We extend the Multi-Level Monte Carlo (MLMC) algorithm in order to quantify uncertainty in the solutions of multi-dimensional hyperbolic systems of conservation laws with uncertain initial data and sources. The algorithm together with the novel load balancing procedure is presented and the scalability on the massively parallel hardware is verified. A new code ALSVID-UQ is described and applied to simulate uncertain solutions of the Euler equations, ideal magnetohydrodynamics (MHD) equations and shallow water equations. Numerical experiments showing the robustness, efficiency and scalability of the proposed algorithm are presented.

120118120348

Centroidal Voronoi tessellations (CVTs) are special Voronoi diagrams for which the generators of the diagrams are also the centers of mass (with respect to a given density function) of the Voronoi cells. CVTs have many uses and applications, several of which we discuss. These may include data compression, image segmentation, clustering, cell biology, territorial behavior of animals, resource allocation, grid generation in volumes and on surfaces, meshless computing, hypercube sampling, and reduced-order modeling. We also discuss a little bit of the theory associated with CVTs and deterministic and probabilistic methods for determining CVTs, including some probabilistic methods that are amenable to parallel processing.

120126110847

In the talk we will consider Hamiltonian perturbations of hyperbolic systems of partial differential equations (PDEs) with one spatial variable. The deformation theory of integrable PDEs will also be discussed. We also consider the behaviour of solutions to such systems at the point of "phase transition" from regular to oscillatory behaviour.

111205111904

Earthquakes are a process in which the internal workings (such as the physical processes of earthquake generation) are only observed indirectly, although the final effects are all too observable! Hidden Markov models (HMMs) are an intuitively attractive idea for analyzing seismicity. The challenge with HMMs is the interpretation of the resulting hidden state process. I will discuss two related applications.

We propose a new model – the Markov-modulated Hawkes process with stepwise decay (MMHPSD) – to investigate long-term patterns in seismicity rate. The MMHPSD is a self-exciting process which switches among different states, in each of which the process has distinguishable background seismicity and decay rates. A variant on the EM algorithm is constructed to fit the model to data possessing immigration-birth features. This is applied to the Landers earthquake sequence, demonstrating that it is capable of capturing changes in the temporal seismicity patterns and the behaviour of main shocks, major aftershocks, secondary aftershocks and periods of quiescence.

This decomposition of the earthquake cycle motivates the construction of a non-linear filter measuring short-term deformation rate changes to extract signals from GPS data. For two case studies of a) deep earthquakes in central North Island, New Zealand, and b) shallow earthquakes in Southern California, an HMM is fitted to the output from the filter. Mutual information analysis indicates that the state having the largest variation of deformation rate contains precursory information that indicates an elevated probability for earthquake occurrence.

111102093050

The evolution of genomes has traditionally been thought to follow a single tree-like pattern of ‘vertical’ inheritance from ancestors to descendents. However, there are a number of biological reasons that individual genes or parts of genes within a genome might not have evolved along the same tree. Identifying discordant gene trees allows biologists to quantify the importance of ‘horizontal’ evolution and to identify the different relationships that constitute the history of genomes. I will present two methods for assessing disagreement between trees. First, I will describe a hierarchical likelihood ratio test that is powerful, but computationally intensive. Second, I will present a clustering method that is more suitable for larger data sets. As the number of complete genome sequences grows, methods for evaluating discordance are becoming increasingly important to evolutionary biologists.

111102092630

In this talk I will present a definition of confounding of effect measures in nonrandomized studies. Although the definition does not require explicit use of counterfactuals or directed acyclic graphs, I will discuss its relationship to them. I will present necessary and sufficient conditions for a variable to be a confounder.

110718104808

The total magnetic charge of particle-like solutions of the EYM equations are determined by the asymptotic behaviour of the Yang-Mills fields. By examining this behaviour we can investigate the question of whether magnetically charged particle-like solutions exist. I will introduce the various ideas and explain what we know about this so far and what remains to be determined.

111028101702

Through the use of microarray technology, researchers are now able to simultaneously measure the expression levels of tens of thousands of genes. Among other things, this allows the construction of profiles of activation of various pathways within tumour samples.

Using breast cancer data, this talk will explore various Bayesian factor regression methods to estimate the probability of pathway activation using gene expression data. The relationship between these probabilities and various histological methods will also be examined.

110923152241

With the success of the Hamilton-Perelman program for proving the Geometrization Conjecture, Ricci flow has become a mathematical celebrity. Almost all discussions of Ricci flow focus on the behavior of the flow on families of three and four dimensional geometries. Why are two dimensional geometries neglected? After a brief review of Ricci flow, we discuss some interesting questions involving surfaces, and answer some of these questions.

111011090644

Eman Alhassan
Dedekind Domains

Fatemah Al Kalaf
Conformal Mapping

Boris Daszuta
Spectral Methods, Wave Equations and the 2-Sphere

Richard McNamara
Parseval Frames

Sam Primrose
Leavitt Path Algebras

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