Seminars

Title: Mathematical model of sexual response
Speaker: Dr Konstantin Blyuss, University of Sussex, UK
Date: 7 March 2023
Abstract: In this talk I will discuss a mathematical model of Masters-Johnson human sexual response cycle. As a starting point, I will review cusp catastrophe and will show why earlier studies that interpreted sexual response cycle using this catastrophe were incorrect. I will then present a derivation of a phenomenological psycho-physiological model of human sexual response cycle. Bifurcation analysis is performed to identify stability properties of the model’s steady state, and numerical simulations are performed to illustrated different types of dynamics associated with the cycle. We will then look at the stochastic version of the model, where I will discuss properties of the spectrum and variance of stochastic oscillations around deterministically stable steady state, as well as the computation of confidence regions. To make a better understanding of stochastic dynamics, I will show how large deviation theory can be used to compute optimal escape paths from the neighbourhood of the steady state, and will discuss clinical implications of results.

TBA (Discussion)
Speaker: Prof. Lorenzo Fioramonti, Surrey Institute for Sustainability, University of Surrey, UK
Date: 21 February 2023

A talk of two halves:  “Practical catastrophe theory”, and “Hidden dynamics of maps and sleep cycles”
Speaker: Dr Mike Jeffrey, University of Bristol
Date: 7 February 2023
Abstract: During covid I did the unusual thing of discovering something that might actually be useful. Actually two things, so I’d like to present them both briefly. One concerns how to handle discontinuities in maps, and one concerns how we locate bifurcations in (also unusually for me) smooth dynamical systems. I’ll give examples taken from reaction-diffusion PDEs in part 1 (Practical catastrophe theory for the modern age), and from sleep-wake cycle maps in part 2 (Hidden dynamics of maps and sleep cycles, and when “period 1+2 implies chaos”)

Modelling dryland vegetation patterns: the impact of non-local seed dispersal and mechanisms of species coexistence
Speaker: Dr Lukas Eigentler, University of Bielefeld, Germany
Date: 27 January 2023

Geometric singular perturbation analysis of the multiple-timescale Hodgkin-Huxley equations
Speaker: Dr Panos Kaklamoanos,  Maxwell Institute for Mathematical Sciences, University of Edinburgh
Date: 17 January 2023

Accommodating data structure in clinical trials and other applied studies. 
Speaker: Professor Simon Skene, Professor of Medical Statistics and Director of Surrey Clinical Trials Unit

Date: 6 December 2022

Modelling in early discovery for large molecules
Speaker: Dr Adam Nasim, GSK
Date: 15 November 2022

Open quantum dynamics for plant motions
Speaker: Professor Dorje Brody, Department of Mathematics, Surrey
Date: 25 October 2022

Computational modelling of neural dynamics: From basic principles to biomedical research
Speaker: Dr Roman Bauer
Date: Thursday 10 December 2020
Abstract: The development of the brain is a highly complex process, involving various mechanisms on different spatial and temporal scales.

While technological advances have allowed to extract valuable information from the brain, the complex nature of these data renders it often challenging to compare and validate theoretical concepts. However, a better understanding of changes during brain development could help elucidate driving factors of disorders, as well as give rise to potential treatment strategies.

Here, I will present some lines of work where computational modelling and analysis is used to study changes in neural tissue during brain development and degeneration. These changes range from axonal arborizations on the single neuron level to inter-areal fibre tracts on the scale of large populations of neurons. Notably, several characteristics associated with pathological conditions can be reproduced, establishing a quantitative framework for the study of neurodevelopmental disorders and degenerative diseases.

Systems biology for single cell RNA-Seq data
Speaker: Dr Tom Thorne
Date: Thursday 10 December 2020
Abstract: Single cell RNA-Seq data is challenging to analyse due to problems like dropout and cell type identification. We present a novel clustering approach that applies mixture models to learn interpretable clusters from RNA-Seq data, and demonstrate how it can be applied to publicly available scRNA-Seq data. Having inferred groupings of the cells, we can then also attempt to learn networks from the data. These approaches are widely applicable to single cell RNA-Seq datasets where there is a need to identify and characterise sub-populations of cells.

