Previous Seminars and Events
Seminars and Events that have been held in the Department of Mathematics and Statistics can be found below:
Nonlinear evolutionary processes, operator theory for the study of differential and integral equations. Enumerative, bijective and algebraic combinatorics.
Title: Distribution of mesh patterns
Date: 2.00pm Tuesday 23rd January 2024
Venue: LT907
Abstract: The notion of a mesh pattern, generalizing several classes of permutation patterns, was introduced in 2011 by Branden and Claesson to provide explicit expansions for certain permutation statistics as, possibly infinite, linear combinations of (classical) permutation patterns. There is a long line of research papers dedicated to the study of mesh patterns and their generalizations.
In this talk, I will discuss a systematic study of avoidance and distribution of mesh patterns of short length, and also some other more general results
Title: Coagulation and Combinatorics
Date: 2.00pm on Tuesday 20th February 2024
Venue: LT907
Abstract: I will review the recent combinatorics approach to discrete coagulation equations due to 艁epek and coworkers and the open problems that arise in that area.
Title: Vortex stretching in Navier-Stokes turbulence
Date: 3.00pm on Tuesday 27th February 2024
Venue: LT907
Abstract: Turbulence in the Navier-Stokes equations is a major nonlinear problem, that cannot be tackled with existing analytical methods. I discuss key characteristics of turbulence, explaining its physical content and the momentum balance it encodes. I indicate the key analytical difficulty and past failures to tackle it in the velocity-pressure space. I introduce the vortex dynamical viewpoint and explain the association between the latter and key turbulent physics. By employing the vortex dynamical viewpoint, I compute key aspects of turbulent vortex stretching, including, among other, the Lyapunov exponents of the tangent system, and the correlations between strain rate eigendirections and coherent, filamentary vorticity.
Title: Coagulation, non-associative algebras and combinatorial trees
Date: 2.00pm Tuesday 12th March 2024
Venue: LT907
Abstract: We consider the classical Smoluchowski coagulation equation with a general frequency kernel. We show that there exists a natural deterministic solution expansion in the non-associative algebra generated by the convolution product of the coalescence term. The non-associative solution expansion is equivalently represented by binary trees. We demonstrate that the existence of such solutions corresponds to establishing the compatibility of two binary-tree generating procedures, by:
- grafting together the roots of all pairs of order-compatible trees at preceding orders, or
- attaching binary branches to all free branches of trees at the previous order.
We then show that the solution represents a linearised flow, and also establish a new numerical simulation method based on truncation of the solution tree expansion and approximating the integral terms at each order by fast Fourier transform. In particular, for general separable frequency kernels, the complexity of the method is linear-loglinear in the number of spatial modes/nodes.
Title: Asymptotic enumeration of monotone permutation grid classes
Date: 2.00pm Tuesday 26th March 2024
Venue: LT907
Abstract: A monotone grid class Grid(M) is a set of permutations whose shape satisfies constraints specifies by the matrix M, all of whose entries are in {1,鈭�1, 0}. Each entry of the matrix corresponds to a cell in a gridding of a permutation. If the entry is 1, then the points in the cell must increase. If it is 鈭�1, they must decrease. If it is 0, the cell must be empty. To find the exact number of permutations of length n in Grid(M) is hard, because a permutation may have more than one gridding, so we only determine the asymptotic enumeration. To do this, we find the number of gridded permutations, the typical proportion of points in each cell, and the ways in which permutations can be gridded. Our focus is mainly on L-shaped, T-shaped, and X-shaped classes.
Title: Non-interpenetration of matter in lower-dimensional structures
Date: 3pm Wednesday 19th June 2024
Venue: LT907
Abstract: Non-interpenetration of matter is a well-known challenge for solid elastic materials combining analytical and geometrical aspects. In the bulk model, at least on the conceptual level, non-interpenetration is quite understood even if many challenges still remain open. In lower-dimensional structures (plates, rods), the situation seems to be even less clear. Focusing on rods in the plane, we will introduce a possible concept of noninterpenetration and show density and 螕-limit results in this case. This is a joint work in progress with B. Bene拧ov谩, D. Campbell, and S. Hencl (all from Prague).
Title: A storm in a tea-cup(?)
Date: 2pm Tuesday 12th November 2024
Venue: LT907
Abstract: This talk has two parts. In the first part I will talk about the amazing results obtained recently by using techniques that originate with Nash and Gromov, and in the second part I will talk about implications of these results for admissibility criteria, which is ongoing work with H. Gimperlein, R. J. Knops and M. Slemrod. Some audience participation will be required in the first part.
Title: The 1-11-representability of graphs
Date: 2.00pm Tuesday 19th November 2024
Venue: LT907
Abstract:
A graph is word-representable if it can be represented by rules concerning the alternation of letters in words. While many well-studied classes of graphs are word-representable, not all graphs can be represented in this way. By relaxing the conditions that define an edge, we can represent all graphs in a so-called 2-11 manner. In the new terminology, word-representable graphs are precisely 0-11-representable graphs. Whether all graphs can be 1-11-represented remains unknown, and the 1-11-representation of graphs has gained attention in the literature. In this talk, I will discuss methods and tools for proving the word-representability and 1-11-representability of graphs.
Title: Ribbon Tilings
Date: 2.00pm Tuesday 26th November 2024
Venue: LT907
Abstract: A ribbon tile consists of a finite edge-connected sequence of unit squares in the plane, each square either directly above or directly to the right of the previous square in the sequence. An n-ribbon tile is a ribbon tile made up of n unit squares. Which finite regions of the plane can be tiled with n-ribbon tiles? How many n-ribbon tilings can a region have? In this talk I will give an introduction to n-ribbon tilings, focussing on these questions. The new material in the talk is based on joint work with Yinsong Chen and Vladislav Kargin (arXiv:2408.09272).
Title: Topology and Transcription in 3D Chromatin Loop Networks
Date: 2.00pm Thursday 28th November 2024
Venue: LT908
Abstract: The 3D folding of a mammalian gene can be studied by polymer models, where the chromatin fiber is represented by a semiflexible polymer which interacts with multivalent proteins, representing complexes of DNA-binding transcription factors and RNA polymerases. This physical model leads to microphase separation and the natural emergence of clusters of proteins and binding sites, which can be understood via a mean field theory. The clustering is accompanied by the folding of chromatin into a set of topologies, each associated with a different network of loops. By combining Brownian dynamic simulations, statistical mechanics and combinatorics, we first classify these networks, and then find their relative importance or statistical weight, when the properties of the underlying polymer are those relevant to chromatin. Unlike polymer networks previously studied, our chromatin networks have finite average distances between successive binding sites, and we show that this feature leads to giant differences between the weights of topologies with the same number of edges and nodes but different wiring. These weights strongly favor rosette-like structures with a local cloud of loops with respect to more complicated nonlocal topologies. Our results suggest that genes should overwhelmingly fold into a small fraction of all possible 3D topologies, which can be robustly characterized by the framework we propose here.
Title: Irrational Enumeration
Date: Tuesday 11th February 2025, 2.00pm
Venue: LT907
Abstract: It is well known that the asymptotic behaviour of the number of objects in a combinatorial class can be determined from the singularities on the circle of convergence of its generating function. In this talk we extend the scope of analytic combinatorics to classes whose objects have irrational sizes by establishing an analogous result when it is no longer required that the size of an object must be an integer.
The generating function for such a class is a power series that admits irrational exponents (which we call a Ribenboim series). A transformation then yields a generalised Dirichlet series from which the asymptotics of the coefficients can be extracted by singularity analysis using an appropriate Tauberian theorem. In practice, the asymptotics can often be determined directly from the original generating function. The technique will be illustrated with a variety of applications, including tilings with tiles of irrational area, lattice walks enumerated by Euclidean length, and trees with vertices of irrational size. We will also explore phase transitions in the asymptotics of families of irrational combinatorial classes.
Title: A Variational Perspective on Auxetic Metamaterials of Checkerboard Type
Date: Tuesday 18th March 2025, 2.00pm
Venue: LT907
Abstract: Auxetic metamaterials have the counterintuitive property that they expand perpendicular to applied forces under stretching. In this talk, we discuss homogenization via Gamma-convergence for elastic materials with stiff checkerboard-type heterogeneities under the assumption of non-self-interpenetration. Our result rigorously confirms these structures as auxetic. The challenging part of the proof is determining the admissible macroscopic deformation behavior, or in other words, characterizing the weak Sobolev limits of deformation maps whose gradients are locally close to rotations on the stiff components. To this end, we establish an asymptotic rigidity result showing that, under suitable scaling assumptions, the attainable macroscopic deformations are affine conformal contractions. Our strategy is to tackle first an idealized model with full rigidity on the stiff tiles and then transfer the findings to a model with diverging elastic constants. The latter requires a new quantitative geometric rigidity estimate for non-connected touching squares and a tailored Poincaré-type inequality for checkerboard structures.
This is joint work with Wolf-Patrick Düll (University of Stuttgart) and Carolin Kreisbeck (KU Eichstätt-Ingolstadt).
Title: On the Connection of the Prandtl Equations and the Harmonic Oscillator
Date: Tuesday 25th March 2025, 2.00pm
Venue: LT907
Abstract: A deep connection is established between the Prandtl equations linearised around a quadratic shear flow, confluent hypergeometric functions of the first kind, and the Schrödinger operator. The first result concerns a spectral condition associated with unstable quasimodes of the Prandtl equations. We give all solutions of the governing ODE in terms of Kummer's functions. By classifying their asymptotic behaviour, we determine that the spectral condition has unique, determined eigenvalue and eigenfunction, the latter being expressible as a combination of elementary functions.
Moreover, we prove that any quasi-eigenmode solution of the linearised Prandtl equations around a quadratic shear flow can be explicitly determined from algebraic eigenfunctions of the Schrödinger operator with a quadratic potential. We show finally that the obtained analytical formulation of the velocity align with previous numerical simulations in the literature.
Title: A sheaf-theoretic framework for beta-diversity
Date: Wednesday 26th November 3 pm - 4 pm
Venue: LT907
Abstract: It is customary to decompose biodiversity (for example, using richness as a proxy) into local (alpha) and global (gamma) diversity. These are not controversial, but the desire to understand how alpha and gamma diversities are connected has led to a vast literature the "intermediate" (beta) diversity, which is claimed to be of relevance in bioconservation. The definitions in the literature are ad-hoc and we seek to remedy the situation by bringing to bear on the matter concepts from sheaf theory. The resulting object (a sheaf graph Laplacian) is easily computable and our very preliminary results show that even its spectrum has more discrimination power than the classical beta diversity. The new Laplacian is a construction that can be used in a variety of data-centred applications and leads to an interesting combinatorics problem.
Continuum mechanics & industrial mathematics
Liquid crystals, Droplet evaporation, Thin-film flow, Complex fluids, Medical product design, Flows in porous & complex media, Non-linear waves.
