This talk will describe methods for computing sharp upper bounds on the probability of a random vector falling outside of a convex set, or on the expected value of a convex loss function, for situations in which limited information is available about the probability distribution. Such bounds are of interest across many application areas in control theory, mathematical finance, machine learning and signal processing. If only the first two moments of the distribution are available, then Chebyshev-like worst-case bounds can be computed via solution of a single semidefinite program. However, the results can be very conservative since they are typically achieved by a discrete worst-case distribution. The talk will show that considerable improvement is possible if the probability distribution can be assumed unimodal, in which case less pessimistic Gauss-like bounds can be computed instead. Additionally, both the Chebyshev- and Gauss-like bounds for such problems can be derived as special cases of a bound based on a generalised definition of unmodality.

Accurate simulation of coastal and hydraulic structures is challenging due to a range of complex processes such as turbulent air-water flow and breaking waves. Many engineering studies are based on scale models in laboratory flumes, which are often expensive and insufficient for fully exploring these complex processes. To extend the physical laboratory facility, the US Army Engineer Research and Development Center has developed a computational flume capability for this class of problems. I will discuss the turbulent air-water flow model equations, which govern the computational flume, and the order-independent, unstructured finite element discretization on which our implementation is based. Results from our air-water verification and validation test set, which is being developed along with the computational flume, demonstrate the ability of the computational flume to predict the target phenomena, but the test results and our experience developing the computational flume suggest that significant improvements in accuracy, efficiency, and robustness may be obtained by incorporating recent improvements in numerical methods.

Key Words:

Multiphase flow, Navier-Stokes, level set methods, finite element methods, water waves

A recommendation system for multi-modal journey planning could be useful to travellers in making their journeys more efficient and pleasant, and to transport operators in encouraging travellers to make more effective use of infrastructure capacity.

Journeys will have multiple quantifiable attributes (e.g. time, cost, likelihood of getting a seat) and other attributes that we might infer indirectly (e.g. a pleasant view).  Individual travellers will have different preferences that will affect the most appropriate recommendations.  The recommendation system might build profiles for travellers, quantifying their preferences.  These could be inferred indirectly, based on the information they provide, choices they make and feedback they give.  These profiles might then be used to compare and rank different travel options.

Classically, basin modelling is undertaken with very little a priori knowledge. Alongside the challenge of improving the general fidelity and utility of the modelling systems, is the challenge of constraining these systems with unknowns and uncertainties in such a way that models (and derived simulation results) can be readily regenerated/reevaluated in the light of new empirical data obtained during the course of exploration, development and production activities.

This talk investigates the discovery of an intriguing and fundamental connection between the famous but apparently unrelated work of two mathematicians of late antiquity, Pappus and Diophantus. This link went unnoticed for well over 1500 years until the publication of two groundbreaking but again ostensibly unrelated works by two German mathematicians at the close of the 19th century. In the interim, mathematics changed out of all recognition, with the creation of numerous new mathematical subjects and disciplines, without which the connection might never have been noticed in the first place. This talk examines the chain of mathematical events that led to the discovery of this remarkable link between two seemingly distinct areas of mathematics, encompassing number theory, finite-dimensional real normed algebras, combinatorial design theory, and projective geometry, and including contributions from mathematicians of all kinds, from the most distinguished to the relatively unknown.

Adrian Rice is Professor of Mathematics at Randolph-Macon College in Ashland, Virginia, where his research focuses on the history of 19th- and early 20th-century mathematics. He is a three-time recipient of the Mathematical Association of America's awards for outstanding expository writing.