Past events

We will discuss the mixing rate of the standard random walk on the giant

component of the random graph G(n,p). We tie down the mixing rate precisely

for all values of p greater than (1+c)/n for any positive constant c. We need

to develop a new bound on the mixing time of general Markov chains, inspired

by and extending work of Kannan and Lovasz. This is joint work with Nick

Fountoulakis.

We consider an investment model that can operate in two different

modes. The transition from one mode to the other one is immediate and forms a

sequence of costly decisions made by the investment's management. Each of the

two modes is associated with a rate of payoff that is a function of a state

process which can be an economic indicator such as the price of a given

comodity. We model the state process by a general one-dimensional

diffusion. The objective of the problem is to determine the switching

strategy that maximises a long-term average criterion in a pathwise

sense. Our analysis results in analytic solutions that can easily be

computed, and exhibit qualitatively different optimal behaviours.

The process industries are one of the UK's major sectors and include

petrochemicals, pharmaceuticals, water, energy and the food industry,

amongst others. The design of a processing plant is a difficult task. This

is due to both the need to cater for multiple criteria (such as economics,

environmental and safety) and the use highly complex nonlinear models to

describe the behaviour of individual unit operations in the process. Early

in the design stages, an engineer may wish to use automated design tools to

generate conceptual plant designs which have potentially positive attributes

with respect to the main criteria. Such automated tools typically rely on

optimization for solving large mixed integer nonlinear programming models.

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This talk presents an overview of some of the work done in the Computer

Aided Process Engineering group at UCL. Primary emphasis will be given to

recent developments in hybrid optimization methods, including the use of

graphical interfaces based on problem specific visualization techniques to

allow the engineer to interact with embedded optimization procedures. Case

studies from petrochemical and water industries will be presented to

demonstrate the complexities involved and illustrate the potential benefits

of hybrid approaches.

http://www.maths.ox.ac.uk/notices/events/abstracts/stochastic-analysis/…