BMC-BAMC 2025
BMC-BAMC 2025
A poster session will run from 14:40-15:40 on Tuesday 24th June. We can accommodate posters that are either A0 in portrait format, or A1 in either landscape or portrait format.
PO1: 14:40-15:40, 24th June 2025, Room DH/GR8 HALL
Dominic Aku (University of Chester)
Title: Mathematical Modelling of Folate Metabolism and DNA Methylation with its Implications for Ageing and Human Health
Abstract: Ageing is directly connected with many physical and mental conditions that lead to the deterioration of human pathological conditions, which comprises Alzheimer’s disease, cardiovascular disease, chronic kidney disease, stroke, neurogenerative disease, and common cancers such as colorectal, prostate, and breast cancer. Interestingly, several researchers have investigated and insinuated that DNA methylation could be vital in the regulation of the ageing process in an organism. This implies that in the mammalian genome, DNA methylation could be used to deduce health conditions that are associated with ageing. Furthermore, folate is nutritionally vital for the enhancement of human health and growth. Besides, folate is essential in the activity of mammalian epigenetics, via its transfer of methyl groups for DNA methylation reaction. More so, folate as part of the B12 vitamins not only plays a key role in our diet but is involved in the mechanism of DNA synthesis, maintenance of DNA methylation and metabolizing the amino acids required for growth and cell division, especially during pregnancy and infancy. Furthermore, investigations have shown that deficiency in B12 vitamins has effects on all age groups, though with a higher degree among aged people, infants, and pregnant women. Over the years, many mathematical models have been constructed, but none has captured explicitly the complexity of the interdependent biochemical and molecular mechanisms of folate metabolism and the DNA methylation cycle. In this mathematical modelling research, we intend to construct a comprehensive mathematical model that will link folate metabolism and DNA methylation and use the model to buttress our understanding of its implications for ageing and human diseases.
PO1: 14:40-15:40, 24th June 2025, Room DH/GR8 HALL
Salam Al-Bayati (University of Technology)
Title: Advanced DRBEM Modelling of Coupled Transport Phenomena in Thermo-Fluid Systems
Abstract: 1. Motivation / Problem Statement: Driven by the new applications and rapid growth for many disciplines in engineering and mathematics, the demands for a powerful and robustness alternative technique for the classical numerical method such as finite element method (FEM) and finite difference method (FDM) has been increased. Furthermore, due to the lack of researches on boundary element method (BEM) for convective-diffusive-reactive problems for a wide range of applications in engineering and sciences. These issues motivate the search for modern techniques that will utilise more efficient and accurate method. To this end, we need some alternative techniques to improve the accuracy and the performance for the solution behavior. 2. Methodology: This work presents a comprehensive study based on a novel computational technique for modelling two-dimensional steady-state and transient convective-diffusive-reactive problems with variable fluid velocity by using the dual reciprocity boundary element method (DRBEM). For the transient fluid problems, the FDM is used to simulate the time evolution procedure for solving the resulting system of equations. 3. Results: The simulated results obtained for different thermo-fluids problems show that the BEM results are in excellent agreement with the analytical solutions and do not present oscillations or damping of the wave front, as it appears in other numerical techniques. 4. Conclusions: This work has a novel study and numerical modelling for both steady-state and transient convective-diffusive-reactive problems in thermo-fluids using BEM combined with DRM. These findings will enrich the research based on BEM with novel modelling for these types of problems.
PO1: 14:40-15:40, 24th June 2025, Room DH/GR8 HALL
Ahlam Alhadbani (School of mathematics-University of Exeter)
Title: Hopf bifurcation for delay equations
Abstract: The research studies how periodic solutions can emerge in differential equations with state-dependent delay. We consider delay differential equations near the Hopf bifurcation, where we know that small-amplitude periodic solutions should exist. We use the LyapunovâSchmidt reduction technique to reduce the infinite-dimensional problem to a two-dimensional subspace. This technique will then be generalised to the case with state-dependent delays, where the nonlinearity is not differentiable.
PO1: 14:40-15:40, 24th June 2025, Room DH/GR8 HALL
Maryam Alka (University of Birmingham)
Title: Mathematical Modelling of Tumour Response to Paclitaxel Under Hypoxic Conditions
Abstract: Tumours often exist in hypoxic environments, where low oxygen levels alter therapeutic efficacy, complicating cancer treatment. This study uses a mathematical modelling framework to explore the synergistic effects of Paclitaxel (PTX), a chemotherapeutic agent, and cobalt chloride (CoClâ), a hypoxia-mimicking agent, on tumour population dynamics. We developed ordinary differential equation (ODE)-based modelsâexponential, logistic, and Gompertzâto simulate tumour growth, incorporating proliferation, PTX-induced apoptosis, and hypoxia-driven effects. Experimental data from the HCC1806 breast cancer cell line, treated with PTX (100 nM, 200 nM), CoClâ (100 ”M), and their combinations over 48/72 hours, were used to validate the models. Cell viability, measured via the CellTiter-Glo assay, informed parameter estimation through Bayesian inversion with the Metropolis-Hastings Markov Chain Monte Carlo (MCMC) algorithm, enabling robust quantification of model parameters and their uncertainties. Model selection, guided by the Akaike Information Criterion (AIC), identified the best-fitting growth model for capturing tumour response. The framework explicitly accounts for nonlinear chemotherapy-hypoxia interactions, revealing how hypoxia modulates PTX efficacy through proliferation and death rates. Key parameters, such as maximum proliferation/apoptosis rates (P_max, Q_max) and interaction terms (Îł_P, Îł_Q), highlight the critical balance between tumour growth and death under hypoxic conditions. These findings underscore the importance of microenvironmental factors in treatment outcomes and provide a predictive tool for optimizing PTX-based strategies in hypoxic tumours. This study integrates experimental data with mathematical modelling to advance our understanding of tumour dynamics, offering insights for tailored therapeutic regimens.
