Thu, 23 Nov 2017

16:00 - 16:30
L1

A Bio-inspired Design for a Switchable Elastocapillary Adhesive

Matthew Butler
(University of Oxford)
Abstract

Many species of insects adhere to vertical and inverted surfaces using footpads that secrete thin films of a mediating fluid. The fluid bridges the gap between the foot and the target surface. The precise role of this liquid is still subject to debate, but it is thought that the contribution of surface tension to the adhesive force may be significant. It is also known that the footpad is soft, suggesting that capillary forces might deform its surface. Inspired by these physical ingredients, we study a model problem in which a thin, deformable membrane under tension is adhered to a flat, rigid surface by a liquid droplet. We find that there can be multiple possible equilibrium states, with the number depending on the applied tension and aspect ratio of the system. The presence of elastic deformation  ignificantly enhances the adhesion force compared to a rigid footpad. A mathematical model shows that the equilibria of the system can be controlled via two key parameters depending on the imposed separation of the foot and target surface, and the tension applied to the membrane. We confirm this finding experimentally and show that the system may transition rapidly between two states as the two parameters are varied. This suggests that different strategies may be used to adhere strongly and then detach quickly.

Tue, 17 Oct 2017

14:00 - 14:30
L5

Multilevel weighted least squares polynomial approximation

Abdul-Lateef Haji-Ali
(University of Oxford)
Abstract

We propose and analyze a multilevel weighted least squares polynomial approximation method. Weighted least squares polynomial approximation uses random samples to determine projections of functions onto spaces of polynomials. It has been shown that using an optimal distribution of sample locations, the number of samples required to achieve quasi-optimal approximation in a given polynomial subspace scales, up to a logarithmic factor, linearly in the dimension of this space. However, in many applications, the computation of samples includes a numerical discretization error. Thus, obtaining polynomial approximations with a single level method can become prohibitively expensive, as it requires a sufficiently large number of samples, each computed with a sufficiently small discretization error. As a solution to this problem, we propose a multilevel method, which employs samples with different accuracies and is able to match the accuracy of single level approximations at reduced computational work. We prove complexity bounds under certain assumptions on polynomial approximability and sample work. Furthermore, we propose an adaptive
algorithm for situations where such assumptions cannot be verified a priori. Numerical experiments underline the practical applicability of our method.

Mon, 20 Nov 2017

15:45 - 16:45
L3

Detecting early signs of depressive and manic episodes in patients with bipolar disorder using the signature-based model

ANDREY KORMILITZIN
(University of Oxford)
Abstract

Recurrent major mood episodes and subsyndromal mood instability cause substantial disability in patients with bipolar disorder. Early identification of mood episodes enabling timely mood stabilisation is an important clinical goal. The signature method is derived from stochastic analysis (rough paths theory) and has the ability to capture important properties of complex ordered time series data. To explore whether the onset of episodes of mania and depression can be identified using self-reported mood data.

Mon, 20 Nov 2017

14:15 - 15:15
L3

SLE and Rough Paths Theory

VLAD MARGARINT
(University of Oxford)
Abstract

In this talk, I am going to report on some on-going research at the interface between Rough Paths Theory and Schramm-Loewner evolutions (SLE). In this project, we try to adapt techniques from Rough Differential Equations to the study of the Loewner Differential Equation. The main ideas concern the restart of the backward Loewner differential equation from the singularity in the upper half plane. I am going to describe some general tools that we developed in the last months that lead to a better understanding of the dynamics in the closed upper half plane under the backward Loewner flow.
Joint work with Prof. Dmitry Belyaev and Prof. Terry Lyons

Mon, 06 Nov 2017

15:45 - 16:45
L3

Karhunen Loeve expansions in regularity structures.

SINA NEJAD
(University of Oxford)
Abstract

We consider L^2-approximations of white noise within the framework of regularity structures. Possible applications include support theorems for SPDEs driven by degenerate noises and numerics. Joint work with Ilya Chevyrev, Peter Friz and Tom Klose. 

Mon, 16 Oct 2017

15:45 - 16:45
L3

A signature-based machine learning model for bipolar disorder and borderline personality disorder

IMANOL PEREZ
(University of Oxford)
Abstract

The signature of a path has many properties that make it an excellent feature to be used in machine learning. We exploit this properties to analyse a stream of data that arises from a psychiatric study whose objective is to analyse bipolar and borderline personality disorders. We build a machine learning model based on signatures that tries to answer two clinically relevant questions, based on observations of their reported state over a short period of time: is it possible to predict if a person is healthy, has bipolar disorder or has borderline personality disorder? And given a person or borderline personality disorder, it is possible to predict his or her future mood? Signatures proved to be very effective to tackle these two problems.

Mon, 09 Oct 2017

14:15 - 15:15
L3

Inverting the signature of a path

JIAWEI CHANG
(University of Oxford)
Abstract

Inverting the signature of a path with ideas from linear algebra with implementations.

Wed, 07 Feb 2018

17:00 - 18:00
L1

Michael Bonsall - Scaling the Maths of Life

Michael Bonsall
(University of Oxford)
Abstract

In this talk Michael Bonsall will explore how we can use mathematics to link between scales of organisation in biology. He will delve in to developmental biology, ecology and neurosciences, all illustrated and explored with real life examples, simple games and, of course, some neat maths.

Michael Bonsall is Professor of Mathematical Biology in Oxford.

7 February 2018, 5pm-6pm, Mathematical Institute, Oxford

Please email @email to register or watch online: https://livestream.com/oxuni/bonsall

Wed, 14 Jun 2017

11:30 - 12:30
N3.12

Finiteness properties and subdirect products of groups

Claudio Llosa Isenrich
(University of Oxford)
Abstract

In my talk I will give a basic introduction to the finiteness properties of groups and their relation to subgroups of direct products of groups. I will explain the relation between such subgroups and fibre products of groups, and then proceed with a discussion of the n-(n+1)-(n+2)-Conjecture and the Virtual Surjections Conjecture. While both conjectures are still open in general, they are known to hold in special cases. I will explain how these results can be applied to prove that there are groups with arbitrary (non-)finiteness properties.

Wed, 17 May 2017

11:30 - 12:30
N3.12

Nearly exponential functions of order 4

David Hume
(University of Oxford)
Abstract

For every $\epsilon>0$ does there exist some $n\in\mathbb{N}$ and a bijection $f:\mathbb{Z}_n\to\mathbb{Z}_n$ such that $f(x+1)=2f(x)$ for at least $(1-\epsilon)n$ elements of $\mathbb{Z}_n$ and $f(f(f(f(x))))=(x)$ for all $x\in\mathbb{Z}_n$? I will discuss this question and its relation to an important open problem in the theory of countable discrete groups.

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