MSI Weekly Bulletin - Week starting Monday 25 June, 2007

The (direct) first passage problem is a well known problem in the theory of stochastic processes: Given a stochastic process $X_t$ and a function $c(t): [0,\infty) \to \mathbb{R}$, and defining $\tau(c) := \inf \{ t >0 : W_t \geq c(t) \}$, the direct problem is to find the probability distribution of $\tau(c)$. The {\em inverse} first passage problem is as follows: Given a stochastic process $X_t$ and a probability measure $Q$ on $(0,\infty]$, find a function $c(t): [0,\infty) \to \mathbb{R} $ for which the first passage time $\tau(c)$ has distribution $Q$. We will discuss a solution to the inverse first passage problem for one-dimensional Brownian motion. BIO: http://www.ms.unimelb.edu.au/~zab/

There is a great deal of statistical regularity in the way that organisms age and die. Biologists and biodemographers have sought to explain these patterns as a response to natural selection. In this lecture Professor Evans will help explain some topics such as the asymmetric segregation of damage between daughter cells in bacteria and yeast, the flattening of mortaility rates for complex organisms in extreme old age, and the ubiquitous Gompertz mortality curve. He will also show how some relatively simple ideas from probability theory shed light on these phenomena.

A code is simply a set of n-tuples, called codewords, over a finite alphabet -- the most commonly studied being binary codes, where the alphabet is {0, 1}. If the alphabet is a finite field F and the code forms a vector space over F then the code is called linear. Two codes are equivalent if one can be obtained from the other via a permutation of the coordinates. Deciding equivalence of linear codes is an analogue of the famous Graph Isomorphism Problem. Both have been shown to be almost certainly not NP-complete and both have eluded all efforts of finding a polynomial time solution. Despite this complexity theoretical limbo, extensive work has been done over the years on developing practical algorithms for solving these problems; that is, algorithms that are efficient for most instances of their respective problems. Brendan McKay's nauty software package provides such functionality for graphs whereas the Magma package does so for linear codes. This talk will introduce the abstract commonalities of such algorithms and then touch on current work to develop a linear code algorithm that gives better performance than those currently used. This work includes implementing the algorithm using nauty's existing machinery; a demonstration of this new software on a few examples will be given.

Molecular dynamics (MD) simulations have become a popular tool to study proteins. Based on Dr. Conrad Burden & Dr. Aaron Oakley's protein analysis R software, we have developed in this work a user-friendly tool that can compare atom trajectories from these MD simulations with experimental data from x-ray crystallography. In this talk we present two software implementations. The first one, R software that compares two experimental data type PDB files, and the second one, a binary software that analyses MD simulated trajectories and generates one or more PDB files.

The optimal transport problem was introduced by the French mathematician Gaspard Monge around 1780: given an initial and a final distributions of mass, how should one match the initial and final positions so as to minimize the total cost of transportation? Independent discoveries by Brenier, Cullen and Mather at the end of the eighties have led to a complete reshaping of the field, with connections to partial differential equations, dynamical systems and fluid mechanics. Unexpected connections with Riemannian geometry were discovered in the past few years. It was found in particular that the evolution of mass distributions along optimal transport is a robust synthetic way to characterize bounds on the Ricci curvature, which led to the solution of some longstanding problems in nonsmooth Riemannian geometry.

It is common in applied statistics to carry out a preliminary model selection using e.g. AIC, BIC or hypothesis tests. This is usually followed by the statistical inference of interest, using the same data, based on the assumption that the selected model had been given to us a priori. This assumption is false and it leads to invalid inferences. Breiman (1992) calls this "a quiet scandal in the statistical community". The purpose of the talk is to (a) describe the depth of this scandal and (b) to describe the speaker's proposed solution to this problem.