# Mathematics & Statistics Seminars and colloquia

### Department Colloquia

25th January: Dr Elaine C M Crooks (University of Swansea)

Title:  ﻿ Compensated convexity, Hausdorff-stable singularity extraction, and image processing﻿

Date: 3.30pm Wednesday 25th January

Venue: Livingstone Tower﻿, 9th floor, room LT908

Abstract:  Compensated convex transforms enjoy tight-approximation and locality properties that can be exploited to develop multi-scale, parametrised methods for identifying singularities in functions.  These tools can then be used, via a numerical implementation, to detect features in images or data, remove noise from images, identify intersections between surfaces, etc, and thus produce new geometric techniques for image processing, feature extraction and geometric interrogation.

Advantages of such an approach include the use of blind global methods that are Hausdorff-stable under perturbation and different sampling techniques, and are also multi-scale, providing scales for features that allow users to select which size of feature they wish to detect.

This is joint work with Kewei Zhang, Nottingham, and Antonio Orlando, Tucumán.﻿

1st February: Dr Thomas Byrne (NPL Scotland)

Title:  tbc

Date: 2pm Wednesday 1st February

Venue: Livingstone Tower﻿, 9th floor, room LT908

Abstract:

15th February: Dr Marie-Therese Wolfram (University of Warwick)

Title:  ﻿Applied PDE in the socio-economic sciences﻿

Date: 3.30pm Wednesday 15th February

Venue: Livingstone Tower﻿, 9th floor, room LT908

Abstract: In recent years nonlinear PDE models have been used successfully in various applications in socio-economic sciences. For example to describe opinion formation and knowledge growth in a society, or the collective dynamics of large pedestrian crowds. In this talk we focus on two PDE models for socio-economic problems. First a Boltzmann mean-field game approach to describe knowledge and economic growth in a society; and second a nonlinear PDE model for interacting pedestrian flows. We start by discussing the underlying microscopic modelling assumptions as well as the corresponding mean-field equations. Then we focus on the existence and linear stability of solutions in either case. Finally we construct special solutions, which relate to sustained economic growth or segregation of flows, and illustrate the dynamics of both models with numerical simulations.﻿

15th March: Dr Young-Ho Eom (Mathematics and Statistics)

Title:  ﻿ Tipping points leading to catastrophic shifts in networked populations﻿

Date: 4pm Wednesday 15th March

Venue: Livingstone Tower﻿, 9th floor, room LT908

Abstract:  ﻿Complex systems often shift drastically from one state to a radically different state when they cross certain thresholds, referred to as tipping points. However, what causes these catastrophic behaviors in such diverse systems is still elusive. Here we consider weakly-connected heterogeneous populations of dynamical systems to identify the role of underlying network topology on the occurrence of tipping points. Specifically we demonstrate that long-range short-cuts can alter how networked populations respond to external conditions or internal perturbations and small-world topology can induce tipping points. We observe that the suppression of local bifurcation in individual nodes due to small-world topology results in tipping point at system level. Our results suggest that particular topological properties of connected systems may provide warning indicators of unexpected collapse in their states﻿.

1st March: Dr Mohammud Foondun (Mathematics and Statistics)

Title:  ﻿Some recent qualitative properties of some stochastic equations﻿

Date: 3.30pm Wednesday 1st March

Venue: Livingstone Tower﻿, 9th floor, room LT908

Abstract:   In this talk, I will review some recently discovered  properties of a class of stochastic heat equations. More precisely, I will discuss how the presence of the random forcing term influence the solutions to the heat equation. If time permits, I will talk about fractional equations.﻿

10th May: Prof Epifanio Virga (University of Pavia)

Title:  ﻿ Onsager's roots of density functional theory﻿

Date: 3.30pm Wednesday 10th May

Venue: Livingstone Tower﻿, 9th floor, room LT908

Abstract:   Onsager's celebrated theory for liquid crystals, put forward in 1949, showed that purely steric, repulsive interactions between molecules can explain the ordering transition that underpins the formation of the nematic phase. Often Onsager's theory is considered as the first successful instance of modern density functional theory. It was however a theory rooted in its time, in the theory that Mayer had proposed in the late 1930's with the aim of explaining condensation of real gases. Despite its undeniable success, Onsager's theory lacks rigour at its onset. This lecture will review in a historical perspective the conceptual basis of Onsager's theory and it will show how this theory can be made rigorous by use of Penrose's tree identity, a powerful technical tool already exploited to ensure convergence to Mayer's cluster expansion. Against all appearances, this is not a technical lecture; it is concerned more with the ideas underneath a successful mathematical theory of ordering in soft matter systems than with the equally precious details of analysis.

