# Mathematics & Statistics Seminars and colloquia

### Department Colloquia

19 September 2018: Dr Sascha Trostorff, (TU Dresden)

Title:  ﻿ Well-posedness for a general class of differential inclusions﻿

Date: 3.30pm Wednesday 19th September 2018

Venue: Livingstone Tower﻿, 9th floor, room LT908

Abstract: The abstract is attached.

7 November 2018: Prof Herbert Huppert (University of Cambridge)

Title:   How long does it take to get there?

Date: 3.30pm Wednesday 7th November 2018

Venue: Livingstone Tower, 9th floor, room LT908

Abstract: There are a huge number of nonlinear partial differential equations that do not have analytic solutions.   Often one can find similarity solutions, which reduce the number of independent variables, but still leads, generally, to a nonlinear equation.  This can, only sometimes, be solved analytically.  But always the solution is independent of the initial conditions.   What role do they play?   It is generally stated that the similarity  solution agrees with the (not determined) exact solution when (for some variable say t) obeys t >>t_1.   But what is  t_1?   How does it depend on the initial conditions?  How large must  t be for the similarity solution to be within 15, 10, 5, 1, 0.1, ….. percent of the real solution?   And how does this depend on the parameters and initial conditions of the problem?   I will explain how a number such typical, but somewhat different, fundamental problems can be solved, both analytically and numerically,  and compare some of the results with small scale laboratory experiments, performed during the talk.  It will be suggested that many members of the audience could take away the ideas and apply them in their own special areas.

14 November 2018: Prof Volker John (Weierstrass Institute for Applied Analysis and Stochastics and FU Berlin)

Title:   Variational Multiscale (VMS) methods for the simulation of turbulent incompressible flows

Date: 3.30pm Wednesday 14th November 2018

Venue: Livingstone Tower, 9th floor, room LT908

Abstract: VMS methods are a comparably new class of methods for simulating convection-dominated problems, like turbulent incompressible flows. The talk will start with an introduction to the difficulties of turbulent flow simulations. Next, principal ideas of the classical Large Eddy Simulation (LES) approach will be presented. Then, the basic ideas of VMS methods will be discussed, together with highlighting the differences to LES methods.

Various realizations of VMS methods for simulating turbulent incompressible flows have been proposed in the past fifteen years.  All of these realizations obey the basic principles of VMS methods: They are based on the variational formulation of the equations and the scale separation is defined by projections.  However, apart from these common basic features, the various VMS methods look quite different.

In this talk, the derivation of the different VMS methods is presented in some detail, their relation among each other and their behavior in numerical simulations are discussed.

5 December 2018: Dr Paul Johnson (University of Glasgow)

Title:   Combining livestock movement network data with a risk map to inform Rift Valley fever control in Northern Tanzania

Date: 3.30pm Wednesday 5th December 2018

Venue: Livingstone Tower, 9th floor, room LT908

Abstract: The potential of modelling to inform infectious disease control in low-income countries, where need is generally greatest, is hampered by a lack of data that is routinely available in many high-income countries, in particular livestock movement data. I will present recent progress from a project that aims to simulate the spread of zoonoses (animal infectious diseases that infect humans) such as Rift valley fever (RVF) across three regions of northern Tanzania (Arusha, Manyara and Kilimanjaro, covering an area slightly larger than Portugal, and home to 5 million people and 4 million cattle).  The simulation model combines three components: a model of livestock movement among the 398 wards (administrative subunits) in the study regions, fitted to data from archived livestock movement permits; a map of habitat suitability for the mosquito vectors of RVF; and a stochastic SEIR model of RVF transmission within wards. I will illustrate the simulation model’s potential to predict the effects of interventions (vaccination, market closure) on disease transmission, the potential to use the movement network to target interventions, and the model's main limitations, including the general lack of availability of good quality data on relevant parameters.

### Applied Analysis﻿

9th October: Grant Silver (Department of Mathematics and Statistics)

Title:   Parameterised communicability metrics in networks: The case of alternative routes for urban traffic﻿

Date:   3pm Tuesday 9th October

Venue: Livingstone Tower﻿, 9th floor, room LT907

Abstract:  Many systems in the real world are represented as networks and methods of network theory make it possible to analyse their properties. We demonstrate how communicability functions can be used to define node centrality indices, which gives a ranking of nodes based on their importance to the network. We then introduce a novel communicability function which makes greater use of longer walks in the network. We introduced a parameter that can be interpreted as the temperature in the network. We use the parameterised function to define a communicability distance between each pair of adjacent nodes. We show in Relative Neighbourhood Graphs how varying the parameter significantly changes the shortest communicability path between pairs of nodes. As the parameter increases, the length of the shortest communicability path increases, while the nodes themselves have, on average, decreased centrality values. We then apply the parameterised communicability function to the street network of Isfahan, where the parameter is interpreted as the level of traffic within the network. We show that for a particular parameter choice, the shortest communicability path becomes the preferred way to travel between nodes. This new path will be longer; however it will contain fewer nodes of high centrality, which corresponds to the avoidance of street intersections which are more likely to be congested with traffic. ﻿

