Fri, 09 Nov 2018

12:30 - 13:00
L4

Using signatures to predict amyotrophic lateral sclerosis progression

Imanol Pérez
(University of Oxford)
Abstract

Medical data often comes in multi-modal, streamed data. The challenge is to extract useful information from this data in an environment where gathering data is expensive. In this talk, I show how signatures can be used to predict the progression of the ALS disease.

Fri, 09 Nov 2018

12:00 - 12:30
L4

Detection of Transient Data using the Signature Features

Hao Ni
(University College London)
Abstract

In this talk, we consider the supervised learning problem where the explanatory variable is a data stream. We provide an approach based on identifying carefully chosen features of the stream which allows linear regression to be used to characterise the functional relationship between explanatory variables and the conditional distribution of the response; the methods used to develop and justify this approach, such as the signature of a stream and the shuffle product of tensors, are standard tools in the theory of rough paths and provide a unified and non-parametric approach with potential significant dimension reduction. We apply it to the example of detecting transient datasets and demonstrate the superior effectiveness of this method benchmarked with supervised learning methods with raw data.

Fri, 16 Nov 2018

12:00 - 13:00
L4

Topological adventures in neuroscience

Kathryn Hess
(École Polytechnique Fédérale de Lausanne (EPFL))
Abstract

Over the past decade, and particularly over the past five years, research at the interface of topology and neuroscience has grown remarkably fast.  In this talk I will briefly survey a few quite different applications of topology to neuroscience in which members of my lab have been involved over the past four years: the algebraic topology of brain structure and function, topological characterization and classification of neuron morphologies, and (if time allows) topological detection of network dynamics.

Mon, 03 Dec 2018

16:00 - 17:00
L6

Uniqueness and stability for shock reflection problem

Mikhail Feldman
(University of Wisconsin)
Abstract

We discuss shock reflection problem for compressible gas dynamics, von Neumann conjectures on transition between regular and Mach reflections, and existence of regular reflection solutions for potential flow equation. Then we will talk about recent results on uniqueness and stability of regular reflection solutions for potential flow equation in a natural class of self-similar solutions. The approach is to reduce the shock reflection problem to a free boundary problem for a nonlinear elliptic equation, and prove uniqueness by a version of method of continuity. A property of solutions important for the proof of uniqueness is convexity of the free boundary. 

This talk is based on joint works with G.-Q. Chen and W. Xiang.

Mon, 19 Nov 2018

17:00 - 18:00
L4

Higher Regularity of the p-Poisson Equation in the Plane

Lars Diening
(Bielefeld University)
Abstract

In recent years it has been discovered that also non-linear, degenerate equations like the p-Poisson equation div(A(u))=div(|u|p2u)=divF allow for optimal regularity. This equation has similarities to the one of power-law fluids. In particular, the non-linear mapping FA(u) satisfies surprisingly the linear, optimal estimate for several choices of spaces X. In particular, this estimate holds for Lebesgue spaces L^q (with q \geq p'), spaces of bounded mean oscillations and Holder spacesC^{0,\alpha} (for some \alpha>0).

In this talk we show that we can extend this theory to Sobolev and Besov spaces of (almost) one derivative. Our result are restricted to the case of the plane, since we use complex analysis in our proof. Moreover, we are restricted to the super-linear case p \geq 2, since the result fails p < 2. Joint work with Anna Kh. Balci, Markus Weimar.

Tue, 13 Nov 2018

14:00 - 14:30
L5

Nonlinear low-rank matrix completion

Florentin Goyens
(Oxford)
Abstract

The talk introduces the problem of completing a partially observed matrix whose columns obey a nonlinear structure. This is an extension of classical low-rank matrix completion where the structure is linear. Such matrices are in general full rank, but it is often possible to exhibit a low rank structure when the data is lifted to a higher dimensional space of features. The presence of a nonlinear lifting makes it impossible to write the problem using common low-rank matrix completion formulations. We investigate formulations as a nonconvex optimisation problem and optimisation on Riemannian manifolds.

Tue, 13 Nov 2018

14:30 - 15:00
L5

An Application of Markov Decision Processes to Optimise Darts Strategy

Graham Baird
(Oxford)
Abstract

This work determines an aim point selection strategy for players in order to improve their chances of winning at the classic darts game of 501. Although many previous studies have considered the problem of aim point selection in order to maximise the expected score a player can achieve, few have considered the more general strategical question of minimising the expected number of turns required for a player to finish. By casting the problem as a Markov decision process, a framework is derived for the identification of the optimal aim point for a player in an arbitrary game scenario.

Tue, 06 Nov 2018

14:00 - 14:30
L5

Solving Laplace's equation in a polygon

Lloyd N. Trefethen
(Oxford)
Abstract

There is no more classical problem of numerical PDE than the Laplace equation in a polygon, but Abi Gopal and I think we are on to a big step forward. The traditional approaches would be finite elements, giving a 2D representation of the solution, or integral equations, giving a 1D representation. The new approach, inspired by an approximation theory result of Donald Newman in 1964, leads to a "0D representation" -- the solution is the real part of a rational function with poles clustered exponentially near the corners of the polygon. The speed and accuracy of this approach are remarkable. For typical polygons of up to 8 vertices, we can solve the problem in less than a second on a laptop and evaluate the result in a few microseconds per point, with 6-digit accuracy all the way up to the corner singularities. We don't think existing methods come close to such performance. Next step: Helmholtz?
 

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