers must be respected and the fact that the travel time between two points depends on the time of departure has to be taken into account. The latter assumption is particularly important in an urban context where the traffic plays a significant role. A shortcoming of univariate marginal distribution algorithm for vehicle routing problems is that,customers are not independent events in probabilistic model. Hence,we propose a novel probabilistic model that probability of the distribution of customers delivered by the same vehicle. Moreover,the new population is generated by two phase insertion heuristics method. Computational results with 56 Solomon benchmark problems confirm the benefits of other algorithms,the resulting algorithm turns out to be competitive,matching or improving the best known results.%针对带硬时间窗的车辆路径问题(VRPHTW)求解，提出了一种混合单变量边缘分布算法(hybrid UDMA，hUDMA)，改进了基本UMDA的概率模型.统计节点按路径分布的概率，使其能够在解空间上找到节点—路径的分布关系，提高了UMDA的全局搜索能力.采用两阶段插入法进行最佳节点搜索和路径分配完成UMDA采样操作，通过种群进化来获取最优解.计算Solomon 100客户的6类问题56个算例的实验结果表明：在最优解的取得方面，C类算例能够全部取得最优解，R、RC类算例能以50%左右概率取得最优解；在平均误差方面，C类算例计算结果与已知最优解一致，R、RC类算例计算误差率与已知最优解比较接近，平均误差率为1.03%.
A Novel Approach to Hardness Testing
Spiegel, F. Xavier; West, Harvey A.
1996-01-01
This paper gives a description of the application of a simple rebound time measuring device and relates the determination of relative hardness of a variety of common engineering metals. A relation between rebound time and hardness will be sought. The effect of geometry and surface condition will also be discussed in order to acquaint the student with the problems associated with this type of method.
Hard processes in hadronic interactions
Satz, H. [CERN, Geneva (Switzerland)]|[Universitat Bielefeld (Germany); Wang, X.N. [Lawrence Berkeley Lab., CA (United States)
1995-07-01
Quantum chromodynamics is today accepted as the fundamental theory of strong interactions, even though most hadronic collisions lead to final states for which quantitative QCD predictions are still lacking. It therefore seems worthwhile to take stock of where we stand today and to what extent the presently available data on hard processes in hadronic collisions can be accounted for in terms of QCD. This is one reason for this work. The second reason - and in fact its original trigger - is the search for the quark-gluon plasma in high energy nuclear collisions. The hard processes to be considered here are the production of prompt photons, Drell-Yan dileptons, open charm, quarkonium states, and hard jets. For each of these, we discuss the present theoretical understanding, compare the resulting predictions to available data, and then show what behaviour it leads to at RHIC and LHC energies. All of these processes have the structure mentioned above: they contain a hard partonic interaction, calculable perturbatively, but also the non-perturbative parton distribution within a hadron. These parton distributions, however, can be studied theoretically in terms of counting rule arguments, and they can be checked independently by measurements of the parton structure functions in deep inelastic lepton-hadron scattering. The present volume is the work of Hard Probe Collaboration, a group of theorists who are interested in the problem and were willing to dedicate a considerable amount of their time and work on it. The necessary preparation, planning and coordination of the project were carried out in two workshops of two weeks` duration each, in February 1994 at CERn in Geneva andin July 1994 at LBL in Berkeley.
Aono, Masashi; Naruse, Makoto; Kim, Song-Ju; Wakabayashi, Masamitsu; Hori, Hirokazu; Ohtsu, Motoichi; Hara, Masahiko
2013-06-18
Biologically inspired computing devices and architectures are expected to overcome the limitations of conventional technologies in terms of solving computationally demanding problems, adapting to complex environments, reducing energy consumption, and so on. We previously demonstrated that a primitive single-celled amoeba (a plasmodial slime mold), which exhibits complex spatiotemporal oscillatory dynamics and sophisticated computing capabilities, can be used to search for a solution to a very hard combinatorial optimization problem. We successfully extracted the essential spatiotemporal dynamics by which the amoeba solves the problem. This amoeba-inspired computing paradigm can be implemented by various physical systems that exhibit suitable spatiotemporal dynamics resembling the amoeba's problem-solving process. In this Article, we demonstrate that photoexcitation transfer phenomena in certain quantum nanostructures mediated by optical near-field interactions generate the amoebalike spatiotemporal dynamics and can be used to solve the satisfiability problem (SAT), which is the problem of judging whether a given logical proposition (a Boolean formula) is self-consistent. SAT is related to diverse application problems in artificial intelligence, information security, and bioinformatics and is a crucially important nondeterministic polynomial time (NP)-complete problem, which is believed to become intractable for conventional digital computers when the problem size increases. We show that our amoeba-inspired computing paradigm dramatically outperforms a conventional stochastic search method. These results indicate the potential for developing highly versatile nanoarchitectonic computers that realize powerful solution searching with low energy consumption.
Leading log expansion of combinatorial Dyson Schwinger equations
Delage, Lucas
2016-01-01
We study combinatorial Dyson Schwinger equations, expressed in the Hopf algebra of words with a quasi shuffle product. We map them into an algebra of polynomials in one indeterminate L and show that the leading log expansion one obtains with such a mapping are simple power law like expression
Dynamic Combinatorial Libraries of Disulfide Cages in Water
West, Kevin R.; Bake, Kyle D.; Otto, Sijbren
2005-01-01
Dynamic combinatorial libraries (DCLs) containing water-soluble disulfide-linked cages (alongside macrocyclic structures) have been generated and characterized. Unlike most other strategies for generating molecular cages, the structures are held together by covalent bonds, which are formed under the
A Synthetic Receptor for Nicotine from a Dynamic Combinatorial Library
Hamieh, Saleh; Ludlow, R. Frederick; Perraud, Olivier; West, Kevin R.; Mattia, Elio; Otto, Sijbren
2012-01-01
Designing synthetic receptors that bind biologically relevant guests in an aqueous solution remains a considerable challenge. We now report a new synthetic receptor for nicotine, selected from a dynamic combinatorial library, that binds this guest in water at neutral pH through a combination of hydr
Combinatorial conditions for low rank solutions in semidefinite programming
Varvitsiotis, A.
2013-01-01
In this thesis we investigate combinatorial conditions that guarantee the existence of low-rank optimal solutions to semidefinite programs. Results of this type are important for approximation algorithms and for the study of geometric representations of graphs. The structure of the thesis is as
Combinatorial conditions for low rank solutions in semidefinite programming
A. Varvitsiotis (Antonios)
2013-01-01
htmlabstractIn this thesis we investigate combinatorial conditions that guarantee the existence of low-rank optimal solutions to semidefinite programs. Results of this type are important for approximation algorithms and for the study of geometric representations of graphs. The structure of the
Isocyanide based multi component reactions in combinatorial chemistry.
Dömling, A.
1998-01-01
Although usually regarded as a recent development, the combinatorial approach to the synthesis of libraries of new drug candidates was first described as early as 1961 using the isocyanide-based one-pot multicomponent Ugi reaction. Isocyanide-based multi component reactions (MCR's) markedly differ f
Combinatorial structures and processing in neural blackboard architectures
van der Velde, Frank; van der Velde, Frank; de Kamps, Marc; Besold, Tarek R.; d'Avila Garcez, Artur; Marcus, Gary F.; Miikkulainen, Risto
2015-01-01
We discuss and illustrate Neural Blackboard Architectures (NBAs) as the basis for variable binding and combinatorial processing the brain. We focus on the NBA for sentence structure. NBAs are based on the notion that conceptual representations are in situ, hence cannot be copied or transported.