23rd October: Grant Ross (Department of Mathematics and Statistics)

Title:   Applications of Centrality Measures to Simplicial Complexes﻿

Date:   3pm Tuesday 23rd October

Venue: Livingstone Tower﻿, 9th floor, room LT907

Abstract: Networks are a well-established method of representing complex systems mathematically. By representing individual entities by nodes and the connections between them as edges, we are able to model systems such as the interactions of proteins in a cell and the communication between wireless sensors. One limitation of networks is that there is no way to model three (or more) way interactions between nodes. Simplicial Complexes are one of the ways to remedy this situation. Centrality measures are ways of measuring the “importance” of a node, edge, triangle or higher order simplex to a simplicial complex in various situations. We shall focus on two applications of these centrality measures, the first to protein protein interaction networks and the second to random geometric simplicial complexes.

6th November: Dominic Breit (Heriot-Watt University)

Title:   Compressible Fluids Interacting with a Linear-Elastic Shell

Date:   4pm Tuesday 6th November

Venue: Livingstone Tower, 9th floor, room LT908

Abstract: We study the Navier–Stokes equations governing the motion of an isentropic compressible fluid in three dimensions interacting with a flexible shell of Koiter type. The latter one constitutes a moving part of the boundary of the physical domain. Its deformation is modeled by a linearized version of Koiter’s elastic energy. We show the existence of weak solutions to the corresponding system of PDEs provided the adiabatic exponent satisfies γ > 12/7 (γ > 1 in two dimensions).  The solution exists until the moving boundary approaches a self-intersection.  This provides a compressible counterpart of the results in Lengeler and R°užiˇcka (Arch RationMech Anal 211(1):205–255, 2014) on incompressible Navier–Stokes equations.

13th November: James Gaunt (Strathclyde Maths Skills Support Centre)

Title:   TBA﻿

Date:   3pm Tuesday 13th November

Venue: Livingstone Tower﻿, 9th floor, room LT907

Abstract:  TBA

### Continuum mechanics & industrial mathematics﻿

5th October: L Kahouadji (Imperial College London)

Title: Vortex formation and aeration in an air-water mixing system using a pitched blade turbine﻿

Date:  2.00pm Friday 5th October

Venue: Livingstone Tower﻿, 9th floor, room LT907

Abstract:

Three-dimensional DNS of an air-water mixing system by a pitched blade turbine in an open vessel is carried out using a hybrid front-tracking/level-set solver for parallel simulations of fully three-dimensional multiphase flows. The pitched blade turbine is constructed through a module that defines immersed objects using a distance function that accounts for the objects interaction with the flow and treated as a fictitious fluid in the Navier-Stokes solution where its velocity is corrected in order to satisfy rigid body motion constraint. In addition of ordinary primary vortices occurring in any kind of rotating flow, our configuration generates several secondary eddy structures resembling to Kelvin-Helmholtz, vortex breakdown, blade tip vortices and End-Wall corner vortices. Extreme situation, called "aeration" corresponding to bubble formation when the interface reaches the rotating blades is also highlighted through this study.﻿

9th October: Marcello Lappa (MechEng, Strathclyde)

Title:Solid Particle "Attractors" in Oscillatory Thermal Flows

Date:  1.00pm Tuesday 9th October

Venue: Livingstone Tower﻿, 9th floor, room LT907

Abstract:

The main overarching principle governing such dynamics is that, because of "inertial effects", a set of particles when transported by a fluid can behave as a "compressible medium", i.e. the spacing among particles can change significantly, even if the surrounding fluid and carrier flow are incompressible. This remarkable property can produce fluctuations of concentration of the dispersed matter and, hence, support mechanisms for particle accumulation and ordering. The subsets of space where particle clustering occurs are generally referred to as "attractors" (a terminology borrowed from the general field concerned with the study of non-linear systems). Even though the genesis of these phenomena can be associated to the inertia of particles, the new categories of attractors mentioned above do not conform to a simple definition or classification with respect to existing knowledge on particle accumulation phenomena. While inter-particle forces are not essential for the emergence of these structures, the presence of waves travelling in the fluid and their interaction with particles play a fundamental role.﻿

Can solid particles "spontaneously" self-assemble in a moving fluid forming complex, beautiful and aesthetically appealing geometrical curves and surfaces? Very recent discoveries have shown this might indeed be the case even if the considered flows are relatively simple.

Even though the ability of turbulence to promote particle clustering or accumulation has been described over many years, it has only recently been discovered that very common (non-turbulent, i.e. simply "laminar") thermal flows induced by gravity, surface tension or vibrational effects may produce very interesting phenomena in terms of patterning behaviour and structures. While particle aggregates formed in turbulent flows have, in general, an irregular appearance (forming fractal-like structures), these new classes of items display a variety of highly ordered, reproducible, high resolution structures ranging from 1D helical curves to 3D surfaces resembling the "quadrics" of projective geometry.