### Department Colloquia joint with EEE

10th May: Prof Phil Whiting (Technical University of Eindhoven)

Title:  ﻿ Lazy Max Weight Scheduling Algorithms for Maximum Stability in Networks with Recon guration Delays﻿

Date: 3.30pm Tuesday 23rd May

Venue: Livingstone Tower﻿, 9th floor, room LT908

Abstract:   We consider the scheduling problem for networks with interference constraints and recon_guration (switching) delays, which is the duration of time when one (feasible) service schedule is dropped and a distinct service schedule is adopted. Such delays occur in many telecommunication applications e.g. optical transceiver tuning a light-path or mobile servers gathering data from sensors. Under zero recon_guration delay it is well known that the Max-Weight scheduling algorithm is throughput-optimal without requiring knowledge of arrival rates. We show that this property of Max-Weight no longer holds when there is a nonzero recon_guration delay. We then go on to show that a class of algorithms which can be loosely termed Lazy Max-Weight policies in which service con_gurations are persisted do achieve the full stability region. These include Variable frame-based Max-Weight (VFMW) algorithms, as well as Switching Curve Based (SCB) policies. For these latter algorithms the time to the next recon_guration is not determined in advance. In the final part of the talk, Numerical results are presented for the SCB and VFMW policies and some issues connected with delay performance are discussed. This is joint work with Sem Borst, Guner Celik and Eytan Modiano.

### Applied Analysis﻿

30th January: Professor Ernesto Estrada

Title: k-path Laplacians, super-diffusion and super-fast random walks on graphs﻿

Date:  4.00pm Monday 30th January

Venue: Livingstone Tower﻿, 9th floor, room LT907

Abstract: I will start by a short introduction to the problem of diffusion on graphs, defining the graph Laplacian and some applications in areas ranging from autonomous robots to diffusion of innovations. Then, I will motivate the necessity of incorporating long-range interactions to account for certain physical diffusive processes. I will then introduce the k-path Laplacians as operators in l_2 Hilbert space and prove a few of their properties (boundedness, self-adjointnes). At this point I will introduce a generalisation of the diffusion equation on graphs by using Mellin- and Laplace-transformed k-path Laplacians. I will prove the existence of super-diffusive regimes for certain values of the parameter in the Mellin-transformed k-path Laplacian in one-dimension. Finally, I will introduce a multi-hopper model, that generalises the random walk model on graphs, by allowing non-nearest neighbours jumps. I will show the differences between this model and the random walk with Levy flights, which is valid only in the continuous space. I will prove that for certain asymptotic value of the parameters in the transforms of the k-path Laplacians, the multi-hopper reaches the minimum hitting and commute times in graphs of any topology. I will illustrate the results in certain classes of graphs and real-world networks.﻿

6th February: Dr Matthias Langer

Title: TBA﻿

Date:  4.00pm Monday 6th February

Venue: Livingstone Tower﻿, 9th floor, room LT907

Abstract:

### Continuum Mechanics and Industrial Mathematics

14th February: Professor Ranga Narayanan (University of Florida, visiting Durham)

Title: Interfacial Dynamics of Phase Change in  Evaporation and Electrodeposition

Date:  1.00pm Tuesday 14th february

Venue: Livingstone Tower﻿, 9th floor, room LT907

Abstract:

A large class of hydrodynamic problems involves interfacial instabilities and within that class, phase change is an important physical process.  xamples of phase -change phenomena are evaporation, solidification, and electrodeposition.  They play an important role in materials processing, food preservation and in energy management. The interfacial instability associated with phase-change processes lead to pattern formation. Determining the conditions and form of pattern selection depend on the judicious use of analytical and computational schemes. This talk will focus on the physical and mathematical analogies between two phase-change instabilities viz., evaporation and electrodeposition. We will relate the results of theory arising from analysis and computations and compare them to experiments.

21st February: Dr Ben Goddard (University of Edinburgh)

Title: Dynamic Density functional Theory: Modelling, Analysis and Numerics

Date:  1.00pm Tuesday 21st February

Venue: Livingstone Tower﻿, 9th floor, room LT907

Abstract:

In recent years, a number of dynamic density functional theories (DDFTs) have been developed to describe colloid particle dynamics. These DDFTs aim to overcome the high-dimensionality of systems with large numbers of particles by reducing to the dynamics of the one-body density, described by a PDE in only three spatial dimensions, independently of the number of particles. The standard derivations are via stochastic equations of motion, but there are fundamental differences in the underlying assumptions in each DDFT. I will begin by giving an overview of some DDFTs, highlighting the assumptions and range of applicability.