A graphical formalism for mixed multi-unit combinatorial auctions
Gionvannucci, A.; Cerquides, J.; Endriss, U.; Rodríguez-Aguilar, J.A.
2010-01-01
Mixed multi-unit combinatorial auctions are auctions that allow participants to bid for bundles of goods to buy, for bundles of goods to sell, and for transformations of goods. The intuitive meaning of a bid for a transformation is that the bidder is offering to produce a set of output goods after h
Solids: a combinatorial auction for a housing corporation
Goossens, D.R.; Onderstal, S.; Spieksma, F.C.R.; Coles, P.; Das, S.; Lahaie, S.; Szymanski, B.
2012-01-01
On May 7, 2011, over one hundred bidders took part in a combinatorial auction for housing space in a newly erected building in Amsterdam (the Netherlands). This paper describes the development of this auction. We sketch our collaboration with the housing corporation that resulted in design choices
Combinatorial Model Involving Stochastic Choices of Destination, Mode and Route
无
2001-01-01
Traffic assignment models are one of the basic tools for the analysis and design of transportation systems. However, the existing models have some defects. Considering the characteristics of Chinese urban mixed traffic and the randomness of transportation information, the author develops a combinatorial model involving stochastic choices of destination, mode and route. Its uniqueness and equivalance are also proved by the optimization theory.
Dithioacetal Exchange: A New Reversible Reaction for Dynamic Combinatorial Chemistry.
Orrillo, A Gastón; Escalante, Andrea M; Furlan, Ricardo L E
2016-05-10
Reversibility of dithioacetal bond formation is reported under acidic mild conditions. Its utility for dynamic combinatorial chemistry was explored by combining it with orthogonal disulfide exchange. In such a setup, thiols are positioned at the intersection of both chemistries, constituting a connecting node between temporally separated networks.
Automated Combinatorial Chemistry in the Organic Chemistry Majors Laboratory
Nichols, Christopher J.; Hanne, Larry F.
2010-01-01
A multidisciplinary experiment has been developed in which students each synthesize a combinatorial library of 48 hydrazones with the aid of a liquid-handling robot. Each product is then subjected to a Kirby-Bauer disk diffusion assay to assess its antibacterial activity. Students gain experience working with automation and at the…
Synthetic receptors for ammonium ions using dynamic combinatorial chemistry
Hamieh, Saleh
2015-01-01
The general topic of this dissertation is the development of synthetic receptors for organic ammonium ions in near physiological conditions using disulfide dynamic combinatorial chemistry (DCC). Chapter 1 explains the importance of this development and the associated difficulties when using the conv
Combinatorial conditions for low rank solutions in semidefinite programming
Varvitsiotis, A.
2013-01-01
In this thesis we investigate combinatorial conditions that guarantee the existence of low-rank optimal solutions to semidefinite programs. Results of this type are important for approximation algorithms and for the study of geometric representations of graphs. The structure of the thesis is as foll
Isocyanide based multi component reactions in combinatorial chemistry.
Dömling, A.
1998-01-01
Although usually regarded as a recent development, the combinatorial approach to the synthesis of libraries of new drug candidates was first described as early as 1961 using the isocyanide-based one-pot multicomponent Ugi reaction. Isocyanide-based multi component reactions (MCR's) markedly differ
Dynamic combinatorial chemistry at the phospholipid bilayer interface
Mansfeld, Friederike M.; Au-Yeung, Ho Yu; Sanders, Jeremy K.M.; Otto, Sijbren
2010-01-01
Background: Molecular recognition at the environment provided by the phospholipid bilayer interface plays an important role in biology and is subject of intense investigation. Dynamic combinatorial chemistry is a powerful approach for exploring molecular recognition, but has thus far not been
Proceedings of the 8th Nordic Combinatorial Conference
Geil, Olav; Andersen, Lars Døvling
The Nordic Combinatorial Conferences were initiated in 1981 by mathematicians from Stavanger. Held approximately every three years since then, the conferences have been able to sustain the interest from combinatorialists all over the Nordic countries. In 2004 the 8th conference is held in Aalborg...
A combinatorial divisibility question from noncommutative algebra
2016-01-01
We present a general conjecture on the divisibility of a certain expression in terms of Kostka numbers and their close variants. This conjecture is closely related to a variant of the period-index problem of noncommutative algebra, with partial implications in both directions. We present a description of the connection between these two problems via Schubert calculus as motivation and evidence for the conjecture before turning to a proof of the conjecture in a family of cases.
Hauser, D. L.; Buras, D. F.; Corbin, J. M.
1987-01-01
Rubber-hardness tester modified for use on rigid polyurethane foam. Provides objective basis for evaluation of improvements in foam manufacturing and inspection. Typical acceptance criterion requires minimum hardness reading of 80 on modified tester. With adequate correlation tests, modified tester used to measure indirectly tensile and compressive strengths of foam.
2014-01-01
Comprehensive Hard Materials deals with the production, uses and properties of the carbides, nitrides and borides of these metals and those of titanium, as well as tools of ceramics, the superhard boron nitrides and diamond and related compounds. Articles include the technologies of powder production (including their precursor materials), milling, granulation, cold and hot compaction, sintering, hot isostatic pressing, hot-pressing, injection moulding, as well as on the coating technologies for refractory metals, hard metals and hard materials. The characterization, testing, quality assurance and applications are also covered. Comprehensive Hard Materials provides meaningful insights on materials at the leading edge of technology. It aids continued research and development of these materials and as such it is a critical information resource to academics and industry professionals facing the technological challenges of the future. Hard materials operate at the leading edge of technology, and continued res...
An effective co-evolutionary quantum genetic algorithm for the no-wait flow shop scheduling problem
Guanlong Deng
2015-12-01
Full Text Available This article proposes a competitive co-evolutionary quantum genetic algorithm for the no-wait flow shop scheduling problem with the criterion to minimize makespan, which is a renowned NP-hard combinatorial optimization problem. An innovative coding and decoding mechanism is proposed. The mechanism uses square matrix to represent the quantum individual and adapts the quantum rotation gate to update the quantum individual. In the algorithm framework, the store-with-diversity is proposed to maintain the diversity of the population. Moreover, a competitive co-evolution strategy is introduced to enhance the evolutionary pressure and accelerate the convergence. The store-with-diversity and competitive co-evolution are designed to keep a balance between exploration and exploitation. Simulations based on a benchmark set and comparisons with several existing algorithms demonstrate the effectiveness and robustness of the proposed algorithm.
A Heuristic Algorithm for 3D Bin-packing Problem%三维装箱问题的启发式算法
罗建军; 吴东辉; 罗细飞
2012-01-01
The 3D bin-packing problem is a classic NP-hard combinatorial optimization problem. On the basis of ID and 2D bin-packing problems, this paper develops a heuristic algorithm to overcome the over-reliance on "experience" of the general heuristic algorithm. This algorithm is structurally simple and has high convergence speed as is demonstrated in an experimental study.%三维装箱问题是一类典型的NP-hard组合优化问题.在一维、二维装箱问题基础上,设计了一种启发式算法,借以克服一般启发式算法依赖“经验”的不足,该算法结构简单,实验表明算法收敛速度快.