30th October: Alex Wray

Title: Low-order modelling of fluid systems

Date:  1.00pm Tuesday 30th October

Venue: Livingstone Tower, 9th floor, room LT907

Abstract:

Fluid dynamical systems of all types are widely studied due to their ubiquitous importance. This can cover everything from controlling the stability of high performance supercars, to the flight of jet planes, to the optimisation of the printing of Organic LED systems. Such systems are typically governed by complex partial differential equations such as the Navier-Stokes equations which are not generally analytically tractable.

Nonetheless, we often wish to be able to make analytical inferences about such systems. A very common approach is to use a `thin-film' approximation to reduce such systems to a lubrication-style situation, and indeed this technique is common within the CMIM group. I give three examples of other approaches that may be taken to derive asymptotic approximations outside the classic lubrication limit. These include:

- the modelling of multiple drops evaporating in proximity (using a boundary-integral method)

- the spreading and retraction of a drop on a hydrophobic substrate (using an energy method)

- the Moffatt problem: the maximum liquid load sustained by a rotating cylinder (using a combined weighted-residual/thick-film formulation)

6th November: Angela Busse (University of Glasgow)

Title: Equivalent sand grain roughness and surface topography

Date:  1.00pm Tuesday 6th November

Venue: Livingstone Tower, 9th floor, room LT907

Abstract:

Surface roughness affects near-wall turbulence if its height is significant compared to the viscous length scale of the flow. The fluid dynamical roughness effect is known to increase with the height of the roughness, but the influence of the roughness topography on the equivalent sand grain roughness and the near-wall flow is not fully understood. Historically, investigations on the fundamental fluid dynamic effects of surface roughness have mainly focused on simple, regular rough surfaces constructed using ordered arrangements of roughness elements such as cubes, hemispherical caps, or bars. In recent years, the focus has started to shift to irregular forms of roughness with complex topographies that are more representative of forms of surface roughness found in applications, e.g., roughness caused by erosion or fouling.  In this talk, relevant surface topographical parameters will be discussed in the context of recent results from direct numerical simulations of turbulent flow over irregular rough surfaces

27th November: Georgy Kitavtsev (University of Oxford)

Title: Approaching biological cell motility through thin-film models for active gels

Date:  1.00pm Tuesday 27th November

Venue: Livingstone Tower, 9th floor, room LT907

Abstract:

"In this talk, the complex problem of description of cell motility as the Adenosinetriphosphate (ATP) driven motion of a thin film of an actin filament network will be modelled in 2D. This model is based on the Ericksen theory that couples director and scalar order parameters and additionally includes active contributions to the stress tensor. The small aspect ratio of the film geometry allows for an asymptotic approximation of the free-boundary problem in the limit of weak elasticity of the network and strong active terms. The new thin-film model captures the defect dynamics in the bulk as well as wall defects and thus presents a significant extension of previous models based on the Lesli-Erickson-Parodi theory. As an example I will present an explicit stationary solution with a discontinuous director field of the derived lubrication model which induces a bidirectional flow in the presence of active forces."

4th December: Josh Walton (Strathclyde)

Title: Spontaneous flow transitions in active nematic liquid crystals

Date:  1.00pm Tuesday 4th December

Venue: Livingstone Tower, 9th floor, room LT907

Abstract:

Active liquid crystals are fluids in which continuous internal energy generation, such as in
bacterial suspensions and microtubule-forming suspensions, allows for spontaneous flow gen-
eration. In such fluids, the flow-generating agent is usually anisotropic (de ned by, for in-
stance, the long axis of the bacterium or microtubule) with such symmetry giving rise to a
liquid crystalline-like phase. Internally driven flows can lead to interesting effects such as
self-organisation and non-equilibrium defect confi gurations.

We consider the behaviour of an active liquid crystal con fined between two parallel
glass plates. Our theoretical analysis is based on extended Ericksen-Leslie equations such
that the stress tensor comprises of the usual liquid crystal viscous stress and an additional
active stress term which accounts for the activity of the fluid. We assume planar anchoring
of the director on the plates and no-slip conditions for the flow velocity.

By decoupling the Ericksen-Leslie equations, we show that it is possible to analytically
calculate critical activity strengths, at which, a transition to spontaneous flow occurs. These
results agree very well with the corresponding numerical calculations of the full nonlinear
model. The steady state Ericksen-Leslie equations are then solved numerically to obtain
non-trivial solutions for varying activity. The stability of these non-trivial solutions is also
determined. We find that changes in the activity magnitude leads to interesting effects such
as flow alignment. Finally, we consider how the results change when a constant pressure
gradient is applied across the cell in the horizontal direction.

Keywords: Ericksen-Leslie equations, active nematic, spontaneous flow generation.