Particular attention will be given to  the inclusion of inertia and hydrodynamic interactions, both of which strongly influence non-equilibrium properties of the system.  I will then demonstrate the very good agreement with the underlying stochastic dynamics for a wide range of systems.  I will also discuss an accurate and efficient numerical code, based on pseudospectral techniques, which is applicable both to the integro-PDEs of DDFT and to many other systems. Finally I will describe the rigorous passage to the high-friction limit, where the one-body density satisfies a nonlinear, non-local Smoluchowski-like equation with a novel diffusion tensor.  I will also describe the (somewhat less rigorous) limit of being close to local equilibrium, in which we obtain a Navier-Stokes-like equation with additional non-local terms.

Joint work with Serafim Kalliadasis, Greg Pavliotis, and Andreas Nold.

28th February: Dr Ed Llewellin (University of Durham)

Title: Slugs and plugs: multiphase magma flow in basaltic volcanic conduits

Date:  1.00pm Tuesday 28th February

Venue: Livingstone Tower﻿, 9th floor, room LT907

Abstract:  Basaltic volcanoes produce a wide spectrum of eruption types, from passive outgassing, through effusion, spattering, and fountaining of lava, to the explosive production of ash. The nature of the eruption - and therefore of the hazard that it poses - is shaped mainly by processes that take place out of sight, in the sub-volcanic plumbing system. Scaled laboratory analogue experiments provide a window into this plumbing system, allowing us to identify and characterize the fluid dynamic processes that occur, and link them to eruption style. I will present the results of analogue experiments performed at a range of scales. The experiments reveal a rich diversity of multiphase fluid dynamic phenomena, and demonstrate that a critical control on eruptive style is the degree to which gas and magma become separated during ascent: when gas and magma are well coupled, effusive activity is favoured; when gas separates from, and rises through the magma, more impulsive or explosive activity results. The spectrum of eruption types, therefore, represents the surface expression of diverse multiphase fluid dynamic processes that occur in the volcanic plumbing system.

14th March: Dr Winnie Mukutu (Kenyatta University)

Title: tbc

Date:  1.00pm Tuesday 14th March

Venue: Livingstone Tower﻿, 9th floor, room LT907

28th March: Professor Andrew Lacey (Heriot-Watt University)

Title: A Coupled Fluid-Layer and Plate Model for Micro-Electro-Mechanical Systems

Date:  2.00pm Tuesday 28th March

Venue: Livingstone Tower﻿, 9th floor, room LT907

Abstract: An electrostatic micro-electro-mechanical system (MEMS) is modelled as a flexible plate or membrane moving under the influence of electrical attraction towards a fixed base plate. Motion is resisted by pressure of a gas in the thin gap between the plates which results in a damping effect.

A two-ODE version of the coupled problem is first looked at, to gain a qualitative understanding of possible behaviour. In particular, it is of interest as to whether the solution to the mathematical model tends to a steady state or instead ceases to exist after a finite time. The latter corresponds to "touch-down" in the MEMS device, when the flexible plate comes into contact with the base plate.

The time scale for the motion of the plate can be much smaller than that for the fluid flow in the narrow gap, allowing the method of multiple scales to be used.

This is joint work with Tim Simmons.

25th April: Tamsin Spelman (Cambridge University)

Title: Artificial micro-devices: armoured microbubbles and a magnetically driven cilium

Date:  1.00pm Tuesday 25th April

Venue: Livingstone Tower﻿, 9th floor, room LT907

Abstract: Micro-devices are built to mix fluid, transport fluid or self-propel on small scales, with long term aims to use them in medicine through targeted drug delivery and micro-diagnostic tools. The Armoured Microbubble (AMB) was designed by our experimental collaborators (group of Philippe Marmottant, University Grenoble Alpes) and consists of a partial hollow sphere, inside which a bubble is caught. Under ultrasound the bubble oscillates, generating a streaming flow in the surrounding fluid and producing a net force. We numerically and analytically analyse the resonances of a single AMB and the streaming flow it generates, as well as the streaming flow around arrays of AMBs in a channel, comparing with experiments. Our second system is a cilium containing aligned paramagnetic filings actuated by a rotating magnetic field, motivated by experimental work on a similar ferromagnetic cilium. We analyse the force the cilium applies to the surrounding fluid for transporting fluid, identifying this is maximal at an intermediate value of two important non-dimensional parameters.