PO1: 14:40-15:40, 24th June 2025, Room DH/GR8 HALL
Hessah Almaaz (University of Glasgow)
Title: Pulsatile fluid flow through porous membranes
Abstract: In a number of physiological and industrial systems, particles are transported and filtered through permeable membranes. The net filtration depends on the form of the fluid delivery, such as whether the flow is steady or pulsatile. We explore the effects of fluid pulsation on the transport of particles through porous hollow fibres, which are typically long and thin. Despite initial indications that fluid pulsation may enhance filtration efficiency, the underlying mechanisms are not well understood. We aim to bridge this gap by developing a fluid-mechanical model of the viscous flow that accounts for rapid changes in the fluid flux between pulses. Our model has been developed for an idealised single fibre, assuming that the membrane is a uniform porous medium. We derive an evolution equation for the fluid flux, which we examine using numerical computation and asymptotic analysis. Our theoretical framework is extendable to various geometries relevant to different applications and gives insight into the extent to which fluid pulsation offers an efficient filtration mechanism.
PO1: 14:40-15:40, 24th June 2025, Room DH/GR8 HALL
Eman Alnuwaysir (university of Exeter)
Title: Modelling freezing episodes in Parkinsonâs Disease as a stochastic transition
Abstract: This research investigates the freezing of gait (FOG) phenomenon in Parkinsonâs Disease (PD) through mathematical modelling and time series analysis. Utilising data from stepping-in-place experiments by Nantel et al., we model transitions from regular stepping to freezing as stochastic escapes between dynamic states. A generalised Hopf (GH) bifurcation framework forms the basis of our model, extended to include shear effects and stochastic noise, providing a more realistic depiction of patient behaviour. The project develops a new null model capturing the bistability between oscillations and steady states, addressing deficiencies in previous models. Through Hilbert Transform embeddings, Markov chain analysis, and escape phase determination, we systematically characterise the timing and dynamics of freezing events. Additionally, we propose a correction for elliptical distortions in Hilbert embeddings and introduce methods for estimating shear parameters from data. Future work includes refining escape angle detection algorithms and testing them on corrected synthetic datasets to enhance their predictive power. This study aims to bridge the gap between mathematical theory and clinical observations, offering potential advancements in early detection and intervention strategies for FOG in PD patients.
PO1: 14:40-15:40, 24th June 2025, Room DH/GR8 HALL
Zubaydah Alotaibi (University of Glasgow)
Title: A model for droplets walking over submerged barriers
Abstract: Small droplets bouncing and self-propelling across the surface of a vibrating liquid bath can behave like quantum particles. In this research, we study how variations in the liquid depth affect the movement of these droplets. Specifically, we model the influence of submerged barriers on the wave field by varying the amplitude and slope of the waves generated by the bouncing droplet. By combining mathematical methods from dynamical systems with numerical simulation, we analyse how droplets stay confined in corrals, tunnel across barriers and interact with obstacles. Our model provides insight into how a classical wave-particle system can give rise to quantum-like behaviour.
PO1: 14:40-15:40, 24th June 2025, Room DH/GR8 HALL
Ohood Althagafi (University of Manchester)
Title: Numerical Evaluation of H Function
Abstract: In recent years, there has been significant advancement in the numerical computation of MellinBarnes integrals. This study focuses on employing Mellin-Barnes integrals for the representation of stable LĂ©vy distributions, utilizing the H-Fox function. We evaluate existing methods for the precise and dependable calculation of this integral across various parameters and variable ranges. Our investigation encompasses both asymptotic series and contour integral techniques. Through numerical experiments, we identify the most effective strategy for specific parameters and variable conditions. Our findings for the optimal methods to be applied in each scenario, are presented.
PO1: 14:40-15:40, 24th June 2025, Room DH/GR8 HALL
James Arthur (University of Exeter)
Title: Multilayer Shallow Water Equations with full rotation vectors via variational principles
Abstract: Much work has been done on using Variational methods to derive shallow water equations. However, most of the preceeding work, such as Dellar and Salmon 2005 and Stewart and Dellar 2016, neglect a centrifugal force term that dominates small scale motion. In this work we rederive these equations with that extra term and then use these equations to derive Poisson Brackets for these more complex systems. These Poisson brackets will then be used for numerics in later work.