### Numerical Analysis and Scientific Computing﻿

2nd October: Dr Dante Kalise (Imperial College London)

Title: TBA

Date:  4.00pm Tuesday 2ndOctober

Venue: Livingstone Tower﻿, 9th floor, room LT907

Abstract:

23rd October: Dr Kirk Soodhalter (Trinity College Dublin)

Title:  ﻿﻿TBA

Date:  4.00pm Tuesday 23rd October

Venue: Livingstone Tower﻿, 9th floor, room LT907

Abstract:  TBA

7th November: Dr Kitty Meeks (University of Glasgow)

Title:  Reducing Reachability in Temporal Networks

Date:  2.00pm Tuesday 6th November

Venue: Livingstone Tower, 9th floor, room LT907

Abstract:   The concept of reachability sets (i.e. which vertices in a network can be reached by travelling along edges from a given starting vertex) is central to many network-based processes, including the dissemination of information or the spread of disease through a network. Depending on the application, it might be desirable to increase or decrease the number of vertices that are reachable from any one starting vertex. In most applications, time plays a crucial role: each contact between individuals, represented by an edge, will only occur at certain time(s), when the corresponding edge is "active". The relative timing of edges is clearly crucial in determining the reachability set of any vertex in the network.

In this talk, I will address the problems of reducing the maximum reachability of any vertex in a given temporal network by two different means:
(1) we can remove a limited number of time-edges (times at which a single edge is active) from the network, or
(2) the number of timesteps at which each edge is active is fixed, but we can change the relative order in which different edges are active (perhaps subject to constraints on which edges must be active simultaneously, or restrictions on the timesteps available for each edge).
Mostly, we find that these problems are computationally intractable even when very strong restrictions are placed on the input, but we identify a small number of special cases which admit polynomial-time algorithms, as well as some general upper and lower bounds on what can be achieved.

Everything in this talk is based on joint work with Jessica Enright (University of Edinburgh); I will also mention some joint results with George B. Mertzios and Viktor Zamaraev (University of Durham) and Fiona Skerman (Uppsala University).

13th November: Dr Lehel Banjai (Heriot Watt University)

Title:   TBA

Date:  4.00pm Tuesday 13th November﻿

Venue: Livingstone Tower﻿, 9th floor, room LT907

Abstract:   TBA

31st January 2019: Dr Stefano Serra Capizzano (Università degli Studi dell'Insubria)

Title: TBA

Date:  1pm Thursday 31st January 2019

Venue: Livingstone Tower, 9th floor, room LT908

Abstract:

7th February 2019: Dr Pierre-Louis Giscard (Université du littoral Cote d'Opale)

Title: TBA

Date:  1pm Thursday 7th February 2019

Venue: Livingstone Tower, 9th floor, room LT907

Abstract:

14th February 2019: Dr Stefano Pozza (Charles University Prague)

Title: TBA

Date:  1pm Thursday 14th February 2019

Venue: Livingstone Tower, 9th floor, room LT907

Abstract:

7th March 2019: Dr Irene Kyza (University of Dundee)

Title: TBA

Date:  1pm Thursday 7th March 2019

Venue: Livingstone Tower, 9th floor, room LT907

Abstract:

21st March 2019: Dr Silvia Gazzola (University of Bath)

Title: TBA

Date:  1pm Thursday 21st March 2019

Venue: Livingstone Tower, 9th floor, room LT907

Abstract:

### Population Modelling and Epidemiology﻿

16th January 2019: Mel Consentino, Florence Tydeman (University of Strathclyde)

Title:  A New High-Accuracy Click Classifier to Study Harbour Porpoises in the Wild

Date: Wednesday 16th January, 1.00pm

Venue: Livingstone Tower, LT907

Abstract:  Harbour porpoises are difficult to observe at sea, even with good weather conditions, due to their small size and cryptic behaviour. However, they are highly vocal, producing narrow-band high-frequency (NBHF) echolocation clicks, which are produced as a series of clicks or ‘click trains’, making them well suited for passive acoustic monitoring (PAM). The first part of my PhD project includes the development of a new porpoise classifier (PorCC) that can be coupled to PAM systems to identify the likely porpoise signals among transient sounds. PorCC works on full-waveform signals and shows an improved performance over current classifiers. It was developed in MATLAB and uses the coefficients of two logistic regression models in a decision-making pathway to assign each signal to one of three categories: high-quality click (HQ), low-quality click (LQ), or high-frequency noise (N). PorCC achieved hit rates > 90% for HQ clicks while keeping false alarm levels < 1%. Moreover, PorCC could be applied for real time monitoring, as well as to study harbour porpoises, and potentially other NBHF species from data collected by towed hydrophones or static recorders. The following step is to separate overlapping click trains to then assess the likely behaviour the animals are engaged in, as evidence suggest the patterns of the click trains are indicative of at least some behaviours (e.g., feeding). The objective of the second part of my project is to study the acoustic behaviour of Kylie, a solitary female common dolphin who inhabits in the Firth of Clyde and interacts with harbour porpoises since at least 2004. Preliminary results suggest Kylie produces signals similar to those of the harbour porpoise when interacts with them. This would be the first case of vocal interaction between two species in the wild.