2nd May: Andrew Croudace and Fatemah Al Mukahal (Mathematics and Statistics)

Title: tbc

Date:  1.00pm Tuesday 2nd May

Venue: Livingstone Tower﻿, 9th floor, room LT907

9th May: Dr Lindsey Corson (University of Strathclyde)

Title: tbc

Date:  1.00pm Tuesday 9th May

Venue: Livingstone Tower﻿, 9th floor, room LT907

16th May: Dr Qing Xiao (University of Strathclyde)

Title: Computational Fluid Dynamics Study of Fish Swimming

Date:  1.00pm Tuesday 16th May

Venue: Livingstone Tower﻿, 9th floor, room LT907

In this talk, the research work currently being performed in a CFD research group in the NAOME department will be introduced. Particular interests will focus on the investigation for the fish swimming behaviour with its application in bio-inspired underwater robots and pharmaceutical influences on aquatic animal locomotion behaviour change. This will further extend to the recently developed industrial biomimetic applications in marine renewable energy devices.

### Numerical Analysis and Scientific Computing﻿

7th February: Dr Marco Fossati (Mechanical and Aerospace Engineering, University of Strathclyde)

Title: Towards Inexpensive Computational Aerodynamics using Reduced Basis﻿

Date:  3.00pm Tuesday 7th February

Venue: Livingstone Tower﻿, 9th floor, room LT907

Abstract:  The design of future airliners and access-to-space systems is faced with many challenges and requirements, the most compelling being increased safety and aerothermodynamic performance, reduced fuel consumption / emissions and minimum acoustic signature. Numerical approaches based on Computational Fluid Dynamics (CFD) have become a widely used tool for aerodynamic design, but unfortunately the cost to obtain accurate CFD solutions is quite high and can easily become prohibitive if multiple different configurations and design solutions have to be evaluated. A numerical approach to cost reduction referred to as modal-based Reduced Order Modeling (ROM) or Reduced Basis Modeling will be discussed that uses modal identification as a means to reduce the computational complexity while preserving almost entirely the physics of the problem. Modal ROM uses an existing set of observations of the flow field to identify a small number of fundamental flow structures, also known as reduced basis or modes, that can be combined togheter to make fast predictions of the aircraft aerodynamic environment with CFD-like accuracy.  The mathematical and numerical theory behind the approach will be discussed in its most relevant aspects and the application of the approach to the parametric analysis of steady and unsteady aerodynamic problems will also be presented.﻿

14th February: Dr Alison Ramage (Mathematics and Statistics)

Title: A multilevel preconditioner for data assimilation with 4D-Var﻿

Date:  3.00pm Tuesday 14th February

Venue: Livingstone Tower﻿, 9th floor, room LT907

Abstract:  Large-scale variational data assimilation problems are commonly found in applications like numerical weather prediction and oceanographic modelling. The 4D-Var method is frequently used to calculate a forecast model trajectory that best fits the available observations to within the observational error over a period of time. One key challenge is that the state vectors used in realistic applications could contain billions or trillions of unknowns so, due to memory limitations, in practice it is often impossible to assemble, store or manipulate the matrices involved explicitly. In this talk we present a limited memory approximation to the Hessian of the linearised quadratic minimisation subproblems, computed using the Lanczos method, based on a multilevel approach. We then use this approximation as a preconditioner within 4D-Var and show that it can reduce memory requirements and increase computational efficiency.

This is joint work with Kirsty Brown (University of Strathclyde) and Igor Gejadze (IRSTEA, Montpellier).﻿

14th February: Dr Christopher Rowlatt (Mathematics and Statistics)

Title: Bubble collapse near a fluid-fluid interface using the spectral element marker particle method﻿

Date:  3.00pm Tuesday 14th February

Venue: Livingstone Tower﻿, 9th floor, room LT907

Abstract:  The spectral element marker particle (SEMP) method is a high-order numerical scheme for modelling multiphase flow where the governing equations are discretised using the spectral element method and the (compressible) fluid phases are tracked using marker particles. Thus far, the method has been successfully applied to two-phase problems involving the collapse of a two-dimensional bubble in the vicinity of a rigid wall (Lind and Phillips, 2012). A simplified model of (micro)bubble-cell interaction is presented, with the aim of gaining initial insights into the flow mechanisms behind sonoporation and microbubble-enhanced targeted drug delivery. Results from this model indicate that the non-local cell membrane distortion (blebbing) phenomenon often observed experimentally may result from stress propagation along the cell surface and so be hydrodynamical in origin.﻿