PO1: 14:40-15:40, 24th June 2025, Room DH/GR8 HALL
Mia Beard (University of Oxford)
Title: On the Relationship Between Einstein Four-Manifolds AND Minimal Surfaces
Abstract: Minimal surfaces and Einstein manifolds are among the most natural structures within differential geometry. While Einstein manifolds remain poorly understood, particularly in the four-dimensional case, minimal surfaces have a far deeper theoretical foundation. When embedding a minimal surface into a three-dimensional manifold, one discovers profound parallels intersecting geometry, topology, and analysis. These parallels include variational principles, topological constraints, monotonicity formulas, compactness results, epsilon-regularity theorems, and thick/thin or sheeted/non-sheeted decompositions. Although minimal surfaces and Einstein four-manifolds are fundamentally distinct objects, these similarities invite the question of whether there exist scenarios in which these objects are manifestations of the same thing. In research undertaken for my Master’s dissertation, I propose a novel connection between these two classes of geometric objects. By synthesising several existing results, including Jensenâs theorem, Takahashiâs theorem, and a conjecture by Song, I demonstrate that when an Einstein four-manifold is globally symmetric, it admits an embedding into a higher-dimensional sphere as a minimal surface. A notable example is provided by the Veronese embedding, through which the complex projective plane elegantly arises as a minimal surface within the seven dimensional sphere.
PO1: 14:40-15:40, 24th June 2025, Room DH/GR8 HALL
Benedetta Bertoli (Imperial College London)
Title: Phase transitions for interacting particle systems on random graphs
Abstract: We investigate phase transitions and metastability in weakly interacting diffusion processes on random graphs, combining bifurcation theory, spectral analysis, and large-scale numerical simulations. These systems, relevant in opinion dynamics, neural networks, and synchronization models, exhibit complex behaviour due to the interplay between interaction potentials and network topology. Using bifurcation theory, we determine the conditions under which the system transitions from one stable state to multiple coexisting states. We further explore how these bifurcations relate to the systemâs energy landscape, where energy acts as a natural measure of order in the system. To better understand stability, we use spectral analysis of the McKean-Vlasov operator, which helps us determine whether small disturbances grow or decay over time. This allows us to classify which stationary states are stable and which are susceptible to change. To support our theoretical findings, we run large-scale numerical simulations of interacting particles on different types of random networks, including ErdĆs-RĂ©nyi, Small-World, and Power-Law graphs. These simulations confirm our predicted transition points and provide additional insights into the systemâs behaviour. Our results emphasize how the underlying network structure plays a fundamental role in shaping the long-term dynamics of these systems.
PO1: 14:40-15:40, 24th June 2025, Room DH/GR8 HALL
James Binnie (Cardiff University)
Title: A Survey Of Dimension Estimation Methods
Abstract: Dimension estimation is a useful tool for data analysis. Given a high dimensional data set, this set may lie on or close to a much lower dimensional manifold. Dimension estimators try to estimate the dimension of the underlying manifold. Our survey of estimators reveals that they fall into different broad families depending on what information is used to infer the intrinsic dimension. On top of the usual local/global divide, we can also group estimators by the underlying geometric information being leveraged. We look at new estimators derived from recent advances in topological and geometric data analysis and find that they have different strengths and weaknesses compared to state of the art estimators. We carry out an extensive survey of the robustness of these estimators to the choice of their hyperparameters, the presence of noise, and the presence of curvature. We find that hyperparameter selection can be crucial and can be overfit to data, making it difficult to determine how to apply an estimator without additional prior knowledge. Different estimators respond to noise and to curvature in different ways, so that the choice of estimator is very important.
PO1: 14:40-15:40, 24th June 2025, Room DH/GR8 HALL
Linus Chang (University of Birmingham)
Title: Quantitative models for the impact of radiotherapy on the aging colon
Abstract: Radiotherapy (RT), an established colorectal cancer treatment modality, is often associated with side-effects that cause premature ageing in exposed tissues, which in turn increases the risk of developing age-related disease. However, the degree of ageing conferred by ionising radiation is currently unknown. By employing experimental lineage-tracing methods combined with stochastic mathematical models and Bayesian inference, we have quantified the impact of RT on the accumulation of mutant clones in normal human colonic epithelium. We use our results to simulate the long-term effects of RT treatment as a function of treatment age and dosage. Furthermore, we define a universal pseudo-age for the colon to estimate the premature aging associated with RT-induced mutant clone expansion. Our study therefore represents one of the first quantitative assessments of the impact of cancer treatment on aging.
PO1: 14:40-15:40, 24th June 2025, Room DH/GR8 HALL
Patiene Chouop Kawe (University of Reading)
Title: A multiscale mathematical modeling approach to predict toxicological outcomes of crop protection chemicals within humans and animals.
