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Combinatorial Optimization
The search for many types of combinatorial matrices can be formulated as a Combinatorial Optimization problem, via certain symmetric matrices that correspond naturally to the concepts of the periodic and non-periodic (aperiodic) functions associated to a finite sequence. Therefore one can use powerful Combinatorial Optimization methods to search efficiently for such matrices.
Combinatorial Designs via Computational Algebra
Many types of Combinatorial Designs such as Hadamard matrices and D-optimal designs can be studied via a Computational Algebra formalism. An ideal in a suitable multivariate polynomial ring, is associated the combinatorial design, thus allowing for Computational Algebra tools (Gröbner bases, Hilbert functions) to be used in the study of combinatorial designs. These ideals exhibit many symmetries and are highly structured. The associated algebraic varieties possess equally interesting properties.
A dual binary tree formalism, enables the use of powerful combinatorial optimization techniques (ranking, pruning, simulated annealing, genetic algorithms) as well as high-performance computing techniques. We are currently using high-performance computing (SHARCnet, WestGrid) to complete exhaustive serches for certain types of combinatorial designs (Hadamard matrices and D-optimal designs). The binary tree formalism is appropriate for developing heuristic search criteria as well.
The search for many types of combinatorial matrices can be formulated as a Combinatorial Optimization problem, via certain symmetric matrices that correspond naturally to the concepts of the periodic and non-periodic (aperiodic) functions associated to a finite sequence. Therefore one can use powerful Combinatorial Optimization methods to search efficiently for such matrices.
Combinatorial Designs via Computational Algebra
Many types of Combinatorial Designs such as Hadamard matrices and D-optimal designs can be studied via a Computational Algebra formalism. An ideal in a suitable multivariate polynomial ring, is associated the combinatorial design, thus allowing for Computational Algebra tools (Gröbner bases, Hilbert functions) to be used in the study of combinatorial designs. These ideals exhibit many symmetries and are highly structured. The associated algebraic varieties possess equally interesting properties.
A dual binary tree formalism, enables the use of powerful combinatorial optimization techniques (ranking, pruning, simulated annealing, genetic algorithms) as well as high-performance computing techniques. We are currently using high-performance computing (SHARCnet, WestGrid) to complete exhaustive serches for certain types of combinatorial designs (Hadamard matrices and D-optimal designs). The binary tree formalism is appropriate for developing heuristic search criteria as well.
Research Interests
Papers共 218 篇Author StatisticsCo-AuthorSimilar Experts
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Distributed Ledger Technol. Res. Pract.no. 1 (2024): 1:1-1:2
APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTINGno. 1 (2024): 1-2
Annals of Mathematics and Artificial Intelligenceno. 2-3 (2023): 107-108
ANNALS OF MATHEMATICS AND ARTIFICIAL INTELLIGENCEno. 6 (2023): 901-901
JOURNAL OF COMBINATORIAL DESIGNSno. 4 (2023): 205-261
ANNALS OF MATHEMATICS AND ARTIFICIAL INTELLIGENCE (2023)
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Kotsireas Ilias S.,Koutschan Christoph,Bulutoglu Dursun A., Arquette David M.,Turner Jonathan S.,Ryan Kenneth J.
Special Matricesno. 1 (2023): 814-841
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