Structure-based design of combinatorial mutagenesis libraries.
Verma, Deeptak; Grigoryan, Gevorg; Bailey-Kellogg, Chris
2015-05-01
The development of protein variants with improved properties (thermostability, binding affinity, catalytic activity, etc.) has greatly benefited from the application of high-throughput screens evaluating large, diverse combinatorial libraries. At the same time, since only a very limited portion of sequence space can be experimentally constructed and tested, an attractive possibility is to use computational protein design to focus libraries on a productive portion of the space. We present a general-purpose method, called "Structure-based Optimization of Combinatorial Mutagenesis" (SOCoM), which can optimize arbitrarily large combinatorial mutagenesis libraries directly based on structural energies of their constituents. SOCoM chooses both positions and substitutions, employing a combinatorial optimization framework based on library-averaged energy potentials in order to avoid explicitly modeling every variant in every possible library. In case study applications to green fluorescent protein, β-lactamase, and lipase A, SOCoM optimizes relatively small, focused libraries whose variants achieve energies comparable to or better than previous library design efforts, as well as larger libraries (previously not designable by structure-based methods) whose variants cover greater diversity while still maintaining substantially better energies than would be achieved by representative random library approaches. By allowing the creation of large-scale combinatorial libraries based on structural calculations, SOCoM promises to increase the scope of applicability of computational protein design and improve the hit rate of discovering beneficial variants. While designs presented here focus on variant stability (predicted by total energy), SOCoM can readily incorporate other structure-based assessments, such as the energy gap between alternative conformational or bound states.
Microfluidic platform for combinatorial synthesis in picolitre droplets.
Theberge, Ashleigh B; Mayot, Estelle; El Harrak, Abdeslam; Kleinschmidt, Felix; Huck, Wilhelm T S; Griffiths, Andrew D
2012-04-07
This paper presents a droplet-based microfluidic platform for miniaturized combinatorial synthesis. As a proof of concept, a library of small molecules for early stage drug screening was produced. We present an efficient strategy for producing a 7 × 3 library of potential thrombin inhibitors that can be utilized for other combinatorial synthesis applications. Picolitre droplets containing the first type of reagent (reagents A(1), A(2), …, A(m)) were formed individually in identical microfluidic chips and then stored off chip with the aid of stabilizing surfactants. These droplets were then mixed to form a library of droplets containing reagents A(1-m), each individually compartmentalized, which was reinjected into a second microfluidic chip and combinatorially fused with picolitre droplets containing the second reagent (reagents B(1), B(2), …, B(n)) that were formed on chip. The concept was demonstrated with a three-component Ugi-type reaction involving an amine (reagents A(1-3)), an aldehyde (reagents B(1-7)), and an isocyanide (held constant), to synthesize a library of small molecules with potential thrombin inhibitory activity. Our technique produced 10(6) droplets of each reaction at a rate of 2.3 kHz. Each droplet had a reaction volume of 3.1 pL, at least six orders of magnitude lower than conventional techniques. The droplets can then be divided into aliquots for different downstream screening applications. In addition to medicinal chemistry applications, this combinatorial droplet-based approach holds great potential for other applications that involve sampling large areas of chemical parameter space with minimal reagent consumption; such an approach could be beneficial when optimizing reaction conditions or performing combinatorial reactions aimed at producing novel materials.
Combinatorial Algorithms for Computing Column Space Bases ThatHave Sparse Inverses
Pinar, Ali; Chow, Edmond; Pothen, Alex
2005-03-18
This paper presents a combinatorial study on the problem ofconstructing a sparse basis forthe null-space of a sparse, underdetermined, full rank matrix, A. Such a null-space is suitable forsolving solving many saddle point problems. Our approach is to form acolumn space basis of A that has a sparse inverse, by selecting suitablecolumns of A. This basis is then used to form a sparse null-space basisin fundamental form. We investigate three different algorithms forcomputing the column space basis: Two greedy approaches that rely onmatching, and a third employing a divide and conquer strategy implementedwith hypergraph partitioning followed by the greedy approach. We alsodiscuss the complexity of selecting a column basis when it is known thata block diagonal basis exists with a small given block size.
A multi-objective stochastic approach to combinatorial technology space exploration
Patel, Chirag B.
Historically, aerospace development programs have frequently been marked by performance shortfalls, cost growth, and schedule slippage. New technologies included in systems are considered to be one of the major sources of this programmatic risk. Decisions regarding the choice of technologies to include in a design are therefore crucial for a successful development program. This problem of technology selection is a challenging exercise in multi-objective decision making. The complexity of this selection problem is compounded by the geometric growth of the combinatorial space with the number of technologies being considered and the uncertainties inherent in the knowledge of the technological attributes. These problems are not typically addressed in the selection methods employed in common practice. Consequently, a method is desired to aid the selection of technologies for complex systems design with consideration of the combinatorial complexity, multi-dimensionality, and the presence of uncertainties. Several categories of techniques are explored to address the shortcomings of current approaches and to realize the goal of an efficient and effective combinatorial technology space exploration method. For the multi-objective decision making, a posteriori preference articulation is implemented. To realize this, a stochastic algorithm for Pareto optimization is formulated based on the concepts of SPEA2. Techniques to address the uncertain nature of technology impact on the system are also examined. Monte Carlo simulations using the surrogate models are used for uncertainty quantification. The concepts of graph theory are used for modeling and analyzing compatibility constraints among technologies and assessing their impact on the technology combinatorial space. The overall decision making approach is enabled by the application of an uncertainty quantification technique under the framework of an efficient probabilistic Pareto optimization algorithm. As a result, multiple
Gunnels, John
2010-06-01
We provide a first demonstration of the idea that matrix-based algorithms for nonlinear combinatorial optimization problems can be efficiently implemented. Such algorithms were mainly conceived by theoretical computer scientists for proving efficiency. We are able to demonstrate the practicality of our approach by developing an implementation on a massively parallel architecture, and exploiting scalable and efficient parallel implementations of algorithms for ultra high-precision linear algebra. Additionally, we have delineated and implemented the necessary algorithmic and coding changes required in order to address problems several orders of magnitude larger, dealing with the limits of scalability from memory footprint, computational efficiency, reliability, and interconnect perspectives. © Springer and Mathematical Programming Society 2010.
Simultaneous Disulfide and Boronic Acid Ester Exchange in Dynamic Combinatorial Libraries
Diemer, Sanna L.; Kristensen, Morten; Rasmussen, Brian
2015-01-01
Dynamic combinatorial chemistry has emerged as a promising tool for the discovery of complex receptors in supramolecular chemistry. At the heart of dynamic combinatorial chemistry are the reversible reactions that enable the exchange of building blocks between library members in dynamic combinato......Dynamic combinatorial chemistry has emerged as a promising tool for the discovery of complex receptors in supramolecular chemistry. At the heart of dynamic combinatorial chemistry are the reversible reactions that enable the exchange of building blocks between library members in dynamic...... combinatorial libraries (DCLs) ensuring thermodynamic control over the system. If more than one reversible reaction operates in a single dynamic combinatorial library, the complexity of the system increases dramatically, and so does its possible applications. One can imagine two reversible reactions...... that operate simultaneously or two reversible reactions that operate independently. Both these scenarios have advantages and disadvantages. In this contribution, we show how disulfide exchange and boronic ester transesterification can function simultaneous in dynamic combinatorial libraries under appropriate...