Abstract: Crop protection chemicals play a crucial role in agriculture by preventing yield losses due to pests and diseases. However, their extensive use raises concerns about environmental contamination and potential risks to human and animal health. Given their impact on cholesterol homeostasis, developing a predictive model to assess their toxicity is essential. This work presents the methodology for developing a novel multiscale mathematical modeling framework that connects chemical-protein interactions, cell-level pathway information, and whole-body physiology to predict when crop protection active ingredient concentrations lead to toxic adverse outcomes. As a first step, a PKPD model of cholesterol dynamics across the gut, blood, and liver has been developed, and it will be used to describe the concentration of an ingested compound, such as a CYP51 inhibitor. This model has been simulated under various scenarios, and local and global sensitivity analyses, as well as structural and practical identifiability analyses, have been performed. It will serve as the foundation for a multiscale approach, integrating a cell-signaling model that captures the interplay between cholesterol biosynthesis and a key regulatory pathway. The signaling model will be refined using machine learning techniques to identify the most relevant proteins, followed by model reduction methods to enhance computational efficiency. Finally, these models will be integrated into a multiscale framework. Once validated with experimental data, this modeling approach could significantly enhance the companyâs ability to predict toxicological outcomes.
PO1: 14:40-15:40, 24th June 2025, Room DH/GR8 HALL
Saeed Farjami (University of Exeter)
Title: Escape Mode: Tadpole Edition – Biologically Realistic Neuromechanical Model Uncovers New Evasion Strategies
Abstract: While forward locomotion in aquatic animals is well-studied, less is known about how they escape a predatorâs grip or back out of confined spaces. We investigated how axial-muscle-driven movements enable young Xenopus tadpoles to break free when grasped. High-speed videos have been recorded to study tadpole behaviour when gripped by forceps. Using markerless pose tracking, we identified four movement types following a grip-and-release: initial coiling, vigorous body flexions (struggling), transitional coiling, and swimming. Electrode recordings of spinal motoneurons and motor nerves during fictive struggling in immobilised tadpoles showed that struggling motor-neuronal activity propagates caudorostrally. To bridge the gap between video recordings of body movements and electrode recordings we use a biologically realistic biomechanical virtual tadpole (VT) model. To explore role of motor commands we VT model subjected to free movement or gripping by virtual forceps. When driven by a reversed swimming motor pattern, VT failed to generate backward swimming. Similarly, struggling rhythms alone produced no thrust for forward or backward movement. However, when VTâs head was restrained, struggling movements allowed it to escape, suggesting that physical interaction with the grip created the necessary force for release. Our findings indicate that the naturally occurring struggling rhythmâcharacterised by prolonged motoneuron bursts and low-frequency propagationâenables tadpoles to break free from predators or retreat from tight spaces. This is joint work with Andrey Palyanov (Ershov Institute of Informatics Systems, Russia), Hong-Yan Zhang, Valentina Saccomanno, Wen-Chang Li (University of St. Andrews, UK), Andrea Ferrario (EPFL, Switzerland), Robert Merrison, Roman Borisyuk, Joel Tabak (University of Exeter).
PO1: 14:40-15:40, 24th June 2025, Room DH/GR8 HALL
Juliana FeijĂł (Universidade de BrasĂlia)
Title: Exact Torsion Solution for Cambered Airfoils
Abstract: We present exact closed-form solutions for the torsion of asymmetric airfoils, a topic previously dominated by numerical methods such as finite elements and the finite difference method. While analytical solutions exist for symmetric airfoils, no comprehensive solutions have been available for asymmetric ones until now. This study enables the computation of key parameters, including maximum shear, maximum axial displacement, and torsional rigidity, which can serve as benchmarks for approximate methods.
PO1: 14:40-15:40, 24th June 2025, Room DH/GR8 HALL
Emily Flicos (University of Cambridge)
Title: Uncertainty quantification through reduced modelling of CO2 injection sites
Abstract: Gravity-driven currents in porous media are observed in many geological settings and have a wide variety of environmental and industrial applications, including geological carbon storage (CCS), geothermal energy storage, and groundwater flow. These systems are of increasing interest as part of the energy transition for their potential to decarbonise both energy generation and many industrial processes. A significant challenge in modelling subsurface flows is the uncertainty of geological properties. Within a storage reservoir, small variations in both the topography of the reservoir and in the permeability structure can have a large impact on the dynamics and hence extent of buoyant currents. In many settings, subsurface flows are long and thin and hence can be modelled as gravity currents, which in certain simplified scenarios yield well characterised similarity solutions. Here we first highlight the impact of permeability variations by performing a perturbation analysis of the self-similar spreading, showing that the sensitivity to permeability variations exhibits characteristic early and late time behaviours. Secondly, we examine the impact of variations in the bounding topography by examining the spreading of a finite volume gravity current moving up a modest slope with small variations to the topography. By varying the amplitude and wavelengths of these variations, we quantify the impact they have on the overall plume dynamics. These models give insight into the situations where spreading is most sensitive to uncertainty in measurements of permeability or topography.
