Title: Mathematical Methods for Analyzing Genomic Data
Speaker: J. B. Nation, University of Hawaii
We describe how some simple modifications of basic methods
give a useful analysis of genetic data, and apply this to
ovarian cancer. A refined singular value decomposition
allows one to look for common biological signals in
gene expression, microRNA and methylation site data.
A clustering technique based on lattice theory identifies
microRNA signals that predict survival. A neural network
using a wavelet transform can be used to choose candidates
for different treatments. Finally, we can identify some
of the biology behind these results, indicating treatment
This is joint work with Gordon Okimoto, Ashkan Zeinalzadeh,
Jenna Maligro, Tammy Yoshioka, and and Tom Wenska of the
University of Hawaii Cancer Center.
Speaker: Anthony Walter, University of Hawaii
Title: Introduction to the Ising model.
Abstract: We will define the Ising model, one of the simplest statistical mechanics
models which exhibits a phase transition. We are looking at a configuration
space on a discrete finite lattice, which is extended to the infinite lattice limit. Depending on some boundary conditions and a parameter $\beta$, in two or more dimensions it can be shown there is a phase transition from a disordered to an ordered phase. In particular we will look at the ferromagnetic case with positive boundary conditions.
We will prove a lower bound of the critical phase transition point.
Title: Bounds on the Number of Covers for Lattices and Related Posets
Abstract: How many covers can there be in a lattice of order n? This question has gone unanswered for decades. In the pursuit of a couple of conjectures, one of which is nearly 40 years old, we have obtained novel results primarily related to asymptotic bounds for lattices and related posets. This talk will involve lattice theory, order theory, combinatorics, graph theory, and analysis.
Reconfiguration in Graph Coloring
In mathematics, as in life, there are often multiple solutions to a question.
Reconfiguration studies whether it is possible to move from one solution to
another following a given set of rules. Is it possible? How long will it take?
In this talk, we will consider reconfiguration of graph coloring.
A proper coloring of a graph is an assignment of a color to each vertex of the
graph so that neighboring vertices have different colors. Suppose we change the
color of just one vertex in a graph coloring. Can we get from one coloring to
another by a sequence of vertex changes so that each step along the way is a
proper coloring? The answer is yes, if we are allowed an unlimited number of
colors. But, what is the fewest colors we can have for this to work? How many
steps might it take? We will look at this, related questions and generalizations.