Genetic control of BMI dynamics: a tale of longitudinal growth models and instrumental variables
Speaker: Dr. Alex Couto Alves
Date: Thursday 27 February 2020
Abstract: Critical periods in body mass index (BMI) trajectory predict childhood obesity and cardio-metabolic conditions. BMI trajectory is nonlinear and nonmonotonic reflecting the influence of genetics, pre-conceptional, gestational, and chilldhood environment. However, the regulation of BMI dynamics in childhood is poorly understood.

Here, we discuss the application of growth models to longitudinal BMI data, which we then use to identify genes controlling BMI dynamics. We estimate model parameters reflecting age and BMI at different critical periods in infancy and childhood and demonstrate that different genetic factors control BMI in these periods.

In the second part of this talk, I will present preliminary results delineating a mechanism linking birth weight to BMI dynamics using an instrumental variable approach. We show that childhood BMI partly mediates the influence of birth weight on adult BMI. However, this study also reveals that alternative pathways must exist, suggesting that prevention of childhood obesity may need to start earlier than originally thought.

This work informs on the targets and periods for prevention and treatment of childhood obesity and adult cardiometabolic conditions

New developments in global sensitivity analysis of engineering models
Speaker: Oleksiy Klymenko
Date: Thursday 28 November 2019
Abstract: Mathematical modelling plays crucial role in the design and operation of man-made systems ranging from small appliances to industrial manufacturing and distribution facilities and further to overarching approaches such as Life Cycle Analysis. Many ensuing models encompass numerous physical, chemical, biological, economic, etc. phenomena in multi-scale settings and involve making optimal decisions regarding system configuration and its optimal model-predictive control.

However, optimal design and operation of such process systems is subject to multiple sources of uncertainty, the effect of which on model outputs (e.g., Key Performance Indicators (KPIs) of a process or Critical Quality Attributes (CQAs) of a product) must be quantified in order to ensure robust system design and operational performance.

In this talk I will give an overview of Global Sensitivity Analysis (GSA) – a tool for model analysis under uncertainty, its applications in engineering and new computational approaches for models involving inequality constraints.

The role of noise in quantum decoherence in cellular systems
Speaker: Lester Buxton
Date: Thursday 10 October 2019
Abstract: Quantum mechanics has been applied to many areas of physics ranging from semiconductors, to computing, to cryptography. In recent years the study of quantum biology has gained momentum, highlighting the fundamental problem of explaining how biological systems may remain coherent in warm and wet cellular environments.

Making use of the Caldeira-Leggett model for open quantum systems, where the quantum system of interest is linearly coupled to a bath of harmonics oscillators, we study the effect of environmental noise on quantum decoherence. Adapting the Caldeira-Leggett model for this noisy system requires first the introduction of the Caldirola-Kanai Hamiltonian into the influence functional, in order to mimic environmental induced damping terms in the oscillators' equations of motion. This will be followed by including appropriate noise terms in the CK Hamiltonian.

The general aim of this project is to see if this model can extend decoherence times of quantum systems.

The effect of spectral density on decoherence dynamics of open quantum systems
Speaker: Sapphire Lally
Date: Thursday 10 October 2019
Abstract: The Caldeira-Leggett model is a successful way of describing the reduced dynamics of a multi-level quantum system in constant interaction with a reservoir of harmonic oscillators.

In open quantum systems, the spectral density describes the distribution of reservoir frequency modes. The Caldeira-Leggett model assumes a spectral density which is Ohmic and Markovian. Initial experimental results suggest that a reservoir of harmonic oscillators has a strongly sub-Ohmic, non-Markovian spectral density.

Here, the Caldeira-Leggett model is extended to an Ohmic non-Markovian spectral density, with the prospect of generalising to non-Ohmic spectral densities. This extended model should be applicable to a wide range of systems and may predict increased decoherence times of the quantum system.

