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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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