28th February: Dr Vanni Noferini (University of Essex)

Title: The structured condition number of a differentiable map between matrix manifolds﻿

Date:  3.00pm Tuesday 28th February

Venue: Livingstone Tower﻿, 9th floor, room LT907

Abstract: We discuss the structured condition number of differentiable maps between differentiable matrix manifolds, thus developing a theoretical framework that extends previous results on vector subspaces. We develop algorithms to compute the structured condition number. Then, we derive a lower bound on the structured condition number which can be much cheaper to compute, and an algorithm for computing the bound.

Finally, as an application, we provide numerical comparisons between the structured and unstructured condition numbers for matrices in automorphism groups and various maps: the matrix logarithm, the matrix square root, the polar decomposition, and the sign decomposition. We argue that the cheaply computable lower bound is often a good estimate of the structured condition number; moreover, we show experimentally that the structured and unstructured condition numbers can differ by several order of magnitude, thus motivating the future development of more structure-preserving algorithms.

This talk is based on joint work with Bahar Arslan and Françoise Tisseur, both from the University of Manchester.﻿

14th March: Kostas Zygalakis (University of Edinburgh)

Title: Bayesian Uncertainty Quantification in the Classification of High Dimensional Data ﻿

Date:  3.00pm Tuesday 14th March

Venue: Livingstone Tower﻿, 9th floor, room LT907

Abstract: In this talk, we present a Bayesian framework for semi-supervised binary classification on graphs. We develop several Bayesian models through the construction of a Gaussian prior from the graph Laplacian. Connections to the Ginzburg-Landau model are also made through the notion of a push-forward of the Gaussian prior under the double-well thresholding. We introduce efficient MCMC methods designed for large data sets to effectively sample from the posterior distribution for large scale problems. Through a variety of numerical experiments, we demonstrate the ability to perform uncertainty quantification by sampling from the posterior distribution. In particular, we observe empirically that the posterior mean and variance aligns well with certain external notions of uncertainty.

28th March: Professor Anotida Madzvamuse (University of Sussex)

Title: A robust and efficient adaptive multigrid solver for the optimal control of phase field formulations of geometric evolution laws﻿

Date:  3.00pm Tuesday 28th March

Venue: Livingstone Tower﻿, 9th floor, room LT907

Abstract: In this talk, I will present a novel solution strategy to efficiently and accurately compute approximate solutions to semilinear optimal control problems, focusing on the optimal control of phase field formulations of geometric evolution laws. The optimal control of geometric evolution laws arises in a number of applications in fields including material science, image processing, tumour growth and cell motility. Despite this, many open problems remain in the analysis and approximation of such problems. In the current work we focus on a phase field formulation of the optimal control problem, hence exploiting the well developed mathematical theory for the optimal control of semilinear parabolic partial differential equations. Approximation of the resulting optimal control problem is computationally challenging, requiring massive amounts of computational time and memory storage. The main focus of this work is to propose, derive, implement and test an efficient solution method for such problems. The solver for the discretised partial differential equations is based upon a geometric multigrid method incorporating advanced techniques to deal with the nonlinearities in the problem and utilising adaptive mesh refinement. An in-house two-grid solution strategy for the forward and adjoint problems, that significantly reduces memory requirements and CPU time, is proposed and investigated computationally. Furthermore, parallelisation as well as an adaptive-step gradient update for the control are employed to further improve efficiency. Along with a detailed description of our proposed solution method together with its implementation we present a number of computational results that demonstrate and evaluate our algorithms with respect to accuracy and efficiency. A highlight of the present work is simulation results on the optimal control of phase field formulations of geometric evolution laws in 3-D which would be computationally infeasible without the solution strategies proposed in the present work.

### Population Modelling and Epidemiology

30th March: Dr Robert Wilson (Mathematics and Statistics, University of Strathclyde)

Title: Zooplankton Diapause in a Warmer World: Modelling the Impact of 21st Century Climate Change on Calanus Finmarchicus

Date: 1pm Wednesday 30th March 2016

Venue: Livingstone Tower﻿, 9th floor, room LT907

Abstract:  To avoid starving  in winter, many zooplankton species spend over six months dormant in deep waters. The time animals can remain dormant will likely be reduced by global warming.  We therefore modelled changes in potential dormancy duration in the key species Calanus finmarchicus under 21st century climate change. Climate change impacts varied markedly. Western Atlantic populations see large reductions in potential dormancy duration, but the Norwegian Sea experiences only marginal change. The reductions in the Western Atlantic will likely cause important changes to the populations of C. finmarchicus and species that prey on it.

