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The Encyclopedia of Integer Sequences
"... This article gives a brief introduction to the OnLine Encyclopedia of Integer Sequences (or OEIS). The OEIS is a database of nearly 90,000 sequences of integers, arranged lexicographically. The entry for a sequence lists the initial terms (50 to 100, if available), a description, formulae, programs ..."
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Cited by 631 (15 self)
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This article gives a brief introduction to the OnLine Encyclopedia of Integer Sequences (or OEIS). The OEIS is a database of nearly 90,000 sequences of integers, arranged lexicographically. The entry for a sequence lists the initial terms (50 to 100, if available), a description, formulae, programs to generate the sequence, references, links to relevant web pages, and other
A new approach to the construction of optimal designs
 J. Statistical Planning and Inference
, 1993
"... By combining a modified version of Hooke and Jeeves ’ pattern search with exact or Monte Carlo moment calculations, it is possible to find I, D and Aoptimal (or nearly optimal) designs for a wide range of responsesurface problems. The algorithm routinely handles problems involving the minimizati ..."
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Cited by 31 (10 self)
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By combining a modified version of Hooke and Jeeves ’ pattern search with exact or Monte Carlo moment calculations, it is possible to find I, D and Aoptimal (or nearly optimal) designs for a wide range of responsesurface problems. The algorithm routinely handles problems involving the minimization of functions of 1000 variables, and so for example can construct designs for a full quadratic responsesurface depending on 12 continuous process variables. The algorithm handles continuous or discrete variables, linear equality or inequality constraints, and a response surface that is any low degree polynomial. The design may be required to include a specified set of points, so a sequence of designs can be obtained, each optimal given that the earlier runs have been made. The modeling region need not coincide with the measurement region. The algorithm has been implemented in a program called gosset, which has been used to compute extensive tables of designs. Many of these are more efficient than the best designs previously known.
Largest jSimplices In dCubes: Some Relatives Of The Hadamard Maximum Determinant Problem
, 1996
"... . This paper studies the computationally difficult problem of finding a largest jdimensional simplex in a given ddimensional cube. The case in which j = d is of special interest, for it is equivalent to the Hadamard maximum determinant problem; it has been solved for infinitely many values of d ..."
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Cited by 12 (0 self)
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. This paper studies the computationally difficult problem of finding a largest jdimensional simplex in a given ddimensional cube. The case in which j = d is of special interest, for it is equivalent to the Hadamard maximum determinant problem; it has been solved for infinitely many values of d but not for d = 14. (The subcase in which j = d j 3 (mod 4) subsumes the famous problem on the existence of Hadamard matrices.) The known results for the case j = d are here summarized and used, but the main focus is on fixed small values of j. When j = 1, the problem is trivial, and when j = 2 or j = 3 it is here solved completely (i.e., for all d). Beyond that, the results are fragmentary but numerous, and they lead to several attractive conjectures. Some other problems involving simplices in cubes are mentioned, and the relationship of largest simplices to Doptimal weighing designs is discussed. Introduction The setting for everything in this paper is a finitedimensional Euclidean sp...
What is known about unit cubes
 K. Weiss & L. De Floriani / Simplex and Diamond Hierarchies 27 submitted to COMPUTER GRAPHICS Forum
, 2011
"... Abstract. Unit cubes, from any point of view, are among the simplest and the most important objects in ndimensional Euclidean space. In fact, as one will see from this survey, they are not simple at all. On the one hand, the known results about them have been achieved by employing complicated ..."
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Cited by 9 (0 self)
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Abstract. Unit cubes, from any point of view, are among the simplest and the most important objects in ndimensional Euclidean space. In fact, as one will see from this survey, they are not simple at all. On the one hand, the known results about them have been achieved by employing complicated
An Experimental Search and New Combinatorial Designs via a Generalisation of Cyclotomy
 J. Combin. Math. Combin. Comput
, 1997
"... Cyclotomy can be used to construct a variety of combinatorial designs, for example, supplementary difference sets, weighing matrices and T matrices. These designs may be obtained by using linear combinations of the incidence matrices of the cyclotomic cosets. However, cyclotomy only works in the p ..."
