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DEFORMATIONS, DISCRETE SAMPLING, AND ROBUST TORIC IDEALS

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Material Information

Title:
DEFORMATIONS, DISCRETE SAMPLING, AND ROBUST TORIC IDEALS
Physical Description:
Book
Language:
English
Creator:
Duff, Timothy F.E.
Publisher:
New College of Florida
Place of Publication:
Sarasota, Fla.
Publication Date:

Thesis/Dissertation Information

Degree:
Bachelor's ( B.A.)
Degree Grantor:
New College of Florida
Degree Divisions:
Natural Sciences
Area of Concentration:
Mathematics
Faculty Sponsor:
McDonald, Patrick

Subjects

Genre:
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, territorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract:
A fundamental theorem of algebraic statistics is that a very general class of sampling problems is equivalent to the problem of computing a presentation for a (not necessarily normal) toric ideal. A special case of this problem is that of generating a random multigraph on a fixed vertex set with fixed degrees; algebraically, this problem is formulated in the setting of toric graph ideals. A basic deficiency of many presentations obtained in solving the algebraic problem is that they do not transfer to the generalized problem in which certain edges are restricted. This deficiency is avoided in the case of a robust graph - one whose corresponding toric ideal is minimally generated by its universal Grobner basis. Such toric ideals are interesting in an algebro-geometric setting, as their zeroth Betti numbers are preserved under at deformation. This thesis provides a review of commutative algebra and Grobner basis theory in the context of deformations and algebraic statistics, as well as a classifi- cation of robust graph ideals. The classification is given in terms of combinatorial conditions on a special class of elementary walks. As an application, we show that the operation of barycentric subdivision from simplicial topology always produces a robust graph, and discuss the implications for certain independence problems in algebraic statistics. We conclude with a discussion of some possible generalizations and open problems.
Statement of Responsibility:
by Timothy F.E. Duff
Thesis:
Thesis (B.A.) -- New College of Florida, 2014
General Note:
RESTRICTED TO NCF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE
Bibliography:
Includes bibliographical references.
General Note:
This bibliographic record is available under the Creative Commons CC0 public domain dedication. The New College of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
General Note:
Faculty Sponsor: McDonald, Patrick

Record Information

Source Institution:
New College of Florida
Holding Location:
New College of Florida
Rights Management:
Applicable rights reserved.
Resource Identifier:
Classification:
S.T. 2014 D84
System ID:
AA00024733:00001

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