Title: Resonant free-surface water waves in closed basins
Date: 1.00pm Thursday 25th January 2024
Title: Data-driven design optimisation of chemical reactors
Date: 1.00pm Thursday 1st February 2024
Title: Oscillatory bodily flows: the eye and the brain
Date: 1.00pm Thursday 8th February 2024
Title: Determination of the index of refraction of anti-reflection coatings
Date: 1.00pm Thursday 22nd February 2024
Title: Electrostatics and variational perturbation theory
Date: 1.00pm Thursday 29th February 2024
Title: TBC
Date: 1.00pm Thursday 7th March 2024
Title: Interplay between zonal jets, waves and turbulence: application to gas giants
Date: 1.00pm Thursday 14th March 2024
Title: Growing in the wind - an interdisciplinary investigation of wind influence on plant growth
Date: 1.00pm Thursday 21st March 2024
Title: The effect of imbibition on the deposition from an evaporating droplet
Date: 1.00pm Wednesday 25th September 2024
Title: Recent progress on modelling of interfacial flows with soluble surfactants including micelle formation, contact-line, and interfacial viscosity effects
Date: 1.00pm Wednesday 2nd October 2024
Title: Droplet dynamics: evaporation, hydrodynamics and particle transport
Date: 1.00pm Wednesday 9th October 2024
Title: Droplet Dynamics and Self-Cleaning Mechanisms on Liquid-Repellent Surfaces
Date: 1.00pm Wednesday 16th October 2024
Title: TBC
Date: 1.00pm Wednesday 23rd October 2024
Title: The Ouzo effect: adding a splash of dynamics to the water-ethanol-oil phase diagram
Date: 1.00pm Wednesday 30th October 2024
Title: TBC
Date: 1.00pm Wednesday 6th November 2024
Title: Shear-induced dispersion in reactive Hele-Shaw flows
Date: 1.00pm Wednesday 20th November 2024
Title: New in-orbit self-assembly principles: experimental results and high-fidelity simulations
Date: 1.00pm Wednesday 4th December 2024
Title: A conservative finite element method for the Navier-Stokes equation with free surface
Date: 1.00pm Wednesday 22nd January 2025
Title: Granular Material Mechanics and Rheology - From Discrete Simulations to Continuum Models
Date: 1.00pm Wednesday 5th February 2025
Title: Fluid Mechanics of Biological Cells
Date: 1.00pm Tuesday 11th February 2025
Title: Active nematic multipoles: a threefold application of nematic harmonics
Date: 1.00pm Wednesday 19th February 2025
Title: A Multicompartment Darcy Flow Model for Myocardial Perfusion Incorporating Patient-Specific Microvasculature
Date: 1.00pm Wednesday 5th March 2025
Title: A tractable framework for modelling hydrophilic large-swelling gels
Date: Wednesday 1st October 2025, 1.00pm
Venue: LT908
Abstract: TBA
Title: Patient-Specific Multiscale Modelling of Glioblastoma: Targeted Modulation of
Interstitial Fluid Flow Using Electric Field
Date: Wednesday 15th October 2025, 1.00pm
Venue: LT907
Abstract: TBA
Title: Patient- The Lean Azimuthal Flame (LEAF) combustor concept: exhaust emissions and
flame topology
Date: Wednesday 29th October 2025, 1.00pm
Venue: LT907
Abstract: TBA
Title: Patient- TBC
Date: Wednesday 3rd December 2025, 1.00pm
Venue: LT907
Abstract: TBA
Title: Patient- TBC
Date: Wednesday 5th November 2025, 1.00pm
Venue: LT907
Abstract: TBA
Title: Patient- TBC
Date: Wednesday 26th November 2025, 1.00pm
Venue: LT907
Abstract: TBA
Title: Multi-scale modelling of blood rheology in sickle cell disease
Date: Wednesday 28th January 2026, 1.00pm
Venue: LT907
Abstract: Sickle cell disease (SCD) is a haematological disorder, caused by a genetic mutation, in which mutant haemoglobin molecules can polymerise under low-oxygen conditions, altering the biophysical properties of the red blood cells. These cell-level differences then result in changes in the whole-blood rheology -- and those rheological properties are in turn linked to the pathophysiology of SCD. I use mathematical modelling and numerical simulation to develop descriptions of cell-cell interactions within blood flow, and validate these against experimental data.
Title: Modelling the Ouzo Effect: Making Clear Why Clear Things Go Cloudy
Date: Wednesday 11th February 2026, 1.00pm
Venue: LT907
Abstract: Ouzo, and many other similar spirits such as pastis and sambuca, is clear when purchased in a bottle, but after adding a very small amount of water it becomes cloudy (it forms an emulsion). This spontaneous emulsification is known as the ouzo effect, and is due to the trace amount of anise oil present in the drink. It is of fundamental scientific interest, and also has a range of potential industrial applications. One of the key open questions is why the emulsion is stable over very long timescales (months and years), despite requiring essentially no energy to form.
Using a combination of experiment, mathematical modelling, and numerics, we have begun to answer this question. I will present a lattice density functional theory model, based on the statistical mechanics of multicomponent fluids, which provides very good agreement with experimental data. I will then explain what this model, combined with experiments, can tell us about the cloudiness of ouzo. Using the model I will also say something about the shapes of droplets in multicomponent systems, the behaviour of alcohol at the interface of these droplets, and how effective interactions between them may relate to long-time stability. Finally, I will discuss how a dynamical version of the model can further inform us about the stability of ouzo emulsions.
Samples will be provided.
Joint work with Andy Archer, Dave Fairhurst, Fouzia Ouali, and David Sibley.
Title: TBA
Date: Wednesday 25th February 2026, 1.00pm
Venue: LT907
Abstract: TBA
Title: TBA
Date: Wednesday 4th March 2026, 1.00pm
Venue: LT907
Abstract: TBA
Title: Multiscale modelling of soft tissue tearing
Date: Wednesday 18th March 2026, 1.00pm
Venue: LT907
Abstract: We present a mathematically rigorous derivation of a multiscale elastic damage phase-field model using asymptotic homogenisation. Starting from the classical phase-field description of damage, we establish a consistent formulation satisfying the Karush–Kuhn–Tucker conditions, ensuring irreversibility of material degradation. The model is defined over an arbitrary composite domain of continua, enhancing general applicability. By applying asymptotic homogenisation under standard assumptions of local periodicity and smoothness, we derive a multiscale framework linking the microscopic structure to macroscopic behaviour. A detailed asymptotic expansion with respect to the scale separation parameter reveals a leading-order macroscale model free from microscale dependencies, with microscopic effects captured through a set of homogenised coefficients. Numerical simulations in one dimension confirm theoretical convergence of micro- and macroscale models as the scale separation parameter tends to zero. We further specify a representative microscale geometry and constitutive choices enabling simulation of aortic dissection, illustrating the framework’s applicability to complex soft tissue tearing phenomena. The proposed approach provides a mathematically sound and computationally efficient alternative to resolved microscale simulations.
Title: Fracture, by design: topology-programmed damage in Maxwell lattices
Date: Wednesday 25th March 2026, 1.00pm
Venue: LT907
Abstract: Fracture is usually treated as an outcome to be avoided; here we see it as something we may write into a lattice's microstructure. Maxwell lattices sit at the edge of mechanical stability, where robust topological properties provide a way on how stress localises and delocalises across the structure with directional preference. Building on this, we propose a direct relationship between lattice topology and damage propagation. We identify a set of topology- and geometry-dependent parameters that gives a simple, predictive framework for nonideal Maxwell lattices and their damage processes. We will discuss how topological polarisation and domain walls steer and arrest damage in a repeatable way. Experiments confirm the theoretical predicted localisation and the resulting tuneable progression of damage and show how this control mechanism can be used to enhance dissipation and raise the apparent fracture energy.
Title: tbc
Date: 3.00pm Wednesday 7th February 2024
Venue: tbc
Abstract: tbc
Title: tbc
Date: 3.00pm Wednesday 28th February 2024
Venue: LT908
Abstract: tbc
Title: Droplet dynamics: evaporation, hydrodynamics and particle transport
Date: 3.00pm Wednesday 9th October 2024
Venue: LT908
Abstract: The evaporation of droplets has been a much-studied problem in recent years, finding applications everywhere from the spraying of pesticides on leaves to diagnostic applications of blood drying. Many of the most critical industrial applications, such as the printing of OLED screens, involve arrays of droplets with polygonal footprints in close proximity to one another, resulting in complex interactions via the vapour phase.
Unfortunately, the theoretical literature has thus far only treated droplets with circular or elliptic footprints, and even then, only for such droplets in isolation. Similarly, existing models in the literature ignore effects such as asymmetric flow profiles, particle diffusion, and substrate deposition.
We discuss recent advancements in this area relaxing all of these constraints, demonstrating how arbitrary arrays of non-circular droplets may be analysed theoretically. We examine a variety of industrially relevant problems, including the evaporative behaviours of rectangular droplets (used for OLED screens), as well as a continuum formulation designed to cope with the extremely large arrays observed in 8K screens (O(10^8) droplets). We briefly discuss the uses of these solutions in other physical contexts.
Title: Preconditioners and Linear Solvers for PDE Problems
Date: 3.00pm Wednesday 23rd October 2024
Venue: LT908
Abstract: Accurate mathematical models of scientific phenomena provide insights into, and solutions to, pressing challenges in a wide range of applications. Many of these models involve complicated PDEs that require fine-scale solution by numerical methods, e.g., finite difference, finite element or finite volume methods. Critical to these discretisations is the solution of one or more linear systems Ax = b involving hundreds of thousands, or millions, of equations. Accordingly, tailored numerical methods are vital to achieve acceptable solve times, especially when multiple linear systems are involved, as in time-dependent, parameter-dependent, optimisation, inverse and uncertainty quantification problems.
This talk will explore recent research into the solution of some of these systems. In particular, we will describe solution methodologies for singular systems arising from the discretisation of the (Navier-)Stokes equations, and will explore the convergence of iterative methods for structured non-self-adjoint problems.
Title: Remodelling Selection: from a vision to a method
Date: 3.00pm Wednesday 30th October 2024
Venue: LT908
Abstract: “Selective Depletion Bias” is a new term that applies when the population mean value of a trait changes over time or across environments due to selective depletion of frail individuals, and this is misinterpreted as individuals (rather than population composition) changing. This demographic phenomenon was identified and formulated mathematically in the 1970s (when the related “frailty variation” term was introduced), and since applied in econometrics, demography, biostatistics, epidemiology, ecology and evolution. There is growing evidence that the phenomenon is more widespread than initially thought, but still frequently neglected due to the challenges of identifying distributions of individual traits that are under selection.
In this context, I propose that identifiability can be achieved by collecting data at different points of a selection gradient and fitting a model that includes the distribution of interest - “Remodelling Selection”. I have applied this approach to estimate the efficacy of vaccines and to model the initial waves of the COVID-19 pandemic. I am currently applying it to a very different system where bacterial populations grow in laboratory environments under different levels of stress and models are fitted to estimate distributions of individual division rates.
I envision the elimination of selective depletion biases in scientific research by remodelling selection in study design and analysis.
Title: Signatures from rough path theory and their applications in machine learning and AI
Date: 3.00pm Wednesday 20th November 2024
Venue: LT908
Abstract: Rough path theory is a mathematical toolbox providing for the deterministic modelling of interactions between highly oscillatory systems (rough paths). The theory is rich enough to capture and extend classical Ito stochastic calculus but has far wider significance. Fundamental to this approach is the realisation that the evolving state of the system is best described or measured over short time intervals by considering the realised effect of the system on certain controlled systems (the measurement instruments), i.e., the path signature.
The path signature, initially introduced by K.T. Chen, is a homomorphism from the monoid of paths into the grouplike elements of a closed tensor algebra (non-commutative). Defined as the collection of coordinate iterated integrals of path, it offers a graded summary of the path and can, through linear combinations, approximate solutions to controlled systems driven by the path (universal property). Moreover, the expected signature of a random path plays a similar role as that the moment generating function of a random variable does (characteristic property). These properties make the path signature a natural and straightforward choice for a feature set of time series in machine learning, as it effectively captures the sequence of events and the nonlinear impact on multimodal stream data. Besides, the logarithm of the path signature, which is indeed a Lie series, offers a more compact and concise representation of the path and can act as a dimension-reduced version of the path features for machine learning tasks. In the first part of the talk, you will learn how path signatures have been applied in areas such as character recognition, clinical diagnosis, battery health prediction and data generation in finance.