Title: Investigating the Variation of Antibiotic Prescribing Rates between NHS Scotland Health-boards and GP Practices Through the use of Maps, Principal Components and Spatial Analysis.

Date: Wednesday 16th January, 1.00pm

Venue: Livingstone Tower, LT907

Abstract:

Background: In Scotland, there is a goal to raise awareness of unnecessary prescribing and inappropriate use of antibiotics, advocated by the Scottish Antibiotics Prescribing Group (SAPG), with the aim to lower the persistence of resistant organisms and control infections such as Clostridium-difficile infection (CDI). The aim of this analysis is to investigate the variation of antibiotic prescribing rates between NHS Scotland health boards and GP practices through the use of maps, principal components and spatial analysis.

Methods: This analysis began with multiple open source ISD prescription data files which were converted into a linked dataset. Other GP descriptive information and locations of GP practices were also merged to this dataset and were used to investigate how the rates of antibiotic prescribing vary across Scotland. Through the use of maps, it was possible to visualise total antibiotic prescribing rates, and individual antibiotic drug group rates, between NHS health boards in Scotland. Creating a spatial point data frame allowed for visualisation of the difference between antibiotic prescribing rates of individual GP practices, within the same health boards, assessing close proximity rates.

Principal Component Analysis (PCA) on the 13 Antibiotic groups was used to indicate GP practices that follow similar prescribing trends of antibiotic drug groups. A Poisson generalised linear regression model of total antibiotic prescribing was constructed, investigating potential explanatory variables. The residuals from this model were then assessed for spatial association, this was achieved using Monte Carlo Envelopes to test for spatial association.

Results: This analysis has shown that the variation in antibiotic prescribing rate between Scottish GP practices can be partly explained by practice demographics. Higher proportions of practice populations Over 74, Under 15 and in the Most Deprived quintile suggests higher prescribing at GP-level, whereas increasing proportion of Least Deprived suggests lower prescribing rates. The PCA has shown that 25% of the total variation can be explained, approximately, by an average across all antibiotic drug groups therefore total antibiotics is a reasonable representation of prescribing at GP-level. After adjusting for GP practice characteristics, there is no evidence of spatial association between GP practices.

28th November: Soizic Garnier, Hazel Smith (University of Strathclyde)

Title: Optimal-detail circulation models for fjords and sea lochs: an application to the Puget Sound

Date: Wednesday 28th November, 1.00pm

Venue: Livingstone Tower, LT907

Abstract:  The Puget Sound is a fjord on the west coast of the USA near Seattle. It is an important habitat for marine life, but in the last 30 years three species of wild salmon have declined dramatically. A possible explanation for this decline is the impact of water circulation and salinity variations on plankton production. This context motivates the investigation of long-term changes in circulation due to environmental dynamic conditions and their impacts on primary production. Our long-term goal is to create a new circulation model that runs over decades and to couple it with a bio-chemical model. Here we focus on the development of the physical model. We use a tidally and laterally averaged framework to describe the estuarine circulation over a long time-scale. However, this requires us to define tidally averaged eddy coefficients. We present a new tidally averaged mixing parametrization for the fjord of the Puget Sound. We show that different physical processes drive the mixing in the bottom and surface layers. For the bottom layer the eddy viscosity relies only on the tidal velocity. However, for the surface layer, wind stress also needs to be considered.

Title: Assessing the Impact of Offshore Windfarm Developments on Marine Mammal Populations

Date: Wednesday 28th November, 1.00pm

Venue: Livingstone Tower, LT907

Abstract: The construction of offshore windfarms can impact marine mammals via the underwater noise generated by the installation of foundations. Potential consequences for extended or repeated disturbance include behavioural and physiological changes which can affect the health and vital rates of individual animals. This, in turn, can translate into population effects.

Consents have been granted for a number of major windfarm developments on the East Coast of Scotland, with further applications anticipated. These major developments each have the potential to input construction noise over tens of kilometres and, taken cumulatively, will input construction noise over a substantial number of years. In this talk we use the iPCoD (Interim Population Consequences of Disturbance) model to assess the impact of proposed developments on the East Coast of Scotland on the long term population dynamics of several key species of marine mammals: bottlenose dolphin, grey seal, harbour porpoise and minke whale.

14th November: Melinda Chou, Kate Pyper (University of Strathclyde)

Title: Effect of Viral Plasticity on the Survival of Host-Virus Systems

Date: Wednesday 14th November, 1.00pm

Venue: Livingstone Tower, LT907

Abstract: Phenotypic plasticity is the ability of an individual to vary their features when environmental conditions change. It can be found in organisms at any trophic level and many studies pointed out the importance of plasticity in the survival of individuals. However, the effects of plasticity on the ecological interactions are not well characterized. Here, we focus on viral plasticity (i.e. viruses are more virulent when the host growth rate increases) and we use models to investigate how plastic viruses affect the interaction with bacteria under a diversity of hosts size and under different environmental conditions. We investigate under which conditions plasticity translates into an increase of coexistence between host and virus and how plasticity influences oscillations as typically observed for antagonistic. We will discuss the stability regions that we compare with a non-plastic system (i.e. viral traits are fixed). The self-regulation involved by the plasticity can have important general applications such as for predator-prey systems.

