Numerical Analysis Group Internal Seminar

27 February 2018
14:00
Tabea Tscherpel
Abstract

The object of this talk is a class of generalised Newtonian fluids with implicit constitutive law.
Both in the steady and the unsteady case, existence of weak solutions was proven by Bul\'\i{}\v{c}ek et al. (2009, 2012) and the main challenge is the small growth exponent qq and the implicit law.
I will discuss the application of a splitting and regularising strategy to show convergence of FEM approximations to weak solutions of the flow. 
In the steady case this allows to cover the full range of growth exponents and thus generalises existing work of Diening et al. (2013). If time permits, I will also address the unsteady case.
This is joint work with Endre Suli.

  • Numerical Analysis Group Internal Seminar
27 February 2018
14:30
Simon Vary
Abstract

Low-rank plus sparse matrices arise in many data-oriented applications, most notably in a foreground-background separation from a moving camera. It is known that low-rank matrix recovery from a few entries (low-rank matrix completion) requires low coherence (Candes et al 2009) as in the extreme cases when the low-rank matrix is also sparse, where matrix completion can miss information and be unrecoverable. However, the requirement of low coherence does not suffice in the low-rank plus sparse model, as the set of low-rank plus sparse matrices is not closed. We will discuss the relation of non-closedness of the low-rank plus sparse model to the notion of matrix rigidity function in complexity theory.

  • Numerical Analysis Group Internal Seminar
6 March 2018
14:00
Oliver Sheridan-Methven
Abstract

The latest CPUs by Intel and ARM support vectorised operations, where a single set of instructions (e.g. add, multiple, bit shift, XOR, etc.) are performed in parallel for small batches of data. This can provide great performance improvements if each parallel instruction performs the same operation, but carries the risk of performance loss if each needs to perform different tasks (e.g. if else conditions). I will present the work I have done so far looking into how to recover the full performance of the hardware, and some of the challenges faced when trading off between ever larger parallel tasks, risks of tasks diverging, and how certain coding styles might be modified for memory bandwidth limited applications. Examples will be taken from finance and Monte Carlo applications, inspecting some standard maths library functions and possibly random number generation.

  • Numerical Analysis Group Internal Seminar
6 March 2018
14:30
Paul Moore
Abstract

Forecasting a diagnosis of Alzheimer’s disease is a promising means of selection for clinical trials of Alzheimer’s disease therapies. A positive PET scan is commonly used as part of the inclusion criteria for clinical trials, but PET imaging is expensive, so when a positive scan is one of the trial inclusion criteria it is desirable to avoid screening failures. In this talk I will describe a scheme for pre-selecting participants using statistical learning methods, and investigate how brain regions change as the disease progresses.  As a means of generating features I apply the Chen path signature. This is a systematic way of providing feature sets for multimodal data that can probe the nonlinear interactions in the data as an extension of the usual linear features. While it can easily perform a traditional analysis, it can also probe second and higher order events for their predictive value. Combined with Lasso regularisation one can auto detect situations where the observed data has nonlinear information.

  • Numerical Analysis Group Internal Seminar