MSI Weekly Bulletin - Week starting Monday 20 February, 2006

This talk will outline the surrogate management framework, which is presently built on the filter MADS method for general nonlinear programming without derivatives. The focus is on the numerical results, with a brief introduction to the MADS algorithm and a slight mention of the convergence results. This line of research was motivated by industrial applications, indeed, by a question I was asked by Paul Frank of Boeing Phantom Works. His group was often asked for help in dealing with very low dimensional design problems driven by expensive simulations. Everyone there was dissatisfied with the common practice of substituting inexpensive surrogates for the expensive "true" objective and constraint functions in the optimal design formulation. I hope to demonstrate in this talk just how simple the answer to Paul's question is. The surrogate management framework has been implemented successfully by several different groups, and it is unreasonably effective in practice, where most of the application are extended valued and certainly nondifferentiable. This has forced my colleagues and me to begin to learn some nonsmooth analysis, which in turn has led to MADS, a replacement for the GPS infrastructure algorithm.

In this talk, I will try to give the flavor of the process of applying optimization for the first time to a class of problems. In this case, the problem requires collaboration between a group of tsunami experts and a group of optimizers, but there are more general lessons here to be learned. It is typical that neither group knew much about the other\'s capabilities and concerns at the start. The major goal of thhe collaboration is to help formulate realistic goals for the project and then to achieve those goals. The first step entails learning a bit of the client\'s terminology, and finding out what can be computed by the client group that might feed an optimization package. The burden is largely on the optimization group for this process, but in the present case, the tsunami experts were used to working with their own client groups, like the state and local governments where tsunamis threaten, and so they were remarkably helpful in the process. A major milestone is the formulation of a test problem. Another is to successfully run optimization on the test problem and then interpret the results and reformulate the test problem. However, a great deal of progress must be made before this is possible. First it is necessary to formulate a reasonable test problem to see how difficult the optimization problem will be. The tsunami problem is of fairly low dimension, but nasty. It is at least nondifferentiable, if not discontinuous. Our optimization group is experienced in working on real-world applications, and so we are used to such problems, which motivated the development of our NOMAD package. The project is now at a point that we can tackle the real buoy location problem, and it has led us to plans to direct our research towards modifications of NOMAD that will make it more efficient for the increasingly important class of sensor location problems.

The information content of DNA can be qualitatively classed into two types: "digital", pertaining especially to the genetic code, while regulatory features, for example, can be thought of as having "analog" functionality. Traditionally Bioinformatics has placed emphasis on applications of the former kind. On the other hand numerous experiments suggest base sequence often determines local structural and mechanical properties of the B-DNA helix, which play key roles in regulatory processes. In this talk I will describe, using simple models of DNA deformation, how one can investigate the hypothesis that DNA-binding proteins have higher affinity for target sites in regions which are susceptible to deformation. In particular in the Escherichia coli genome we find characteristic correlations between local helix flexibility and binding sites for RNA polymerase plus other DNA-bending proteins such as FIS and CAP. Finally potential applications, such as extraction of such "analog" information from genome sequences will be briefly discussed.

The populations of seals in the Eastern North Atlantic continue to grow and their large numbers raise concerns among fisherman who feel that they contributed substantially to the collapse of the code stock and are preventing the recovery of this stock. There is both scientific and political interest in determining what seals eat. In this talk, I will describe the statistical approach we've taken in answering this question. To do this requires we look at the data, formulate a model, fit the data, assess the uncertainty in our estimates and validate our results. A key biological fact is that as seals eat, the fatty acid compisition of their prey is reflected in the fatty acid composition of the seal. My collaborators, Sara Iverson (Biology, Dalhousie) and Don Bowen (Fisheries and Oceans) have obtained reliable fatty acid profiles of both seals and their potential prey on the Scotian Shelf giving us the data required to do the estimation. Much of the data analysis and model fitting was done in collaboration with Wade Blanchard (Dalhousie). Connie Steward (UNBSJ) made very good progress in developing reliable confidence interval estimates in her PhD thesis.