PO1: 14:40-15:40, 24th June 2025, Room DH/GR8 HALL
Yong See Foo (University of Melbourne)
Title: Quantifying structural uncertainty in chemical reaction network inference
Abstract: Dynamical systems of chemistry and biology are complex, and one often does not have comprehensive knowledge about the interactions involved. Chemical reaction network (CRN) inference aims to identify, from observing species concentrations, the unknown reactions between the species. Most approaches focus on identifying a single, most likely CRN, without addressing uncertainty about the resulting network structure. However, it is important to quantify structural uncertainty to have confidence in our inference and predictions. In this work, we do so by constructing an approximate posterior distribution over CRN structures. This is done by keeping a large set of suboptimal solutions found in an optimisation framework with sparse regularisation, in contrast to existing optimisation approaches which discard suboptimal solutions. We find that inducing reaction sparsity with nonconvex penalty functions results in more parsimonious CRNs compared to the popular lasso regularisation. In a real-data example where multiple CRNs have been previously proposed, we simultaneously recover reactions proposed from different literature under structural uncertainty. We demonstrate how posterior correlations between reactions help identify where structural ambiguities are present. This can be translated into alternative reaction pathways suggested by the available data, which guide the efforts of future experimental design.
PO1: 14:40-15:40, 24th June 2025, Room DH/GR8 HALL
William Gillow (University of Oxford)
Title: Injection driven spreading of a surfactant-laden droplet on a prewetted substrate.
Abstract: We consider the spreading of a thin viscous surfactant-laden droplet onto a shallow precursor layer of clean fluid. The spreading is driven by injection of fluid and surfactant through a slot in the base. We utilise lubrication theory to derive a model for the evolution of the height of the interface as well as the concentration of the surfactant both within the bulk and on the surface. We explore this model numerically through transforming into a self-similar spatial coordinate so that we can use a piecewise constant step size within the mesh to efficiently simulate long time behaviour whilst capturing features that appear over widely separated length scales. We also use asymptotic techniques to deduce the scalings of characteristics of the droplet shape in the large time limit and how these are influenced by the relative sizes of parameters in the model, finding a good agreement with those found from the numerical simulations.
PO1: 14:40-15:40, 24th June 2025, Room DH/GR8 HALL
Hanan Hozan (University of reading)
Title: The influence of water wave motion on oil slick spreading dynamics
Abstract: We hypothesise that the spread of oil slicks on the waterâs surface during oil spills is significantly influenced by water wave motion at the initial or intermediate spreading stages, well before emulsification processes have a substantial impact on the oil filmâs state. We demonstrate that the spreading dynamics of an oil slick on the water surface are facilitated by water waves, employing the thin film approximation. It is shown that water wave motion can rapidly deplete any oil slick, reducing the oil layerâs thickness to nearly zero. This mechanism may act as a precursor to emulsification processes, leading to the accelerated depletion of oil spills into a distribution of droplets that form an emulsion
PO1: 14:40-15:40, 24th June 2025, Room DH/GR8 HALL
Esha Joshi (University of Surrey, United Kingdom)
Title: Mechanistic Modelling of Pre-clinical Drug Trials of Tumour Cells
Abstract: Translating findings from pre-clinical to clinical drug trials remains a significant challenge in pharmacology. The main issue is that most pre-clinical studies rely on mouse xenograft models, whereas clinical trials are conducted in humans, where tumours exhibit greater structural constraints and biological differences. A key step toward improving this translation is developing a robust mathematical understanding of pre-clinical trials outcomes, which can enhance predictive modelling, refine drug development strategies, and reduce reliance on animal models. In this study, we analyse tumour growth data from patient-derived xenograft (PDX) models used in pre-clinical trials of small-molecule cytotoxic chemotherapy. The dataset (source: Novartis, open-source dataset) includes longitudinal tumour volume measurements across multiple cancer types capturing both untreated tumour growth and responses to various drug treatments. To characterise tumour growth dynamics, we fit non-linear mixed effects mechanistic tumour growth models for empirical growth laws that account for inter-tumour variability and treatment effects. Beyond model fitting, we explore optimal dosing strategies for small-molecule drugs by integrating our models with RECIST (Response Evaluation Criteria in Solid Tumours)-based response criteria, a set of guidelines used to assess the response of cancer patients to treatment for nutrient diffusion models. Our findings contribute to a deeper understanding of pre-clinical tumour growth patterns and provide a framework for improving dose optimisation, an important step in mathematical oncology. Longer term, this project, in collaboration with GlaxoSmithKline (GSK), aims to establish mechanistic modelling approaches incorporating spatial, pharmacokinetic and pharmacodynamic (PKPD) effects to create models that are fit-for-use in drug development.
PO1: 14:40-15:40, 24th June 2025, Room DH/GR8 HALL
Paraskevi Katsiavria (Durham University)
Title: Effects of Shear and Rotation on Convective Instabilities and Heat Transport
Abstract: Convection plays a crucial role in heat transport within astrophysical bodies. In this study, we investigate how shear flow and rotation influence convective onset and heat transport. Using a linear stability analysis, we examine the critical Rayleigh number required for onset under different shear profilesâlinear and sinusoidalâand compare our findings with existing literature. We also analyse the growth rates of convective instabilities and extend our study to include rotation, both independently and in combination with shear. In the non-linear regime, we assess how these factors affect heat transport by evaluating the Nusselt number, for a given Rayleigh number. Our motivation for future work is to provide insight into the interplay between shear, rotation, magnetic fields and convection, contributing to a better understanding of astrophysical fluid dynamics.
