Forthcoming events in this series


Tue, 29 Nov 2016

12:45 - 13:30
C5

Community Detection in Annotated Bipartite Networks

Roxana Pamfil
(University of Oxford)
Abstract

A successful programme of personalised discounts and recommendations relies on identifying products that customers want, based both on items bought in the past and on relevant products that the customers have not yet purchased. Using basket-level grocery shopping data, we aim to use clustering ("community detection") techniques to identify groups of shoppers with similar preferences, along with the corresponding products that they purchase, in order to design better recommendation systems.


Stochastic block models (SBMs) are an increasingly popular class of methods for community detection. In this talk, I will expand on some work done by Newman and Clauset [1] that uses a modified SBM for community detection in annotated networks. In these networks, additional information in the form of node metadata is used to improve the quality of the inferred community structure. The method can be extended to bipartite networks, which contain two types of nodes and edges only between nodes of different types. I will show some results obtained from applying this method to a bipartite network of customers and products. Finally, I will discuss some desirable extensions to this method such as incorporating edge weights and assessing the relationship between metadata and network structure in a statistically robust way.


[1] Structure and inference in annotated networks, MEJ Newman and A Clauset, Nature Communications 7, 11863 (2016).


Note: This talk will cover similar topics to my presentation in the InFoMM group meeting on Friday, November 25 but it won't be exactly the same. I will focus more on the mathematical details for my JAMS talk.
 

Tue, 01 Nov 2016

12:45 - 13:30
C5

Stretching and deformation of thin viscous sheets: glass redraw through a long heater zone

Doireann O'Kiely
(University of Oxford)
Abstract

Thin glass sheets are used in smartphone, battery and semiconductor technology, and may be manufactured by first producing a relatively thick glass slab (known as a preform) and subsequently redrawing it to a required thickness. Theoretically, if the sheet is redrawn through an infinitely long heater zone, a product with the same aspect ratio as the preform may be manufactured. However, in reality the effect of surface tension and the restriction to factories of finite size prevent this. In this talk I will present a mathematical model for a viscous sheet undergoing redraw, and use asymptotic analysis in the thin-sheet, low-Reynolds-number limit to investigate how the product shape is affected by process parameters. 

Tue, 18 Oct 2016

12:45 - 13:30
C5

Scalable Two-Phase Flow Solvers

Niall Bootland
(University of Oxford)
Abstract

My research focuses on numerical techniques that help provide scalable computation within simulations of two-phase fluid flow problems. The efficient solution of the linear systems which arise is key to obtaining practical computation. I will motivate and discuss new methods which seek to generalise effective techniques for a single phase to the more challenging setting of two-phase flow where the governing equations have discontinuous coefficients.

Tue, 17 May 2016

12:45 - 13:30
C5

Sorting of micro-swimmers in flowing visco-elastic fluids

Arnold Mathijssen
(University of Oxford)
Abstract

Interactions between micro-swimmers and their complex flow environments are important in many biological systems, such as sperm cells swimming in cervical mucus or bacteria in biofilm initiation areas. We present a theoretical model describing the dynamics of micro-organisms swimming in a plane Poiseuille flow of a viscoelastic fluid, accounting for hydrodynamic interactions and biological noise. General non-Newtonian effects are investigated, including shear-thinning and normal stress differences that lead to migration of the organisms across the streamlines of the background flow. We show that micro-swimmers are driven towards the centre-line of the channel, even if countered by hydrodynamic interactions with the channel walls that typically lead to boundary accumulation. Furthermore, we demonstrate that the normal stress differences reorient the swimmers at the centre-line in the direction against the flow so that they swim upstream. This suggests a natural sorting mechanism to select swimmers with a given swimming speed larger than the tunable Poiseuille flow velocity. This framework is then extended to study trapping and colony formation of pathogens near surfaces, in corners and crevices. 

Tue, 03 May 2016

13:00 - 13:30
C5

√T, or not √T, that is the question

Matthew Saxton
(Mathematical Institute, University of Oxford)
Abstract

We consider the motion of a thin liquid drop on a smooth substrate as the drop evaporates into an inert gas. Many experiments suggest that, at times close to the drop’s extinction, the drop radius scales as the square root of the time remaining until extinction. However, other experiments observe slightly different scaling laws. We use the method of matched asymptotic expansions to investigate whether this different behaviour is systematic or an artefact of experiment.

Tue, 21 Oct 2014

12:45 - 13:45
C4

TBA

Alexander Vervuurt, Jochen Kursawe, Linus Schumacher
(Mathematical Institute, Oxford)
Tue, 17 Jun 2014

13:15 - 14:00
C4

Community structure in temporal multilayer networks

Marya Bazzi
(University of Oxford)
Abstract

Networks provide a convenient way to represent complex systems of interacting entities. Many networks contain "communities" of nodes that are more strongly connected to each other than to nodes in the rest of the network. Most methods for detecting communities are designed for static networks. However, in many applications, entities and/or interactions between entities evolve in time. To incorporate temporal variation into the detection of a network's community structure, two main approaches have been adopted. The first approach entails aggregating different snapshots of a network over time to form a static network and then using static techniques on the resulting network. The second approach entails using static techniques on a sequence of snapshots or aggregations over time, and then tracking the temporal evolution of communities across the sequence in some ad hoc manner. We represent a temporal network as a multilayer network (a sequence of coupled snapshots), and discuss  a method that can find communities that extend across time. 