The second part of the talk will highlight recent advancements in the field: the 2D signature, a generalised version of the path signature for surfaces, which effectively represents image data and retains universal and characteristic properties on surfaces. I will demonstrate how the 2D signature can aid in detecting adversarial attacks.
Title: Trusted Research and Innovation: Protecting our People, Academic Endeavour, and Reputation
Date: 3.00pm Wednesday 11th December 2024
Venue: LT908
Abstract: This session will cover relevant UK Government legislation along with the University of 海角论坛 approach to Trusted Research & Innovation and support available to staff in this area.
Title: Homogenization of a Coupled Electrical and Mechanical Bidomain Model for the Myocardium
Date: 3.00pm Wednesday 29th January 2025
Venue: LT908
Abstract: We propose a coupled electrical and mechanical bidomain model for the myocardium tissue. The heart muscle structure that we investigate possesses an elastic matrix with embedded cardiac myocytes. We are able to apply the asymptotic homogenization technique by exploiting the length scale separation that exists between the microscale where we see the individual myocytes and the overall size of the heart muscle. We derive the macroscale model which describes the electrical conductivity and elastic deformation of the myocardium driven by the existence of a Lorentz body force. The model comprises balance equations for the current densities and for the stresses, with the novel coefficients accounting for the difference in the electric potentials and elastic properties at different points in the microstructure. The novel coefficients of the model are to be computed by solving the periodic cell differential problems arising from application of the asymptotic homogenization technique. By combining both the mechanical and electrical behaviours, we obtain a macroscale model that highlights how the elastic deformation of the heart tissue is influenced and driven by the application of a body force that varies with the difference in electric potentials at different points in the microstructure. We numerically investigate the novel model as well as various extensions and consider properties such as the effective electrical conductivities and elastic parameters and find behaviours that replicate physiological observations.
Title: Plankton thermal diversity modulates the responses of primary production to ocean warming
Date: 3.00pm Wednesday 12th February 2025
Venue: LT908
Abstract: Marine phytoplankton plays a pivotal role in taking up CO2 from the atmosphere and supporting marine fisheries. As our ocean is warming at an unprecedented rate due to anthropogenic activities, it is imperative to understand how the phytoplankton community and primary production will respond to warming. However, a fixed rate of increase of phytoplankton photosynthetic rate to increasing temperature is assumed in most Earth System Models used for projecting how the Earth system will respond to climate warming, which ignores phytoplankton diversity and leads to great uncertainties in future projection. Here, I explore how the differences in the thermal responses of phytoplankton species affect our perception of how to parameterize phytoplankton thermal responses in plankton models and the implications for how primary production will change in a warming ocean.
Title: A Riemannian View on PDE-constrained Shape Optimisation
Date: 3.00pm Wednesday 26th February 2025
Venue: LT908
Abstract: Shape optimisation involves finding the optimal shape of a domain (e.g., a boundary or region in space) to minimise or maximise an objective function. This process is often subject to constraints, many of which are governed by partial differential equations (PDEs) since physical phenomena—such as fluid flow, heat conduction, or elasticity—are typically described by these equations. Common examples include minimising drag in fluid dynamics, maximising structural strength, and optimising material distribution within a design domain.
A significant challenge in shape optimisation is modelling the shapes themselves, as no universal consensus exists on the best approach. Current methods include level set techniques, the method of mappings, and boundary parametrisation, each with its own advantages and limitations. In this talk, we focus on the Riemannian view of shape optimisation. Here, Riemannian geometry provides a mathematical framework for understanding and navigating the space of shapes. The key idea is to treat the space of admissible shapes as a Riemannian manifold, where each shape (e.g., a curve in 2D or a surface in 3D) represents a point in either a finite- or infinite-dimensional manifold. Additionally, Riemannian metrics define distances and gradients on this manifold, enabling the rigorous application of optimisation techniques such as gradient descent.
Title: Equation-Free Toolbox: Efficient Multiscale Computation of Microscale Systems
Date: 2.00pm Wednesday 21st May 2025
Venue: LT908
Abstract:
The Equation-Free approach empowers the computer-assisted analysis of complex, multiscale systems. Micro-scale code is often the best available description of a system, but it is typically impractical for macroscale predictions. The toolbox functions non-invasively ‘wrap around’ microscopic simulators to empower scientists and engineers to perform macro-scale, system-level tasks and analysis. The methodology bypasses the derivation of macroscopic evolution equations by computing the micro-scale simulator only over short bursts in time (Projective Integration) and/or on small patches in space (Patch Scheme). For efficiency, the bursts and patches are sparse in time and space, respectively.
For proven macroscale accuracy, we adjust standard time integration methods and establish excellent inter-patch coupling, respectively. The proofs of highly controllable accuracy encompass microscale heterogeneous systems, such as modern meta-materials, to underpin macro scale ‘homogenised’ predictions. In the Equation-Gree approach, no epsilon need be identified, nor any slow or fast variables - it is non-invasive. Download the Matlab toolbox to try it. Open challenge: discover how microscope particle/agent systems may achieve similar accuracy and efficiency.
Health and Ecology Modelling
Marine Population Modelling, Mathematical Biology, Epidemiology and Statistical Informatics
Title: The Role of Individuals in Determining the Impacts of Changing Environments on Population Level Dynamics
Date: Wednesday 7th February, 1.00-2.00pm
Venue: LT907
Abstract:
Climate change is having profound effects on the incidence of vector borne disease, such as dengue, chikungunya and West Nile virus. However, developing effective measures of disease risk on a global scale are challenged by the complex ways in which environmental variation acts in vector-host-pathogen systems. One way in which insect vectors, such as mosquitos, respond to environmental variation is to change their traits this can result in populations comprised of groups of individuals which differ in their traits (e.g. size, fecundity). For example, if food is scarce for juvenile mosquitos then when they become adults they are smaller, and lay fewer eggs to ensure there is less competition for food in the next generation. The environment of the juvenile determines the trait the individual has as an adult. In this way the individuals adapt to the environment as well as shape the environment for future generations.
Current models over-simplify the interaction between individuals, populations and the environment, so risk misestimating predictors of disease risk. Here, we derive a mathematical framework for capturing the interaction of individuals, their traits and the population dynamics. I will show how this new mathematical framework leads to both interesting mathematical questions and can be used to help explain the location, magnitude and timing of historical dengue outbreaks.
Title: Estimating the Size of Aedes Aegypti Populations from Dengue Incidence Data: Implications for the Risk of Yellow Fever, Zika Virus and Chikungunya Outbreaks
Date: Wednesday 17th April, 1.00-2.00pm
Venue: TBC
Abstract: In this talk I present a model to estimate the density of aedes mosquitoes in a community affected by dengue. The model is based on the fitting of a continuous function to the incidence of dengue infections, from which the density of infected mosquitoes is derived straightforwardly. Further derivations allows the calculation of the latent and susceptible mosquitoes' densities, the sum of the three equals the total mosquitoes' density. The model is illustrated with the case of the risk of urban yellow fever resurgence in dengue infested areas but the same methods apply for other aedes-transmitted infections like Zika and chikungunya viruses.
Title: Quantifying Performance and Resilience in Marine Assemblages with Complex Life-Histories
Date: Wednesday 21st February, 1.00-2.00pm
Venue: LT908
Abstract: Ongoing global change challenges our ability to predict how natural populations will both respond to novel climatic regimes and utilise available habitat space. Corals are critical to the functioning of coastal reef ecosystems and, yet, in spite of their intrinsic and economic value, are threatened by an increasing plethora of abiotic and biotic disturbances. Preventing the ensuing loss of coral coverage and diversity calls for a mechanistic understanding of resilience across coral species and populations that is currently lacking in coral reef science. Meanwhile, changing coastal conditions and our ever-expanding exploitation of marine resources, has heralded a perceived increase in the abundance of coastal jellyfish assemblages. While jellyfish are also an important component of coastal marine communities, their public perception is often tainted by their proclivity for aggregating in vast numbers, known as jellyfish blooms, which can disrupt fishing and tourism activities. However, despite the socioeconomic ramifications associated with the formation of these jellyfish blooms, the complex and cryptic lifecycles exhibited by jellyfish species largely precludes accurate predictions into their timing and location, restricting our ability to manage and mitigate their ecological and economic impacts. Here, I will introduce research comprising state-structured population modelling, novel transient demographic approaches, and state-of-the-art hydrodynamic simulations, that offers valuable insight into the performance and resilience of these complex and cryptic marine assemblages under future climate scenarios; frameworks that represent key decision-support tools for informing both the conservation of global coral reefs and our management of the socioeconomic impacts of jellyfish bloom formation.
Title: Some Data-Driven Approaches to Surveillance of Covid-19 in the UK
Date: Wednesday 28th February, 1.00-2.00pm
Venue: LT908
Abstract: Whilst much of the work in modelling transmission of the pandemic was conducted using mathematical transmission models, the quantity of data made available through open data portals, such as the Covid Dashboard, provided alternatives to understanding and intervening to improve public health outcomes. In this talk I will outline some statistical approaches using surveillance data from varying spatial scales to study underlying dynamics of transmission of Covid-19 in the UK. In particular, multivariate flexible regression models and dimension spatial dimension reduction techniques will be used to estimate relative transmissibility of emerging variants of concern, as well as nowcasting current states of pandemic from noisy multivariate time series, respectively.
Title: Using Minimalistic Food-Web Models to Inform Fisheries Management
Date: Wednesday 1st May, 1.00-2.00pm
Venue: TBC
Abstract: Chance and Necessity (CaN) modelling is a minimalistic food-web modelling framework integrating the existing knowledge about an entire or part of the ecosystem, the available data, and uncertainties. Unlike most of the large ecosystem models, the CaN framework does not aim at predicting the future state of commercial stocks, but rather to reconstruct possible past dynamics of a food-web. Reconstructions result from the delimitation of the possible 鈥渟tate-space鈥� of the food-web based on ecological survey data and expert knowledge, and the exploration of this 鈥渟tate-space鈥�. Here, I will present the underlying concepts of CaN modelling, present case studies of CaN modelling applications and provide examples on how the model outputs can be used to improve the management of commercial fisheries in the future.
Title: How Lifestyle Differences Affect Epidemic Spread: Heterogeneous Density Dependence in Infectious Contact Rates
Date: Wednesday 10th July, 1.00-2.00pm
Venue: LT908
Abstract:
Title: Modelling and Inference and Heterogeneity in Bacterial Growth
Date: Wednesday 22nd May, 1.00-2.00pm
Venue: LT908
Abstract: E. coli is a common bacterium found in the intestines of humans and animals. While many strains are harmless, some can cause serious illness, such as diarrhoea, urinary tract infections, and in severe cases, even kidney failure or death. Understanding its behaviour and mechanisms of infection is therefore vital for public health. Like many bacteria, E. coli can also develop resistance to antibiotics. Persister cells are a small subpopulation of bacterial cells which are slow-growing, which allows them to survive in harsh conditions such as exposure to antibiotics or other stressful environments. These cells are distinct from regular bacterial cells because they are not killed by antibiotics. Studying how resistance emerges and spreads within bacterial populations helps in developing strategies to combat antibiotic-resistant strains. The aim of this talk is to discuss the range of modelling approaches to determine the impact non-inheritable variation between individual cells has on population growth and population response to stressful environments. Various models will be considered including systems of ODEs, age-structured PDEs, renewal equations, and stochastic branching process. Where possible, comparisons and connections will be made between the different modelling approaches. We also discuss some initial work on model inference, where the objective is to indirectly determine the possibility of heterogenous sub-populations from total population data. These techniques will be applied to a probabilistic model of data generated from a microfluidic dynamic cytometer.