Morgan, Gary
2014-01-01
Languages are composed of a conventionalized system of parts which allow speakers and signers to generate an infinite number of form-meaning mappings through phonological and morphological combinations. This level of linguistic organization distinguishes language from other communicative acts such as gestures. In contrast to signs, gestures are made up of meaning units that are mostly holistic. Children exposed to signed and spoken languages from early in life develop grammatical structure following similar rates and patterns. This is interesting, because signed languages are perceived and articulated in very different ways to their spoken counterparts with many signs displaying surface resemblances to gestures. The acquisition of forms and meanings in child signers and talkers might thus have been a different process. Yet in one sense both groups are faced with a similar problem: "how do I make a language with combinatorial structure"? In this paper I argue first language development itself enables this to happen and by broadly similar mechanisms across modalities. Combinatorial structure is the outcome of phonological simplifications and productivity in using verb morphology by children in sign and speech.
Gary eMorgan
2014-11-01
Full Text Available Languages are composed of a conventionalized system of parts which allow speakers and signers to compose an infinite number of form-meaning mappings through phonological and morphological combinations. This level of linguistic organization distinguishes language from other communicative acts such as gestures. In contrast to signs, gestures are made up of meaning units that are mostly holistic. Children exposed to signed and spoken languages from early in life develop grammatical structure following similar rates and patterns. This is interesting, because signed languages are perceived and articulated in very different ways to their spoken counterparts with many signs displaying surface resemblances to gestures. The acquisition of forms and meanings in child signers and talkers might thus have been a different process. Yet in one sense both groups are faced with a similar problem: 'how do I make a language with combinatorial structure’? In this paper I argue first language development itself enables this to happen and by broadly similar mechanisms across modalities. Combinatorial structure is the outcome of phonological simplifications and productivity in using verb morphology by children in sign and speech.
Combinatorial chemistry as a tool for targeting different stages of the replicative HIV-1 cycle.
Mugnaini, Claudia; Petricci, Elena; Corelli, Federico; Botta, Maurizio
2005-08-01
In the present era, acquired immunodeficiency syndrome (AIDS) is the most fatal disorder for which no completely successful chemotherapy has been developed so far. The pandemic spread of this disease has prompted an unprecedented scientific and clinical effort to understand and combat it. A number of targets has been identified to stop the replication of the virus at different stages of its life cycle: Reverse Transcriptase (RT), protease (PR) and CCR5 are the most promising targets. Although highly active antiretroviral therapy (HAART) has been effective in reducing the mortality and morbidity in recent years, adverse side effects of the chemotherapy, patient non-compliance and the development of viral resistance remain major problems. With the aim to find better drug candidates with minor adverse side effects in recent years, several groups have investigated combinatorial approaches for the generation of libraries of HIV PR inhibitors while only few contributions to the preparation of libraries of HIV Reverse Transcriptase (RT) and CCR5 inhibitors are available. This review summarizes the recent developments of combinatorial chemistry in this area.
ANALYSIS AND PERFORMANCE MEASUREMENT OF EXISTING SOLUTION METHODS OF QUADRATIC ASSIGNMENT PROBLEM
Morteza KARAMI
2014-01-01
Full Text Available Quadratic Assignment Problem (QAP is known as one of the most difficult combinatorial optimization problems that is classified in the category of NP-hard problems. Quadratic Assignment Problem Library (QAPLIB is a full database of QAPs which contains several problems from different authors and different sizes. Many exact and meta-heuristic solution methods have been introduced to solve QAP. In this study we focus on previously introduced solution methods of QAP e.g. Branch and Bound (B&B, Simulated Annealing (SA Algorithm, Greedy Randomized Adaptive Search Procedure (GRASP for dense and sparse QAPs. The codes of FORTRAN for these methods were downloaded from QAPLIB. All problems of QAPLIB were solved by the abovementioned methods. Several results were obtained from the computational experiments part. The Results show that the Branch and Bound method is able to introduce a feasible solution for all problems while Simulated Annealing Algorithm and GRASP methods are not able to find any solution for some problems. On the other hand, Simulated Annealing and GRASP methods have shorter run time comparing to the Branch and Bound method. In addition, the performance of the methods on the objective function value is discussed.
A GPU Implementation of Local Search Operators for Symmetric Travelling Salesman Problem
Juraj Fosin
2013-06-01
Full Text Available The Travelling Salesman Problem (TSP is one of the most studied combinatorial optimization problem which is significant in many practical applications in transportation problems. The TSP problem is NP-hard problem and requires large computation power to be solved by the exact algorithms. In the past few years, fast development of general-purpose Graphics Processing Units (GPUs has brought huge improvement in decreasing the applications’ execution time. In this paper, we implement 2-opt and 3-opt local search operators for solving the TSP on the GPU using CUDA. The novelty presented in this paper is a new parallel iterated local search approach with 2-opt and 3-opt operators for symmetric TSP, optimized for the execution on GPUs. With our implementation large TSP problems (up to 85,900 cities can be solved using the GPU. We will show that our GPU implementation can be up to 20x faster without losing quality for all TSPlib problems as well as for our CRO TSP problem.
Liang, Xuecheng
Dynamic hardness (Pd) of 22 different pure metals and alloys having a wide range of elastic modulus, static hardness, and crystal structure were measured in a gas pulse system. The indentation contact diameter with an indenting sphere and the radius (r2) of curvature of the indentation were determined by the curve fitting of the indentation profile data. r 2 measured by the profilometer was compared with that calculated from Hertz equation in both dynamic and static conditions. The results indicated that the curvature change due to elastic recovery after unloading is approximately proportional to the parameters predicted by Hertz equation. However, r 2 is less than the radius of indenting sphere in many cases which is contradictory to Hertz analysis. This discrepancy is believed due to the difference between Hertzian and actual stress distributions underneath the indentation. Factors which influence indentation elastic recovery were also discussed. It was found that Tabor dynamic hardness formula always gives a lower value than that directly from dynamic hardness definition DeltaE/V because of errors mainly from Tabor's rebound equation and the assumption that dynamic hardness at the beginning of rebound process (Pr) is equal to kinetic energy change of an impact sphere over the formed crater volume (Pd) in the derivation process for Tabor's dynamic hardness formula. Experimental results also suggested that dynamic to static hardness ratio of a material is primarily determined by its crystal structure and static hardness. The effects of strain rate and temperature rise on this ratio were discussed. A vacuum rotating arm apparatus was built to measure Pd at 70, 127, and 381 mum sphere sizes, these results exhibited that Pd is highly depended on the sphere size due to the strain rate effects. P d was also used to substitute for static hardness to correlate with abrasion and erosion resistance of metals and alloys. The particle size effects observed in erosion were
Circle Packing for Origami Design Is Hard
Demaine, Erik D; Lang, Robert J
2010-01-01
We show that deciding whether a given set of circles can be packed into a rectangle, an equilateral triangle, or a unit square are NP-hard problems, settling the complexity of these natural packing problems. On the positive side, we show that any set of circles of total area 1 can be packed into a square of size 8/pi=2.546... These results are motivated by problems arising in the context of origami design.