Tue, 03 Jun 2014

13:00 - 14:00
C4

`When you say "Jump!"; I say "How far ?"': non-local jumping for stochastic lattice-based position jump simulations.

Paul Taylor and Mark Gilbert
(University of Oxford)
Abstract
Position jump models of diffusion are a valuable tool in biology, but stochastic simulations can be very computationally intensive, especially when the number of particles involved grows large. It will be seen that time-savings can be made by allowing particles to jump with a range of distances and rates, rather than being restricted to moving to adjacent boxes on the lattice. Since diffusive systems can often be described with a PDE in the diffusive limit when particle numbers are large, we also discuss the derivation of equivalent boundary conditions for the discrete, non-local system, as well as variations on the basic scheme such as biased jumping and hybrid systems.
Tue, 13 May 2014 13:00 -
Wed, 14 May 2014 14:00
C4

Making Exact Bayesian Inference on Cox Processes

Yves-Lauren Kom Samo
(University of Oxford)
Abstract

Cox processes arise as a natural extension of inhomogeneous Poisson Processes, when the intensity function itself is taken to be stochastic. In multiple applications one is often concerned with characterizing the posterior distribution over the intensity process (given some observed data). Markov Chain Monte Carlo methods have historically been successful at such tasks. However, direct methods are doubly intractable, especially when the intensity process takes values in a space of continuous functions.

In this talk I'll be presenting a method to overcome this intractability that is based on the idea of "thinning" and that does not resort to approximations.

Tue, 11 Mar 2014

13:15 - 14:00
C4

Understanding the Dynamics of Embryonic Stem Cell Differentiation: A Combined Experimental and Modeling Approach

Stanley Strawbridge
(University of Cambridge)
Abstract

Pluripotency is a key feature of embryonic stem cells (ESCs), and is defined as the ability to give rise to all cell lineages in the adult body. Currently, there is a good understanding of the signals required to maintain ESCs in the pluripotent state and the transcription factors that comprise their gene regulatory network. However, little is known about how ESCs exit the pluripotent state and begin the process of differentiation. We aim to understand the molecular events associated with this process via an experiment-model cycle.

Tue, 25 Feb 2014

13:15 - 14:00
C4

Onset of menisci

Doireann O'Kiely
(OCIAM)
Abstract

A solid object placed at a liquid-gas interface causes the formation of a meniscus around it. In the case of a vertical circular cylinder, the final state of the static meniscus is well understood, from both experimental and theoretical viewpoints. Experimental investigations suggest the presence of two different power laws in the growth of the meniscus. In this talk I will introduce a theoretical model for the dynamics and show that the early-time growth of the meniscus is self-similar, in agreement with one of the experimental predictions. I will also discuss the use of a numerical solution to investigate the validity of the second power law.

Tue, 18 Feb 2014

13:15 - 14:00
C2

A non-parametric test for dependence based on the entropy rate

Pedro Vitoria (Stochastic Analysis group) and Galen Sher (Economics)
(Oxford University)
Abstract

A non-parametric test for dependence between sets of random variables based on the entropy rate is proposed. The test has correct size, unit asymptotic power, and can be applied to test setwise cross sectional and serial dependence. Using Monte Carlo experiments, we show that the test has favourable small-sample properties when compared to other tests for dependence. The ‘trick’ of the test relies on using universal codes to estimate the entropy rate of the stochastic process generating the data, and simulating the null distribution of the estimator through subsampling. This approach avoids having to estimate joint densities and therefore allows for large classes of dependence relationships to be tested. Potential economic applications include model specification, variable and lag selection, data mining, goodness-of-fit testing and measuring predictability.

Tue, 03 Dec 2013

13:15 - 14:00
C4

Modelling cell population growth in tissue engineering

Lloyd Chapman
(OCIAM Oxford)
Abstract

It is often difficult to include sufficient biological detail when modelling cell population growth to make models with real predictive power. Continuum models often fail to capture physical and chemical processes happening at the level of individual cells and discrete cell-based models are often very computationally expensive to solve. In the first part of this talk, I will describe a phenomenological continuum model of cell aggregate growth in a specific perfusion bioreactor cell culture system, and the results of numerical simulations of the model to determine the effects of the bioreactor operating conditions and cell seeding on the growth. In the second part of the talk, I will introduce a modelling approach used to derive continuum models for cell population growth from discrete cell-based models, and consider possible extensions to this framework.