PO1: 14:40-15:40, 24th June 2025, Room DH/GR8 HALL
Tanisha Kumari (University of Glasgow)
Title: Mathematical modelling of ice sheet dynamics
Abstract: This study presents the mathematical modelling and analysis of ice sheet dynamics, such as those of Antarctica and Greenland, seeking specifically to bridge the gap in the understanding of the role of subglacial till on the large-scale dynamics of ice sheets and its pronounced impacts on potential sea level rise in light of the changing climate. Over large length and time scales, such as that of all of Antarctica or Greenland, ice in fact behaves as a viscous fluid because of the tremendous pressure gradients within the ice, which causes it to slowly deform, or flow. We model the ice sheet lying over the grounded subglacial till in contact with the bedrock. Initially, source flux is supplied to both the ice sheet and the till, after which the upper layer begins to float at the grounding line, say the shelf. The shear stress dominated ice sheet and till are coupled by continuity of thickness and flux at the grounding line. The mathematical modelling is carried out by using fluid mechanics principles for viscous fluids, Glenâs flow law, shallow ice and shallow shelf approximation. The theoretical analysis and numerical computation of solution is done for Newtonian case. The subglacial till lubricates the overlying ice sheet which results in the in the shear thinning and acceleration of fast flowing ice stream. References [1] Glen, J. W., âThe Creep of Polycrystalline Ice,â Proc. R. Soc. Lond. A, Vol. 228, No. 1175, 2024, pp. 519-538. [2] Schoof, C. and Hewitt, I. J., âIce-sheet dynamics,â Annu. Rev. Fluid Mech., Vol.45, 2013, pp. 214-239. [3] Robinson, Rosalyna A. V., Huppert, H. E. and Worster, M. G., J.,âDynamics of viscous grounding lines,â Fluid Mech., Vol.648, 2010, pp. 363-380.
PO1: 14:40-15:40, 24th June 2025, Room DH/GR8 HALL
Anthony Miller (University of Essex)
Title: Simple Neural Networks and Prediction Horizons of Chaotic Dynamics
Abstract: In this work, we conduct a comprehensive study of a simple artificial neural network and its ability to predict the time-series evolution of the well-known Lorenz 63 system. While numerous studies have focused on maximising the prediction horizon of the Lorenz 63 system, many results are unreliable due to limited testing and the selective choice of initial conditions that yield favourable outcomes. We demonstrate that achieving accurate predictions requires a deeper understanding of both the neural network and the chaotic dynamical system under study. One of the avenues we explore shows that when strong chaotic synchronisation exists within the training data, it introduces bias into the model and, consequently, its predictions. Thus, our study highlights the importance of eliminating any potential bias from the training data to improve predictive accuracy.
PO1: 14:40-15:40, 24th June 2025, Room DH/GR8 HALL
Adam Onus (Queen Mary University of London)
Title: Distance-from-flats persistent homology transform
Abstract: The Persistent Homology Transform (PHT) was introduced in the field of Topological Data Analysis about 10 years ago, and has since been proven to be a very powerful descriptor of Euclidean shapes. The PHT consists of scanning a shape from all possible directions and then computing the persistent homology of sublevel set filtrations of the respective height functions; this results in a sufficient and continuous descriptor of Euclidean shapes. The PHT can be generalised to consider arbitrary parameter spaces and sublevel sets with respect to any function. In particular, we study “distance-from-flat” PHTs defined on the Grassmannian of affine subspaces of Euclidean space, that allow to scan a shape by probing it with all possible affine m-dimensional subspaces (“flats”) for fixed dimension m, and by computing persistent homology of sublevel set filtrations of the function encoding the distance from the flat. We show that these transforms are injective and continuous and that they provide computational advantages over the classical PHT. This provides a very powerful and computationally advantageous tool for examining shapes, which in a previous work by a subset of the authors has proven to significantly outperform state-of-the-art neural networks for shape classification tasks.
