Home > ~mathmeet > Newplymouth

Here is the preliminary timetable, indicating who will be speaking when.

More details as they come to hand.

Sunday | Monday | Tuesday | Thursday | Friday | Saturday | ||
---|---|---|---|---|---|---|---|

0845 - 1015 |
Andreas Dress | Neil Robertson | Terry Speed |
Richard Stanley | Karl Broman | Lior Pachter | |

1030 - 1130 |
Martin Grohe | Tandy Warnow | Richard Stanley |
Mike Hallet | Mike Hallet | Karl Broman | |

1145 - 1245 |
Tandy Warnow | Paul Seymour | Neil Robertson |
Martin Grohe | Terry Speed | Tandy Warnow | |

1900 - 2000 |
Andreas Dress | Martin Grohe | Paul Seymour |
Lior Pachter | |

**Andreas Dress**-
- 1.
__Crypto-Isomorphisms in Combinatorial Phylogenetics__ Like other combinatorial structures, the so-called X-trees much studied in phylogenetic analysis also have many rather distinct, yet perfectly equivalent descriptions. They can be described:

- in graph-theoretical terms as leaf-labelled (and edge-weighted) trees,
- in terms of 'certain' metrics defined on X,
- in terms of 'certain' collections of (weighted) X-splits, and
- in terms of 'certain' collections of (weighted) quartet trees whose leaves are drawn from X.

While proving the corresponding "crypto-isomorphism theorems" (i.e. the equivalence of those various descriptions) is not very hard, the point of keeping all those concepts in mind when dealing with phylogenetic analysis is that

- each one has distinct --- and not any more equivalent ---
*relaxations*derived by relaxing one or the other of the requirements necessary and sufficient for the existence of an associated X-tree, and - trying to relate these relaxations to each other as well as to
real-world data can reveal
- important aspects of those concepts themselves, as well as
- intrinsic inconsistencies of any data set in question.

The lecture will provide a review of the various combinatorial concepts mentioned above and discuss how these concepts and, in particular, their various relaxations are related with each other.

- 2.
__Quartets and Ranks in Phylogenetic Combinatorics and Cluster Analysis__ -
Based on the previous lecture, the evening lecture will deal specifically with recent progress regarding "quartet analysis" and "rank-based methods in biological data analysis".

**Neil Robertson****Terry Speed**-
Terry suggests weeks 7 and 8 of http://www.stat.Berkeley.EDU/users/terry/Classes/s246.2002/index.html as background reading.

**Richard Stanley**-
Richard Stanley's overall title is

__An introduction to generating functions__. He intends to cover:- The idea of generating functions.
- Rational generating functions.
- Algebraic generating functions.
- Exponential generating functions, trees and Lagrange inversion.

However, he is currently undecided as to how to allocate the topics over his two lectures.

He suggests that the closest paper to the topic is his own paper, "Generating Functions", in

*Studies in Combinatorics*(G.-C. Rota, ed.), Mathematical Association of America, 1978, pp 100-141, or (for the very keen) his books,*Enumerative Combinatorics*, volumes 1 and 2.- Slides
**Karl Broman**-
Karl suggests the following background readings:

- McPeak, M S (1996), Introduction to recombination and linkage analysis.
In: Speed T P, Waterman M S (eds)
*Genetic mapping and DNA sequencing, IMA volumes on Mathematics and its Applications, Volume 81*, Springer-Verlag, or available here. - Broman K W (2001), Review of statistical methods for QTL mapping in
experimental crosses.
*Lab Animal*30(7):44-52, or here.

- McPeak, M S (1996), Introduction to recombination and linkage analysis.
In: Speed T P, Waterman M S (eds)
**Lior Pachter**-
__Mathematics of Gene Finding and Alignment__Lior Pachter plans to talk about hidden Markov models and their applications to gene finding and alignment.

His first talk (more introductory) will survey the basics of alignment and gene finding, highlighting interesting connections to combinatorics.

The second talk will go more in detail into comparative genomics and current research on probabilistic methods for alignment, gene finding, and phylogeny (time permitting) using HMMs.

**Martin Grohe**-
__Logic, Graph Theory and Complexity__ **Tandy Warnow**-
- 1.
__Fast Converging Phylogenetic Reconstruction Methods__ In this talk we address a statistical aspect of the performance of phylogeny reconstruction methods -- namely, the number of sites (i.e. the sequence length) needed for the method to reconstruct the true tree with high probability. We present results showing that standard polynomial time methods will reconstruct the true tree given sequences of lengths that are exponential in the largest evolutionary distance in the tree. We then describe new methods (some developed in collaboration with Mike Steel) which reconstruct the true tree with high probability from polynomial length sequences. These methods are graph-theoretic, and exploit chordal graph theory to obtain their performance guarantees.

- 2.
__Open problems in phylogenetics__ - 3.
__Historical Linguistics__ A beautiful graph theory question, "triangulating colored graphs", turns out to be the foundation of the inference of evolutionary history of languages. Here we will present the theory, describe both combinatorial and graph theoretic algorithms to solve this problem, and describe our analysis of the Indo-European family of languages.

- 1.
**Mike Hallet****Paul Seymour**

- 1.