Breaking the bonds of weak coupling: the dynamic causal modelling of oscillator amplitudes
Speaker: Erik Fagerholm (King's College London)
Date: Thursday 6 June 2019
Abstract: Models of coupled oscillators are useful in describing a wide variety of phenomena in physics, biology and economics. These models typically rest on the premise that the oscillators are weakly coupled, meaning that amplitudes can be assumed to be constant and dynamics can therefore be described purely in terms of phase differences. Whilst mathematically convenient, the restrictive nature of the weak coupling assumption can limit the explanatory power of these phase-coupled oscillator models. We therefore propose an extension to the weakly-coupled oscillator model that incorporates both amplitude and phase as dependent variables. We use the bilinear neuronal state equations of dynamic causal modelling as a foundation in deriving coupled differential equations that describe the activity of both weakly and strongly coupled oscillators. We show that weakly-coupled oscillator models are inadequate in describing the processes underlying the temporally variable signals observed in a variety of systems. We demonstrate that phase-coupled models perform well on simulations of weakly coupled systems but fail when connectivity is no longer weak. On the other hand, using Bayesian model selection, we show that our phase-amplitude coupling model can describe non-weakly coupled systems more effectively despite the added complexity associated with using amplitude as an extra dependent variable. We demonstrate the advantage of our phase-amplitude model in the context of model-generated data, as well as of a simulation of inter-connected pendula, neural local field potential recordings in rodents under anaesthesia and international economic gross domestic product data.

Predictive policing: myth or reality?
Speaker: Sylvain Delahaies (Surrey)
Date: Thursday 7 February 2019
Abstract: Predictive policing aims at forecasting where and when crime will take place in the future. While millions are currently invested in unproven predictive softwares we focus on self-excited point processes which have recently become popular to predict crime. We consider a police patrol allocation experiment and investigate under what parameter regimes the model might prove useful. Then we consider a novel Bayesian sequential data assimilation algorithm for joint state-parameter estimation by deriving an approximation Poisson Gamma Kalman filter. Finally we apply the data assimilation scheme and police patrol experiment to real Chicago crime data.

Dynamic modulation of brain states using brain stimulation
Speaker: Dr Ines Violante (Psychology, Surrey)
Date: Thursday 10 January 2019
Abstract: Electrical brain stimulation is a key technique in research and clinical neuroscience studies because it can provide causal relationships between brain and behaviour and offers the possibility of manipulating abnormal brain dynamics. I will discuss our recent work showing that fMRI can provide meaningful information regarding how brain networks are affected by transcranial brain stimulation. I will discuss the importance of combining multimodal approaches to reveal insights about the mechanisms associated with cognitive functions in humans, and to develop clinical tools to target dysfunctional brain dynamics occurring as a result of brain pathologies. In particular, I will discuss the use of neuroadaptive Bayesian optimisation to define individual stimulation parameters to modulate the function of specific brain networks.

Threshold activated coupling stabilizes the chaotic states to steady states
Speaker: Chandrakala Meena (Bar-Ilan University, Ramat Gan, Israel)
Date: Thursday 20 December 2018
Abstract: In this talk, Chandrakala Meena would like to talk about a chaos control mechanism in random scale-free networks of population dynamics. For the population dynamics we consider the chaotic Ricker map on each node and nodes in the network are connected by transport that is triggered when population density in a patch is in excess of a critical threshold level.

Our central result is that threshold-activated dispersal leads to stable fixed populations, for a wide range of threshold levels. Further, suppression of chaos is facilitated when the threshold-activated migration is more rapid than the intrinsic population dynamics of a patch. Additionally, networks with a large number of nodes open to the environment, readily yield stable steady states and in the networks with very few open nodes, the degree and betweeness centrality of the node open to the environment has a pronounced influence on control. All qualitative trends are corroborated by quantitative measures, reflecting the efficiency of control, and the width of the steady state window.

Seizure prediction: a computer science challenge?
Speaker: Lucas Franca (University College London)
Date: Thursday 29 November 2018
Abstract: Over the last decades, researchers have thoroughly searched for a seizure prediction method. Such a technology further became a ‘Holy Grail’ of epileptology due to its potential to revolutionise healthcare and symptoms management in patients with intractable epilepsies. 

Achieving such an ambitious aim requires, nevertheless, some insight on the mechanisms of ictogenesis and how these properties manifest in brain signals. Every year, extensive recordings of brain signals of pre-ictal and ictal states are obtained during pre-surgical evaluation in patients with intractable epilepsies. Applying mathematical and/or statistical techniques to study and model such data might  provide new hints on how epileptic seizures arise and evolve.