6th April: Dr Amanda Weir (Health Protection Scotland)

Title: TBA

Date: 1pm Wednesday 6th April 2016

Venue: Livingstone Tower﻿, 9th floor, room LT907

Abstract: TBA

26th October: Dr Gary Napier (University of Glasgow)

Title: A General Methodological Framework for Identifying Disease Risk Spatial Clusters Based Upon Mixtures of Temporal Trends

Date: 1pm Wednesday 26th October 2016

Venue: Livingstone Tower﻿, 9th floor, room LT907

Abstract:   We present a novel general Bayesian hierarchical mixture model for clustering areas based on their temporal trends. Our approach is general in that it allows the user to choose the shape of the temporal trends to include in the model, and examples include linear, general monotonic, and changepoint trends. Inference from the model is based on Metropolis coupled Markov chain Monte Carlo (MC)^3 techniques in order to prevent issues pertaining to multimodality often associated with mixture models. The effectiveness of (MC)^3 is demonstrated in a simulation study, before applying the model to hospital admission rates due to respiratory disease in the city of Glasgow between 2002 and 2011. Software for implementing this model will be made freely available as part of the R package CARBayesST.

25th May: Raphael Ximenes (Department of Mathematics & Statistics, University of Strathclyde)

Title: The Risk of Dengue for Non-Immune Foreign Visitors to the 2016 Summer Olympic Games in Rio de Janeiro, Brazil

Date: 1.00pm, Wednesday 25th May 2016

Venue: Livingstone Tower, 9th Floor, LT9.07

Abstract:  Dengue is a viral infection caused by 4 dengue serotypes transmitted by mosquitoes that is an increasing problem in Brazil and other countries in the tropics and subtropics. As Brazil is the country with the highest number of dengue cases worldwide. Rio de Janeiro, the venue for the 2016 Olympic Games, has been of major importance for the epidemiology of dengue in Brazil. After the DENV 1–4 introductions in 1986, 1990, 2000 and 2011, respectively, the city has suffered explosive outbreaks. Properly quantifying the risk of dengue for foreign visitors to the Olympics is important. A mathematical model to calculate the risk of developing dengue for foreign tourists attending the Olympic Games in Rio de Janeiro in 2016 is proposed. A system of differential equation models the spread of dengue amongst the resident population and a stochastic approximation is used to assess the risk to tourists.

2nd November: Sandra Maier (University of Strathclyde)

Title: Optimal Vaccination Age for Dengue in Brazil with a Tetravalent Dengue Vaccine

Date: 1pm Wednesday 2nd November 2016

Venue: Livingstone Tower﻿, 9th floor, room LT907

Abstract:  With the first vaccine against Dengue being licensed in several endemic countries an important aspect that needs to be considered is the age at which it should be administered. If vaccination is done too early it is ineffective as individuals are protected by maternal antibodies, but if it is done later the infection may spread in the younger age groups, also the risks of hospitalisation and mortality change with age of infection, which is influenced by vaccination. However, to find the optimal vaccination age the possible coexistence of up to four distinct Dengue serotypes and the cross-reactions between these serotypes and Dengue antibodies need to be taken into account. We adapt a method previously applied to other infectious diseases and define the lifetime expected risk due to Dengue with respect to two different risk measures (hospitalization and lethality) which we then seek to minimize for a given three-dose vaccination strategy. Our results show that the optimal vaccination age not only depends on the risk measure but also on the number and combination of serotypes in circulation, as well as on underlying assumptions about cross-immunity and antibody dependent enhancement (ADE).