Title: Heterogeneity and Identifiability in Mathematical Biology
Date: Wednesday 29th May, 1.00-2.00pm
Venue: LT908
Abstract: Heterogeneity is a dominant factor in the behaviour of many biological processes and is often a significant source of the variation observed in biological data. Despite this, it is relatively rare for mathematical models of biological systems to incorporate variability in model parameters as a source of noise. In the first part of talk, I motivate and present a new computationally efficient method for inference and identifiability analysis of so-called random parameter models based on an approximate moment-matched solution constructed through a multivariate Taylor expansion.
Effective application of mathematical models to interpret biological data and make accurate predictions typically requires that model parameters are identifiable. Yet, there are no commonly adopted approaches that can be applied to assess the structural identifiability of the partial differential equation (PDE) models that are requisite to capture the spatial heterogeneities features inherent to many phenomena. In the second part of this talk, I provide an introduction to structural identifiability before presenting a new methodology applicable to a broad class of PDE models. I then conclude by discussing the future of identifiability analysis for the spatial, random parameter, and stochastic models that are fast becoming pervasive throughout mathematical biology.
Title: Cascading and Multi-Stressor Effects in Coastal Ecosystems
Date: Monday 19th August, 3.00-4.00pm
Venue: LT511
Abstract: Coastal ecosystems are simultaneously exposed to a plethora of human-induced stressors, such as climate warming, eutrophication, pollution, overfishing, and pathogens. These stressors interact with each other, driving counter-intuitive responses and undesirable results in management efforts. For example, the reduction of nutrient loads is widely believed to be the solution for eutrophication problems in coastal ecosystems. However, we show that these efforts have not always resulted in, and may not in the future result in, the desired reduction of phytoplankton biomass. Instead, the effects of de-eutrophication are overridden by climate warming, which intensifies temperature-dependent grazing of zooplankton by small carnivores, such as juvenile fish, leading to reduced herbivory (by zooplankton on phytoplankton) and thus increased standing stock of algae. This effect is especially strong in the shallow and turbid waters of coastal seas worldwide. High turbidity persistently limits the rates of photosynthesis, shifting bottom-up control towards top-down control and a stronger influence of higher trophic levels. In another case study, we show the compounding effects of climate warming and marine viruses on food web dynamics in a coastal environment, leading to a decline in primary production and carbon export, and higher retention of nutrients in the upper water column. Our results highlight the importance of stressor interactions and cascading effects in understanding responses in coastal ecosystems, a benchmark for ecosystem modelling and the effective development of management and conservation strategies.
Title: TBC
Date: Wednesday 4th September, 1.00-2.00pm
Venue: LT908
Abstract:
Mathematics of Life Sciences
Marine Science, Variation and Selection, Epidemiological Modelling
Title: Two Epidemiological Problems: Birds and Cows
Date: Wednesday 22nd January, 2.00-3.00pm
Venue: LT908
Abstract: I would like to present an analysis of two questions, and they are only faintly connected. The first is: should we recommend carcass removal as a method of mitigating outbreaks of avian influenza in sea bird colonies. This remains an urgent policy question around which there is very little relevant empirical evidence. What has modelling to offer policy makers? The second is, if we only had a few virus genome sequences from a monophyletic outbreak of disease, could we estimate how many people had been infected in total? This would be an importantly useful estimate to be able to make. I will describe some progress towards solving this problem, using data from foot-and-mouth disease outbreaks.
Title: Extracting Hidden Trait Distributions from Population-Level Data
Date: Wednesday 19th February, 2.00-3.00pm
Venue: LT907
Abstract: Individual variation in traits that respond to selection can have puzzling effects on the dynamics of populations. These traits are often unobservable, which leads to the neglect of their variation among individuals, and consequent biases in the interpretation and modelling of population-level data. In this chalk-talk, I will sketch the approach that our group has been developing to extract hidden trait distributions from specifically designed population experiments.
Title: AI for Green Future – Reliable, Novel, Efficient and Trustworthy AI Development in Agriculture
Date: Wednesday 19th March, 2.00-3.00pm
Venue: LT511
Abstract: Artificial intelligence (AI) will play a key role in tackling current economic and environmental challenges and has seen significant investment over the past 5 years, with the market valued at $86.9 billion in 2022 and predicted to grow at a CAGR of 36.2% to reach $407 billion by 2027. The state-of-the-art of AI is dominated by deep learning and model-centric approaches, but these are data and computation intensive and prone to data drift-related errors, which are critical limitations for agricultural applications. To address these drawbacks, we operationalise an alternative paradigm – holistic data-centric AI with lifelong learning – which emerged in 2021. We are one of the first to (1) focus on the agricultural applications of data-centric AI and (2) integrate socio-ethnic and ethical principles, which are typically overlooked in AI applications. Such human-in-the-loop hybrid AI models will accommodate aspects of the social sciences and humanities (SSH) that are important for agricultural applications due to the widespread gender, ethnic and social inequity in this sector. We address the slow adoption of AI by jump-starting the use of novel, sustainable AI-based solutions in European agriculture in collaboration with India. This is important because temperature rises of ~1.5 °C in the coming decade are likely to shift the climate in Europe to the equivalent of India today. The co-development of solutions for agriculture in India will therefore better position the EU to adapt to climate change in the future. India’s collaboration with the EU, a leader in AI/data/robotics, will accelerate its already booming AI sector, particularly in agriculture. We thus respond to the India–EU roadmap for the exploitation of AI/data/robotics platforms, providing an entry point into Asia and encouraging the transition to circular and sustainable agriculture. In this talk, I will talk about the general principles underlying the AI for Green Future ideas, and discuss some examples of project that show how this approach can be developed in practice.
Title: Breezes, Blazes, and Stats: A Research Journey
Date: Wednesday 9th April, 2.00-3.00pm
Venue: LT907
Abstract: In this talk, I will present my research on estimating wildlife fatalities at onshore wind farms and, more recently, on modelling the occurrence of both urban and rural fires. Understanding the impact of onshore wind farms on avian and bat populations requires mortality estimation. In this context, we want to estimate the number of deaths driven by collision with the wind farm structures. Mortality assessment is typically based on counting detected carcasses underneath turbines. However, there are several sources of uncertainty, including carcass removal (e.g., by scavengers) and the observers’ detection ability that must be accounted for. Moreover, mortality rates vary across space and time, influenced by turbine placement and changing collision risks. Urban fires remain a major threat, contributing to property damage, psychological trauma, physical injury, and loss of life. High population density and some socio-economic factors can further amplify fire risk and firefighting costs. On the other hand, wildfires represent a global challenge. In Portugal, despite a declining trend in the number of rural fires, the total burned area has increased in the last years, reaching 110,097 hectares in 2022. This shift is tied to a rise in large, intense fires, which are often linked to climate change and result in more extensive environmental impact and higher socio-economic costs. I will conclude by sharing some recent ongoing work on modelling the occurrence and size of rural fires.
Title: Incorporating Spatial, Ecological and Societal Dimensions into Bioeco-nomic Models of Environmental Decision-Making
Date: Wednesday 16th April, 2.00-3.00pm
Venue: LT907
Abstract: Woodland conservation and expansion plans often fail because the effort is not targeted at an appropriate spatial scale required by ecological processes and does not address the needs and preferences of the population. These different requirements often lead to trade-offs which need to be addressed by planners and managers. Models incorporating ecology, economics and stakeholder views can assist in designing Payment for Ecosystem Services (PES) schemes that can balance different requirements. Such models often involve interesting mathematical problems, from percolation and asymmetric diffusion to large-scale simulations and web application development.
I will first address the efficacy of a local PES scheme in creating a network of conserved land patches on a heterogeneous landscape, combining birth-death and migration dynamics with a simple economic model. A long-term survival of representative species is used to quantify the out-comes of an irreversible land-use change caused when its owner accepts the payment exceeding their opportunity cost. We compare the outcomes of uniform and aggregated payment schemes, showing that simple uniform payment is often the most cost-effective solution.
Secondly, we apply a portfolio modelling approach to address the spatial allocation of resources across a landscape, based on a combination of ecological and social benefits to inform woodland expansion schemes. The model incorporates multiple societal preferences over ecosystem benefits, such as the parcel’s potential to contribute to carbon capture, biodiversity and health and well-being. Connectivity is incorporated by gravity models, with the values depending on the distance and size of the site and/or city. We show how landscape locations with different characteristics are selected depending on the manager’s preferences and how the choice affects the ecosystem services. The model is applied to England’s National Forest and the web application based on it is included into the Tree Council toolbox, for use across the country.
Title: Inference of Mixed-Effects State-Space Models with Unknown Initial Condition and Heteroschedastic Measurement Error
Date: Wednesday 14th May, 2.00-3.00pm
Venue: LT718
Abstract: Important dynamical systems in nature can be faithfully described by differential equations. Often the parameters of such systems are unknown, and it is a fundamental step to estimate them. If data is available the model parameters can be calibrated to reproduce experimental findings. However, standard inference methods can be computationally expensive, especially in high dimensional settings, and do not necessarily account for missing measurements, experimental confounders, and heterogeneity in the parameters across different groups/conditions. Furthermore, these methods usually require the initial state of the system, i.e. the initial condition, whose value is not necessarily available from experiments.
A statistical framework is proposed to infer the parameters of dynamical systems written in a mixed-effects state-space formulation. The initial condition is treated as an extra unknown vector parameter. Measurement error noise is modelled as a function of confounding factors, thus accounting for heteroscedasticity. The mixed-effects on the parameters describe heterogeneity in the dynamics across groups/conditions, whilst reducing parameter dimensionality. Inference is performed by minimizing a loss function between model predictions and measurements. The method is first tested in simulation studies and then applied to describe the molecular mechanisms underlying clonal haematopoiesis, a biological process whereby the expansion of mutated cells can result in tumour development.
Title: Quantifying the Stochastic Dynamics of Transcription-Coupled DNA Repair
Date: Wednesday 28th May, 2.00-3.00pm
Venue: LT908
Abstract: DNA damage is a major source of cancer-causing mutations and disruption to gene expression, particularly in ageing. Transcription-coupled repair (TCR) minimises the risk of damage within genes, but experimental measurement of this DNA repair process is challenging. Here, we combined a well powered murine model of cancer development with a new stochastic model of damage and repair to quantify the mechanisms of repair on DNA alkylation adducts. We show that RNA-polymerases frequently bypass lesions without triggering repair, indicating that small alkylation adducts are unlikely to be an efficient barrier to gene expression but are likely to be a source of mutant RNA. The efficiency of TCR gradually decays through gene bodies leading to a rejection of the standard conceptual model that transcription immediately resumes after repair. Our results have implications for the accurate inference of driver mutations in cancer and the effects of DNA damage on expression, especially for genes with a large genomic span.
