Journal of Molecular Graphics and Modelling, ISSN 1093-3263, 06/2017, Volume 74, pp. 89 - 99

[Display omitted] •We report iMOLSDOCK, an induced-fit docking algorithm using mutually orthogonal Latin squares (MOLS).•The benchmarking results of iMOLSDOCK...

Side-chain flexibility | MOLSDOCK | Mutually orthogonal Latin squares | Peptide-protein docking | Docking tool | Receptor flexibility | Induced-fit docking | Molecular docking | SMALL MOLECULE DOCKING | LIGAND-BINDING | PROTEIN | BIOCHEMISTRY & MOLECULAR BIOLOGY | BIOCHEMICAL RESEARCH METHODS | CRYSTALLOGRAPHY | GENETIC ALGORITHM | PEPTIDE DOCKING | 3-DIMENSIONAL STRUCTURE | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MEAN-FIELD TECHNIQUE | ENERGY FUNCTION | MATHEMATICAL & COMPUTATIONAL BIOLOGY | FLEXIBLE DOCKING | Amino Acid Sequence | Thermodynamics | Molecular Docking Simulation - methods | Animals | Hydrogen Bonding | Protein Conformation, beta-Strand | Humans | Protein Binding | Receptors, Cell Surface - chemistry | Software | Binding Sites | Oligopeptides - chemistry | Benchmarks | Algorithms | Peptides | Analysis

Side-chain flexibility | MOLSDOCK | Mutually orthogonal Latin squares | Peptide-protein docking | Docking tool | Receptor flexibility | Induced-fit docking | Molecular docking | SMALL MOLECULE DOCKING | LIGAND-BINDING | PROTEIN | BIOCHEMISTRY & MOLECULAR BIOLOGY | BIOCHEMICAL RESEARCH METHODS | CRYSTALLOGRAPHY | GENETIC ALGORITHM | PEPTIDE DOCKING | 3-DIMENSIONAL STRUCTURE | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MEAN-FIELD TECHNIQUE | ENERGY FUNCTION | MATHEMATICAL & COMPUTATIONAL BIOLOGY | FLEXIBLE DOCKING | Amino Acid Sequence | Thermodynamics | Molecular Docking Simulation - methods | Animals | Hydrogen Bonding | Protein Conformation, beta-Strand | Humans | Protein Binding | Receptors, Cell Surface - chemistry | Software | Binding Sites | Oligopeptides - chemistry | Benchmarks | Algorithms | Peptides | Analysis

Journal Article

Journal of Combinatorial Designs, ISSN 1063-8539, 09/2019, Volume 27, Issue 9, pp. 541 - 551

Commonly, the direct construction and the description of mutually orthogonal Latin squares (MOLS) make use of difference or quasi‐difference matrices. Now...

bounds | permutation code | mutually orthogonal Latin squares | isometry | permutation arrays | MATHEMATICS

bounds | permutation code | mutually orthogonal Latin squares | isometry | permutation arrays | MATHEMATICS

Journal Article

Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, 10/2014, Volume 47, Issue 43, pp. 435303 - 23

We show there is a natural connection between Latin squares and commutative sets of monomials defining geometric structures in finite phase-space of prime...

Latin squares | finite fields | phase space | mutually unbiased bases | DIMENSIONS | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL | UNBIASED BASES | Isomorphism | Permutations | Equivalence | Arrays | Mathematical analysis | Joints | Physics - Quantum Physics

Latin squares | finite fields | phase space | mutually unbiased bases | DIMENSIONS | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL | UNBIASED BASES | Isomorphism | Permutations | Equivalence | Arrays | Mathematical analysis | Joints | Physics - Quantum Physics

Journal Article

IEEE Transactions on Information Theory, ISSN 0018-9448, 06/2004, Volume 50, Issue 6, pp. 1289 - 1291

We develop a connection between permutation arrays that are used in powerline communication and well-studied combinatorial objects, mutually orthogonal latin...

Computer science | Geometry | Algebra | Poles and towers | Mathematics | Error correction codes | Application software | Galois fields | Mutually orthogonal latin squares (MOLS) | Permutation array | Doubly resolvable design | Powerline communications | Permutation code | doubly resolvable design | permutation array | powerline communications | COMPUTER SCIENCE, INFORMATION SYSTEMS | permutation code | CONSTRUCTIONS | mutually orthogonal Latin squares (MOLS) | ENGINEERING, ELECTRICAL & ELECTRONIC | Research | Information theory | Permutations | Arrays | Joints | Combinatorial analysis

Computer science | Geometry | Algebra | Poles and towers | Mathematics | Error correction codes | Application software | Galois fields | Mutually orthogonal latin squares (MOLS) | Permutation array | Doubly resolvable design | Powerline communications | Permutation code | doubly resolvable design | permutation array | powerline communications | COMPUTER SCIENCE, INFORMATION SYSTEMS | permutation code | CONSTRUCTIONS | mutually orthogonal Latin squares (MOLS) | ENGINEERING, ELECTRICAL & ELECTRONIC | Research | Information theory | Permutations | Arrays | Joints | Combinatorial analysis

Journal Article

Theoretical Computer Science, ISSN 0304-3975, 11/2019, Volume 795, pp. 312 - 325

We introduce the orthogonal colouring game, in which two players alternately colour vertices (from a choice of m∈N colours) of a pair of isomorphic graphs...