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Cited by 8 (5 self)
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Cyclotomy can be used to construct a variety of combinatorial designs, for example, supplementary difference sets, weighing matrices and T matrices. These designs may be obtained by using linear combinations of the incidence matrices of the cyclotomic cosets. However, cyclotomy only works in the prime and prime power cases. We present a generalisation of cyclotomy and introduce generalised cosets. Combinatorial designs can now be obtained by a search through all linear combinations of the incidence matrices of the generalised cosets. We believe that this search method is new. The generalisation works for all cases and is not restricted to prime powers. The paper presents some new combinatorial designs. We give a new construction for T matrices of order 87 and hence an OD(4 \Theta 87; 87; 87; 87; 87). We also give some Doptimal designs of order n = 2v = 2 \Theta 145; 2 \Theta 157; 2 \Theta 181. Keywords: Cyclotomy, Galois field, Galois domain, autocorrelation function, supplemen...
Using factorial experiments to evaluate the effect of genetic programming parameters
 Genetic Programming, Proceedings of EuroGP’2000, volume 1802 of LNCS
, 2000
"... Abstract. Statistical techniques for designing and analysing experiments are used to evaluate the individual and combined effects of genetic programming parameters. Three binary classification problems are investigated in a total of seven experiments consisting of 1108 runs of a machine code genetic ..."
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Cited by 5 (0 self)
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Abstract. Statistical techniques for designing and analysing experiments are used to evaluate the individual and combined effects of genetic programming parameters. Three binary classification problems are investigated in a total of seven experiments consisting of 1108 runs of a machine code genetic programming system. The parameters having the largest effect in these experiments are the population size and the number of generations. A large number of parameters have negligible effects. The experiments indicate that the investigated genetic programming system is robust to parameter variations, with the exception of a few important parameters. 1
Largedeterminant sign matrices of order 4k + 1
 Discrete Math
"... Abstract. The Hadamard maximal determinant problem asks for the largest n × n determinant with entries ±1. When n ≡ 1 (mod 4) , the maximal excess construction of Farmakis & Kounias [FK] has been the most successful general method for constructing large (though seldom maximal) determinants. For cert ..."
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Cited by 4 (4 self)
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Abstract. The Hadamard maximal determinant problem asks for the largest n × n determinant with entries ±1. When n ≡ 1 (mod 4) , the maximal excess construction of Farmakis & Kounias [FK] has been the most successful general method for constructing large (though seldom maximal) determinants. For certain small n, however, still larger determinants have been known; several new records were recently reported in [OSDS]. Here, we define “3normalized ” n × n Hadamard matrices, and construct largedeterminant matrices of order n + 1 from them. Our constructions account for most of the previous “small n ” records,
NEW LOWER BOUNDS FOR THE MAXIMAL DETERMINANT PROBLEM
, 2003
"... Abstract. We report new world records for the maximal determinant of an n×n matrix with entries ±1. Using various techniques, we beat existing records for ..."
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Cited by 3 (3 self)
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Abstract. We report new world records for the maximal determinant of an n×n matrix with entries ±1. Using various techniques, we beat existing records for
On the enumeration of some Doptimal designs
 Journal of Statistical Planning and Inference
, 2008
"... Abstract. Two matrices with elements taken from the set {−1, 1} are Hadamard equivalent if one can be converted into the other by a sequence of permutations of rows and columns, and negations of rows and columns. In this paper we summarize what is known about the number of equivalence classes of mat ..."
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Cited by 2 (0 self)
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Abstract. Two matrices with elements taken from the set {−1, 1} are Hadamard equivalent if one can be converted into the other by a sequence of permutations of rows and columns, and negations of rows and columns. In this paper we summarize what is known about the number of equivalence classes of matrices having maximal determinant. We establish that there are 7 equivalence classes for matrices of order 21 and that there are at least 9,884 equivalence classes for matrices of order 26. The latter result is obtained primarily using a switching technique for producing new designs from old. 1.