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EXPANDING THE TUTTE POLYNOMIAL OF A MATROID OVER THE INDEPENDENT SETS

Koko Kalambay Kayibi

in Combinatorics, Complexity, and Chance: A Tribute to Dominic Welsh

Published in print:
2007
Published Online:
September 2007
ISBN:
9780198571278
eISBN:
9780191718885
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198571278.003.0011
Subject:
Mathematics, Probability / Statistics

This chapter provides direct combinatorial proof of an expansion of the Tutte polynomial by independent sets of the matroid. Another expansion of the Tutte polynomial is presented in terms of ... More


FLOWS AND FERROMAGNETS

Geoffrey Grimmett

in Combinatorics, Complexity, and Chance: A Tribute to Dominic Welsh

Published in print:
2007
Published Online:
September 2007
ISBN:
9780198571278
eISBN:
9780191718885
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198571278.003.0008
Subject:
Mathematics, Probability / Statistics

The Tutte polynomial and its relatives play important roles in matroid theory, computational complexity, and models of statistical physics. They provide the natural way to count and relate a variety ... More


Case studies in Bayesian screening for time-varying model structure: the partition problem

Zesong Liu, Jesse Windle, and James G. Scott

in Bayesian Theory and Applications

Published in print:
2013
Published Online:
May 2013
ISBN:
9780199695607
eISBN:
9780191744167
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199695607.003.0021
Subject:
Mathematics, Probability / Statistics

This chapter presents two case studies involving the problem of time-varying model uncertainty for many different time series observed in parallel. In the first case study, time-varying graphical ... More


Latent Variable Models for Analyzing DNA Methylation

E. Andrés Houseman

in Probabilistic Graphical Models for Genetics, Genomics, and Postgenomics

Published in print:
2014
Published Online:
December 2014
ISBN:
9780198709022
eISBN:
9780191779619
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198709022.003.0015
Subject:
Mathematics, Probability / Statistics, Biostatistics

Deoxyribonucleic acid (DNA) methylation is tightly linked with cellular differentiation. For instance, it has been observed that DNA methylation in tumor cells encodes phenotypic information about ... More


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