# Mathematics & Statistics Seminars and colloquia

## Departmental Colloquia

8 May 2019: Professor Kees Vuik (Delft University of Technology, The Netherlands)

Title:   Deflation with POD vectors for porous media flow

Date: 2.00pm Wednesday 8th May 2019

Venue: Livingstone Tower, 9th floor, room LT908

Abstract: We consider systems originating from the simulation of multi-phase flow through porous media.  The spatially discretized coupled nonlinear equations are solved with a two-stage preconditioner.  We consider the first step of this procedure, i.e. solving of the pressure equation.  We develop preconditioners based on deflation and a selection of deflation vectors motivated by Proper Orthogonal Decomposition (POD) to a number of pre-computed solutions.  We investigate alternatives using different varieties of reduced-order modelling.  Furthermore we explore the connection between POD-based preconditioning and deflation methods.  One of the difficulties for deflation methods is to find the right deflation vectors for general problems. The combination of deflation with the POD methods looks very promising in this respect.

13 November 2019: Professor John Z. Shi (Shanghai Jiao Tong University; currently University of Cambridge)

Title:  Coastal Processes: with Special Reference to Physical Processes in the Changjiang River estuary, China

Date: 3.30pm Wednesday 13th November 2019

Venue: Livingstone Tower, 9th floor, room LT908

Abstract: Numerous studies have been undertaken to understand the physics of circulation and mixing in estuaries around the world. This present study builds on and adds to these existing studies through a case study of the Changjiang River estuary, China.

Simultaneous field observations were made of time series of water level, current velocity, salinity and suspended sediment concentration at ten hydrological gauging stations along the North Passage in the Changjiang River estuary. Quantitative analyses of those data are attempted to understand circulation, mixing and fine sediment transport along the Deepwater Navigational Chanel in this estuary. Landward subtidal flow only appears during the neap tide. The maximum bottom landward velocity is in the order of 0.05 ~ 0.1 m·s-1 in the dry season and 0.15 ~ 0.2 m·s-1 in the wet season, respectively. In both dry and wet seasons, calculated mixing parameter (M), which is the ratio of the tidal timescale to the vertical mixing timescale, is below the critical value (1.0) on a neap tide but above it on a spring tide within the middle and lower reaches of the Channel. This suggests that tidal variation of mixing may be able to generate the tidal straining circulation during the periodic stratified spring tide. The interaction between significant river shear flow and longitudinal density gradient, a process termed "river effect" in this study, is revealed as the major reason for seasonal variation of stratification. The competition between tidal stirring, gravitational circulation and river effect could produce an increase in tidal mean value of the potential energy anomaly from neap to spring tides. Tidal mean value of the Simpson number (Si) over a neap tide surpasses the critical value (8.4×10-1) within the middle reach of the Channel, suggesting the occurrence of persistent stratification there. Tidal mean Si over a spring tide is in the order of 8.4×10-1~8.8×10-2 within the middle reach, suggesting the occurrence of strain induced periodic stratification (SIPS). Shear prevails within the pycnocline in the middle and lower reaches of the Channel on a neap tide, with the value of squared shear (S2) exceeding 10-3 s-2. Calculated gradient Richardson number (Ri) is small at the salt-fresh water interface, indicating the occurrence of Kelvin–Helmholtz instability there.

The TELEMAC-3D, incorporating a stability function, and the potential energy anomaly equation (ϕ-equation), are used to analyze neap-spring tidal and intratidal variability of intermittent mixing and stratification within the North Passage of the Changjiang (Yangtze) River estuary in the wet season. Eight terms in the ϕ-equation are used to examine physical mechanisms and the relative importance of each term for the lower reach of the North Passage. As revealed by the gradient Richardson number (Ri), the Simpson number (Si) and the potential energy anomaly (ϕ), weak mixing and persistent stratification appear on a neap tide, while strong mixing and periodic stratification on a spring tide within the main channel in the middle and lower reaches of the North Passage. The landward subtidal flow is much stronger on a neap tide than that on a spring tide. Within the main channel in the lower reach, large magnitude of longitudinal ϕ-advection (Au) reflects the important effect of saltwedge movement on stratification. Large magnitude of lateral ϕ-advection (Av) may be enhanced by large lateral gradient of ϕ due to the complex bathymetry and artificial structures. Both longitudinal (Au) and lateral ϕ-advections (Av) are temporally and spatially intermittent. Large longitudinal depth-mean straining (Bu) overlays the combined effect of tidal straining, circulation and river discharge. Large lateral depth-mean straining (Bv) is generated by large lateral density gradient interacting with the shear flow. The magnitude of integrated vertical turbulent buoyancy flux (E) mainly depends on tidal stirring at the bottom, while wind stirring at the surface and shear instability at the pycnocline are secondary contributors. The magnitudes of the other physical mechanisms including longitudinal non-mean straining (Cu), lateral non-mean straining (Cv) and vertical advection (D) are relatively smaller than those above. Neap-spring tidal variability of mixing and stratification mainly results from combined effect of three principal physical mechanisms, i.e. tidal stirring, longitudinal (Bu) and lateral depth-mean strainings (Bv). Intratidal variability of mixing and stratification is apparent on a spring tide. It seems that Advection, Straining and Stirring Induced Periodic Stratification (ASSIPS), rather than Advection and Straining Induced Periodic Stratification (ASIPS) and Straining Induced Periodic Stratification (SIPS), controls intratidal variability of mixing and stratification within the North Passage.

