**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.

Title: ** TBA**

Date: 3.30pm Wednesday 7th November 2018

Venue: Livingstone Tower, 9th floor, room LT908

Abstract: TBA

### 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.

Title: TBA

Date: 3pm Tuesday 23rd October

Venue: Livingstone Tower, 9th floor, room LT907

Abstract: TBA

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.

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.

### Numerical Analysis and Scientific Computing

10th October: Dr Prashanth Nadukandi (University of Manchester)Title: Stable computation of the trigonometric matrix functions: cos(sqrt(A)) and sinc(sqrt(A))

Date: 4.00pm Tuesday 10th October

Venue: Livingstone Tower, 9th floor, room LT907

Abstract:

Title: Perron-Frobenius theorem for multi-homogeneous maps and some applications

Date: 4.00pm Tuesday 24th October

Venue: Livingstone Tower, 9th floor, room LT907

Abstract: The nonlinear Perron-Frobenius theory addresses existence, uniqueness and maximality of positive eigenpairs for order-preserving homogeneous functions. This is an important and relatively recent generalization of the famous results for nonnegative matrices. In this talk I present a further generalization of this theory to "multi-dimensional" order-preserving and homogeneous maps, which we briefly call multi-homogeneous maps. The results presented are then used to discuss some nonlinear matrix and tensor eigenvalue problems and some of their applications.

Title: An introduction to multitrace formulations and associated domain decomposition solvers

Date: 4.00pm Tuesday 7th November

Venue: Livingstone Tower, 9th floor, room LT907

Abstract: Multitrace formulations (MTFs) are based on a decomposition of the problem domain into subdomains, and thus domain decomposition solvers are of interest. The fully rigorous mathematical MTF can however be daunting for the non-specialist. We introduce in this work MTFs on a simple model problem using concepts familiar to researchers in domain decomposition. This allows us to get a new understanding of MTFs and a natural block Jacobi iteration, for which we determine optimal relaxation parameters. We then show how iterative multitrace formulation solvers are related to a well known domain decomposition method called optimal Schwarz method: a method which used Dirichlet to Neumann maps in the transmission condition. We finally show that the insight gained from the simple model problem leads to remarkable identities for Calder ́on projectors and related operators, and the convergence results and optimal choice of the relaxation parameter we obtained is independent of the geometry, the space dimension of the problem, and the precise form of the spatial elliptic operator, like for optimal Schwarz methods. We illustrate our analysis with numerical experiments. This is a joint work with X. Claeys and M.J. Gander

Title: Direct Solution of Sparse Linear Equations on Parallel Computers

Date: 4.00pm Tuesday 14th November

Venue: Livingstone Tower, 9th floor, room LT907

Abstract: As part of the H2020 FET-HPC Project NLAFET (http://www.nlafet.eu/), we are studying the scalability of algorithms and software for using direct methods for solving large sparse equations. In this talk we briefly discuss the structure of NLAFET and the scope of the Project. We then focus on algorithmic approaches for solving sparse systems: positive definite, symmetric indefinite, and unsymmetric. An important aspect of most of our algorithms is that although we are solving sparse equations most of the kernels are for dense linear algebra. We show why this is the case with a simple example before illustrating the various levels of parallelism available in the sparse case. The work described in this talk has been conducted by the STFC NLAFET Team who comprise: Florent Lopez, Stojce Nakov, and Philippe Gambron.

Title: The p-Laplacian on a segment. Spectral and time evolution problem

Date: 4.00pm Tuesday 21st November

Venue: Livingstone Tower, 9th floor, room LT907

Abstract: The non-linear spectral and time evolution problems associated to the p-Laplacian have attracted significant attention in recent years. In this talk we will examine various analytical properties of these two problems, when posed on a segment of finite length and subject to homogeneous Dirichlet boundary conditions at the end points. An explicit expression for the eigenfunctions can be found in terms of special functions. These eigenfunctions are naturally called p-sine functions, a terminology introduced by Elbert, Otani and others in the 1980s. The p-sine functions play a fundamental role in the theory of Sobolev embeddings, yet many questions about them remain open. During the talk we will discuss partial answers and challenges associated to some of these open questions. We only known, for example, that the p-sine functions form a Riesz basis of the Hilbert space L^2(0,1) for all p larger than or equal to a threshold p_1, where p_1 is the solution of a transcendental equation and is approximately equal to 1.043817. The confirmation of this threshold relies on the Beurling representation of the change of coordinate operator in terms of Dirichlet series and the answer to the basis question remains completely open for 1

Title:

Date: 4.00pm Tuesday 30 January 2018

Venue: Livingstone Tower, 9th floor, room LT907

Abstract:

Title: Stochastic Separation Theorems and One-trial corrections of Legacy AI systems

Date: 3.00pm Tuesday 20 February 2018

Venue: Livingstone Tower, 9th floor, room LT907

Abstract: In this talk we shall consider the problem of mistakes in Artificial Intelligence (AI) systems and motivate a technology for simple, real-time, computationally-efficient, and non-iterative improvements of the systems. The improvements are, in essence, shallow networks constructed on top of the existing AI computational architectures. Theoretical foundation of the technology is based on Stochastic Separation Theorems and the ideas of measure concentration. We show that, subject to mild technical assumptions on statistical properties of internal signals in the original AI, with probability close to one the technology enables instantaneous ''learning away'' of spurious and systematic errors. The method is illustrated with applications in image processing and face/human shape recognition/detection.