Title: AI for Decision Support to Smallholder Farming
Date: Tuesday 16th September 2025, 2.00pm
Venue: LT908
Abstract: Pests and diseases contribute to an estimated 40% reduction in global crop yields annually, necessitating scalable, data-driven interventions to help smallholder farmers. Recent advances in artificial intelligence (AI) and machine learning (ML) have demonstrated significant potential in augmenting plant health diagnostics and decision support at field scale. A forthcoming initiative, the AgriLLM Project, scheduled for launch at COP30 (Brazil, November 2025), integrates Large Language Models (LLMs) with CGIAR’s domain expertise to generate context-specific, real-time agronomic advisories. This innovation addresses persistent gaps in extension delivery across the Global South, where resource-constrained systems limit access to expert recommendations during critical phenological stages. Among operational examples, the Plantix platform has emerged as a large scale AI application, capable of automatically diagnosing over 700 biotic and abiotic stresses across 45 crops. Advisories were offered for over 150 million targeted farmer problems using plant damage symptoms. Complementing this, ICRISAT’s Plant Health Detector employs supervised ML classifiers to automate recognition of 50 crop damages. An Intelligent Agricultural Systems Advisory Tool is being piloted to provide climate smart pre-season and in-season advisories in India and Africa. Parallel advances in computer vision have facilitated spatially explicit tracking of invasive pests such as Spodoptera frugiperda, while citizen science models enhance surveillance. Collectively, these AI-enabled systems exemplify transformative pathways for resilient, data-driven crop advisory management for smallholders in Asia and Africa.
Title: Identifying the Effect of Climate Warming on Ocean Chlorophyll from Satellite Records Using Deep Learning and Multiple Regression Methods
Date: Wednesday 15th October 2025, 2.00pm
Venue: LT908
Abstract: Anthropogenic climate warming is expected to cause long-term changes in global marine phytoplankton, affecting the marine ecosystem and fishery production. However, it is challenging to distinguish the effects of long-term climate warming from natural variability in satellite chlorophyll-a (Chl-a, a proxy for phytoplankton biomass) records—the only global-scale observations of phytoplankton—due to limited data length and interference from natural fluctuations. As a result, we still cannot confidently determine whether observed changes in global Chl-a from limited satellite records are caused by long-term climate warming or how quickly warming-induced Chl-a changes occur.
In this talk, I will introduce our recent two studies on this topic. First, we developed a deep learning model and trained it using an ensemble of Earth System Models’ simulations, which successfully detected the climate warming signal from satellite observations of global Chl-a. This validates the model’s predictions and highlights the emerging anthropogenic impacts on global marine phytoplankton. Second, using multiple regression models, we reduced the influence of natural climate variability on trend analysis of satellite Chl-a in the tropical Pacific from 1997–2023, revealing a long-term decline in Chl-a at a rate of about −4‰/yr. Global warming contributed to this decline at a rate of −14.5%/鈩�. This finding offers solid estimates of the global warming-driven trend in tropical marine phytoplankton biomass, helping to forecast future changes in marine ecosystems.
Title: Application of GAM in Exploring Long-Term Productivity-Biodiversity Relationships in Marine Microzooplankton Assemblages
Date: Wednesday 22nd October 2025, 2.00pm
Venue: LT511
Abstract: Although the productivity-biodiversity relationship (PBR) has been a hot topic, few studies have considered how anthropogenic pressures affect PBRs in marine microzooplankton. Here, we applied GAMs to provide the first insights into PBRs in tintinnid assemblages using 18-year data from Jiaozhou Bay, a typical coastal bay in the Yellow Sea. We hypothesized and verified that PBRs vary across contrasting anthropogenic nutrient inputs and that functional and phylogenetic diversity would provide more information than conventional species richness. High productivity promotes higher diversity under low to medium rather than high anthropogenic nutrient inputs. Compared to species richness, functional and phylogenetic diversity reveal more PBR patterns and respond more rapidly to varying anthropogenic inputs. A concave PBR is revealed for functional diversity in the ecozone with highly active water exchange. Our study contributes to the understanding of PBRs in marine unicellular secondary producers and their responses to anthropogenic nutrient inputs in coastal ecosystems.
Title: Improving Predictions of Drug-Induced Arrhythmias Through Calibration of Action Potential Models
Date: Wednesday 26th November 2025, 2.00pm
Venue: LT907
Abstract:
Mathematical action potential (AP) models describe changes in cell membrane voltage arising from a complex interplay of ionic currents and their potential interactions with drug compounds. These models can support preclinical risk assessment for drug-induced cardiac arrhythmias and help extract richer information from animal-based experiments.
The rabbit Purkinje fiber assay is widely used in preclinical safety studies because it incorporates the major electrophysiological mechanisms present in human ventricular myocytes. When combined with such experiments, mathematical AP models can provide predictions of drug effects on cardiac electrophysiology. However, in practice, these models sometimes fail to reproduce key experimental findings.
This work aims to improve AP models by calibrating their parameters to reduce discrepancies between model predictions and experimental recordings. After introducing the modeling and calibration methods, preliminary results will be presented and discussed.
Title: Dissecting the Role of Phenotypic Variation in Cell Population Growth and Collective Self-Generated Chemotaxis
Date: Wednesday 28th January 2026, 2.00pm
Venue: LT907
Abstract: Phenotypic variation is a ubiquitous feature of biological cell populations, even in genetically identical cells growing in uniform environments. Such variability can have profound consequences for population-level behaviour, particularly under stress, yet it is often neglected in classical modelling frameworks.
In the first part of this talk, I consider mathematical models of bacterial population growth that explicitly incorporate non-heritable variation in individual cell growth rates. I examine how phenotypic heterogeneity and environmental selection shape population growth and the dynamics of phenotypic subpopulations. We derive theoretical results for population growth rates and compare them with predictions from homogeneous models, identifying regimes in which variability qualitatively alters population outcomes. I also address the inverse problem of inferring distributions of generation times and phenotypic abundances from data, showing that competing model assumptions can be robustly distinguished.
In the second part of the talk, I turn to self-generated chemotaxis, a collective process in which cells modify their chemical environment to guide movement. Using a hybrid discrete–continuum model that couples stochastic cell motion with a continuum description of the chemoattractant, I investigate how phenotypic variation in motility, sensing, and chemical degradation affects the robustness of collective migration. Simulations and inference results highlight which sources of variability are most influential. The results and tools developed have broader implications for collective behaviour in cell biology, ecology, and evolution.
Title: Estimating the Role of Heterogeneities in the First-Wave Dynamics of COVID-19 in Nigeria
Date: Wednesday 18th February 2026, 2.00pm
Venue: LT907
Abstract: Variation in individual specific traits such as susceptibility or connectivity that are not subject to short-term change can have an important influence on the dynamics and potential to control infectious disease outbreaks. This is because the distribution of these heterogeneities in the susceptible population changes over the course of an outbreak as a result of higher levels of transmission between infected and more susceptible or more connected individuals, leading to additional reductions in the effective reproduction number and the herd immunity threshold. This study estimates heterogeneities in susceptibility in COVID-19 transmission by fitting a modified Susceptible, Infected, Recovered model to incidence data. We estimate the parameters of the model using Markov Chain Monte Carlo techniques, first testing the proposed method on simulated data to determine its effectiveness before applying it to real-world incidence time-series from ten different Nigerian States supplied by their Centre for Disease Control. We estimated the average basic reproduction number to be 1.360 (95% credible intervals (CrI): 1.356 - 1.366), the heterogeneity parameter to be 2.561 (2.247 - 2.884), and the reporting probability to be 0.005 (0.004 - 0.006). Information criteria indicated that the model with heterogeneity was substantially better supported compared to an analogous homogenous model. The estimated value of the herd immunity threshold and final epidemic size with this estimated level of heterogeneity is much reduced compared to the homogenous model. Including heterogeneities in epidemiological models can improve the reliability of model-based inferences, and lead to better-informed decisions for managing emerging and re-emerging infectious disease outbreaks like COVID-19.
Title: On the Simultaneous Inference of Susceptibility Distributions and Intervention Effects from Epidemic Curves
Date: Wednesday 18th February 2026, 2.30pm
Venue: LT907
Abstract: Individual variation in susceptibility lowers herd-immunity thresholds by causing highly susceptible individuals to be infected early, accelerating selective depletion of the susceptible pool. In Susceptible–Exposed–Infectious–Recovered (SEIR) models, this heterogeneity is often summarised by the coefficient of variation (ν). Although heterogeneity in susceptibility and non-pharmaceutical interventions (NPIs) act through different mechanisms—intrinsic depletion versus time-varying contact reduction—their effects on observed epidemic curves can be similar. As a result, when fitting a single epidemic trajectory, these components can lie along a pronounced “compensation ridge,” making them practically non-identifiable.
We first investigate this challenge using stochastic simulations of synthetic epidemics. Single-epidemic inference via maximum likelihood and Bayesian MCMC yields strong posterior/ likelihood dependence between ν and intervention strength c , with correspondingly wide uncertainty intervals. We then systematically study a multi-epidemic framework that jointly analyses 2–3 concurrent epidemics (e.g. distinct regions) under shared heterogeneity but differing initial conditions. This design reduces the ν–c dependence and improves numerical stability by roughly an order of magnitude, indicating that variation in timing and scale across epidemics can help constrain the trade-off.
We apply the approach to first-wave COVID-19 mortality in England and Scotland using a hierarchical Bayesian model with an explicit delay-based observation process. The real-data fits confirm that the compensation ridge persists: joint fitting narrows the feasible parameter region relative to single-country analyses, yet mortality data alone cannot fully disentangle depletion from lockdown effects without informative priors or additional information.
Finally, we study model misspecification: does the shape of the susceptibility distribution matter when mean and variance are matched? Comparing Gamma and Lognormal susceptibility models matched on moments, we find systematic differences driven by tail behaviour, with Gamma-based models tending to be structurally “optimistic” relative to Lognormal alternatives. Importantly, we show that although multi-epidemic fitting improves precision, it can also produce confident but biased inference when the susceptibility distribution is misspecified.
Title: An Adaptive Tolerance Selection Procedure to Avoid Local Minima in Approximate Bayesian Computation Algorithms for Use in Coagulation-Fragmentation Models of DNA Methylation
Date: Wednesday 25th February 2026, 2.00pm
Venue: LT907
Abstract: DNA methylation is an important epigenetic phenomenon in which methyl groups are added to sequences of DNA. The addition of these chemical groups regulates gene expression and erroneous methylation patterns are associated with various diseases including Alzheimer’s and cancer. In this talk a mathematical model of DNA methylation will be developed using a coagulation-fragmentation based framework which allows the formation and break-up of clusters of methylated sites across DNA to be investigated. Model calibration requires the comparison of model output to experimental data to infer model parameters. However, for our model the likelihood function quickly becomes intractable as the system is scaled to realistically relevant lengths of DNA. This inability to obtain a likelihood is common when studying physically relevant systems and hence likelihood-free inference approaches are generally used. In this talk we will employ Approximate Bayesian Computation Sequential Monte Carlo (ABC SMC) for parameter estimation. ABC is a rejection sampling technique in which the intractable likelihood is replaced by a simulation-based comparison of experimental (observed) data and simulated data. The difference between experimental and observed data yields a discrepancy, with the accept/reject criteria then conditioned on whether this discrepancy is less than some tolerance value. We investigate the role of the tolerance sequence used in ABC SMC to iteratively navigate from a given prior distribution to posterior. Choosing a suitable tolerance sequence is critical to the success of ABC SMC and we have found that established techniques such as selecting pre-defined fixed tolerance sequences and adaptively updating tolerance selection as the inference process evolves can both result in the ABC SMC algorithm becoming trapped in regions of local minima in discrepancy space. Here we present an improved ABC SMC algorithm which overcomes this issue largely through simple sampling from the prior. The discrepancy associated with each parameter vector sampled from the prior is calculated and analysis of the corresponding discrepancy distribution using the Kneedle algorithm leads to the specification of an appropriate starting tolerance, allowing ABC SMC to begin near the global minimum in discrepancy space. Subsequent iterations of ABC SMC then refine inference around the true parameter values. We have found this new approach allows ABC SMC to infer parameter values reliably for systems which contain local minima in their discrepancy space. We will then move on to discuss some recent work related to the additional challenges faced when applying ABC SMC to stochastic systems of reaction networks. Firstly, it can be common for experimental data to consist of only a single realisation, which can then prove challenging to compare with stochastic models. We test the ability of the ABC SMC algorithm to successfully estimate parameter values when the simulated data consists of only single stochastic realisations of the model under investigation. We then conclude by investigating the role that stochastic statistics can play in improving parameter identifiability.
