Past

http://www.maths.ox.ac.uk/arg/

The talk starts with a general introduction of the convex

quadratic semidefinite programming problem (QSDP), followed by a number of

interesting examples arising from finance, statistics and computer sciences.

We then discuss the concept of primal nondegeneracy for QSDP and show that

some QSDPs are nondegenerate and others are not even under the linear

independence assumption. The talk then moves on to the algorithmic side by

introducing the dual approach and how it naturally leads to Newton's method,

which is quadratically convergent for degenerate problems. On the

implementation side of the Newton method, we stress that direct methods for

the linear equations in Newton's method are impossible simply because the

equations are quite large in size and dense. Our numerical experiments use

the conjugate gradient method, which works quite well for the nearest

correlation matrix problem. We also discuss difficulties for us to find

appropriate preconditioners for the linear system encountered. The talk

concludes in discussing some other available methods and some future topics.

http://www.maths.ox.ac.uk/oxmos/meetings

\\Common\dfs\htdocs\www\maintainers\reception\enb\abstracts\topology\mt06\cobordism.shtml

\\Common\dfs\htdocs\www\maintainers\reception\enb\abstracts\string-theory\mt06\pioline.shtml

Aggregation refers to the thermodynamically favoured coalescence of individual molecular units (monomers) into dense clusters. The formation of liquid drops in oversaturated vapour, or the precipitation of solids from liquid solutions, are 'everyday' examples. A more exotic example, the crystallization of hydrophobic proteins in lipid bilayers, comes from current biophysics.

This talk begins with the basic physics of the simplest classical model, in which clusters grow by absorbing or expelling monomers, and the free monomers are transported by diffusion. Next, comes the description of three successive 'eras' of the aggregation process: NUCLEATION is the initial creation of clusters whose sizes are sufficiently large that they most likely continue to grow, instead of dissolving back into monomers.

The essential physical idea is growth by unlikely fluctuations past a high free energy barrier. The GROWTH of the clusters after nucleation depletes the initial oversaturation of monomer. The free energy barrier against nucleation increases, effectively shutting off any further nucleation. Finally, the oversaturation is so depleted, that the largest clusters grow only by dissolution of the smallest. This final era is called COARSENING.

The initial rate of nucleation and the evolution of the cluster size distribution during coarsening are the subjects of classical, well known models. The 'new meat' of this talk is a 'global' model of aggregation that quantitates the nucleation era, and provides an effective initial condition for the evolution of the cluster size distribution during growth and coarsening. One by-product is the determination of explicit scales of time and cluster size for all three eras. In particular, if G_* is the initial free energy barrier against nucleation, then the characteristic time of the nucleation era is proportional to exp(2G_*/5k_bT), and the characteristic number of monomers in a cluster during the nucleation era is exp(3G_*/5k_bT). Finally, the 'global' model of aggregation informs the selection of the self similar cluster size distribution that characterizes 'mature' coarsening.

\\Common\dfs\htdocs\www\maintainers\reception\enb\abstracts\logic\mt06\taylor