EDITORIAL: Combinatorial and High-Throughput Materials Research
Potyrailo, Radislav A.; Takeuchi, Ichiro
2005-01-01
The success of combinatorial and high-throughput methodologies relies greatly on the availability of various characterization tools with new and improved capabilities [1]. Indeed, how useful can a combinatorial library of 250, 400, 25 000 or 2 000 000 compounds be [2-5] if one is unable to characterize its properties of interest fairly quickly? How useful can a set of thousands of spectra or chromatograms be if one is unable to analyse them in a timely manner? For these reasons, the development of new approaches for materials characterization is one of the most active areas in combinatorial materials science. The importance of this aspect of research in the field has been discussed in numerous conferences including the Pittsburgh Conferences, the American Chemical Society Meetings, the American Physical Society Meetings, the Materials Research Society Symposia and various Gordon Research Conferences. Naturally, the development of new measurement instrumentation attracts the attention not only of practitioners of combinatorial materials science but also of those who design new software for data manipulation and mining. Experimental designs of combinatorial libraries are pursued with available and realistic synthetic and characterization capabilities in mind. It is becoming increasingly critical to link the design of new equipment for high-throughput parallel materials synthesis with integrated measurement tools in order to enhance the efficacy of the overall experimental strategy. We have received an overwhelming response to our proposal and call for papers for this Special Issue on Combinatorial Materials Science. The papers in this issue of Measurement Science and Technology are a very timely collection that captures the state of modern combinatorial materials science. They demonstrate the significant advances that are taking place in the field. In some cases, characterization tools are now being operated in the factory mode. At the same time, major challenges
Hardness and excitation energy
Á Nagy
2005-09-01
The concept of the ensemble Kohn-Sham hardness is introduced. It is shown that the first excitation energy can be given by the Kohn-Sham hardness (i.e. the energy difference of the ground-state lowest unoccupied and highest occupied levels) plus an extra term coming from the partial derivative of the ensemble exchange-correlation energy with respect to the weighting factor in the limit → 0. It is proposed that the first excitation energy can be used as a reactivity index instead of the hardness.
Su, Naifang; Dai, Ding; Deng, Chao; Qian, Minping; Deng, Minghua
2014-06-01
Discovering the regulation of cancer-related gene is of great importance in cancer biology. Transcription factors and microRNAs are two kinds of crucial regulators in gene expression, and they compose a combinatorial regulatory network with their target genes. Revealing the structure of this network could improve the authors' understanding of gene regulation, and further explore the molecular pathway in cancer. In this article, the authors propose a novel approach graphical adaptive lasso (GALASSO) to construct the regulatory network in breast cancer. GALASSO use a Gaussian graphical model with adaptive lasso penalties to integrate the sequence information as well as gene expression profiles. The simulation study and the experimental profiles verify the accuracy of the authors' approach. The authors further reveal the structure of the regulatory network, and explore the role of feedforward loops in gene regulation. In addition, the authors discuss the combinatorial regulatory effect between transcription factors and microRNAs, and select miR-155 for detailed analysis of microRNA's role in cancer. The proposed GALASSO approach is an efficient method to construct the combinatorial regulatory network. It also provides a new way to integrate different data sources and could find more applications in meta-analysis problem.
2006-01-01
"The second international conference on hard and electromagnetic probes of high-energy nuclear collisions was held June 9 to 16, 2006 at the Asilomar Conference grounds in Pacific Grove, California" (photo and 1/2 page)
Claes H. de Vreese; Boomgaarden, Hajo G.; Semetko, Holli A.
2008-01-01
Abstract Support for European integration is a function no longer only of `hard' economic and utilitarian predictors but also of `soft' predictors such as feelings of identity and attitudes towards immigrants. Focusing on the issue of the potential membership of Turkey in the European Union (EU), this study demonstrates that the importance of `soft' predictors outweighs the role of `hard' predictors in understanding public opinion about Turkish membership. The study draws on survey...
Laguerre-type derivatives: Dobinski relations and combinatorial identities
Penson, K A; Horzela, A; Solomon, A I; Duchamp, G H E
2009-01-01
We consider properties of the operators D(r,M)=a^r(a^\\dag a)^M (which we call generalized Laguerre-type derivatives), with r=1,2,..., M=0,1,..., where a and a^\\dag are boson annihilation and creation operators respectively, satisfying [a,a^\\dag]=1. We obtain explicit formulas for the normally ordered form of arbitrary Taylor-expandable functions of D(r,M) with the help of an operator relation which generalizes the Dobinski formula. Coherent state expectation values of certain operator functions of D(r,M) turn out to be generating functions of combinatorial numbers. In many cases the corresponding combinatorial structures can be explicitly identified.
Combinatorial Gene Regulation through Kinetic Control of the Transcription Cycle.
Scholes, Clarissa; DePace, Angela H; Sánchez, Álvaro
2017-01-25
Cells decide when, where, and to what level to express their genes by "computing" information from transcription factors (TFs) binding to regulatory DNA. How is the information contained in multiple TF-binding sites integrated to dictate the rate of transcription? The dominant conceptual and quantitative model is that TFs combinatorially recruit one another and RNA polymerase to the promoter by direct physical interactions. Here, we develop a quantitative framework to explore kinetic control, an alternative model in which combinatorial gene regulation can result from TFs working on different kinetic steps of the transcription cycle. Kinetic control can generate a wide range of analog and Boolean computations without requiring the input TFs to be simultaneously bound to regulatory DNA. We propose experiments that will illuminate the role of kinetic control in transcription and discuss implications for deciphering the cis-regulatory "code."
An Atlas of Combinatorial Transcriptional Regulation in Mouse and Man
Ravasi, Timothy
2010-03-01
Combinatorial interactions among transcription factors are critical to directing tissue-specific gene expression. To build a global atlas of these combinations, we have screened for physical interactions among the majority of human and mouse DNA-binding transcription factors (TFs). The complete networks contain 762 human and 877 mouse interactions. Analysis of the networks reveals that highly connected TFs are broadly expressed across tissues, and that roughly half of the measured interactions are conserved between mouse and human. The data highlight the importance of TF combinations for determining cell fate, and they lead to the identification of a SMAD3/FLI1 complex expressed during development of immunity. The availability of large TF combinatorial networks in both human and mouse will provide many opportunities to study gene regulation, tissue differentiation, and mammalian evolution.
Time Complexity of Evolutionary Algorithms for Combinatorial Optimization: A Decade of Results
Pietro S. Oliveto; Jun He; Xin Yao
2007-01-01
Computational time complexity analyzes of evolutionary algorithms (EAs) have been performed since the mid-nineties. The first results were related to very simple algorithms, such as the (1+1)-EA, on toy problems. These efforts produced a deeper understanding of how EAs perform on different kinds of fitness landscapes and general mathematical tools that may be extended to the analysis of more complicated EAs on more realistic problems. In fact, in recent years, it has been possible to analyze the (1+1)-EA on combinatorial optimization problems with practical applications and more realistic population-based EAs on structured toy problems. This paper presents a survey of the results obtained in the last decade along these two research lines. The most common mathematical techniques are introduced, the basic ideas behind them are discussed and their elective applications are highlighted. Solved problems that were still open are enumerated as are those still awaiting for a solution. New questions and problems arisen in the meantime are also considered.