Title: The World’s Largest Macroalgal Bloom in the Yellow Sea, China: Formation and Implications
Date: Wednesday 4th March 2026, 2.00pm
Venue: LT907
Abstract: The world’s largest trans-regional macroalgal blooms during 2008-2025 occurred in the Yellow Sea, China. A decadal study reveals the causes, development and future challenges in this unique case. Satellite imagery and field observations showed that the macroalgal blooms in the Yellow Sea originated from the coast of Jiangsu province and that favorable geographic and oceanographic conditions brought the green macroalgae from the coast offshore. Statistically, optimal temperature, light, nutrients and wind contributed to the formation and transport of the massive bloom north into the Yellow Sea and its deposition onshore along the coast of Shandong province. Certain biological traits of Ulva prolifera-efficient photosynthesis, rapid growth rates, high capacity for nutrient uptake, and diverse reproductive systems allowed growth of the original thousands of tonnes of biomass into more than one million tonnes of biomass in just two months. The proliferation of U. prolifera in the Yellow Sea resulted from a complex contingency of circumstances, including human activity (eutrophication by release of nutrients from wastewater, agriculture, and aquaculture), natural geographic and hydrodynamic conditions (current, wind) and the key organism’s biological attributes. Hydro-bio-model was developed for monitoring of green tide. Better understanding of the complex biological-chemical-physical interactions in coastal ecosystems and the development of an effective integrated coastal zone management with consideration of scientific, social and political implications are critical to solving the conflicts between human activity and nature.
Title: Fragility in a Togashi-Kaneko Stochastic Model with Mutations
Date: Wednesday 18th March 2026, 2.00pm
Venue: LT907
Abstract: In biochemical and biological contexts, autocatalytic interactions—where a species promotes its own production, often through feedback with other components—play a central role. They capture nonlinear feedback loops capable of generating rich dynamical phenomena such as bistability, sustained oscillations, and stochastic switching between metastable states. These mechanisms are not only fundamental in chemical kinetics, where autocatalysis underlies classical models of pattern formation and self-organization, but they also appear in biological settings ranging from gene regulation and signalling cascades to ecological interactions and evolutionary dynamics. They have also appeared in models of opinion dynamics in populations.
The Togashi-Kaneko (TK) stochastic model is a prototypical example of an autocatalytic reaction network exhibiting dramatic switching behaviour. The desire to understand this unusual behaviour has attracted considerable attention in recent years. In this talk, we study the TK model with additional mutations. We establish a rigorous stochastic averaging principle that describes slow dynamics in terms of certain ergodic means of fast variables. Beginning with two species, we demonstrate a sensitivity of the model to even slight departures from symmetry in the autocatalytic reactions. We accomplish this through a detailed analysis of the stationary distribution of the fast process when the state of the slow process is fixed. We call this high sensitivity property "fragility". We give some examples of behaviour that can occur when there are more than two species. These preliminary explorations for multiple species point to a wealth of open questions for future research. This is a joint work with Yi Fu, Hye-Won Kang, Lea Popovic, Greg Rempala, and Ruth J. Williams. (SIAM Journal of Life Sciences, in press)
Title: Multiscale Modelling, Analysis and Simulation of Cancer Invasion Processes
Date: Wednesday 22nd April 2026, 2.00pm
Venue: LT907
Abstract: Invasion, one of the hallmarks of cancer, is a complex process involving numerous interactions between cancer cells and the extracellular matrix, facilitated by matrix degrading enzymes (MDEs). It was demonstrated experimentally that there are two important types of MDEs, membrane-bound and diffusible metalloproteinases, involved in cancer invasion. To analyse the impact of those two types of MDEs on cancer invasion, we formulate a microscopic cell-scale model for the degradation of the extra-cellular matrix by matrix degrading enzymes produced by cancer cells. Using tools from the theory of homogenisation we propose a macroscopic tissue-level model for cancer cell invasion into the extra-cellular matrix mediated by bound and soluble MDEs. For the macroscopic model we prove the well-posedness result and propose a finite element method for the numerical approximation. Simulation results illustrate the role of the bound and soluble enzymes in cancer invasion processes.
Title: Colorectal Cancer Screening: Trends in Pathology Diagnoses
Date: Wednesday 20th May 2026, 2.00pm
Venue: LT907
Abstract: Colorectal cancer (CRC) is the third most common incident cancer worldwide and second most common cause of cancer-related death. Population-based CRC or bowel cancer screening (BCS) programmes have been established in many countries worldwide, with the aim of reducing CRC-related deaths through detection and removal of precancerous adenomatous polyps and of earlier-stage CRC for which excision is curative. Summary data and trends in pathology diagnoses and clinicopathological features of screen-detected cancers from the 铿乺st 10 years of the Northern Ireland Bowel Cancer Screening Programme are presented. Pathology data demonstrates success in the form of reduced diagnoses of cancer and advanced colorectal polyps.
Title: Estimating the Rate of Mutation to Mutator Phenotypes (the Mutation-Mutator Rate)
Date: Wednesday 20th May 2026, 2.00pm
Venue: LT907
Abstract: Mutators, defined as variants with an increased mutation rate, are known co-conspirators in things like cancer and the evolution of antibiotic resistance. Mutators themselves are produced by mutation, often in genes like mismatch repair genes and polymerase genes. But the problem is that there are lots of such genes and it is quite possible, even probable, that mutators can arise by mutation in other genes that we don't know about. In other words, the mutational target for mutators is large and incompletely known. So a mutator-mutation rate can't be estimated by brute-force sequencing methods, i.e., it cannot be directly observed and is therefore an inherently hidden or latent parameter. Here, we develop a method to estimate the mutator-mutation rate based only on numbers of observable mutations. The math is fun but the feasibility of the experimental protocol deriving from our "first-order" math is questionable. This is where you come in! We need creative ideas. I hope the talk sparks some fruitful conversation. A couple cancer groups are already interested but deterred a bit by these experimental hurdles.
Title: Identifying Alternative Explanations for Population Growth Rate Behaviour between Ancestor and Mutant Strains of Chlamydomonas Reinhardtii Across Stress Gradients
Date: Wednesday 27th May 2026, 2.00pm
Venue: LT907
Abstract: Trends in population growth rates in increasingly stressful environments are often attributed to individuals in one group (ancestor or mutant) being more vulnerable to the stressful environment than individuals in the other group. However, modelling the behaviour of these groups with the assumption of there being intra-group variation in the division rates can provide the explanation that it is the level of this variation that drives the differences in behaviour. To demonstrate this phenomenon, population growth rate data of the micro-algae Chlamydomonas reinhardtii in salt environments was modelled using both the conventional single-phenotype model and the alternative multi-phenotype models, where the inference of the different parameters provide competitive fits and differing explanations for the difference in behaviour between the ancestor and mutant populations.
Title: What is Remodelling Selection?
Date: Wednesday 24th June 2026, 2.00pm
Venue: LT907
Abstract: Every population consists of individuals who vary in their traits, and each trait may, or may not, be associated with frailty or fitness. Variation in frailty and fitness traits makes population studies prone to selective depletion bias (SDB). The issue is widespread across fields, with equivalent questions awaiting firm answers. When an ageing cohort exhibits declining mortality, is it individuals becoming healthier or selective depletion of the frail? In an epidemic, when growth in cumulative infections decelerates, is it individuals cautiously changing behaviour or selective depletion of the most susceptible? In microbial populations, when mutations increase population vulnerability to stress, it is individuals becoming more vulnerable or mutant populations having higher variance in fitness? This list can be expanded for many problems in diverse fields. In each case, the first explanation invokes individuals changing, while the second recognises that populations change due to selection on pre-existing variation. While the former are intuitive and widely adopted, explanations that rely on selective depletion are more neutral and less commonly considered due to cognitive biases and challenges in estimating all variation that matters. Until a practical means is found to estimating the relevant variation that exists in populations, its effects on observations will continue to be largely ignored, leading to over-attribution of results to other processes, biased predictions, bad policy decisions and poor reproducibility, with significant negative impacts on science, economics and ethics.
For 10 years, I have been proposing remodelling selection (ReMS) as a general solution to the SDB problem. Using specific case studies, collaborators and I have shown how it works in practice. However, when we apply for funding to establish the critical methodology for scalable use, we get reviewers who are clearly very knowledgeable saying things like: "A concrete description of what ReMS is, is missing. What is it 'made' of, how is it similar or different to other methods. Is it specific equations? Types of Datasets?..."
We clearly need a more rigorous mathematical description of ReMS rather than more case studies. This session will be an informal discussion featuring work involving Ibrahim Mohammed and Chris Robertson, Adam Hillman and John Mackenzie, Luca Del Core, and more. Please come and collaborate if you are interested... or even just intrigued!
Title: Elucidating and Identifying Phenotypic Heterogeneity
Date: Wednesday 8th July 2026, 2.00pm
Venue: LT907
Abstract: Many biological systems regulate phenotypic heterogeneity as a fitness-maximising strategy in uncertain and dynamic environments. Analysis of such strategies is typically confined both to a discrete set of environmental conditions, and to a discrete (often binary) set of phenotypes specialised to each condition. In the first part of this talk, we extend on both fronts to encapsulate both a discrete and continuous spectrum of phenotypes arising in response to two broad classes of environmental fluctuations that drive changes in the phenotype-dependent growth rates. We present a series of analytical and semi-analytical results that reveal regimes in which both discrete and continuous phenotypic heterogeneity is evolutionary advantageous. In the second part of this talk, we study the identifiability of a continuously structured model of phenotype transitions in cancer from commonly-reported cell count data.
Title: Inference of Qualitative Models and Analysis of (Dis)assembly Trajectories in Ecological Communities
Date: Wednesday 15th July 2026, 2.00pm
Venue: LT907
Abstract: The order of species invasions and extinctions determines the paths of community assembly. Mapping these paths beyond available observations requires models able to represent all possible orderings of events. Yet, quantitative models require parameters that are rarely available, while qualitative models are still mostly built by hand, without systematic inference from empirical data. From the observed extinctions and invasions of a six-species experimental microcosm, we automatically inferred, without estimating any parameter, an ensemble of qualitative models consistent with the data. These possibilistic models predict, for each tested invasion, the resulting stable states and extinction sequences, organized into an assembly graph. The analysis of this graph reveals behaviors such as species playing a purely transient role before going extinct, or states that are unreachable through sequential invasion. We also explore the impact of simultaneous versus sequential invasions on the structure of the assembly graph. Such qualitative models can be built from observations of extinctions and invasions alone, which are more readily available than the quantitative parameters required by classical approaches. Where richer data are available, the inferred model structure can in turn constrain and guide the construction of quantitative, timed or probabilistic models.
Numerical solutions of PDEs, Stochastic computation, Numerical linear algebra, Computational physics & engineering
Title: A model of the spread of a disease through a population with different age groups.