27 November 2019: Prof Sheila Bird OBE FRSE (MRC Biostatistics Unit, University of Cambridge)

Title:  How record-linkage has shed light on age-related increases in drugs-related deaths

Date: 3.30pm Wednesday 27th November 2019

Venue: Livingstone Tower, 9th floor, room LT908

Abstract: Strongly age-related increases in drugs-related deaths (DRDs) in the 21st century are the late sequelae of UK’s heroin-injector epidemics of the early 1980s. DRDs are mainly opioid-related deaths (ORDs); opioid-dependent clients’ DRD-rate not only increases as clients age beyond 35 and 45 years of age but females’ advantage is lost. Briefly, I explain how the before/after evaluation of Scotland’s National Naloxone Programme (NNP) was designed to circumvent the first of these epidemic forces. Secondly, I will show how record-linkage, an approach in which data from diverse records are combined, has been applied to Scotland’s methadone-client cohort (2009-2015) and has shed light on the effects of both age and gender as well as methadone-dose.

### Applied Analysis﻿

8th October: Ji-Hwan Jung (Seoul National University)

Title:   Riordan graphs and their properties

Date:   3pm Tuesday 8th October 2019

Venue: Livingstone Tower, 9th floor, room LT907

Abstract: In this talk, we use the theory of Riordan matrices to introduce the notion of a Riordan graph. The Riordan graphs are a far-reaching generalization of the well known and well studied Pascal graphs and Toeplitz graphs, and also some other families of graphs. The Riordan graphs are proved to have a number of interesting (fractal) properties, which can be useful in creating computer networks with certain desirable features, or in obtaining useful information when designing algorithms to compute values of graph invariants. The main focus in this talk is the study of structural properties which find certain conditions on Riordan graphs to have an Eulerian trail/cycle or a Hamiltonian cycle, diameter of io-decomposable Riordan graphs, and so on. Finally we pose several open questions and conjectures.

22nd October: Sven-Ake Wegner (Teesside)

Title:   Port-Hamiltonian differential equations on infinite networks

Date:   3pm Tuesday 22nd October 2019

Venue: Livingstone Tower, 9th floor, room LT907

Abstract: Given a graph G=(V,E) we associate with each edge an interval. On each interval we consider a port-Hamiltonian partial differential equation x_t = P_1*(Hx)_xi + P_0*Hx with matrices P_1, P_0 and Hamiltonian density function H. In the talk, we discuss which boundary conditions, imposed at the vertices, guarantee that solutions of the above equation are given by a (contraction) semigroup. Our results cover infinite graphs, graphs with edge length tending to zero and Hamiltonians H that can approach zero or be unbounded.

29th October: Lukas Eigentler (Heriot-Watt University)

Title:   Modelling dryland vegetation patterns: Nonlocal dispersal and species coexistence

Date:   3pm Tuesday 29th October 2019

Venue: Livingstone Tower, 9th floor, room LT907

Abstract: Vegetation patterns are a ubiquitous feature of semi-arid regions and are a prime example of a self-organisation principle in ecology, caused by a positive feedback between local plant growth and water redistribution. The Klausmeier reaction-advection-diffusion model is a deliberately simple system describing the formation of vegetation stripes on sloped terrain. In this talk, I present two model extensions to (i) investigate the effects of nonlocal seed dispersal, and (ii) propose mechanisms that enables species coexistence in patterned vegetation and savannas.

For mathematical simplicity, plant dispersal is modelled by diffusion in many mathematical models. Backed up by empirical data, plant diffusion is replaced by a convolution term, to account for nonlocal effects. Asymptotic analysis of the model is possible, due to a scale difference between plant dispersal and water transport. I show that a condition for pattern onset in the model can be derived analytically, which indicates that long-range seed dispersal inhibits the onset of spatial patterns. Results on pattern existence and stability, obtained via a numerical continuation method, further show a change in the type of stability boundaries in the pattern's Busse balloon as dispersal distance is varied. The difference in destabilisation mechanisms between different types of stability boundaries suggests increased resilience of patterns to reductions in precipitation due to long dispersal distances. Stability results further propose a resolution of a mismatch between previous mathematical models predicting an uphill movement of vegetation bands and some field studies reporting stationary patterns.