Orthogonal colouring game | Orthogonal graph colouring | Scoring game | Mutually orthogonal Latin squares | Games on graphs | Strictly matched involution | CHROMATIC NUMBER | COMPUTER SCIENCE, THEORY & METHODS | Computer Science | Discrete Mathematics

Orthogonal colouring game | Orthogonal graph colouring | Scoring game | Mutually orthogonal Latin squares | Games on graphs | Strictly matched involution | CHROMATIC NUMBER | COMPUTER SCIENCE, THEORY & METHODS | Computer Science | Discrete Mathematics

Journal Article

Graphs and Combinatorics, ISSN 0911-0119, 7/2016, Volume 32, Issue 4, pp. 1353 - 1374

A pair of Latin squares, A and B, of order n, is said to be pseudo-orthogonal if each symbol in A is paired with every symbol in B precisely once, except for...

Mutually nearly orthogonal Latin squares | Difference covering array | Latin squares | Mathematics | Pseudo-orthogonal Latin squares | Engineering Design | Combinatorics | 05B15 | MATHEMATICS | MATRICES | COMBINATORIAL DESIGN | Graphs | Construction | Arrays | Symbols | Combinatorial analysis | Mathematics - Combinatorics

Mutually nearly orthogonal Latin squares | Difference covering array | Latin squares | Mathematics | Pseudo-orthogonal Latin squares | Engineering Design | Combinatorics | 05B15 | MATHEMATICS | MATRICES | COMBINATORIAL DESIGN | Graphs | Construction | Arrays | Symbols | Combinatorial analysis | Mathematics - Combinatorics

Journal Article

Utilitas Mathematica, ISSN 0315-3681, 09/2017, Volume 104, pp. 83 - 102

Let N = {0,1, ... , n-1}. A pair of orthogonal Latin squares A, B of order n is called diagonally ordered (DOOLS(n) for short) if the following properties are...

Elementary | Frame mutually orthogonal Latin squares | Strong symmetric | Diagonally ordered magic square | EXISTENCE | MATHEMATICS, APPLIED | frame mutually orthogonal Latin squares | elementary | strong symmetric | STATISTICS & PROBABILITY | ARRAYS

Elementary | Frame mutually orthogonal Latin squares | Strong symmetric | Diagonally ordered magic square | EXISTENCE | MATHEMATICS, APPLIED | frame mutually orthogonal Latin squares | elementary | strong symmetric | STATISTICS & PROBABILITY | ARRAYS

Journal Article

Journal of Combinatorial Theory. Series A, ISSN 0097-3165, 10/2017, Volume 151, pp. 146 - 201

Our main result essentially reduces the problem of finding an edge-decomposition of a balanced r-partite graph of large minimum degree into r-cliques to the...

Mutually orthogonal Latin squares | Edge-decompositions | MATHEMATICS | DENSE GRAPHS | PACKINGS | MINIMUM DEGREE | INTEGER

Mutually orthogonal Latin squares | Edge-decompositions | MATHEMATICS | DENSE GRAPHS | PACKINGS | MINIMUM DEGREE | INTEGER

Journal Article

9.
Full Text
Corrigendum to “The orthogonal colouring game” [Theor. Comput. Sci. 795 (2019) 312–325]

Theoretical Computer Science, ISSN 0304-3975, 01/2020

Journal Article

Discrete Mathematics, ISSN 0012-365X, 2011, Volume 311, Issue 12, pp. 1015 - 1033

Let a b = n 2 . We define an equitable Latin rectangle as an a × b matrix on a set of n symbols where each symbol appears either ⌈ b n ⌉ or ⌊ b n ⌋ times in...

