Finding maximin latin hypercube designs by Iterated Local Search heuristics

The maximin LHD problem calls for arranging N points in a k-dimensional grid so that no pair of points share a coordinate and the distance of the closest pair of points is as large as possible. In this paper we propose to tackle this problem by heuristic algorithms belonging to the Iterated Local Search (ILS) family and show through some computational experiments that the proposed algorithms compare very well with different heuristic approaches in the established literature.     

Linear CNF formulas and satisfiability

In this paper, we study linear CNF formulas generalizing linear hypergraphs under combinatorial and complexity theoretical aspects w.r.t. SAT. We establish NP-completeness of SAT for the unrestricted linear formula class, and we show the equivalence of NP-completeness of restricted uniform linear formula classes w.r.t. SAT and the existence of unsatisfiable uniform linear witness formulas. On that basis we prove NP-completeness of SAT for uniform linear classes in a resolution-based manner by constructing large-sized formulas. Interested in small witness formulas, we exhibit some combinatorial features of linear hypergraphs closely related to latin squares and finite projective planes helping to construct rather dense, and significantly smaller unsatisfiable k-uniform linear formulas, at least for the cases k=3,4.     

The spectrum for quasigroups with cyclic automorphisms and additional symmetries

We determine necessary and sufficient conditions for the existence of a quasigroup of order n having an automorphism consisting of a single cycle of length m and n−m fixed points, and having any combination of the additional properties of being idempotent, unipotent, commutative, semi-symmetric or totally symmetric. Quasigroups with such additional properties and symmetries are equivalent to various classes of triple systems.     

Uniform Semi‐Latin Squares and Their Schur‐Optimality

Let n and k be integers, with and . An semi‐Latin square S is an array, whose entries are k‐subsets of an ‐set, the set of symbols of S, such that each symbol of S is in exactly one entry in each row and exactly one entry in each column of S. Semi‐Latin squares form an interesting class of combinatorial objects which are useful in the design of comparative experiments. We say that an semi‐Latin square S is uniform if there is a constant μ such that any two entries of S, not in the same row or column, intersect in exactly μ symbols (in which case ). We prove that a uniform semi‐Latin square is Schur‐optimal in the class of semi‐Latin squares, and so is optimal (for use as an experimental design) with respect to a very wide range of statistical optimality criteria. We give a simple construction to make an semi‐Latin square S from a transitive permutation group G of degree n and order , and show how certain properties of S can be determined from permutation group properties of G. If G is 2‐transitive then S is uniform, and this provides us with Schur‐optimal semi‐Latin squares for many values of n and k for which optimal semi‐Latin squares were previously unknown for any optimality criterion. The existence of a uniform semi‐Latin square for all integers is shown to be equivalent to the existence of mutually orthogonal Latin squares (MOLS) of order n. Although there are not even two MOLS of order 6, we construct uniform, and hence Schur‐optimal, semi‐Latin squares for all integers . & 2012 Wiley Periodicals, Inc. J. Combin. Designs 00: 1–13, 2012     

Random Latin square graphs

In this paper we introduce new models of random graphs, arising from Latin squares which include random Cayley graphs as a special case. We investigate some properties of these graphs including their clique, independence and chromatic numbers, their expansion properties as well as their connectivity and Hamiltonicity. The results obtained are compared with other models of random graphs and several similarities and differences are pointed out. For many properties our results for the general case are as strong as the known results for random Cayley graphs and sometimes improve the previously best results for the Cayley case. © 2011 Wiley Periodicals, Inc. Random Struct. Alg., 2011     

Wrap-Around L2-Discrepancy of Random Sampling, Latin Hypercube and Uniform Designs

For comparing random designs and Latin hypercube designs, this paper con- siders a wrap-around version of the L₂-discrepancy (WD). The theoretical expectation and variance of this discrepancy are derived for these two designs. The expectation and variance of Latin hypercube designs are significantly lower than those of the corresponding random designs. We also study construction of the uniform design under the WD and show that one-dimensional uniform design under this discrepancy can be any set of equidistant points. For high dimensional uniform designs we apply the threshold accepting heuristic for finding low discrepancy designs. We also show that the conjecture proposed by K. T. Fang, D. K. J. Lin, P. Winker, and Y. Zhang (2000, Technometrics) is true under the WD when the design is complete.     

Teleportation of n-Particle State via n Pairs of EPR Channels

The teleportation of an arbitrary n-particle state (n ≥ 1) is proposed if n pairs of identical EPR states are utilized as quantum channels. Independent Bell state measurements are performed for joint measurement. By using a special Latin square of order 2n(n ≥ 1), explicit expressions of outcomes after the Bell state measurements by Alice (sender) and the corresponding unitary transformations by Bob (receiver) can be derived. It is shown that the teleportation of n-particle state can be implemented by a series of single-qubit teleportation.     

On the distance between distinct group Latin squares

In an article in 1992, Drápal addressed the question of how far apart the multiplication tables of two groups can be? In this article we continue this investigation; in particular, we study the interaction between partial equalities in the multiplication tables of the two groups and their subgroup structure. © 1997 John Wiley & Sons, Inc. J Combin Designs 5: 235–248, 1997     

基于JMCT-JBURN的燃料棒径向功率分布计算

研究给出基于蒙特卡罗粒子输运软件JMCT耦合燃耗分析软件JBURN计算燃料棒径向功率分布的方法。介绍了计算模型的建立、输运及燃耗计算的相关设置以及裂变功率、俘获功率的统计方法。UO₂燃料棒径向功率分布的计算结果表明,采用JMCT-JBURN软件的结果与工程常用软件符合较好,最大偏差不超过3%,证明了计算方法和计算软件的适用性。该方法可用于工程设计。