Title: A Statistical Assessment of the Utility of TOXBASE in the Emergency Department

Date: Wednesday 14th November, 1.00pm

Venue: Livingstone Tower, LT907

Abstract: The National Poisons Information Service maintain TOXBASE, a system which provides information on the treatment of poisoned patients. It contains information on over 17,000 different toxicants. In this talk, I will focus on work linking TOXBASE usage data with routinely collected attendances and admissions data from England and Wales in order to assess whether usage of TOXBASE in the emergency department has a positive impact on admissions due to poisoning.

This analysis began by comparing temporal patterns in accesses to TOXBASE with emergency admissions due to poisoning. It was then of interest to determine whether there were hospitals which were unusual with respect to their admissions or their use of TOXBASE. An informal assessment of these “unusual” values was carried out in order to assess whether there were any commonalities which may explain why the locations are unusual.

Finally, regression models were fit in order to assess the impact of TOXBASE use. An interaction model was first used to assess the overall effect of TOXBASE use on emergency admissions. This showed that, while admissions will always increase with attendances, locations which use TOXBASE more will see a smaller increase than those which use TOXBASE less. The final piece of analysis used simple models to assess whether accesses to six different drug sub-groups had different effects on admissions.

3rd October 2018: Dr Tanya Englishby (Mathematics and Statistics, University of Strathclyde)
Title: Genetic and non-genetic evaluation tools for accelerating improvement in beef cattle carcass traits within and across country﻿

Date: 3pm Wednesday 3rd October 2018

Venue: Livingstone Tower﻿, 9th floor, room LT907

Abstract: The main revenue source for beef farmers worldwide is carcass value (carcass weight, conformation and fat score). In general, heavier, better conformed (muscular), lean carcasses are awarded premium grades at the abattoirs. The grade a carcass receives is related to a number of factors, such as the genetics (breed) of the animal and the environment in which it is reared. In order to improve the profitability of the herd, breeders need an accurate means of comparing and selecting the best animals to breed from. Beef producers also need information on how their farm management (environmental) practices affect the performance of their animals. For predictive purposes, both Ireland and the UK routinely assess the productivity of animals for carcass traits, to estimate the improvement in these traits by the use of particular animals in breeding programs. The primary purpose of these evaluations is to distinguish the elite breeding stock in the population. These evaluations may be enhanced through employing alternative methods of analysis and by incorporating more information on animals or relatives of animals. This increase in information can be achieved through countries pooling their data. Pooling data also means that farmers in each country will have an accurate means of comparing foreign and domestic bulls, therefore getting access to the best selection candidates.

Using information on beef carcasses from abattoirs in Ireland and the UK, this study makes use of random regression analyses to generate tools for the enhancement of selection and management decisions at a national (within each country) and international (between countries) level. The results from this study show that the influence of the genetic make-up of an animal on carcass traits varies across age and that there is variation between breeding bulls in their growth profiles for carcass traits. This means that the progeny of some bulls develop at different rates compared to the progeny of other bulls, therefore they will be ready for slaughter at different ages. Knowledge of individual sire growth profiles for carcass traits could help farmers identify the most profitable time at which to slaughter the progeny of particular bulls, leading to a more efficient use of farm resources.

This study also showed how data collected for the purpose of genetic evaluations for carcass traits can yield useful information for consideration in farm management practices. The herd environment plays a significant role in carcass trait performance across ages at slaughter and years of slaughter and this information is a useful indicator of management practices across time.

In addition to the enhancement of within country evaluations, this study shows the potential benefits of an international evaluation for carcass traits. Access to international evaluations would allow Irish and UK beef farmers to make more informed decisions on the selection of breeding stock needed to increase genetic gain in carcass traits and subsequently increase herd profitability.

3rd October 2018: Ricardo Gonzalez Gil (Mathematics and Statistics, University of Strathclyde)
Title: Long-term changes in the plankton of the Canabrian Sea

Date: 3pm Wednesday 3rd October 2018

Venue: Livingstone Tower﻿, 9th floor, room LT907

Abstract:Understanding how different hydrographic processes drive long-term changes in plankton is crucial to unveil the marine ecosystem functioning and project the consequences of future climate scenarios. To address this question in the Cantabrian Sea (southern Bay of Biscay), we combined a monthly time-series (1993-2010) of physicochemical and biological data collected in situ and satellite observations. Zooplankton biomass increased during the study period, especially for larger size classes. These results contrast with the decrease in biomass and size expected under global warming, which is shown in the region by the rise in summer sea surface temperature, suggesting the operation of other processes. Indeed, winter mixing and coastal upwelling were key drivers of zooplankton dynamics in spring and autumn, respectively, when zooplankton inter-annual increases were stronger. In particular, winter-mixing control occurs through the spring phytoplankton bloom: deeper and later mixing in winter was followed by later, larger and more productive blooms. We found that winters with weaker mixing (that led to weaker spring blooms) were associated with warmer surface temperatures. Consequently, global warming may lead in the future to smaller and less productive spring blooms in the Bay of Biscay, reversing the observed positive trends in zooplankton.
﻿