16th November: Dr Laura Hobbs (University of Strathclyde)

Title: Dancing in the Moonlight: Vertical Migration of Arctic Zooplankton during the Polar Night

Date: 1pm Wednesday 16th November 2016

Venue: Livingstone Tower﻿, 9th floor, room LT907

Abstract:  This talk will focus on the results from my PhD, which I completed this year at the Scottish Association for Marine Science before starting here at Strathclyde. In recent years, evidence has been found of Diel Vertical Migration (DVM) in zooplankton during the Polar Night in the Arctic Ocean. However, the drivers of this light mediated behaviour during an apparent lack of illumination and food are poorly understood. A novel dataset comprising 58 deployments of moored Acoustic Doppler Current Profilers is used in this study to observe the vertical migratory behaviour of zooplankton on a pan-Arctic scale. Methods of circadian rhythm analysis are applied to detect synchronous activity. During the Polar Night, the moon is seen to control the vertical positioning of zooplankton, and a new type of migratory behaviour is described: Lunar Vertical Migration (LVM). This exists as LVM-day (24.8 hour periodicity) and LVM-month (29.5 day periodicity), and is observed throughout the Arctic Ocean. The results presented here show continuous activity throughout winter, and challenge assumptions of a quiescent Polar Night.

3rd May: Dr Emanuele Giorgi (CHICAS, Lancaster University)

Title: Disease Mapping and Visualization using Data from Spatio-Temporally Referenced Prevalence Surveys

Date: 1pm Wednesday 3rd May 2017

Venue: Livingstone Tower﻿, 9th floor, room LT907

Abstract:   We set out general principles and develop statistical tools for the analysis of data from spatio-temporally referenced prevalence surveys. Our objective is to provide a tutorial guide that can be used in order to identify parsimonious geostatistical models for prevalence mapping. A general variogram-based Monte Carlo procedure is proposed to check the validity of the modelling assumptions. We describe and contrast likelihood-based and Bayesian methods of inference, showing how to account for parameter uncertainty under each of the two paradigms. We also describe extensions of the standard model for disease prevalence that can be used when stationarity of the spatio-temporal covariance function is not supported by the data. We discuss how to define predictive targets and argue that exceedance probabilities provide one of the most effective ways to convey uncertainty in prevalence estimates. We describe statistical software for the visualization of spatio-temporal predictive summaries of prevalence through interactive animations. Finally, we illustrate an application to historical malaria prevalence data from 1334 surveys conducted in Senegal between 1905 and 2014.

1st June: Dr Luigi Sedda(CHICAS, Lancaster University)

Title: Including biology in spatial statistical models. Examples from vector-borne disease studies.

Date: 12.30pm, Thursday 1st June 2017

Venue: Livingstone Tower﻿, 9th floor, room LT907

Abstract:

Vector borne diseases (e.g. Malaria, Dengue, Leishmaniasis) account for 20% of all infectious diseases, causing several million of infections and more than 1 million deaths annually. The majority of the vectors are insects (e.g. mosquitoes, midges and flies) and ticks, which biology and epidemiology are not often fully understood.

Biological and statistical models are used for mapping and modelling vector-borne diseases, however, rarely these methods are combined to produce maps and tools for disease surveillance and control (e.g. vector hot spots).  In this talk I will present some techniques that can make data biologically meaningful; and the use of geo-bio-statistical models for tsetse flies (sleeping sickness) surveillance and control in Zambia. We show how mapping tsetse flies immigration, emigration, mortality and fertility can be the key element for successful disease eradication.

### Stochastic Analysis

15th March: Dr Joszef Lorinczi (Loughborough University)

Title: Non-local Schrodinger Operators and Related Jump Processes

Date: 3pm Wednesday 15th March 2017

Abstract:  Classical Schrödinger operators have been the object of much research involving functional analysis, probability and mathematical physics in the past decades. The recent interest in non-local Schrödinger operators consisting of the sum of a pseudo-differential operator and a multiplication operator greatly extended the range of applications, and inspired much new research in pure mathematics too. I will discuss how Feynman-Kac-type representations can be derived for the non-local cases and which random processes they give rise to. Then I will consider various sample path properties of these jump processes in terms of spectral properties of the generating non-local operators, and will contrast them with diffusions and classical Schrödinger operators.

19th April: Dr Alexandru Hening (Imperial College London)

Title: Stochastic Lotka-Volterra Food Chains

Date: 3.30pm Wednesday 19th April 2017

Abstract:   We study the persistence and extinction of species in a simple food chain that is modelled by a Lotka-Volterra system with environmental stochasticity. There exist sharp results for deterministic Lotka-Volterra systems in the literature but few for their stochastic counterparts. The food chain we analyze consists of one prey and $n-1$ predators for $n\in\{2,3,4,\dots\}$. The $j$th predator eats the $j-1$th species and is eaten by the $j+1$th predator; this way each species only interacts with at most two other species - the ones that are immediately above or below it in the trophic chain. We show that one can classify, based on an explicit quantity depending on the interaction coefficients of the system, which species go extinct and which converge to their unique invariant probability measure. Our work can be seen as a natural extension of the deterministic results of Gard and Hallam '79 to a stochastic setting. A novelty of our analysis is the fact that we can describe the behavior the system when the noise is degenerate. This is relevant because of the possibility of strong correlations between the effects of the environment on the different species. This is joint work with Dang H. Nguyen.