Through the introduction of a second plant species to the Klausmeier model, I present two mechanisms that enable species coexistence despite the species' competition for the same limiting resource. Firstly, coexistence occurs as a metastable state if the average fitness difference between both species, a measure of the species' competitiveness in a spatially uniform setting, is small. Secondly, a stability analysis of the system's single-species patterns, performed through a calculation of their essential spectra, shows that a solution branch in which both species coexist bifurcates off the single-species solution branch as it loses its stability to the introduction of a second species. I present a comprehensive existence and stability analysis to establish key conditions, including a balance between the species' local competitive abilities and their colonisation abilities, for species coexistence in the model.

joint work with Jamie JR Bennett (Ben Gurion Univ.) and Jonathan A Sherratt (Heriot-Watt Univ.)

5th November: David Bourne (Heriot-Watt)

Title:   Optimal Lattice Quantizers and Best Approximation in the Wasserstein Metric

Date:   3pm Tuesday TBC

Venue: Livingstone Tower, 9th floor, room LT907

Abstract: In this talk I will discuss the problem of the best approximation of the three-dimensional Lebesgue measure by a discrete measure supported on a Bravais lattice. Here 'best approximation' means best approximation with respect to the Wasserstein metric W_p, p \in [1,\infty). This problem is known as the quantization problem and it arises in numerical integration, electrical engineering, discrete geometry, and statistics.

19th November: Sabine Boegli (University of Durham)

Title:   Essential numerical ranges for linear operator pencils

Date:   3pm Tuesday 19th November 2019

Venue: Livingstone Tower, 9th floor, room LT907

Abstract: We introduce the notion of essential numerical range for linear operator pencils, that is, for generalised eigenvalue problems Af=zBf with linear operators A and B and eigenvalue z (for B the identity operator we recover the usual eigenvalue equation). The essential numerical range is used to describe the set of spectral pollution when approximating the operator pencil by projection and truncation methods. We apply the results to various differential operator pencils.

This talk is based on joint work with Marco Marletta (to appear in IMA Journal of Numerical Analysis).

### Continuum mechanics & industrial mathematics﻿

15th October 2019 - Alice Thompson (University of Manchester)

Title: Bubble propagation in modified Hele-Shaw channels

Date:  1.00pm Tuesday 15th October 2019

Venue: Livingstone Tower, 9th floor, room LT907

22nd October 2019 - Andrew Mitchell (University of Strathclyde)

Title: Coating flow on a rotating horizontal cylinder subject to an airflow

Date:  1.00pm Tuesday 22nd October 2019

Venue: Livingstone Tower, 9th floor, room LT907

22nd October 2019 - Magdalena Lesniewska (University of Strathclyde)

Title: Near-wall behaviour of a colloid particle in a liquid crystal fluid

Date:  1.00pm Tuesday 22nd October 2019

Venue: Livingstone Tower, 9th floor, room LT907

29th October 2019 - Brian Sleeman (University of Dundee)

Title: Inverse Obstacle Scattering Problems: A Game of Hide and Seek

Date:  1.00pm Tuesday 29th October 2019

Venue: Livingstone Tower, 9th floor, room LT907

12th November 2019 - Daniel Orejon (University of Edinburgh)

Title: Dropwise Condensation on Hierarchical Superhydrophobic Surfaces: Uncoated, Coated and Lubricant infused

Date:  1.00pm Tuesday 12th November 2019

Venue: Livingstone Tower, 9th floor, room LT907

19th November 2019 - Alex Wray (University of Strathclyde)

Title: Topics in thick flows

Date:  1.00pm Tuesday 19th November 2019

Venue: Livingstone Tower, 9th floor, room LT907

26th November 2019 - Jennifer Gaskell (University of Glasgow)

Title: Bayesian Inference-Informed Agent-Based Modelling of Migratory Fish near Energy Infrastructure

Date:  1.00pm Tuesday 26th November 2019

Venue: Livingstone Tower, 9th floor, room LT907

10th December 2019 - Jonny Singh (University of Strathclyde)

Title: Using multiply scattered waves in heterogeneous media

Date:  1.00pm Tuesday 10th December 2019

Venue: Livingstone Tower, 9th floor, room LT907

### Numerical Analysis and Scientific Computing﻿

24th September 2019: Sofiat Olaosebikan (University of Glasgow)

Title: Algorithmics of the Student-Project Allocation problem

Date:  4pm Tuesday 24th September 2019

Venue: Livingstone Tower, 9th floor, room LT907

Abstract:  Matching problems are all around us – they arise when we try to find the “best” allocation between two sets of entities. For example, matching kidney transplant patients with compatible donors, allocating junior doctors to hospitals, and assigning students to projects in a university department.