19th September 2018: Mr Trevor Sloughter (Mathematics and Statistics, University of Strathclyde)
Title: Integrating Seasonal Variation of Light Response in High-Latitude Phytoplankton into Models of Spring Blooms﻿

Date: 1pm Wednesday 19th September 2018

Venue: Livingstone Tower﻿, 9th floor, room LT907

Abstract: The warming of high latitude marine environments presents a challenge to ecosystem models which aim to predict future change in primary production magnitude and phenology. A major difficulty in predicting these changes and their impact on higher trophic levels is that the strong seasonal variations in physiology and strategy of phytoplankton are poorly understood. Further, seasonality is usually not accounted for in ecosystem models. Here, a mechanistic explanation for observed seasonality in light response (the photoparameters µ0 and α) is proposed using a trade-off between photosynthetic efficiency and respiration costs. This seasonality is integrated into an NPZD ecosystem model applied to the eastern Bering Sea, which captures the timing and magnitude of the spring bloom in a cold year more accurately than without seasonality. The final aim of this project is a comparison of the model's ability to reproduce spring blooms in both timing and magnitude for both cold and warm years, using cruise data collected in cold years 2007-2009, and warm years 2014-2015.﻿

19th September 2018: Dr Jiafeng Pan (Mathematics and Statistics, University of Strathclyde)

Title: A pilot project of real world outcomes in patients with metastatic breast cancer treated with taxanes

Date: 1pm Wednesday 19th September 2018

Venue: Livingstone Tower﻿, 9th floor, room LT907

Abstract:  Aim To compare the outcome of two taxane treatments (docetaxel and paclitaxel) in women with metastatic breast cancer.

Design Cohort study via linking existing health datasets (Chemocare, hospitalisation and cancer registry).

Cohort Patients with metastatic breast cancer in GGC who are treated with taxane regimen during Jan 2010 - Dec 2015 - all patients are followed from first treatment date until their death or the censor date March 2017.

Statistical methods Adjusted hazard ratio comparing the survival of two taxane treatments is derived using Cox proportional-hazards regression accounting for the baseline characteristics (eg. Age, social deprivation and comorbidity). Proportionality assumption for the adjusted model is tested using Schoenfeld residuals. Proportionality assumption is failed which means the hazard ratio for taxane treatments is time dependent in the adjusted model. We therefore truncate the data set into three time intervals and derive a step function for the hazard ratio of taxane treatment i.e. a different hazard ratio in each time interval.

Results Compared to docetaxel, patient with paclitaxel are 1.7 times (95% CI 1.03-2.87) more likely to die during first year after treatment, but among survivors, no significant difference in survival after one year.

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.

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.

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.

20th March: Dr Bingzhang Chen (Research & Development Center for Global Change, Japan Agency for Marine-Earth Science and Technology)

Title: Why Primary Production Peaks at Surface During Summer in the Subtropica, Oligotrophic Open Ocean?

Date: 1pm Tuesday 20th March 2018

Venue: Livingstone Tower﻿, 9th floor, room LT908

Abstract:   Classic understanding on environmental controls on primary production (PP) in the subtropical, oligotrophic ocean gyre is that phytoplankton growth and PP are limited by the upward supply of inorganic nutrients delivered largely by diffusion. Since nutrient supply mostly comes from below and light attenuates from surface to the depth, phytoplankton growth rate and PP should peak at some intermediate depth, coinciding with the deep chlorophyll maximum (DCM) layer. However, examination on the PP data measured at three stations (ALOHA, S1, and BATS) in the subtropical North Pacific and Atlantic reveals that PP peaks within the surface mixed layer despite the negligible nutrient concentration at surface and a pronounced deep chlorophyll maximum (DCM) around 100 m. While the formation of DCM can be largely explained by phytoplankton photo-acclimation (adjustments of chlorophyll-to-carbon ratios), the surface peak of phytoplankton growth rate is difficult to explain. I evaluate several hypotheses that try to explain the surface peak of phytoplankton growth rate. The preliminary finding is that the coexistence of high- and low-light adapted ecotypes can best explain the observed patterns of nutrient, chlorophyll, and PP. This is highly consistent with many biodiversity–ecosystem functioning (BEF) studies that biodiversity can enhance productivity and nutrient utilization via niche complementarity.  Thus, evaluation of the effects of climate change on ocean productivity is hard to be reliable without considering biodiversity.