Mathematical Model and Hybrid Scatter Search for Cost Driven Job-shop Scheduling Problem
Bai Jie
2011-07-01
Full Text Available Job-shop scheduling problem (JSP is one of the most well-known machine scheduling problems and one of the strongly NP-hard combinatorial optimization problems. Cost optimization is an attractive and critical research and development area for both academic and industrial societies. This paper presents a cost driven model of the job-shop scheduling problem in which the solutions are driven by business inputs, such as the cost of the product transitions, revenue loss due to the machine idle time and earliness/tardiness penalty. And then, a new hybrid scatter search algorithm is proposed to solve the cost driven job-shop scheduling problem by introducing the simulated annealing (SA into the improvement method of scatter search (SS. In order to illustrate the effectiveness of the hybrid method, some test problems are generated, and the performance of the proposed method is compared with other evolutionary algorithms such as genetic algorithm and simulated annealing. The experimental simulation tests show that the hybrid method is quite effective at solving the cost driven job-shop scheduling problem.
二次分配问题的大洪水算法求解%Great Deluge Algorithm for Quadratic Assignment Problem
魏欣; 马良; 张惠珍
2011-01-01
大洪水算法是一种求解组合优化问题的独特方法,该方法通过模拟洪水上涨的过程来达到求解一些组合优化难题的目的.本文运用该方法求解二次分配问题(QAP),设计了相应的算法程序,并对QAPLIB(二次分配基准问题库)中的算例进行了实验测试,结果表明,大洪水算法可以快速有效地求得二次分配问题的优化解,是求解二次分配问题的一个新的较好方案.%The great deluge algorithm ( GDA) is a special approach for solving combinatorial optimization problems.It can be used to solve some NP-hard combinatorial optimization problems through simulating the process of flood rising.In this paper, we use this algorithm to solve the quadratic assignment problem and design the corresponding program.The instances in the QABLIB are tested experimentally.And the results show that the algorithm is able to find the optimal solution quickly and effectively, and that the CDA is a new and promising method for the QAP.
Combinatorial Solid-Phase Synthesis of Balanol Analogues
Nielsen, John; Lyngsø, Lars Ole
1996-01-01
The natural product balanol has served as a template for the design and synthesis of a combinatorial library using solid-phase chemistry. Using a retrosynthetic analysis, the structural analogues have been assembled from three relatively accessible building blocks. The solid-phase chemistry inclu...... including MSNT-mediated esterification of both support-bound alcohols and carboxylic acids has been implemented successfully. Copyright (C) 1996 Elsevier Science Ltd....
Combinatorial Solid-Phase Synthesis of Balanol Analogues
Nielsen, John; Lyngsø, Lars Ole
1996-01-01
The natural product balanol has served as a template for the design and synthesis of a combinatorial library using solid-phase chemistry. Using a retrosynthetic analysis, the structural analogues have been assembled from three relatively accessible building blocks. The solid-phase chemistry inclu...... including MSNT-mediated esterification of both support-bound alcohols and carboxylic acids has been implemented successfully. Copyright (C) 1996 Elsevier Science Ltd....
Immobilized OBOC combinatorial bead array to facilitate multiplicative screening
Xiao, Wenwu; Bononi, Fernanda C.; Townsend, Jared; Li, Yuanpei; Liu, Ruiwu; Lam, Kit S.
2013-01-01
One-bead-one-compound (OBOC) combinatorial library screening has been broadly utilized for the last two decades to identify small molecules, peptides or peptidomimetics targeting variable screening probes such as cell surface receptors, bacteria, protein kinases, phosphatases, proteases etc. In previous screening methods, library beads were suspended in solution and screened against one single probe. Only the positive beads were tracked and isolated for additional screens and finally selected...
The evolution of combinatorial gene regulation in fungi.
Tuch, Brian B.; Galgoczy, David J.; Hernday, Aaron D.; Hao Li; Johnson, Alexander D.
2008-01-01
It is widely suspected that gene regulatory networks are highly plastic. The rapid turnover of transcription factor binding sites has been predicted on theoretical grounds and has been experimentally demonstrated in closely related species. We combined experimental approaches with comparative genomics to focus on the role of combinatorial control in the evolution of a large transcriptional circuit in the fungal lineage. Our study centers on Mcm1, a transcriptional regulator that, in combinati...
A Combinatorial interpretation of Hofstadter's G-sequence
Rahman, Mustazee
2011-01-01
We give a combinatorial interpretation of a classical meta-Fibonacci sequence defined by G(n) = n - G(G(n-1)) with the initial condition G(1) = 1, which appears in Hofstadter's 'Godel, Escher, Bach: An Eternal Golden Braid'. The interpretation is in terms of an infinite labelled tree. We then show a few corollaries about the behaviour of the sequence G(n) directly from the interpretation.
Nag, S; Banerjee, R; Fraser, H L
2007-05-01
The new generation of metallic biomaterials for prosthesis implantation (orthopedic and dental) typically have a Ti base with fully biocompatible alloying additions such as Nb, Ta, Zr, Mo, Fe and Sn. While the binary Ti-Ta and the ternary Ti-Nb-Ta systems are promising, the large composition space afforded by these systems offers tremendous scope in terms of alloy design via optimization of alloy composition and thermomechanical treatment. In the present paper a novel combinatorial approach has been developed for rapidly exploring the microstructural evolution and microstructure-microhardness (or elastic modulus) relationships in these systems. Using directed laser deposition, compositionally graded alloy samples have been fabricated and subsequently heat-treated to affect different microstructures in terms of the volume fraction and distribution of the alpha phase in the beta matrix as a function of composition. Subsequently, composition-specific indentation-based hardness and modulus information has been obtained from these graded samples, and the resulting data have been used to develop relationships between the composition, microstructure and mechanical properties. Such rapid combinatorial assessments can be very useful in optimizing not only the alloy composition but also the desired microstructure for achieving the best combination of properties for specific orthopedic or dental applications.
What makes a phase transition? Analysis of the random satisfiability problem
Zweig, K A; Vicsek, T; 10.1016/j.physa.2009.12.051
2010-01-01
In the last 30 years it was found that many combinatorial systems undergo phase transitions. One of the most important examples of these can be found among the random k-satisfiability problems (often referred to as k-SAT), asking whether there exists an assignment of Boolean values satisfying a Boolean formula composed of clauses with k random variables each. The random 3-SAT problem is reported to show various phase transitions at different critical values of the ratio of the number of clauses to the number of variables. The most famous of these occurs when the probability of finding a satisfiable instance suddenly drops from 1 to 0. This transition is associated with a rise in the hardness of the problem, but until now the correlation between any of the proposed phase transitions and the hardness is not totally clear. In this paper we will first show numerically that the number of solutions universally follows a lognormal distribution, thereby explaining the puzzling question of why the number of solutions ...
View discovery in OLAP databases through statistical combinatorial optimization
Hengartner, Nick W [Los Alamos National Laboratory; Burke, John [PNNL; Critchlow, Terence [PNNL; Joslyn, Cliff [PNNL; Hogan, Emilie [PNNL
2009-01-01
OnLine Analytical Processing (OLAP) is a relational database technology providing users with rapid access to summary, aggregated views of a single large database, and is widely recognized for knowledge representation and discovery in high-dimensional relational databases. OLAP technologies provide intuitive and graphical access to the massively complex set of possible summary views available in large relational (SQL) structured data repositories. The capability of OLAP database software systems to handle data complexity comes at a high price for analysts, presenting them a combinatorially vast space of views of a relational database. We respond to the need to deploy technologies sufficient to allow users to guide themselves to areas of local structure by casting the space of 'views' of an OLAP database as a combinatorial object of all projections and subsets, and 'view discovery' as an search process over that lattice. We equip the view lattice with statistical information theoretical measures sufficient to support a combinatorial optimization process. We outline 'hop-chaining' as a particular view discovery algorithm over this object, wherein users are guided across a permutation of the dimensions by searching for successive two-dimensional views, pushing seen dimensions into an increasingly large background filter in a 'spiraling' search process. We illustrate this work in the context of data cubes recording summary statistics for radiation portal monitors at US ports.