Tue, 19 Nov 2013

13:15 - 14:00
C4

Optimizing cross-flow-filtration efficacy using variable wall permeabilities (JH) and Volumetric image segmentation (IvG)

James Herterich and Ingrid von Glehn
(OCCAM, University of Oxford)
Abstract

JH: Water filtration systems typically involve flow along a channel with permeable walls and suction applied across the wall. In this ``cross-flow'' arrangement, clean water leaves the channel while impurities remain within it. A limiting factor for the operation of cross-flow devices is the build-up of a high concentration of particles near the wall due to the induced flow. Termed concentration polarization (CP), this effect ultimately leads to the blocking of pores within the permeable wall and the deposition of a ``cake'' on the wall surface. Here we show that, through strategic choices in the spatial variations of the channel-wall permeability, we may reduce the effects of CP by allowing diffusion to smear out any build up of particles that may occur. We demonstrate that, for certain classes of variable permeability, there exist optimal choices that maximize the flux of clean water out of a device.

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IvG: TBC

Tue, 05 Nov 2013

13:15 - 14:00
C4

Introduction to Data Assimilation

Partick Raanes
(OCIAM, Oxford)
Abstract

Data assimilation is a particular form of state estimation. That's partly the "what". We'll also look at the how's, the why's, some who's and some where's.

Tue, 22 Oct 2013

13:00 - 14:00
C4

Singularly perturbed hyperbolic systems

Stuart Thomson
(OCIAM, Oxford)
Abstract

In the first JAM seminar of 2013/2014, I will discuss the topic of singular perturbed hyperbolic systems of PDE arising in physical phenomena, particularly the St Venant equations of shallow water theory. Using a mixture of analytical and numerical techniques, I will demonstrate the dangers of approximating the dynamics of a system by the equations obtained upon taking a singular limit $\epsilon\rightarrow 0$ and furthermore how the dynamics of the system change when the parameter $\epsilon$ is taken to be small but finite. Problems of this type are ubiquitous in the physical sciences, and I intend to motivate another example arising in elastoplasticity, the subject of my DPhil study.

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Note: This seminar is not intended for faculty members, and is available only to current undergraduate and graduate students.

Tue, 28 May 2013

13:00 - 14:00
DH 1st floor SR

Community detection in spatially embedded epidemic networks

Marta Sarzynska
Abstract

We detect communities on time-dependent correlation networks to study the geographical spread of disease. Using data on country-wide dengue fever, rubella, and H1N1 influenza occurrences spanning several years, we create multilayer similarity networks, with the provinces of a country as nodes and the correlations between the time series of case numbers giving weights to the edges.

We perform community detection on these temporal networks of disease outbreaks, looking for groups of provinces in which disease patterns change in similar ways. Optimizing multilayer modularity with a Newman-Girvan null model over a wide parameter range, we observe several partitions that corresponding roughly to relevant historical time points, such as large epidemics and introduction of new disease strains, as well as many strongly spatial partitions.

We develop a novel null model for community detection that takes into account spatial information, thereby allows to uncover additional structure that might otherwise be obscured by spatial proximity. The null model is based on a radiation model that was proposed recently for modelling human mobility, and we believe that it might be better at capturing disease spread than existing spatial null models based on gravity models for interaction between nodes.

The radiation null model performs better than the Newman-Girvan null model and similarly to the gravity model on benchmark spatial networks with distance-dependent links and a known community structure (both static and multislice networks), and it strongly outperforms both on flux-based benchmarks. When applied to the disease networks, the radiation null model uncovers novel, clear temporal partitions, that might shed light on disease patterns, the introduction of new strains, and provide epidemic warning signals.

Tue, 27 Nov 2012

13:15 - 13:45
DH 3rd floor SR

The Mechanics of Multitubes

Stephen O'Keeffe
Abstract

Multi-layered cylinders, or 'multitubes', are ubiquitous throughout the biological world, from microscopic axons to plant stems. Whilst these structures share an underlying common geometry, each one fulfils a different key role in its relevant environment. For example plant stems provide a transport network for nutrients within the organism, whilst the tongue of a chameleon is used for prey capture. This talk will be concerned with the mechanical stability of multitubes. How do the material properties, applied tractions and geometry of elastic rods and tubes influence their critical buckling pressure and mode of buckling? We will discuss the phenomenon of differential growth, an important factor in the mechanical behaviour of such systems and introduce a mathematical framework, which can be used to model differential growth in soft tissues and predict the onset of buckling. We will also present a small number of applications for this research.

Tue, 13 Nov 2012

13:15 - 14:00
DH 1st floor SR

An introduction to mathematical finance : market completeness, arbitrage and backward stochastic differential equations

Arnaud Lionnet
(University of Oxford)
Abstract

I will present the basics of mathematical finance, and what probabilists do there. More specifically, I will present the basic concepts of replication of a derivative contract by trading, market completeness, arbitrage, and the link with Backward Stochastic Differential Equations (BSDEs).