Orthogonal array | Latin rectangle | Mutually orthogonal Latin square | MATHEMATICS | Mathematical analysis | Rectangles | Symbols | Images

Orthogonal array | Latin rectangle | Mutually orthogonal Latin square | MATHEMATICS | Mathematical analysis | Rectangles | Symbols | Images

Journal Article

Communications in Statistics - Theory and Methods, ISSN 0361-0926, 08/2017, Volume 46, Issue 16, pp. 8155 - 8165

Constructions of blocked mixture designs are considered in situations where BLUEs of the block effect contrasts are orthogonal to the BLUEs of the regression...

mutually orthogonal latin squares | incidence matrix | Primary 62K05 | orthogonal arrays | Balanced arrays | Secondary 62K15 | balanced incomplete block design (BIBD) | mixture experiments | orthogonal designs | partially balanced incomplete block design (PBIBD) | STATISTICS & PROBABILITY | Regression coefficients | Orthogonality | Matrices (mathematics) | Incidence | Orthogonal arrays

mutually orthogonal latin squares | incidence matrix | Primary 62K05 | orthogonal arrays | Balanced arrays | Secondary 62K15 | balanced incomplete block design (BIBD) | mixture experiments | orthogonal designs | partially balanced incomplete block design (PBIBD) | STATISTICS & PROBABILITY | Regression coefficients | Orthogonality | Matrices (mathematics) | Incidence | Orthogonal arrays

Journal Article

International Journal of Applied Engineering Research, ISSN 0973-4562, 09/2015, Volume 10, Issue 18, pp. 39425 - 39430

Journal Article

Cryptography and Communications, ISSN 1936-2447, 2010, Volume 2, Issue 2, pp. 221 - 231

There has been much interest in mutually unbiased bases (MUBs) and their connections with various other discrete structures, such as projective planes,...

Finite fields | Mutually unbiased bases | Mutually orthogonal Latin squares | Quantum cryptography | Odd prime powers | MATHEMATICS, APPLIED | COMPUTER SCIENCE, THEORY & METHODS

Finite fields | Mutually unbiased bases | Mutually orthogonal Latin squares | Quantum cryptography | Odd prime powers | MATHEMATICS, APPLIED | COMPUTER SCIENCE, THEORY & METHODS

Journal Article

Discrete Mathematics, ISSN 0012-365X, 2009, Volume 309, Issue 23, pp. 6464 - 6469

The competition graph of a digraph D is the graph which has the same vertex set as D and has an edge between u and v if and only if there exists a vertex x in...

Competition number | Complete multipartite graph | Mutually orthogonal Latin squares | Competition graph | Edge clique cover number | MATHEMATICS

Competition number | Complete multipartite graph | Mutually orthogonal Latin squares | Competition graph | Edge clique cover number | MATHEMATICS

Journal Article

Biochemical and Biophysical Research Communications, ISSN 0006-291X, 2006, Volume 342, Issue 2, pp. 424 - 433

We combine a new, extremely fast technique to generate a library of low energy structures of an oligopeptide (by using mutually orthogonal Latin squares to...

Mutually orthogonal Latin squares | Genetic algorithm | Protein structure prediction | MEAN FIELD-THEORY | INTRAMOLECULAR CONFORMATIONAL OPTIMIZATION | BIOCHEMISTRY & MOLECULAR BIOLOGY | REDUCED REPRESENTATION | mutually orthogonal Latin squares | NUCLEIC-ACIDS | genetic algorithm | BIOPHYSICS | AVIAN PANCREATIC-POLYPEPTIDE | ENERGY FUNCTION | SEQUENCE | FORCE-FIELD | SECONDARY STRUCTURE | protein structure prediction | VILLIN HEADPIECE SUBDOMAIN | Protein Structure, Tertiary | Microfilament Proteins - chemistry | Predictive Value of Tests | Computational Biology - methods | Melitten - chemistry | Oligopeptides - genetics | Pancreatic Polypeptide - chemistry | Tryptophan - genetics | Proto-Oncogene Proteins c-myb - genetics | Tryptophan - chemistry | Pancreatic Polypeptide - genetics | Peptide Library | Algorithms | Animals | Chickens | Protein Conformation | Proto-Oncogene Proteins c-myb - chemistry | Melitten - genetics | Microfilament Proteins - genetics | Oligopeptides - chemistry | Proteins | Oligopeptides

Mutually orthogonal Latin squares | Genetic algorithm | Protein structure prediction | MEAN FIELD-THEORY | INTRAMOLECULAR CONFORMATIONAL OPTIMIZATION | BIOCHEMISTRY & MOLECULAR BIOLOGY | REDUCED REPRESENTATION | mutually orthogonal Latin squares | NUCLEIC-ACIDS | genetic algorithm | BIOPHYSICS | AVIAN PANCREATIC-POLYPEPTIDE | ENERGY FUNCTION | SEQUENCE | FORCE-FIELD | SECONDARY STRUCTURE | protein structure prediction | VILLIN HEADPIECE SUBDOMAIN | Protein Structure, Tertiary | Microfilament Proteins - chemistry | Predictive Value of Tests | Computational Biology - methods | Melitten - chemistry | Oligopeptides - genetics | Pancreatic Polypeptide - chemistry | Tryptophan - genetics | Proto-Oncogene Proteins c-myb - genetics | Tryptophan - chemistry | Pancreatic Polypeptide - genetics | Peptide Library | Algorithms | Animals | Chickens | Protein Conformation | Proto-Oncogene Proteins c-myb - chemistry | Melitten - genetics | Microfilament Proteins - genetics | Oligopeptides - chemistry | Proteins | Oligopeptides

Journal Article

16.
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Searching for Mutually Orthogonal Latin Squares via integer and constraint programming

European Journal of Operational Research, ISSN 0377-2217, 2006, Volume 173, Issue 2, pp. 519 - 530

This paper applies algorithms integrating Integer Programming (IP) and Constraint Programming (CP) to the Mutually Orthogonal Latin Squares (MOLS) problem. We...