Combinatorial study of ceramic tape-casting slurries.
Liu, Zhifu; Wang, Yiling; Li, Yongxiang
2012-03-12
Ceramic tape-casting slurries are complex systems composed of ceramic powder, solvent, and a number of organic components. Conventionally, the development of ceramic tape-casting slurries is time-consuming and of low efficiency. In this work, combinatorial approaches were applied to screen the ethanol and ethyl-acetate binary solvent based slurry for ceramic green tape-casting. The combinatorial libraries were designed considering the variation of the amount of PVB (Poly vinyl-butyral) binder, polyethylene-400, and butyl-benzyl-phthalate plasticizers, and glyceryl triacetate dispersant. A parallel magnetic stirring process was used to make the combinatorial slurry library. The properties mapping of the slurry library was obtained by investigating the sedimentation and rheological characteristics of the slurries. The slurry composition was refined by scaling up the experiments and comparing the microstructure, mechanical property, and sintering behavior of green tapes made from the selected slurries. Finally, a kind of ethanol-ethyl acetate binary solvent based slurry system suitable for making X7R dielectric ceramic green tapes was achieved.
Controlling Combinatorial Complexity in Software and Malware Behavior Computation
Pleszkoch, Mark G [ORNL; Linger, Richard C [ORNL
2015-01-01
Virtually all software is out of intellectual control in that no one knows its full behavior. Software Behavior Computation (SBC) is a new technology for understanding everything software does. SBC applies the mathematics of denotational semantics implemented by function composition in Functional Trace Tables (FTTs) to compute the behavior of programs, expressed as disjoint cases of conditional concurrent assignments. In some circumstances, combinatorial explosions in the number of cases can occur when calculating the behavior of sequences of multiple branching structures. This paper describes computational methods that avoid combinatorial explosions. The predicates that control branching structures such as ifthenelses can be organized into three categories: 1) Independent, resulting in no behavior case explosion, 2) Coordinated, resulting in two behavior cases, or 3) Goaloriented, with potential exponential growth in the number of cases. Traditional FTT-based behavior computation can be augmented by two additional computational methods, namely, Single-Value Function Abstractions (SVFAs) and, introduced in this paper, Relational Trace Tables (RTTs). These methods can be applied to the three predicate categories to avoid combinatorial growth in behavior cases while maintaining mathematical correctness.
Fronczak, Agata
2012-10-01
We present an alternative approach to the problem of interacting fluids, which we believe may provide important insights into microscopic mechanisms that lead to the occurrence of phase transitions. The approach exploits enumerative properties and combinatorial meaning of Bell polynomials. We derive the exact formula for the probability of a general system of N particles at temperature T to consist of k weakly coupled clusters of various sizes. We also show that the grand potential of the system may be considered the exponential generating function for the number of internal states (thermodynamic probability) of these clusters. The microscopic interpretation of the grand potential is surprising, especially if one recalls that until now only the thermodynamic meaning of this free energy was known. We also derive an approximated expression for the density of states.
Fronczak, Agata
2012-01-01
We present a completely new approach to the problem of interacting fluids, which we believe may provide important insights into microscopic mechanisms that lead to the occurrence of phase transitions. The approach exploits enumerative properties and combinatorial meaning of Bell polynomials. We derive the exact formula for probability of a general system of N particles at temperature T to consist of k weakly coupled clusters of various sizes. We also show that the grand potential of the system may be considered as the exponential generating function for the number of internal states (thermodynamic probability) of these clusters. The microscopic interpretation of the grand potential is novel and surprising, especially if one recalls that until now the only thermodynamic meaning of this free energy was known. We also derive an approximated expression for the density of states.
Kille, Sabrina; Acevedo-Rocha, Carlos G; Parra, Loreto P; Zhang, Zhi-Gang; Opperman, Diederik J; Reetz, Manfred T; Acevedo, Juan Pablo
2013-02-15
Saturation mutagenesis probes define sections of the vast protein sequence space. However, even if randomization is limited this way, the combinatorial numbers problem is severe. Because diversity is created at the codon level, codon redundancy is a crucial factor determining the necessary effort for library screening. Additionally, due to the probabilistic nature of the sampling process, oversampling is required to ensure library completeness as well as a high probability to encounter all unique variants. Our trick employs a special mixture of three primers, creating a degeneracy of 22 unique codons coding for the 20 canonical amino acids. Therefore, codon redundancy and subsequent screening effort is significantly reduced, and a balanced distribution of codon per amino acid is achieved, as demonstrated exemplarily for a library of cyclohexanone monooxygenase. We show that this strategy is suitable for any saturation mutagenesis methodology to generate less-redundant libraries.
TART97 a coupled neutron-photon 3-D, combinatorial geometry Monte Carlo transport code
Cullen, D.E.
1997-11-22
TART97 is a coupled neutron-photon, 3 Dimensional, combinatorial geometry, time dependent Monte Carlo transport code. This code can on any modern computer. It is a complete system to assist you with input preparation, running Monte Carlo calculations, and analysis of output results. TART97 is also incredibly FAST; if you have used similar codes, you will be amazed at how fast this code is compared to other similar codes. Use of the entire system can save you a great deal of time and energy. TART97 is distributed on CD. This CD contains on- line documentation for all codes included in the system, the codes configured to run on a variety of computers, and many example problems that you can use to familiarize yourself with the system. TART97 completely supersedes all older versions of TART, and it is strongly recommended that users only use the most recent version of TART97 and its data riles.
Tobias Buer
2010-10-01
Full Text Available The procurement of transportation services via large-scale combinatorial auctions involves a couple of complex decisions whose outcome highly influences the performance of the tender process. This paper examines the shipper's task of selecting a subset of the submitted bids which efficiently trades off total procurement cost against expected carrier performance. To solve this bi-objective winner determination problem, we propose a Pareto-based greedy randomized adaptive search procedure (GRASP. As a post-optimizer we use a path relinking procedure which is hybridized with branch-and-bound. Several variants of this algorithm are evaluated by means of artificial test instances which comply with important real-world characteristics. The two best variants prove superior to a previously published Pareto-based evolutionary algorithm.
Combinatorial Frequency Generation in Quasi-Periodic Stacks of Nonlinear Dielectric Layers
Oksana Shramkova
2014-07-01
Full Text Available Three-wave mixing in quasi-periodic structures (QPSs composed of nonlinear anisotropic dielectric layers, stacked in Fibonacci and Thue-Morse sequences, has been explored at illumination by a pair of pump waves with dissimilar frequencies and incidence angles. A new formulation of the nonlinear scattering problem has enabled the QPS analysis as a perturbed periodic structure with defects. The obtained solutions have revealed the effects of stack composition and constituent layer parameters, including losses, on the properties of combinatorial frequency generation (CFG. The CFG features illustrated by the simulation results are discussed. It is demonstrated that quasi-periodic stacks can achieve a higher efficiency of CFG than regular periodic multilayers.