My talk is centred around the Student-Project Allocation problem (SPA), which, in its natural form, involves finding a many-to-one matching of students to projects offered by lecturers, based on student preferences over projects and the maximum number of students that each project and lecturer can accommodate. Two models of SPA exist in the literature: one permits preferences from the students only, while the other permit preferences from both the students and the lecturers. In the latter case, three different variants have been studied, including lecturer prefereces over (i) students, (ii) projects, and (iii) (student,project) pairs.

For my PhD, I have been exploring SPA with lecturer preferences over Projects (SPA-P) and SPA with lecturer preferences over Students with Ties (SPA-ST). The solution concept that we seek in this context is a “stable matching”, which ensures that no student and lecturer who are not matched together would rather be assigned to each other than remain with their current assigneess. In my talk, I will present the algorithmic results arising from my research on finding stable matchings in SPA-P and SPA-ST. Some of these results include integer programming models and exact polynomial-time algorithms.

Sofiat Olaosebikan is a final year PhD in Computing Science at the University of Glasgow. Her interests lie at the intersection of mathematics and theoretical computer science. You can find out more about her work on her website, and you can follow her on twitter @soolaosebikan.

29th October 2019: Prof Catherine Powell (University of Manchester)

Title: Adaptive & Multilevel Stochastic Galerkin Approximation for Parameter-Dependent PDEs.

Date:  4pm Tuesday 29th October 2019

Venue: Livingstone Tower, 9th floor, room LT907

Abstract:  In this talk, we discuss aspects of numerical analysis associated with stochastic Galerkin approximation for performing forward UQ in PDE models with uncertain (parameter-dependent) inputs. Starting with the standard elliptic test problem, we first describe in general terms, a strategy for performing a posteriori error estimation and developing adaptive solution algorithms. We then discuss how this methodology can be extended to a more challenging linear elasticity problem with uncertain Young’s modulus. We introduce a three-field parametric PDE model and develop an adaptive stochastic Galerkin mixed finite element scheme. We estimate the error in the natural weighted norm with respect to which the weak formulation is stable. Exploiting the connection between this norm and the underlying PDE operator also leads to an efficient block-diagonal preconditioning scheme for the associated discrete problems. It can be shown that both the error estimator and the preconditioner are robust in the incompressible limit.

5th November 2019: Dr Niall Bootland

Title: On coarse spaces for solving the heterogeneous Helmholtz equation with domain decomposition methods

Date:  4pm Tuesday 5th November 2019

Venue: Livingstone Tower, 9th floor, room LT907

Abstract:  The development of effective solvers for high frequency wave propagation problems, such as those described by the Helmholtz equation, presents significant challenges. One promising class of solvers for such problems are parallel domain decomposition methods, however, an appropriate coarse space is typically required in order to obtain robust behaviour (scalable with respect to the number of domains, weakly dependant on the wave number but also on the heterogeneity of the physical parameters). In this talk we introduce a coarse space based on generalised eigenproblems in the overlap (GenEO) for the Helmholtz equation. Numerical results within FreeFEM demonstrate convergence that is effectively independent of the wave number and contrast in the heterogeneous coefficient as well as good performance for minimal overlap.

10th December 2019: Alistair Forbes (NPL)

Title: Effective number of degrees of freedom associated with models

Date:  4pm Tuesday 10th December 2019

Venue: Livingstone Tower, 9th floor, room LT907

Abstract: This talk is concerned with the approximation of data using linear models for which there is prior information associated with some or all of the model parameters. This situation arises, for example, in Tikhonov regularisation, Bayesian inference and approximation with Gaussian process (GP) models [4]. The latter case is particularly important in model calibration [3] in which the measured response of a system is modelled as

y = Ba + e + ; e 2 N(0; V );  2 N(0; 2M I)

where Ba is the response predicted by a hypothesised model,  are random effects associated with measurement process, and e are systematic effects that account for the mismatch between the modelled response Ba and the actual response of the system about which there is prior information encoded by the variance matrix V . In the approximation process, the m-vector of data y is approximated by a linear function Hy of the data, where H is an m x m matrix. The effective number of degrees of freedom associated with the model is given by the sum of the eigenvalues of H [2]. For standard linear regression, the matrix H is a projection and has n eigenvalues equal to 1 and all others zero, where n is the number of parameters in the model. Incorporating prior information about the parameters reduces the effective number of degrees of freedom since the ability of the model to approximate the data vector y is partially constrained by the prior information [1]. We give a general approach for providing bounds on the effect number of degrees of freedom for models with prior information on the parameters and illustrate the approach on common problems. In particular, we show how the effective number of degrees of freedom depends on spatial or temporal correlation lengths associated with Gaussian processes. The correlation lengths are seen to be tuning parameters used to match the model degrees of freedom to the (generally unknown) number of degrees of freedom associated with the system giving rise to the data.