Date: 1pm Tuesday 30th January 2024
Venue: LT907
Abstract: The way in which a disease spreads through a population can depend on the ages of the individuals in that population. In many cases older members of the population are more likely to become seriously ill or die from an infectious disease.
The standard SIR model for the spread of a disease is extended to consider a population split into different age groups and includes features such as births and deaths from causes other than the disease being considered. The model will be used to investigate how varying the parameters for different age groups affect the spread of the disease through the population. In addition the
model will also be modified to incorporate how a vaccination programme can effect the spread of the disease. The methods discussed will be illustrated with a number of typical numerical examples.
Title: Artificial Intelligence and Toxicologic Pathology and drug development
Date: 1pm Tuesday 6th February 2024
Venue: LT907
Abstract: TBA
Title: Dynamical low-rank deep learning
Date: 1pm Tuesday 13th February 2024
Venue: LT907
Abstract: As model and data sizes increase, modern AI faces pressing questions about timing, costs, energy consumption, and accessibility. As a consequence, growing attention has been devoted to network pruning techniques able to reduce model size and computational footprint, while retaining model performance. The majority of these techniques focus on reducing inference costs by pruning the network after a pass of full training. A smaller number of methods address the reduction of training costs, mostly based on compressing the network via low-rank layer factorizations. In fact, a variety of empirical and theoretical evidence has recently shown that deep networks exhibit a form of low-rank bias, hinting at the existence of highly performing low-rank subnetworks. In this talk, I will present our recent work on low-rank models in deep learning, including some of our recent results on implicit low-rank bias and our dynamical low-rank training algorithm, which uses a form of Riemannian optimization to train small factorized network layers while simultaneously adjusting their rank. I will describe several results about convergence and approximation as well as experimental evidence of performance quality as compared to recent pruning techniques on several convolutional network models.
Title: DEM applied in the mining and mineral extraction industry
Date: 1pm Tuesday 19th March 2024
Venue: LT907
Abstract: As the world transitions towards net zero though electrification our reliance upon critical minerals and ores such as copper, iron, lithium, etc is ever increasing. The mining and mineral extraction industry currently uses 4-7% of the worlds available energy supply. Mining and mineral extraction companies are faced with decarbonising their impact on the planet while simultaneously increasing extraction from excavation sites to meet demand using traditional technology. Discrete Element Modelling (DEM) gives us insight into why products behave the way they do and process condition parameter exploration to ultimately drive towards new designs and a more sustainable future. The presentation will cover who the Weir Advanced Research Centre (WARC) is at UoS, our journey so far in using DEM for Weir products and the future direction of coupling such tools with other mathematical tools.
Title: Reducible networks of Prandtl-Ishlinskii operators with economic and financial applications
Date: 1pm Tuesday 26th March 2024
Venue: LT907
Abstract: If the nodes in a network have input-output responses satisfying a certain property (ie. they are Prandtl-Ishlinskii (PI) operators) then remarkable simplifications are possible. For arbitrary network topologies (under mild additional conditions) the entire network can be rigorously reduced to a single aggregated PI operator. This is true even if cascading behaviour, such as bubbles and crashes, can occur in the network.
Two applications will be presented. One is a financial market model incorporating momentum traders. The other is a macroeconomic model with the aggregated PI operator representing inflation expectations in the economy.
Title: Non-interpenetration of matter in lower-dimensional structures
Date: 3pm Wednesday 19th June 2024
Venue: LT907
Abstract: Non-interpenetration of matter is a well-known challenge for solid elastic materials combining analytical and geometrical aspects. In the bulk model, at least on the conceptual level, non-interpenetration is quite understood even if many challenges still remain open. In lower-dimensional structures (plates, rods), the situation seems to be even less clear. Focusing on rods in the plane, we will introduce a possible concept of noninterpenetration and show density and 螕-limit results in this case. This is a joint work in progress with B. Bene拧ov谩, D. Campbell, and S. Hencl (all from Prague).
Date: 3.00pm Thursday 6th February 2025
Venue: LT908
Title: Katz centrality for signed networks (Shuruq Alharbi)
Abstract: Centrality is a widely used concept for determining the node’s importance when analyzing networks. In this work, we extend the idea to signed networks, which include positive relations such as like, alliance, and partnership, and negative relations such as dislike, rivalry, and competition. These have gained attention due to their ability to reflect the real social world, however traditional centrality measures fail to deal with them because of their dynamics, necessitating the development of new tools. In this study, we used the structural balance theory as a base to provide a Katz centrality version for signed networks. We classify Katz’s centrality for signed networks into four types based on walk type (balanced, unbalanced, absolute, and disparity). We observe that each of these centralities can highlight a different aspect of a node. The results indicate that balanced and unbalanced relations can affect centrality measures, which provides a deeper understanding of such network dynamics. This research provides a useful tool for understanding node importance and opens the field to exploring the centrality field in signed networks.
Title: Iterative block matrix inversion algorithm with applications to covariance matrices (Ann Paterson)
Abstract: Obtaining the inverse, or selected elements of the inverse, of a large symmetric positive definite matrix A ∈ R^{n×n} arises in a number of fields, including computational physics, machine learning and Bayesian statistics. In particular, a number of important computations in statistics require the inverse of positive definite matrices, or certain submatrices of these, e.g., within Gaussian process regression. Here we present a novel algorithm which is designed to approximate the inverse of a large symmetric positive definite matrix. An iterative process of partitioning the matrix A and using block matrix inversion is repeated, until the approximated inverse H = A^{−1} reaches a satisfactory level of accuracy. We demonstrate that the two-block, non-overlapping approach converges for any positive definite matrix, while numerical results provide strong evidence that the multi-block, overlapping approach also converges for such matrices.
Date: 3.00pm Thursday 13th March 2025
Venue: LT907
Title: Uniform in time approximations of stochastic
Abstract:
Complicated models, for which a detailed analysis is too far out of reach, are routinely approximated via a variety of procedures; this is the case when we use multiscale methods, when we take many particle limits and obtained a simplified, coarse-grained dynamics, or, simply, when we use numerical methods, which will be the focus of this talk. While approximating, we make an error which is small over small time-intervals but it typically compounds over longer time-horizons. Hence, in general, the approximation error grows in time so that the results of our "predictions" are less reliable when we look at longer time-horizons.
However this is not necessarily the case and one may be able to find dynamics and corresponding approximation procedures for which the error remains bounded, uniformly in time. We will discuss a very general approach to understand when this is possible. I will show how the approach we take is very broad and show how it can be used for all of the approximation procedures mentioned above – however the focus of the talk will be on numerical discretizations for SDEs. This is based on a series of joint works with a number of people
Date: 3.00pm Thursday 27th March 2025
Venue: LT907
Title: GMRES upper bound based on epsilon-pseudospectra for preconditioned Toeplitz systems
Abstract: PDE models typically require numerical discretisation with sufficiently fine meshes to capture solution features, transforming the problem into solving one or more systems of linear equations, Ax=b. Due to several factors, these systems are often large and nonsymmetric and highly nonnormal. Krylov subspace methods, such as GMRES, are powerful tools for solving these sparse systems, but preconditioning is usually required to increase efficiency. While descriptive convergence theory exists to guide preconditioner choice when A is normal, it is less informative for nonnormal ones. Due to the nonnormality, GMRES bounds based on eigenvalues, the field of values and pseudospectra can fail to be descriptive.
Our work aims to also utilise the underlying PDE and discretisation properties to better understand the GMRES convergence. We show that in many instances the preconditioned matrix can be decomposed into the identity plus a low-rank perturbation and a small-norm perturbation, resulting in an eigenvalue clustering near 1 with a few outliers. We characterise the pseudospectra in this case, and present a new GMRES bound that takes into account the outlier in a way that overcomes overestimations seen in other bounds.
Title: Prof. Daniel Appelö (Virginia Tech)
Date: Tuesday 27th January 2026, 3.00pm
Venue: Teams
Abstract: In this paper, we develop a framework for designing arbitrary high order low-rank schemes for the Lindblad equation with time-dependent Hamiltonians. Our approach is based on nested Picard iterative integrators (NPI) and results in schemes in Kraus form that are completely positive and trace preserving (CPTP). The schemes are amenable to low rank formulations, making them suitable for problems where the matrix rank of the density matrix is small.
Title: Optimising Cold Chain Logistics for Net Zero: A Mathematical Framework for Policy Decision-Making
Date: Tuesday 24th February 2026, 3.00pm
Venue: LT908
Abstract: A zero-emissions cold chain (ZECC) involves transporting and storing temperature-sensitive goods, such as food and medicine, without emitting greenhouse gases. Cold-chain logistics present a rich class of combinatorial optimisation problems. In this talk, I will present a mathematical formulation for evaluating decarbonisation strategies in cold chain networks, with the view of informing UK policy. An example of such strategy is the use of alternative fuel types such as electric or hydrogen vehicles over diesel. The framework uses network flow models and vehicle routing problems to identify supply chain structures and optimal routing strategies while balancing competing objectives of minimising operational costs and carbon emissions. We will demonstrate this approach on real supply chain data from Scotland.
and
Title: Using generative AI to accelerate uncertainty quantification in multiscale methods
Abstract: Multiscale methods, including both finite element and finite volume variants, are widely used to solve problems involving features across a broad range of scales. A classic example is the simulation of subsurface flow through porous media, such as the infiltration of gases in geological carbon storage. In such a setting, the rock permeability may vary on the micrometre scale, while the computational domain can span hundreds of metres or even kilometres. Multiscale methods allow fine-scale features to be resolved at a reduced cost by augmenting the approximation space using multiscale basis functions, which are typically obtained by solving relatively small local problems. In this talk, I will present work combining graph convolutional networks with denoising diffusion models and image super-resolution techniques to instead generate the multiscale basis functions conditionally on the problem parameters. This can reduce the overall computation time in the context of uncertainty quantification, where hundreds or thousands of simulations runs are performed.
Title: Structure preserving methods for a class of nonlinear dispersive equations
Date: Tuesday 3rd March 2026, 3.00pm
Venue: LT908
Abstract: In this talk we introduce a structure preserving, second order in time relaxation-type scheme for approximating solutions of a class of nonlinear dispersive equations. We highlight the advantages of such methods with regard to mimicking key properties of the continuous problems. We proceed to discuss the a posteriori error analysis of the scheme for the Schrödinger-Poisson system. In particular, we introduce an appropriate reconstruction and present the main steps of the derivation of optimal order a posteriori error bounds. The main challenges in the analysis arise from the nonlinear nature of the problem and the fact that the potential function, which is also unknown, is linked with the wave function. This means that we should obtain optimal a posteriori error estimates for both the potential and the wave function at the same time. Various numerical experiments verify and complement our findings.
Title: Mixed-precision Computing: High Accuracy With Low Precision
Date: Tuesday 17th March 2026, 3.00pm
Venue: LT908
Abstract: Mixed-precision algorithms have launched an era in which efficiency and accuracy are no longer mutually exclusive. Rather than rely entirely on high-precision formats like double (64-bit) precision, mixed-precision algorithms apply lower precisions such as single (32-bit) or half (16-bit) precision whenever possible, reserving higher precision only for critical steps. Doing so can drastically reduce memory requirements, improve performance, and lessen energy consumption on modern computer hardware without sacrificing accuracy or stability.
In this talk, we discuss the challenges of using low/mixed precision, and present five cases, common in scientific applications, where using mixed precision makes sense.
