Algebraic combinatorics for computational biology
نویسنده
چکیده
Algebraic combinatorics for computational biology by Nicholas Karl Eriksson Doctor of Philosophy in Mathematics University of California, Berkeley Professor Bernd Sturmfels, Chair Algebraic statistics is the study of the algebraic varieties that correspond to discrete statistical models. Such statistical models are used throughout computational biology, for example to describe the evolution of DNA sequences. This perspective on statistics allows us to bring mathematical techniques to bear and also provides a source of new problems in mathematics. The central focus of this thesis is the use of the language of algebraic statistics to translate between biological and statistical problems and algebraic and combinatorial mathematics. The wide range of biological and statistical problems addressed in this work come from phylogenetics, comparative genomics, virology, and the analysis of ranked data. While these problems are varied, the mathematical techniques used in this work share common roots in the field of combinatorial commutative algebra. The main mathematical theme is the use of ideals which correspond to combinatorial objects such as magic squares, trees, or posets. Biological problems suggest new families of ideals, and the study of these ideals can in some cases be useful for biology. Professor Bernd Sturmfels Dissertation Committee Chair
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Sergi Elizalde
My main area of research is combinatorics. I like not only its beauty as a subject but also its wide applicability throughout mathematics and science. I have diverse mathematical interests, and combinatorics is the bridge that connects them. Even though I have a predilection for enumerative questions, I have also worked on algebraic combinatorics, computational biology, number theory, and combi...
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