19th May: Dr Fengzhong Li (Shandong University, China)

Title: Time-Varying Feedback and its Control Ability

Date: 3.00pm Friday 19th May 2017

Abstract:   Comparison to pure feedback control, time-varying feedback control has distinct advantages, e.g., in handling system nonlinearities, counteracting system uncertainties and achieving prescribed performance. But due to the time-variations, time-varying feedback always keeps most people away, and its potential has been investigated far from enough. Here I shall illustrate some good and ability of time-varying feedback, and introduce some applications in SDEs, as well as several problems to be further investigated.

14th June: Dr Nicos Georgiou (University of Sussex)

Title: Last Passage Percolation Models in a Bernoulli Environment

Date: 3.00pm Wednesday 14th June 2017

Venue: Livingstone Tower, LT9.07

Abstract:   We will discuss two different last passage percolation models in an i.i.d. Bernoulli random environment.  In particular, I will show explicit laws of large numbers and order of fluctuations for the last passage time - the maximum number of Bernoulli points one can collect by following a sequence of admissible steps that ends in a predetermined lattice site. I will show how the behaviour of these models change depending on the set of admissible steps (e.g. the LLN changes, directions that belong in a "percolation cluster” change) and also show how the order of fluctuations change if the direction of the path endpoint changes. This is joint work with Janosch Ortmann and Federico Ciech (Univ. of Sussex).

16th June: Dr Gongfei Song (Nanjing University of Information Science and Technology, China)

Title: Quantized Feedback Control for Control Systems with Saturation Nonlinearity

Date: 3.30pm Friday 16th June 2017

Venue: Livingstone Tower, LT9.07

Abstract:   In control systems, every physical actuator or sensor is subject to saturation owing to its maximum and minimum limits. Common examples of such limits are the deflection limits in aircraft actuators, the voltage limits in electrical actuators. Saturation nonlinearities are also purposely introduced into engineering systems such as control systems and neural network systems. In addition, one of the most important research areas in control theory is quantized control. Quantized feedback is found in many engineering systems including mechanical systems and networked systems. Since communication that need to transmit the feedback information from
the sensor to the controller may become less reliable as the bandwidth is limited. Here, I shall investigate quantized feedback control problems for systems subject to saturation nonlinearity.

5th July: Professor Qian Guo (Shanghai Normal University, China)

Title: Stability of Two Kinds of Stochastic Runge-Kutta Methods for Stochastic Differential Equations

Date: 3.30pm Wednesday 5th July 2017

Venue: Livingstone Tower, LT9.07

Abstract:   We present two kinds of explicit Runge–Kutta methods for solving stochastic differential equations by using the three–term recurrence relations of Chebyshev and Legendre polynomials.  The almost sure stability and mean-square stability  of the numerical solutions generated by the two kinds of methods are investigated respectively. Numerical examples are provided to confirm theoretical results.

19th September: Dr Abdul-Lateef Haji-Ali (Oxford University)

Title: MLMC for Value-At-Risk

Date: 4.00pm Tuesday 19th September 2017

Venue: Livingstone Tower, LT9.07

Abstract:   In this talk, I explore Monte Carlo methods to estimate the Value-At-Risk (VaR) of a portfolio, which is a measure of the risk of the portfolio in some short time horizon.  It turns out that estimating VaR involves approximating a nested expectation where the outer expectation is taken with respect to stock values at the risk horizon and the inner expectation is taken with respect to the option index and stock values at some final time.  Following (Giles, 2015), our approach is to use MLMC to approximate the outer expectation where deeper levels use more samples in the Monte Carlo estimate of the inner expectation.  We look at various control variates to reduce the variance of such an estimate.  We also explore using an adaptive strategy (Broadie et al, 2011) to determine the number of samples used in estimating the inner expectation. Finally, we discuss using unbiased MLMC (Rhee et al., 2015) when simulating stocks requires time discretization.  Our results show that using MLMC to approximate a probability of large-loss with an error tolerance of order $\epsilon$, we are able to get an optimal complexity of order $\epsilon^{-2}(\log(\epsilon^{-1})^2$ that is independent of the number of options, for a large enough number of options.