The calculation of effective degrees of freedom associated with GP models leads to some interesting observations that invite further analysis.

References
[1] A. B. Forbes. Empirical functions with pre-assigned correlation behaviour. In F. Pavese, W. Bremser, A. Chunovkina, N. Fischer, and A. B. Forbes, editors, Advanced Mathematical and Computational Tools for Metrology X, pages 17{28, Singapore, 2015. World Scienti c.

[2] T. Hastie, R. Tibshirani, and J. Friedman. Elements of Statistical Learning. Springer, New York, 2nd edition, 2011.

[3] M. C. Kennedy and A. O'Hagan. Bayesian calibration of computer models. J. Roy. Sat. Soc. B, 64(3):425-464, 2001.

[4] C. E. Rasmussen and C. K. I. Williams. Gaussian Processes for Machine Learning. MIT Press, Cambridge, Mass., 2006.

TBA: Nikolaos Sfakianakis (St. Andrews)

Title: The Filament Based Lamellipodium Model and the corresponding Finite Element Method: from cell-cell adhesion to the cell-cluster and monolayer formation

Date:  TBA

Venue: Livingstone Tower, 9th floor, room LT907

Abstract: The lamellipodium is a thin, sheet-like structure that is found in the propagating front of fast moving cells like fibroblasts, keratocytes, cancer cells, and more. It is a dense network of linear biopolymers of the protein actin, termed actin-filaments. These actin-filaments are highly dynamic structures that participate in a plethora of processes such as polymerization, nucleation, capping, fragmentation, and more.

These processes are important for the structure and functionality of the lamellipodium and the motility of the cell. They are, to a large extent, affected by the extracellular environment; for example, the chemical landscape in which the cell of resides and the local composition and architecture of the Extracellular Matrix (ECM), lead to biased motility responses of the cell. When in proximity to each other, they develop cell-cell adhesion via specialized transmembrane proteins of the cadherin family. Collectively, they coagulate to clusters of cells that eventually merge to form cell monolayers.

We model these phenomena using the Filament Based Lamellipodium Model (FBLM); an anisotropic, two-phase, two-dimensional, continuum model that describes the dynamics the lamellipodium at the level of actin-filaments and their interactions. The model distinguishes between two families (phases) of filaments and includes the interactions between them, as well as between the network of the filaments and the extracellular environment. The FBLM was first proposed in [1] and later extended in [2,4,5]. The FBLM is endowed with a problem specific Finite Element Method (FEM) that we have previously developed in [3].

In this talk we present the basic components of the FBLM and the FEM and focus on a series of simulations reproducing fundamental components of the motility of the cells, such us chemotaxis, haptotaxis, interaction with the environment [3,4]. We also present our new findings with respect to cell-cell collision and adhesion, as well as the formation of clusters of cells and cell monolayers [5]. To confront the increased computational needs of the monolayer, we have developed a parallel version of our numerical method which we also address in this talk.

Literature:

[1] D. Oelz, C. Schmeiser. How do cells move? in Cell mechanics: from single scale-based models to multiscale modeling, (2010)

[2] A. Manhart, D. Oelz, C. Schmeiser, N. Sfakianakis, An extended Filament Based Lamellipodium: Model produces various moving cell shapes in the presence of chemotactic signals, (2015)

[3] A. Manhart, D. Oelz, C. Schmeiser, N. Sfakianakis. Numerical treatment of the filament based lamellipodium model (FBLM) (2016)

[4] N. Sfakianakis, A. Brunk, Stability, convergence, and sensitivity analysis of the FBLM and the corresponding FEM, (2018)

[5] N. Sfakianakis, D. Peurichard, C. Schmeiser, and A. Brunk, The FBLM-FEM: from cell-cell adhesion to cluster formation, (2018)

### Population Modelling and Epidemiology﻿

22nd May 2019: Hally Stone (University of Washington, Seattle)

Title: Gone with the Wind: Linking Phytoplankton Biomass and Wind Patterns using Satellite Data in the California Current System

Date: Wednesday 22nd May, 11.00am

Venue: Livingstone Tower, LT907

Abstract:

11th June 2019: Dr Andrew Morozov (University of Leicester)

Title: Towards Constructing a Mathematically Rigorous Framework for Modelling Evolutionary Fitness