PO1: 14:40-15:40, 24th June 2025, Room DH/GR8 HALL
Davide Papapicco (University of Auckland)
Title: Slowly, then all at once: Uncovering the dynamics of a catastrophe
Abstract: The sudden collapse of the population of a species is often used to refer to critical phenomena in nature that have catastrophic, and sometimes even unrecoverable, repercussions for the long-term stability of ecosystems. Generically, models based on stochastically perturbed dynamical systems can feature abrupt and unforeseen transitions between alternative stable states. These phenomena, called tipping points, have been extensively studied in the past 30 years with emphasis on their roles driving significant changes in a warmer earth and its complex systems. Mathematically we characterise different mechanisms of tipping for stochastic differential equations (SDEs). A prevalent analytical method relies on a fast-slow separation of the dynamic variables in which slow passage through a critical parameter region (bifurcation-induced tipping) and stochastic fluctuations around an attractor (noise-induced tipping) interplay with the non-stationarity of the forcing parameter (rate-induced tipping) to give a rich plethora of tipping phenomena. Given the ubiquity of critical transitions in nature, and the vital importance of predicting catastrophic events before the tipping point is reached, early warning signals have been proposed. An effective warning signal, whilst derived from the mathematical analysis of the model, has to scale in generality. Importantly it has to be applicable to scenarios in which scientists have limited or no knowledge of the dynamical systems generating the observed data. We introduce a probability estimate of tipping for systems in quasi-stationary regimes that employs analytical and numerical techniques to recostruct the steady-state solution of the Fokker-Planck equation from timeseries data alone. Statistical error estimates based on the linear least-squares regression show asymptotic converges under the ergodic hypothesis. Applicability to 1âdimensional metastable regimes is discussed and scalability to higher-dimensional models is tested empirically via numerical simulations.
PO1: 14:40-15:40, 24th June 2025, Room DH/GR8 HALL
Zainab Rahman (University of Portsmouth)
Title: Investigating the existence of periodic orbits of renormalisation operators for coupled systems of the FQ and C-type systems
Abstract: We observe universal scaling behaviour in the bifurcation structure of families of maps that represent discrete dynamical systems. In particular, many families exhibit period-doubling cascades in which asymptotic scaling relationships occur in parameter space, state space, and time, as the system approaches the accumulation of period-doublings. We use renormalisation operators that encode the scaling in an attempt to analyse this phenomenon. The existence of periodic points of these operators, and the properties of the associated tangent maps, are studied so as to explain quantitative universality of the dynamics. Our work is on the existence of renormalisation fixed points and cycles for period doubling in coupled pairs of maps. We are formulating rigorous computer-assisted bounds on operations in Banach spaces of pairs of functions of two variables. We have considered the conjectured FQ-type fixed point and the C-type period-two cycle in our work, hoping to explain universality of scaling in qualitatively different classes of coupled dynamical systems. We use renormalisation operators that encode the scaling in an attempt to analyse this phenomenon. The existence of periodic points of these operators, and the properties of the associated tangent maps, are studied so as to explain quantitative universality of the dynamics. Our work is on the existence of renormalisation fixed points and cycles for period doubling in coupled pairs of maps. We are formulating rigorous computer-assisted bounds on operations in Banach spaces of pairs of functions of two variables. We have considered the conjectured FQ-type fixed point and the C-type period-two cycle in our work, hoping to explain universality of scaling in qualitatively different classes of coupled dynamical systems.
PO1: 14:40-15:40, 24th June 2025, Room DH/GR8 HALL
Kaitlyn Ries (Newcastle University)
Title: Spatiotemporal modelling the spread of invasive pests across Great Britain
Abstract: Invasive species pose a significant threat to biodiversity, the environment, and the economy. They are expensive to manage and monitor, in the UK alone the estimated annual cost to the economy is ÂŁ4 billion. The spread of invasive species is increasing at unprecedented rates, as a result of expanding human trade networks and climate change. One invasive species of note is the oak processionary moth (OPM), which became established in the UK in 2006 through accidental importation. OPMs are harmful defoliators of oak trees, leaving them vulnerable to other stressors and diseases. They are also harmful to humans; the caterpillars have urticating hairs which can cause breathing difficulties. The eradication of OPM in the UK has been deemed unfeasible with the current management strategy focused on containing their spread. In partnership with Fera Science, we are combining mathematical and statistical models to describe and predict the spread of OPM across the UK and to inform future management strategies. This poster will showcase our work on an agent-based (individual-based) modelling approach for capturing OPM spread across the South-East of England. This model uses a lattice-based grid where a cell is either infested or susceptible (analogous to an SI model) to OPM, with cells becoming infested based on their distance to infested cells under the assumption of different dispersal kernels. We can then use the model to guide new management strategies and scenario test which may allow better containment.
PO1: 14:40-15:40, 24th June 2025, Room DH/GR8 HALL
Georgina Ryan (University of Oxford)
Title: Mathematical modelling of ion charge asymmetry in electrolytic cells
Abstract: The electrochemical processes found in electrolytic cells are the basis for modern energy technology like batteries and fuel cells. The simplest of these cells consists of an electrolytic solution (salt dissolved in a solvent) incorporated into an electrical circuit. Some electrolytic solutions are made of âsymmetricalâ salts whose constituent anions and cations have the same charge magnitude, while other electrolytic solutions have an ion charge asymmetry. We use asymptotic analysis on the PoissonâNernstâPlanck equations to examine the impact of ion charge asymmetry on the potential and ion concentrations in both the bulk solution and the boundary layers that form at the electrodes.