Title: Computational research on blood flow dynamics and the initiation of atherosclerosis

Date: 4.00pm Tuesday 27 February 2018

Venue: Livingstone Tower, 9th floor, room LT907

Abstract: Atherosclerosis, the leading underlying cause of heart failure and stroke, is an inflammatory disease affecting primarily the larger systemic arteries. Atherosclerotic lesions are non-uniformly distributed along the arterial network, suggesting an important role for hemodynamic factors, particularly wall shear stress, in their development. In this talk, I will present computationally fluid dynamic (CFD)-obtained results on the role of hemodynamics on the distribution of these stresses, around idealized and anatomically correct arterial geometries. The value and sensitivity of this work will be discussed on the basis of a reverse-engineering approach in finding direct correlations with biology. A short description of other ongoing and future group research activities will also be presented.

Title: Generalized locally Toeplitz sequences and some applications to fractional diffusion equations

Date: 4.00pm Tuesday 6th March 2018

Venue: Livingstone Tower, 9th floor, room LT908

Abstract: When discretizing a linear PDE by a linear numerical method, the computation of the numerical solution reduces to solving a linear system. The size of this system grows when the discretization parameter n increases, i.e., when we refine the discretization mesh. We are then in the presence of a sequence of linear systems {Anxn = bn} with increasing size.

It is usually observed in practice that the corresponding sequence of discretization matrices {An} inherits a structure from the continuous problem and enjoys an asymptotic spectral distribution, which is compactly described by a function, known as symbol. The knowledge of the symbol and of its properties has a very crucial role, since it can be used to perform a convergence analysis and to predict the behavior of preconditioned Krylov and multigrid methods applied to An, as well as to design effective preconditioners and multigrid solvers for the associated linear systems.

The main tool for computing the spectral symbol of a PDE discretization matrix is the theory of Generalized locally Toeplitz (GLT) matrix-sequences introduced in [5] as a generalization of both classical Toeplitz sequences and variable coefficient differential operators. In this talk, we give an overview of such a theory and we outline its application to the fractional diffusion equations (FDEs), an extension of classical diffusion equations used to model anomalous diffusion phenomena. Exploiting the GLT machinery, we provide a spectral analysis of some FDE discretization matrices and we use the retrieved spectral information either to discuss the convergence of recently proposed techniques [2, 4] or to design new preconditioning and multigrid strategies for both 1D and 2D FDE problems [1, 3].

References

1. M.Donatelli,M.Mazza,S.Serra-Capizzano,Spectral analysis and structure preserving preconditioners for fractional diffusion equations, J. Comput. Phys., 307 (2016) 262–279.

2. S. L. Lei, H. W. Sun, A circulant preconditioner for fractional diffusion equations, J. Comput. Phys., 242 (2013) 715–725.

3. H. Moghaderi, M. Dehghan, M. Donatelli, M. Mazza, Spectral analysis and multigrid preconditioners for two- dimensional space-fractional diffusion equations, J. Comput. Phys., 350 (2017) 992–1011.

4. H. Pang, H. W. Sun, Multigrid iterative methods for fractional diffusion equations, J. Comput. Phys., 231 (2012) 693–703.

5. S. Serra-Capizzano, Generalized locally Toeplitz sequences: spectral analysis and applications to discretized differential equations, Linear Algebra Appl., 366 (2003) 371–402.

Title: Computing the operator norm of nonnegative matrices

Date: 4.00pm Tuesday 22nd May 2018

Venue: Livingstone Tower, 9th floor, room LT908

Abstract: Computing the subordinate operator norm of a rectangular matrix is known to be NP-hard in general. However, by restricting ourselves to matrices with nonnegative entries, we show that under suitable conditions on the norms, the operator norm of such matrices can be computed efficiently with a nonlinear power method. A linear convergence rate to the global maximizer is discussed. In particular, our conditions include the hypercontractive case for which no similar results were previously known. As an application, we discuss how these results can be used to produce lower bounds on the log-Sobolev constant of finite Markov chains.

Joint work with Francesco Tudisco and Matthias Hein.

### Population Modelling and Epidemiology

3rd October 2018: Dr Tanya Englishby (Mathematics and Statistics, University of Strathclyde)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.

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.

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 µ_{0} 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.

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.

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.

Title: TBA

Date: 1pm Wednesday 6th April 2016

Venue: Livingstone Tower, 9th floor, room LT907

Abstract: TBA

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.

**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.

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).

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.

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.

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.

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

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.

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.

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.

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.

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.

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).

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.

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.

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.

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.

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).

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.