Date: Tuesday 11th June, 12.00pm

Venue: Livingstone Tower, LT907

Abstract: In modelling biological evolution, a major mathematical challenge consists in an adequate quantification of selective advantages of species. Current approaches to modelling natural section are often based on the idea of maximization of a certain prescribed criterion - evolutionary fitness. This paradigm was inspired by the seminal Darwin's idea of the 'survival of the fittest'. However, the concept of evolutionary fitness is still somewhat vague, intuitive and is often subjective. On the other hand, by using different definitions of fitness one can predict conflicting evolutionary outcomes, which is obviously unfortunate. In this talk, I present a novel axiomatic approach to model natural selection in dynamical systems with inheritance in an arbitrary function space. For a generic self-replication system, I introduce a ranking order of inherited units following the underlying measure density dynamics. Using such ranking, it becomes possible to derive a generalized fitness function which maximization will predict long-term evolutionary outcome. The approach justifies the variational principle of determining evolutionarily stable behavioural strategies. I demonstrate a new technique allowing to derive evolutionary fitness for population models with structuring (e.g. in models with time delay) which was so far a mathematical challenge. Finally, I show how the method can be applied to a von Foerster continuous stage population model.

21st August 2019: Dr Antonella Rivera (The Coral Reef Alliance)

Title: Exploring the Drivers for the Sustainability of the Gooseneck Barnacle Fishery in Asturias, Northern Spain

Date: Wednesday 21st August, 1.00pm

Venue: Livingstone Tower, LT907

Abstract: The Asturian gooseneck barnacle fishery is a unique example of a complex social-ecological system that has been co-managed for over 20 years. As part of the co-management system fishers are allotted Territorial User Rights for Fishing and an active participation in management strategies in return for detailed data gathering. Here, we used this extensive time-series to assess the sustainability of the Asturian gooseneck barnacle fishery through time and to disentangle the key socio-ecologic drivers for its success. The fishery has succeeded in maintaining or increasing catch per unit effort in all management areas. Additionally, despite the national economic crisis, mean gooseneck barnacle market prices have remained stable in Asturias. Furthermore, the system has received vast public approval, where 73% of the stakeholders have indicated that the only way to maintain a sustainable gooseneck barnacle fishery in Asturias is through the current management regime. The co-management system has primarily achieved the sustainability of the fishery through 4 key characteristics: (1) the continuous incorporation of scientific information and fishers’ knowledge in management frameworks, (2) a matching of management scales with the main life-history traits of the species, (3) empowerment of the resource users and (4) embracing adaptive capacity through flexible management guidelines, resource diversification and selectivity. The Asturian gooseneck barnacle co-management system provides a set of basic principles for TURFs, which may be conducive to sustainable fisheries.

23rd August 2019: Dr S. Lan Smith (JAMSTEC)

Title: Phenotypic plasticity sustains modelled phytoplankton size diversity by flattening fitness gradients, but may confound observed relationships

Date: Friday 23rd August, 12.00pm

Venue: Livingstone Tower, LT907

Abstract:  Inducible phenotypic plasticity has long been known to impact the growth response of a wide variety of organisms, and more recently has been appreciated as a determinant of biodiversity, production, and ecosystem function. However, considerable uncertainty remains about how intra-specific trait variation may contribute to biodiversity. Photo-acclimation is a well known example of physiological flexibility for phytoplankton, and a variety of models have been developed to represent its effects on their growth, chlorophyll and nutrient content. I apply a sized-structured model accounting for the photo-acclimation response of phytoplankton (FlexPFT), as well as a control model lacking this response, to two contrasting time-series observation sites from the North Pacific ocean: a relatively calm subtropical site (stn. S1) and a more variable subarctic site (stn. K2). As previously reported (Smith et al. J. Plankton Res. 2016), compared to the control, the FlexPFT model reproduced better the available observations of size fractionated chlorophyll, nutrients, and primary production and predicted greater size diversity. Here I clarify that this is because phenotypic plasticity flattens fitness gradients, quantified here as specific growth rate vs. size. This effect contributed more to enhancing size diversity at the more variable subarctic site than at the calmer subtropical site. However, at both sites modelled size diversity differs substantially as calculated in terms of chlorophyll, carbon or nitrogen biomass, because the degree of flexibility differs with cell size, as a result of the size-scaling of traits. Modelled distributions of chlorophyll over size tend to be substantially less even (lower diversity) than those of either fitness or biomass. This suggests that, although much more widely available than observations of biomass or growth rate, chlorophyll-based size distributions should be interpreted with care.

25th September 2019: Dr Markus Schartau, Vanessa Lampe, Dr Eva-Maria Noethig (GEOMAR Kiel and AWI Bremerhaven, Germany)

Title: Why Should we and How Can we Identify Structural Details in Size-Spectra of Marine Microplankton?

Date: Wednesday 25th September, 1.00pm

Venue: Livingstone Tower, LT907

Abstract:  Despite their microscopic size, unicellular marine plankton control how elements like carbon are transformed and distributed in the ocean. Phytoplankton are photosynthetic organisms that assimilate inorganic nutrients into their organic biomass, with cell sizes ranging from less than one up to several hundreds of micrometers. Phytoplankton live as single cells or in colonies, can form large sticky aggregates that may sink, or they become ingested by a variety of zooplankton.