PO1: 14:40-15:40, 24th June 2025, Room DH/GR8 HALL
Kylie Savoye (University of Birmingham)
Title: Integrative Network Analysis of Spatial Transcriptomics Data
Abstract: Spatial transcriptomics is a technique that detects gene expression signals at single-cell resolution. It measures gene expression while preserving the positional information of RNA molecules. This technology generates high-dimensional data, with each cell associated with thousands of genes, making biological interpretation challenging. While existing analytical approaches typically examine spatial relationships and transcriptomic profiles separatelyâpotentially losing critical information through inferenceâour work introduces an integrated methodology. We develop a network-based representation where individual cells serve as nodes, and the edges between them are weighted according to gene expression correlation patterns. From this integrated representation, we apply a range of network analysis approaches, to uncover patterns within the data. This allows us to detect and measure architectural features present in the tissue and enable to detection of structural differences between experimental conditions, such as cancer versus non-cancer or drug versus control. Our integrated analysis aims to preserve important information that could be lost in some more traditional approaches. By simultaneously accounting for both spatial context and transcriptomic profiles, we hope to identify properties that provide deeper insights into the underlying biological processes of different tissues. This method shows promise for improving our understanding of complex cellular systems and could potentially help in identifying new biomarkers and therapeutic targets.
PO1: 14:40-15:40, 24th June 2025, Room DH/GR8 HALL
Nurzhan Serikbayev (Department of Mathematical Sciences, Loughborough University, Loughborough LE11 3TU)
Title: Dispersive shock waves of the extended Korteweg – de Vries equation
Abstract: Dispersive shock waves, or undular bores, can be described as non-stationary waves propagating as oscillatory transitions between two basic states, in which the oscillatory structure gradually expands and grows in amplitude during the propagation of the waves. Recently, an explicit analytical approximation describing a dispersive shock wave solution of the Korteweg – de Vries equation was constructed in terms of the elliptic and hypergeometric functions. We explore the possibility of using this description to construct an approximation of similar solutions to the extended Korteweg – de Vries equation, i.e, the. equation that includes higher-order terms, by using near-identity transformations. This is joint work with Karima Khusnutdinova.
PO1: 14:40-15:40, 24th June 2025, Room DH/GR8 HALL
Josh Shelton (University of St Andrews)
Title: New exact solutions to the water wave problem with vorticity and submerged vortices
Abstract: In an unbounded fluid, an infinite row of point vortices lie at a steady equilibrium. This steady configuration is unstable to subharmonic perturbations, the dominant growth rate of which occurs when the wavelength of the perturbation is twice that of the vortex row. This classic result is known as the pairing instability. However, analogous stability results are unknown for vortex rows submerged within bounded fluids, such as that in the free-surface water wave problem for instance, which motivates this present study on exact steady solutions of this problem. Specifically, we consider the case with constant fluid vorticity and one vortex per wave period. The result is a two-parameter family of solutions parameterised by: (i) the shear strength, and (ii) the vortex depth.
PO1: 14:40-15:40, 24th June 2025, Room DH/GR8 HALL
Elliot Vincent (University of Warwick)
Title: Epidemiological modelling of the effectiveness of Integrated Pest Management strategies for the control of Septoria tritici
Abstract: Reducing reliance on pesticides is an important global challenge. Integrated Pest Management (IPM) is one proposed sustainable solution, which is acknowledged to be effective, but has thus far only seen limited implementation in practice by crop growers. It comprises a set of management strategies which focus on the long-term prevention, detection and control of pests and diseases. Using epidemiological modelling, we investigate the potential outcomes of IPM as a method of disease control. As a case study, we considered Septoria tritici, an economically important disease of wheat, and examined the effect of IPM controls on yield and infection prevalence. We used an existing deterministic, compartmental infectious disease model of S. tritici transmission for the underlying system, and modified the model by implementing a number of IPM control measures. Using experimental data from existing literature we parameterised a number of applicable IPM measures, and investigated the range of probable outcomes for each. We then investigated the outcomes if an individual grower were to implement an IPM regime (consisting of the concurrent implementation of multiple IPM measures) as an alternative to a fungicide-based regime. We found that an IPM regime was able to maintain yields for an individual grower, and that in a system of multiple growers, a high prevalence of IPM could improve outcomes for all members of the system. The results of this modelling work provide valuable evidence for motivating the greater uptake of IPM in practice.
PO1: 14:40-15:40, 24th June 2025, Room DH/GR8 HALL
Adriana Zanca (The University of Melbourne)
Title: A random dynamical systems perspective on cell fate
Abstract: How pluripotent cells give rise to progressively more specialised cells over multiple cell divisions, known as cell fate, remains one of the mysteries of systems biology. During development, it is of the utmost importance that cells uphold certain division regimes for an organism to survive and thrive. Beyond development, cell fate perturbations can result in cancer and other pathological conditions. The theoretical and mathematical biology community has been making contributions to our understanding of cell fate including by quantifying Waddingtonâs seminal landscape using dynamical systems, performing statistical trajectory inference on single-cell sequencing data, or considering geometric and algebraic approaches to cell fate. In this talk, I will present a random dynamical systems interpretation of cell fate. This approach is, arguably, a generalisation of existing models of cell fate that may be able to provide new perspectives into cell fate.