### Stochastic Analysis

7th December 2018: Professor Wei Mao (Donghua University, China)

Title: Asymptotic Properties and Numerical Analysis of the Solution to Hybrid Stochastic Differential Equations with Jumps

Date: Friday 7th December, LT908, 4-5.00pm

Abstract:  In this paper, we are concerned with the asymptotic properties and numerical analysis of the solution to hybrid stochastic differential equations with jumps. By applying the theory of M-matrices, we study the pth moment asymptotic boundedness and stability of the solution. Under the non-linear growth condition, we also show the convergence in probability of the Euler-Maruyama approximate solution to the true solution. Finally, some examples are provided to illustrate our new results.

10th October 2018: Prof Annie Millet (Université Paris 1 Panthéon-Sorbonne)

Title: ﻿﻿﻿﻿On strong convergence of time numerical schemes for the stochastic 2D Navier-Stokes equations﻿

Date: 3pm Wednesday 10th October 2018, LT907

Abstract:  We prove that some time discretization schemes, such as the splitting, fully and semi-implicit ones, of the 2D Navier-Stokes equations subject to a random perturbation converge in $L^2(\Omega)$. The speed of convergence depends on the viscosity. The argument is based on convergence of a localized scheme, and on exponential moments of the solution to the stochastic 2D Navier-Stokes equations. This joint work with H.~Bessaih  improves previous results which only described the speed of convergence in probability of these numerical schemes﻿.

26th September 2018: Mr Ya Wang (University of Science and Technology, China)

Title: Stability in distribution of stochastic functional differential equations

Date: 4pm Wednesday 26th September 2018, LT907

Abstract:  The theory of stochastic functional differential equations (SFDEs) has been developing very quickly.  In particular, many research papers have been devoted to the stability analysis of SFDEs. However, most of these papers are concerned with the stability of the trivial solution in probability or moment and such stability is somehow too strong. In many practical situations it would be more useful to know whether or not the probability distribution of the solution will converge to some distribution). This convergence is called the stability in distribution and the limit distribution is known as the stationary distribution. The talk will review the current research on the stability in distribution of SFDEs and show our new results﻿.

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.

24th August: Dr Leila Setayeshgar (Providence College, USA)

Title: Bayes' Rule and the Law

Date: 3.00pm Thursday 24th August 2017

Venue: Livingstone Tower, LT9.07

Abstract:   Bayesian inference is an approach in mathematical statistics where the probability of a hypothesis is updated as more evidence and data become available.  It has wide applications in many areas such as machine learning, evolutionary biology, medicine and even in the judicial system.  This talk will explore how Bayesian inference can be used in a specific court case to assist jurors in the process of legal decision making, demonstrating the power of mathematics in the court room.

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.

18th October: Dr Eyal Neuman (Imperial College London)

Title: On Uniqueness and Blowup Properties for a Class of Second Order SDEs

Date: 2.30pm Wednesday 18th October 2017

Venue: Livingstone Tower, LT9.07

Abstract:   As the first step for approaching the uniqueness and blowup properties of the solutions of the stochastic wave equations with multiplicative noise, we analyze the conditions for the uniqueness and blowup properties of the solution (X_t; Y_t) of the equations dX_t = Y_tdt, dY_t =|X_t|^\alpha dB_t, (X_0; Y_0) = (x_0; y_0). In particular, we prove that solutions are nonunique if 0 < \apha < 1 and (x_0; y_0) = (0; 0) and unique if 1=2 < \alpha and(x_0; y_0) \not= (0; 0). We also show that blowup in finite time holds if \alpha > 1 and (x_0; y_0) \not= (0; 0).

12th June: Dr Yue Wu (Edinburgh University)

Title: Randomized Numerical Schemes for (S)ODEs/SPDEs

Date: 4.00pm Tuesday 12th June 2018

Venue: Livingstone Tower, LT9.07

Abstract:   A wide range of applications, for instance, in the engineering and physical sciences as well as in computational finance is still spurring the demand for the development of more efficient algorithms and their theoretical justification. In particular, the current focus lies on the approximation of ODEs/S(P)DEs which cannot be treated by standard methods found in textbook.  We, therefore, first developed two randomized explicit Runge–Kutta schemes for ordinary differential equations (ODEs) with time-irregular coeffcient functions. In particular, the methods are applicable to ODEs of Carathéodory type, whose coeffcient functions are only integrable with respect to the time variable but are not assumed to be continuous.  An important ingredient in the analysis are corresponding error bounds for the randomized Riemann sum quadrature rule.  It is demanding to approximate numerical solutions of non-autonomous SDEs where the standard smoothness and growth requirements of standard Milstein-type methods are not fulfilled. In the case of a non-differentiable drift coefficient function f, we proposed a drift-randomized Milstein method to achieve a higher order approximation and discussed the optimality of our convergence rates.  We also pushed the idea to the numerical solution of non-autonomous semilinear stochastic evolution equations (SEEs) driven by an additive Wiener noise. Usually quite restrictive smoothness requirements are imposed in order to achieve high order of convergence rate. It turns out that the resulting method converges with a higher rate with respect to the temporal discretization parameter without requiring any differentiability of the nonlinearity. Our approach also relaxes the smoothness requirements of the coefficients with respect to the time variable considerably.