Variations in size-spectra reveal some of the underlying dynamics involved within the unicellular plankton community. The size-abundance spectrum slope and the corresponding y-intercept are two parameters that are often thought to inform us about the biovolume and transfer efficiency of the microbial plankton community. This paradigm is challenged by measurements when looking at size-spectra precisely. Distinctive structural details are well resolved with the kernel density estimation method. I will present latest results from our analyses of elaborate, repeated microscopic measurements from the Fram Strait (Arctic Ocean). We could identify four ranges of size-selective grazing close to Equivalent Spherical Diameters (ESD) of 4, 9, 30 and 70 μm. These prominent and robust ESD ranges will be discussed in context with plankton size-spectra from other locations (e.g. Equatorial Pacific). Finally, I will discuss with you how size-spectral data could be used for calibrating size-based models.

23rd October 2019: Dr Sarkis Manoukian (Glasgow Caledonian University)

Title: Patient-level probabilistic modelling to investigate the cost-effectiveness of six screening strategies for carbapenemase producingenterobacteriaceae (CPE) in the NHS.

Date: Wednesday 23rd October, 1.00pm

Venue: Livingstone Tower, LT907

Abstract:  Antimicrobial resistance has been recognised as a global threat to public health, with carbapenemase-producing-enterobacteriaceae (CPE) causing significant morbidity and mortality in hospital settings. There is evidence to suggest these pathogens propagate along hospital transmission routes making screening programmes important. At present, there is no gold standard available on which to base a CPE screening and testing programme.  The low incidence of CPE has led to the introduction of a clinical risk assessment (CRA) which identifies patients who may benefit from microbiological screening. In order to limit spread in clinical settings, isolation of suspected positives is being recommended putting a strain on resources. There are different screening technologies available which means screening can be done quickly or more slowly with differential impacts on costs. There is therefore a need for an evidence base for different approaches to screening in order to ensure that these programmes are effective. A patient level simulation approach is the most appropriate when dealing with infectious diseases since it allows modelling heterogeneous patients interacting with each other. Our individual based approach allows population-level costs and health benefits associated with infectious disease prevention and control to be captured.

A decision-analytic model was developed to assess the cost per QALY gained for different NHS screening strategies. Patients can be colonised by CPE making them asymptomatic carriers, patient pathways change according to colonisation status and patient outcomes depend on characteristics. Patients can be discharged and re-admitted to hospital. Different scenarios are modelled to test how cost-effectiveness and patient outcomes change as CPE epidemiology changes. We use a combination of data to parameterise the model with information coming from literature sources and NHS Scotland patient level data. Health and economic benefits of screening are estimated taking into account parameter uncertainty. We report key events and probabilistic sensitivity analyses are also conducted. This is a highly detailed patient level simulation of a NHS hospital which provides estimates under uncertainty.

Screening has the potential to save lives and the recommendation is to continue screening for CPE in NHS hospitals. Screening results in a lower estimated number of infections, cross-infections and hospitalisations due to CPE.

6th November 2019: Dr Paul Seed (Division of Women's Health, Kings college London)

Title: Medical Research - The Essential Role of the Statistician

Date: Wednesday 6th November, 1.00pm

Venue: Livingstone Tower, LT907

Abstract:  An interactive look at the work of a Medical Statistician in a busy environment dedicated to research for patient benefit.

19th November 2019: Dr Frederic Maps (Universite Laval, Quebec, Canada)

Title: Quantification of Individual Zooplankton Traits from in situ Imaging Reveals Ecological Responses to Sea Ice Dynamics in an Arctic Sea.

Date: Tuesday 19th November, 1.00pm

Venue: Livingstone Tower, LT908

Abstract:  Nowhere on Earth are the current climate disruption impacts more pronounced than in the Arctic. The Arctic Ocean is shifting rapidly towards a new oceanographic climate involving warmer water masses, reduced sea ice and altered geochemical properties and circulation patterns. One prevailing ecological paradigm is that ongoing climate changes may have dramatic effects on Arctic hyperspecialized mesozooplanktonic species (animals between about 200 µm and 20 mm), owing to an increased competition with smaller boreal expatriates, effectively depriving the trophic networks from its rich lipid source and profoundly altering ecosystem services. However, the role of the dominant zooplankton should not be assessed only by the bulk amount of primary production they channel up the trophic network or down to the sea floor, but also according to the detailed combination of traits that characterize their communities. Planktonic organisms are essentially small, fragile, transparent and unevenly distributed, but for imagery, these characteristics are an advantage for bringing in abundant and diverse quantitative information. It can indeed reveal internal structures such as the gonads, digestive tract and lipid sac directly related to key functional traits for thousands of individuals at a time. The combination in situ imaging of live individuals and environmental variables obtained at high spatio-temporal resolution has led to the most significant increase in available information for marine ecology since the appearance of satellite data 40 years ago.

