MSOR School Colloquia

In addition to the regular seminar series there is a series of Colloquia delivered by members of the School.

• 19 March 2010; Shirley Pledger: "Fuzzy Ecological Communities"
• 23 April 2010; Noam Greenberg: "What is Model Theory?"
• 28 May 2010; Mark McGuinness: "Exploding Rock"

All talks are at 4pm on Fridays in Laby LT118.

The organiser for the series is Rob.Goldblatt@msor.vuw.ac.nz.

Abstracts and details of previous colloquia are here.

Fuzzy Ecological Communities

Shirley Pledger (4pm Friday 19 March 2010, Laby LT118)

In studies of ecological communities, a typical data set is a matrix with one row per species and one column per sample. The matrix may contain incidence data (presence/absence, binary data 1/0), or abundance data (count data, the number of individuals of each species at each site).

Traditional analyses use multivariate methods such as multidimensional scaling, principal component analysis, cluster analysis, ordination, correspondence analysis, association analysis, and direct and indirect gradient analysis. These methods are essentially mathematical rather than statistical, and they provide dimension reduction and plots in low dimensions in order to illustrate the main features of the data.

By introducing statistical mixture models, we may switch to fuzzy clustering, in which species and/or samples are allocated to groups probabilistically. Exploring these models, we obtain not only low-dimensional graphical results similar to those from traditional analyses, but also the benefits of available methods for comparing models, testing hypotheses and estimating parameters. For example, (i) if species are to be clustered into "functional groups" (occurring in similar habitats), how many clusters are indicated by the data? (ii) can the samples be ordered (using their species compositions) along a single axis, or are more dimensions needed to represent the patterns?

Although the examples will be from community ecology, these models have applications in a wide range of disciplines.

No detailed knowledge of mathematics, statistics or, indeed, ecology is required of the audience.

What is Model Theory?

Noam Greenberg (4pm Friday 23 April 2010, Laby LT118)

Exploding Rock

Mark McGuiness (4pm Friday 28 May 2010, Laby LT118)

The mathematical model presented here is motivated by recent experimental work, in which a vertical column of rock underlarge pressure is suddenly depressurised, so that it explodes, in a sequence of horizontal fractures that forms from the top down. The resulting blocks are lifted off and ejected by the escaping gas. This experiment provides a framework for understanding the way in which catastrophic explosion can occur, and is motivated by the corresponding phenomenon of magmatic explosion during Vulcanian eruptions. I will summarise a theoretical model built to describe these results, and show that it is capable of describing both the primary sequence of fracturing, and the secondary intra-block fracturing.