Doubly diffracted ray from a hard quarterplane
Albertsen, Niels Christian
2000-01-01
The scattering of the electromagnetic field from a half wave dipole source around a quarterplane can be calculated from the solutions to two scalar problems, one with a soft quarterplane and one with a hard quarterplane. In both cases, a doubly diffracted ray may exist, but only in the case of th...
Renormalization Hopf algebras and combinatorial groups
Frabetti, Alessandra
2008-01-01
These are the notes of five lectures given at the Summer School {\\em Geometric and Topological Methods for Quantum Field Theory}, held in Villa de Leyva (Colombia), July 2--20, 2007. The lectures are meant for graduate or almost graduate students in physics or mathematics. They include references, many examples and some exercices. The content is the following. The first lecture is a short introduction to algebraic and proalgebraic groups, based on some examples of groups of matrices and groups of formal series, and their Hopf algebras of coordinate functions. The second lecture presents a very condensed review of classical and quantum field theory, from the Lagrangian formalism to the Euler-Lagrange equation and the Dyson-Schwinger equation for Green's functions. It poses the main problem of solving some non-linear differential equations for interacting fields. In the third lecture we explain the perturbative solution of the previous equations, expanded on Feynman graphs, in the simplest case of the scalar $\\...
Hard and superhard nanocomposite coatings
Musil, J. [Univ. of West Bohemia, Plzen (Czech Republic). Dept. of Phys.
2000-03-01
This article reviews the development of hard coatings from a titanium nitride film through superlattice coatings to nanocomposite coatings. Significant attention is devoted to hard and superhard single layer nanocomposite coatings. A strong correlation between the hardness and structure of nanocomposite coatings is discussed in detail. Trends in development of hard nanocomposite coatings are also outlined. (orig.)
Simulated annealing algorithm for solving chambering student-case assignment problem
Ghazali, Saadiah; Abdul-Rahman, Syariza
2015-12-01
The problem related to project assignment problem is one of popular practical problem that appear nowadays. The challenge of solving the problem raise whenever the complexity related to preferences, the existence of real-world constraints and problem size increased. This study focuses on solving a chambering student-case assignment problem by using a simulated annealing algorithm where this problem is classified under project assignment problem. The project assignment problem is considered as hard combinatorial optimization problem and solving it using a metaheuristic approach is an advantage because it could return a good solution in a reasonable time. The problem of assigning chambering students to cases has never been addressed in the literature before. For the proposed problem, it is essential for law graduates to peruse in chambers before they are qualified to become legal counselor. Thus, assigning the chambering students to cases is a critically needed especially when involving many preferences. Hence, this study presents a preliminary study of the proposed project assignment problem. The objective of the study is to minimize the total completion time for all students in solving the given cases. This study employed a minimum cost greedy heuristic in order to construct a feasible initial solution. The search then is preceded with a simulated annealing algorithm for further improvement of solution quality. The analysis of the obtained result has shown that the proposed simulated annealing algorithm has greatly improved the solution constructed by the minimum cost greedy heuristic. Hence, this research has demonstrated the advantages of solving project assignment problem by using metaheuristic techniques.
Session: Hard Rock Penetration
Tennyson, George P. Jr.; Dunn, James C.; Drumheller, Douglas S.; Glowka, David A.; Lysne, Peter
1992-01-01
This session at the Geothermal Energy Program Review X: Geothermal Energy and the Utility Market consisted of five presentations: ''Hard Rock Penetration - Summary'' by George P. Tennyson, Jr.; ''Overview - Hard Rock Penetration'' by James C. Dunn; ''An Overview of Acoustic Telemetry'' by Douglas S. Drumheller; ''Lost Circulation Technology Development Status'' by David A. Glowka; ''Downhole Memory-Logging Tools'' by Peter Lysne.
2003-01-01
CERN will be organizing a special information day on Friday, 27th June, designed to promote the wearing of hard hats and ensure that they are worn correctly. A new prevention campaign will also be launched.The event will take place in the hall of the Main Building from 11.30 a.m. to 2.00 p.m., when you will be able to come and try on various models of hard hat, including some of the very latest innovative designs, ask questions and pass on any comments and suggestions.
Wuhui Li; Fengzhang Ren; Juanhua Su; Zhanhong Ma; Ke Cao; Baohong Tian
2011-07-01
This paper presents a new formula for calculating the hardness of metallic crystals, resulted from the research on the critical grain size with stable dislocations. The formula is = 6 /[(1 – )], where is the hardness, the coefficient, the shear modulus, the Poisson’s ratio, a function of the radius of an atom () and the electron density at the atom interface (). The formula will not only be used to testify the critical grain size with stable dislocations, but also play an important role in the understanding of mechanical properties of nanocrystalline metals.
Kugler, W.
2007-01-15
Hard exclusive processes in high energy electron proton scattering offer the opportunity to get access to a new generation of parton distributions, the so-called generalized parton distributions (GPDs). This functions provide more detailed informations about the structure of the nucleon than the usual PDFs obtained from DIS. In this work we present a detailed analysis of exclusive processes, especially of hard exclusive meson production. We investigated the influence of exclusive produced mesons on the semi-inclusive production of mesons at fixed target experiments like HERMES. Further we give a detailed analysis of higher order corrections (NLO) for the exclusive production of mesons in a very broad range of kinematics. (orig.)
Gungormus, Mustafa; Fong, Hanson; Kim, Il Won; Evans, John Spencer; Tamerler, Candan; Sarikaya, Mehmet
2008-03-01
We report selection and characterization of hydroxyapatite-binding heptapeptides from a peptide-phage library and demonstrate the effects of two peptides, with different binding affinities and structural properties, on the mineralization of calcium phosphate mineral. In vitro mineralization studies carried out using one strong- and one weak-binding peptide, HABP1 and HABP2, respectively, revealed that the former exhibited a drastic outcome on mineralization kinetics and particle morphology. Strong-binding peptide yielded significantly larger crystals, as observed by electron microscopy, in comparison to those formed in the presence of a weak-binding peptide or in the negative control. Molecular structural studies carried out by circular dichroism revealed that HABP1 and HABP2 differed in their secondary structure and conformational stability. The results indicate that sequence, structure, and molecular stability strongly influence the mineralization activity of these peptides. The implication of the research is that the combinatorially selected short-sequence peptides may be used in the restoration or regeneration of hard tissues through their control over of the formation of calcium phosphate biominerals.
Exact and Metaheuristic Approaches for a Bi-Objective School Bus Scheduling Problem.
Chen, Xiaopan; Kong, Yunfeng; Dang, Lanxue; Hou, Yane; Ye, Xinyue
2015-01-01
As a class of hard combinatorial optimization problems, the school bus routing problem has received considerable attention in the last decades. For a multi-school system, given the bus trips for each school, the school bus scheduling problem aims at optimizing bus schedules to serve all the trips within the school time windows. In this paper, we propose two approaches for solving the bi-objective school bus scheduling problem: an exact method of mixed integer programming (MIP) and a metaheuristic method which combines simulated annealing with local search. We develop MIP formulations for homogenous and heterogeneous fleet problems respectively and solve the models by MIP solver CPLEX. The bus type-based formulation for heterogeneous fleet problem reduces the model complexity in terms of the number of decision variables and constraints. The metaheuristic method is a two-stage framework for minimizing the number of buses to be used as well as the total travel distance of buses. We evaluate the proposed MIP and the metaheuristic method on two benchmark datasets, showing that on both instances, our metaheuristic method significantly outperforms the respective state-of-the-art methods.