Date: Tuesday 24th March 2026, 3.00pm
Venue: LT908
Title: Exploring Scalable Approaches to Network Alignment (CN)
Abstract: Network alignment is the task of identifying matching nodes in different networks. It is a useful tool in data analysis and arises in a wide range of applications, such as in aligning social networks. Despite its broad relevance, the problems on which it has been successfully used are limited in size since network alignment is NP-hard. For an approach that scales in size, one cannot hope to solve the problem exactly and good approximations may be preferred.
One approach for approximation is to formulate graph alignment as an optimisation problem and solve a suitable relaxed version. Another approach is to embed the nodes of two networks into a shared vector space and use a distance measure to match the
nodes, optionally first applying dimensionality reduction to the embedding matrix.
Machine learning is an increasingly popular component of alignment algorithms. Many machine learning based methods generate embeddings, but the inaccessibility of the underlying mathematics motivates an analysis of embedding independent of AI.
Title: Vehicle Routing Problem in Home Health Care Systems (MA)
Abstract: Patients in home healthcare systems (HHC) need a variety of medical treatments to be provided at their residences during time windows. Due to compatibility limitations, not all caregivers can serve all patients and each service has a set duration. The planning difficulty is figuring out how best to assign and route caregivers to patients while meeting all operational and scheduling requirements. Traditionally, home healthcare routing and scheduling problems have focused on minimizing the total travel distance. However, minimizing distance alone does not necessarily lead to efficient or fair schedules, because it ignores the time spent on service delivery and possible waiting times between visits. Therefore, this
study formulates a new variant of the Vehicle Routing Problem with soft time windows (VRPTW) that aims to minimize the total distance,active caretakers
and workload balance based on completion time of all patient visits. The Vehicle Routing Problem with Time Windows (VRPTW) is a complex combinatorial
optimisation problem that extends the classical Vehicle Routing Problem (VRP) by adding time window constraints to serve customers. It is widely studied due
to its real-world applications in logistics, delivery services, and transportation Liu et al. [2023].
References
Xiaobo Liu, Yen-Lin Chen, Lip Yee Por, and Chin Soon Ku. A systematic literature review of vehicle routing problems with time windows. Sustainability,
15(15):12004, 2023.
Date: Tuesday 31st March 2026, 3.00pm
Venue: LT908
Title: Rates of convergence for finite element approximations of mean field game partial differential inclusions
Abstract: Mean Field Games (MFG) are models for Nash equilibria in games of optimal control involving a continuum of players. MFG are typically described by a system of PDE, where a Hamilton—Jacobi—Bellman equation, for the generic player’s value function, is coupled nonlinearly with a Kolmogorov—Fokker—Planck (KFP) equation that determines the player density. A common assumption for such models asserts the uniqueness of players' choice of optimal controls and differentiability of the Hamiltonian of the system. Recently, we proposed that the MFG PDE system be relaxed to a Partial Differential Inclusion (PDI) system based on measurable selections of the partial subdifferential of the convex Hamiltonian, in order to model cases where players of the mean field game have access to (possibly) nonunique optimal controls and the Hamiltonian of the system is not required to be differentiable.
In this talk, we present error bounds for monotone stabilized finite element discretizations of stationary second-order MFG PDI posed on general bounded polytopal Lipschitz domains with strongly monotone running costs, where the Hamiltonian of the system is merely Lipschitz, convex, but (possibly) nondifferentiable. We prove an asymptotic rate
of convergence in the $H^1$-norm for the approximations of the value function and in the $L^2$-norm for the approximations of the player density, despite the density having minimal regularity \emph{a priori} as a function in $H^1$ and there being no continuity of the set-valued partial subdifferential of the Hamiltonian. This talk is based on joint works with Iain Smears.
Stochastic Differential Equations, Stochastic Computation, Time Series, Probability, Image Analysis
Title: Numerical Solutions of a Markov-Switching One-Factor Volatility Model with Non-Globally Lipschitz Continuous Coefficients
Friday 25th January, 2024, 4.00-5.00pm
Venue: LT907
Abstract: We extend the one-factor stochastic volatility model to incorporate coefficient terms of super-linear growth under the Markov-switching framework. Since the proposed model is intractable analytically, we develop various mathematical techniques to investigate convergence in probability of the numerical solutions under the local Lipschitz condition. Finally, we perform simulation examples to demonstrate the theoretical results and justify the theoretical results for the valuation of some financial options.
Title: Explicit Convergence Rates for the M/G/1 Queue under Perturbation
Friday 19th April, 2024, 3.00-4.00pm
Venue: LT907
Abstract: Stochastically ordered Markov process is a topic of special concern to us. As is mentioned by Meyn and Tweedie, many Markov processes are stochastically ordered in their initial state. Thus, we established convergence rates for discrete-time Markov chains on a countable state space that are stochastically ordered starting from a stationary distribution under perturbation. We investigate the explicit criteria to obtain the ordinary ergodicity, geometric ergodicity and polynomial ergodicity for the embedded M/G/1 queue under perturbation. The explicit geometric convergence rates for the original system and the system under perturbation are calculated. Our bounds in the geometric case and polynomial case are closely connected to the first hitting times. Two examples are provided to illustrate our result.
Title: Truncated Euler-Maruyama Method for Time-Changed SDEs with Super-Linear State Variables and H/"older's Continuous Time Variables
Friday 3rd May, 2024, 3.00-4.00pm
Venue: LT907
Abstract: In this work, an explicit numerical method is developed for a class of non-autonomous time-changed stochastic differential equations, whose coefficients obey H\鈥漮lder's continuity in terms of the time variables and are allowed to grow super-linearly in terms of the state variables. The strong convergence of the method in the finite time interval is proved and the convergence rate is obtained. Simulations are provided to demonstrate the theoretical results.
Title: A New Criterion on Stability in Distribution for a Hybrid Stochastic Delay Differential Equation
Friday 17th May, 2024, 3.00-4.00pm
Venue: LT907
Abstract: A new sufficient condition for stability in distribution of a hybrid stochastic delay differential equation (SDDE) has been proposed in this work. Although the new criterion leads to stability for an SDDE, its main component only depends on the coefficients of a corresponding SDE without delay. The Lyapunov method is applied to find an upper bound, so that the SDDE is stable in distribution if the delay is less than the upper bound. Also, the criterion shows that delay terms can be an impetus toward the stability in distribution.
Title: Limit Theorems for Weakly Dependent Random Fields with Applications to High-Dimensional Time Series
Friday 31st May, 2024, 2.00-3.00pm
Venue: LT908
Abstract: We establish limit theorems, law of large numbers (LLN) and central limit theorem (CLT), for weakly dependent arrays of random fields which are not necessarily stationary and may have asymptotically unbounded moments. The weak dependence condition is proved to be inherited through transformation, and this makes our results applicable to statistical inference of high-dimensional time series models. Consistency and asymptotic normality of maximum likelihood estimation can be proved for high dimensional time series models which are checked to be weakly dependent as random fields, allowing for non-stationarity and unbounded trending moments, when sample size and/or dimension go to infinity. As an example for application of our general theory, asymptotic properties of estimation for network autoregression are obtained under mild conditions.
Title: Mathematical Analysis of Refractory Period Distribution and the Underlying Molecular Regulation Mechanisms for Signal Transduction Systems
Friday 28th August, 2024, 3.00-4.00pm
Venue: LT908
Abstract: Cellular decisions are governed by signal transduction pathways involving a series of chemical reactions. The refractory period (RP) represents the time it takes for the reaction system to regain responsiveness after a stimulus, making it a crucial factor in signal transduction pathways. Analytical expressions for RP distributions are essential for understanding its molecular regulation mechanisms. However, it depends on solving CME for systems with second or higher-order reactions, which remain open problems with traditional methods. We are developing new theories and methodologies to solve RP distributions for general time-variant signal transduction systems with second-order reactions. Our recent research shows that using path-wise representations can bypass solving CMEs analytically. Using this method, we solved the RP distribution for a class of nonlinear time-variant systems with A+A-C type of second-order reactions. We will extend to more complicated systems with A+B 鈥� C type of systems.
Title: Stochastic Approximation and Applications
Friday 6th February, 2025, 3.00-4.00pm
Venue: LT907
Abstract: Because of the demand and current interests in using machine learning to solve optimization problems, stochastic gradient algorithms have gained resurgent interests. These, however, are rooted in stochastic approximation (SA). In this talk, we will give a brief introduction to SA, mention the issues involved, main results, and applications in image processing, filtering, system identification, manufacturing, and financial engineering. [The main reference is H.J. Kushner and G. Yin, 2nd Ed., Springer, 2013 together with some of our more recent work that are in the preprint form.]
Title: Ergodicity of Euler-Maruyama Schemes by the Coupling Method
Wednesday 12th March, 2025, 3.00-4.00pm
Venue: LT907
Abstract: In this talk I will explain how to use the probabilistic technique known as the coupling method in order to analyse ergodicity of Euler-Maruyama (EM) schemes for a broad class of stochastic differential equations (SDEs). After a general introduction to the coupling method, I will discuss how to use it to show that the Markov transition kernel of an EM scheme is contractive in an appropriately designed Wasserstein distance, and then I will present several useful consequences of that contractivity, such as obtaining precise convergence rates of the EM scheme to stationarity, or the Poincare inequality for its invariant measure. The talk is based on the following series of papers:
[4] J. Bao, M. B. Majka and J. Wang, Geometric ergodicity of modified Euler schemes for SDEs with super-linearity, submitted, 2024
[3] L. Liu, M. B. Majka and P. Monmarché, L^2-Wasserstein contraction for Euler schemes of elliptic diffusions and interacting particle systems, Stochastic Process. Appl. 179 (2025), 104504
[2] L.-J. Huang, M. B. Majka and J. Wang, Strict Kantorovich contractions for Markov chains and Euler schemes with general noise, Stochastic Process. Appl. 151 (2022), 307-341,
[1] A. Eberle and M. B. Majka, Quantitative contraction rates for Markov chains on general state spaces, Electron. J. Probab. 24 (2019), paper no. 26, 36 pp.
Title: Hybrid Stochastic Functional Differential Equations with Infinite Delay: Approximations and Numerics
Monday 19th May, 2025, 3.00-4.00pm
Venue: LT907
Abstract: This talk is to investigate if the solution of a hybrid stochastic functional differential equation (SFDE) with infinite delay can be approximated by the solution of the corresponding hybrid SFDE with finite delay. A positive result is established for a large class of highly nonlinear hybrid SFDEs with infinite delay. Our new theory makes it possible to numerically approximate the solution of the hybrid SFDE with infinite delay, via the numerical solution of the corresponding hybrid SFDE with finite delay.
Edinburgh Mathematics Society (EMS)
Title: Can We Rely On AI?
Date: 3.00pm Friday 19th January 2024
Venue: LT908
Abstract: Over the last decade, adversarial attack algorithms have revealed instabilities in deep learning tools. These algorithms raise issues regarding safety, reliability and interpretability in artificial intelligence (AI); especially in high risk settings. Mathematics is at the heart of this landscape, with ideas from optimization, numerical analysis and high dimensional stochastic analysis playing key roles. From a practical perspective, there has been a war of escalation between those developing attack and defence strategies. At a more theoretical level, researchers have also studied bigger picture questions concerning the existence and computability of successful attacks. I will present examples of attack algorithms in image classification and optical character recognition. I will also outline recent results on the overarching question of whether, under reasonable assumptions, it is inevitable that AI tools will be vulnerable to attack.
Tea/coffee will also be served in the staff common room (LT911) from 2:30pm.
For those of you who cannot attend in person, the talk will be streamed over zoom.
Meeting ID: 872 9919 5984
Password: 729852