We used data from an in situ imager (Underwater Video Profiler UVP5) deployed during the GreenEdge international campaign that occurred during the ice melt of 2016 in Baffin Bay between Greenland and Canada. Based on numerical descriptors of the images (e.g. area, gray level, perimeter complexity index, etc.) automatically extracted and available in the EcoTaxa data base, we have i) objectively defined morphological groups of mesozooplankton in a continuous space of traits and ii) relate these traits assemblages (groups) to environmental properties. These results revealed clear ecological patterns and led us to new research hypotheses about the physiological state (via colours) or feeding activity (via the visibility of appendages) of the individuals that would have been invisible to classical taxonomic approaches. It is now time to discuss ways to integrate such data into numerical modelling frameworks.

5th December 2019: Dr Emily Grace Simmonds (Department of Mathematical Sciences, Norwegian University of Science & Technology)

Title: Exploring the Causes and Consequences of Phenological Change

Date: Thursday 5th December, 1.00pm

Venue: Livingstone Tower, LT908

Abstract:  Climate change can induce shifts in the timing of life history events in biological organisms. Individual species do not shift their timing uniformly, and the resulting disruption can alter interactions between species, with potentially substantial consequences. Predicting these consequences has proven challenging. We use an evolutionarily explicit integral projection model to project phenological change and population dynamics of a wild great tit population, under three climate change scenarios. We identify thresholds of temporal mismatch between the great tits and their caterpillar prey beyond which the predator population rapidly goes extinct. Phenotypic plasticity initially helped maintain temporal synchrony, but a consequence of this is it slowed an adaptive evolutionary response. Under pessimistic climate change projections, limits to plasticity were reached, directional evolution then accelerated, but not to a point where it could prevent mismatch. Our projections suggest that current population stability, resulting from buffering, could be masking a road to extinction.

### Stochastic Analysis

10th May 2019: Dr Hao Yang (Huazhong University of Science and Technology, China)

Title: The truncated Euler-Maruyama method for stochastic differential equations with H\"{o}lder diffusion coefficients

Date: 5-6.00pm, Friday 10th May 2019, LT907

Abstract:  In stochastic financial and biological models, the diffusion coefficients often involve the term \sqrt{x}, or more general |x|^r for r\in(0,1). In this paper, we study the strong convergence of the truncated Euler-Maruyama (EM) approximation first proposed by Mao for one-dimensional stochastic differential equations (SDEs) with superlinearly growing drifts and the H\"{o}lder continuous diffusion coefficients.

9th October 2019: Dr Chen Fei (Donghua University, China)

Title: Stabilisation of Highly Nonlinear Hybrid Systems by Feedback Control Based on Discrete-Time State Observations

Date: 4-5.00pm, Wednesday 9th October 2019, LT907

Abstract:  Given an unstable hybrid stochastic differential equation (SDE), can we design a feedback control, based on the discrete-time observations of the state at times $0, \tau, 2\tau, \cdots$, so that the controlled hybrid SDE becomes asymptotically stable? It has been proved that this is possible if the drift and diffusion coefficients of the given hybrid SDE satisfy the linear growth condition.

However, many hybrid SDEs in the real world do not satisfy this condition (namely, they are highly nonlinear) and there is no answer to the question yet if the given SDE is highly nonlinear.  The aim of this paper is to tackle the stabilization problem for a class of highly nonlinear hybrid SDEs.  Under some reasonable conditions on the drift and diffusion coefficients, we show how to design the feedback control function and give an explicit bound on $\tau$ (the time duration between two consecutive state observations), whence the new theory established in this paper is implementable.

22nd November 2019: Professor Xiaoyue Li (Northeast Normal University, China)

Title: Stabilisation of Highly Nonlinear Hybrid Stochastic Differential Delay Equations by Delay Feedback Control

Date: 4-5.00pm, Wednesday 22nd November 2019, LT907

Abstract:  Given an unstable hybrid stochastic differential equation (SDDE, also known as an SDDE with Markovian switching),can we design a delay feedback control to make the controlled hybrid SDDE become asymptotically stable? If the feedback control is based on the current state, the stabilisation problem has been studied.  However, there is little known when the  feedback control is based on the past state. The problem becomes even harder when the coefficients of the underlying hybrid SDDE do not satisfy the linear growth condition (namely, the coefficients are highly nonlinear).  The aim of this talk is to address the stabilisation problem for a given unstable highly nonlinear hybrid SDDE.