Integer programming | Mutually Orthogonal Latin Squares | Constraints satisfaction | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | integer programming | constraints satisfaction | mutually orthogonal Latin squares | SETS | Usage | Algorithms | Functions, Orthogonal | Tests, problems and exercises | Management science

Integer programming | Mutually Orthogonal Latin Squares | Constraints satisfaction | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | integer programming | constraints satisfaction | mutually orthogonal Latin squares | SETS | Usage | Algorithms | Functions, Orthogonal | Tests, problems and exercises | Management science

Journal Article

Journal of Statistical Planning and Inference, ISSN 0378-3758, 03/2013, Volume 143, Issue 3, pp. 573 - 582

An (n×n)/ksemi-Latin square is an n×n square array in which nk distinct symbols (representing treatments) are placed in such a way that there are exactly k...

Block design | Block design efficiency measures | Mutually orthogonal Latin squares | Semi-Latin square | DESIGN package for GAP | Construction and enumeration of combinatorial designs | Design optimality | Algebraic computation | STATISTICS & PROBABILITY | BLOCK-DESIGNS

Block design | Block design efficiency measures | Mutually orthogonal Latin squares | Semi-Latin square | DESIGN package for GAP | Construction and enumeration of combinatorial designs | Design optimality | Algebraic computation | STATISTICS & PROBABILITY | BLOCK-DESIGNS

Journal Article

Journal of Combinatorial Designs, ISSN 1063-8539, 06/2012, Volume 20, Issue 6, pp. 265 - 277

Let n and k be integers, with n>1 and k>0. An (n×n)/k semi‐Latin square S is an n×n array, whose entries are k‐subsets of an nk‐set, the set of symbols of S,...

transitive permutation groups | Schur-optimality | mutually orthogonal Latin squares | semi-Latin squares | MATHEMATICS | NON-EXISTENCE | BLOCK-DESIGNS

transitive permutation groups | Schur-optimality | mutually orthogonal Latin squares | semi-Latin squares | MATHEMATICS | NON-EXISTENCE | BLOCK-DESIGNS

Journal Article

Journal of Statistical Planning and Inference, ISSN 0378-3758, 2001, Volume 95, Issue 1, pp. 9 - 48

In the two centuries since Euler first asked about mutually orthogonal latin squares, substantial progress has been made. The biggest breakthroughs came in...

Mutually orthogonal latin squares | Transversal design | Block design | Orthogonal array | 51E10 | 51E21 | 05B15 | 51E05 | 05B25 | 05B05 | EXISTENCE | orthogonal array | FINITE PROJECTIVE PLANES | transversal design | HUGHES PLANE | STATISTICS & PROBABILITY | block design | INCOMPLETE TRANSVERSAL DESIGNS | ORDER | mutually orthogonal latin squares | 4 MOLS | SUBSQUARES | SETS | SUBPLANES | SPECTRUM

Mutually orthogonal latin squares | Transversal design | Block design | Orthogonal array | 51E10 | 51E21 | 05B15 | 51E05 | 05B25 | 05B05 | EXISTENCE | orthogonal array | FINITE PROJECTIVE PLANES | transversal design | HUGHES PLANE | STATISTICS & PROBABILITY | block design | INCOMPLETE TRANSVERSAL DESIGNS | ORDER | mutually orthogonal latin squares | 4 MOLS | SUBSQUARES | SETS | SUBPLANES | SPECTRUM

Journal Article

Journal of the Australian Mathematical Society, ISSN 1446-7887, 12/2009, Volume 87, Issue 3, pp. 409 - 420

For a class of 'linear' sudoku solutions, we construct Mutually orthogonal families of maximal size for all square orders, and we show that all such solutions...

Mutually orthogonal latin squares | Sudoku group | Orthogonal latin squares | Sudoku | MATHEMATICS | mutually orthogonal latin squares | sudoku | orthogonal latin squares | sudoku group

Mutually orthogonal latin squares | Sudoku group | Orthogonal latin squares | Sudoku | MATHEMATICS | mutually orthogonal latin squares | sudoku | orthogonal latin squares | sudoku group

Journal Article

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