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 Łepek 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,−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 −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 Γ-limit results in this case. This is a joint work in progress with B. Benešová, D. Campbell, and S. Hencl (all from Prague).

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: 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 Strathclyde 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.

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 “state-space” of the food-web based on ecological survey data and expert knowledge, and the exploration of this “state-space”. 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:  

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 Γ-limit results in this case. This is a joint work in progress with B. Benešová, 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:  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\”older'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 — 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.

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. 

https://strath.zoom.us/j/87299195984

Meeting ID: 872 9919 5984

Password: 729852