In this talk, Luca Franca will discuss putative mathematical methods to characterise epileptic seizures and the role of machine learning and pattern recognition in seizure prediction and characterisation, as well as common pitfalls in these techniques.

MoLSS/SSRC Mathematical modelling of sleep/wake regulation afternoon
Date: Monday 18 June 2018

Modeling sleep-wake regulation: REM sleep mechanisms and dynamics
Speaker: Victoria Booth (Departments of Mathematics and Anesthesiology, University of Michigan)

What time do you have? Modeling interindividual variability in the human circadian system
Speaker: Cecilia Diniz-Behn (Department of Applied Mathematics and Statistics, Colorado School of Mines and Department of Pediatrics, University of Colorado School of Medicine)

Neglected Tropical Diseases (NTD) control and elimination: Insights from mathematical models
Speaker: Joaquin Prada (University of Surrey)
Date: Thursday 24 May 2018
Abstract: Neglected Tropical Diseases (NTD) are a large morbidity and mortality burden and the World Health Organization (WHO) set a roadmap for NTDs with goals for 2020.

The NTD modelling consortium was formed to help answer key epidemiological questions using mathematical models. One particular question of interest is - are we on target with the current strategies? - if not, what alternatives are available?

Transmission models have been developed to inform WHO guidelines and are now being combined with geo-spatial models of disease to obtain more country relevant predictions. Mathematical models are therefore extremely useful for informing policy decision-making.

The economics of bacterial gene expression
Speaker: Jose Gimenez (University of Surrey)
Date: Thursday 3 May 2018
Abstract: The cellular resources required for gene expression are limited in bacterial cells. Owing to this, the expression of a particular gene can affect the activity of another seemingly unconnected gene and it has been shown that this coupling can be described by linear manifolds.

We combine experimental work and mathematical models to understand how these couplings emerge and how can they be alleviated to improve the performance of synthetic genetic circuits and pathways. In particular, we have investigated the effect of producing partitions of ribosomes that can be allocated differentially to specific mRNAs of interest.

Rigorous derivation of the nonlocal reaction-diffusion FitzHugh-Nagumo system
Speaker: Gregory Faye (University of Toulouse)
Date: Thursday 26 April 2018
Abstract: We introduce a spatially extended transport kinetic FitzHugh-Nagumo model with forced local interactions and prove that its hydrodynamic limit converges towards the classical nonlocal reaction-diffusion FitzHugh-Nagumo system.

Our approach is based on a relative entropy method, where the macroscopic quantities of the kinetic model are compared with the solution to the nonlocal reaction-diffusion system. This approach allows to make the rigorous link between kinetic and reaction-diffusion models. This joint work with Joachim Crevat and Francis Filbet.

Resilience of cocoa farming to climate variation
Speaker: Lorna Wilson (University of Bath)
Date: Thursday 19 April 2018
Abstract: I will provide a brief introduction to the University of Bath’s Institute for Mathematical Innovation, and some of the industrial mathematics that I have undertaken in my unique role as a commercial research associate. I will then present my research into mathematical modelling of the variation in on-farm cocoa yields resulting from weather effects in Ghana.

This project builds upon the initial work carried out on behalf of Mondelez at a three day Agri-Food industry study group with Innovate UK in January 2017. One of the challenges facing cocoa farmers is large variability in crop yield from one year to another. It is believed that climate is one of the biggest drivers of this variation and research into the impact of long term climate change on cocoa production is underway. Such yield variation causes large fluctuations in income for farmers and can hinder investment (either from the farmer or from external lenders). Being able to model the potential variation in on-farm cocoa yields due to climate could significantly aid sustainable development of resilient farming communities.

I will talk about the ODE model proposed at the study group which I found to be insufficient to capture the importance of cocoa pod age. A full age-based PDE model is considered too complex to generate practical results. I will present a delay differential equation (DDE) approach, that is simple enough to be effectively  parameterised with the data available, but still able to capture the ageing of cocoa pods. I will compare the promising results of the model output to the yield data for various statistically selected rainfall inputs.