Applied Mathematics Seminar

The Applied Mathematics Seminar usually takes place on Thursdays at 12:00 during term time in either Nuffield G13 or Lecture Theatre B Watson.

Spring 2020

Statistics of internal equilibria: Evolutionary Game Theory meets Random Polynomial Theory

  • Hong Duong, University of Birmingham
  • Thursday 20 February 2020, 12:00
  • Biosciences 301

Random evolutionary games, where the payoff entries are random variables, play an important role in the modelling of social and biological systems under uncertainty which is due to, for instance, the lack of information or the rapidly change of environment. As in classical game theory with the Nash equilibrium, the analysis of equilibrium points in evolutionary game theory has been of special interest because these equilibrium points provide essential understanding of complexity in a dynamical system, such as its behavioural, cultural or biological diversity and the maintenance of polymorphism.

In this talk, I will discuss our recent works on the statistics of the number of equilibriums in multi-player multi-strategy games. Prior methods involve solving a system of polynomial equations, thus are restricted to systems consisting of small numbers of players and/or strategies due to Abel’s impossibility theorem. By connecting to the rich theory of random polynomial theory, our approach allows overcoming this difficulty, enabling us to study general systems with arbitrarily large numbers of strategies and players.

A coupled bulk-surface model for cell polarisation

  • Anotida Madzvamuse, University of Sussex
  • Thursday 13 February 2020, 12:00
  • Biosciences 301

In this talk we will present a model describing the GTPase cycle between its active membrane-bound and inactive cytosolic form. Rho GTPases are key players in cell polarisation, which is required in several cellular activities, such as migration. The intricate reactions network of such proteins can lead to very complex mathematical models that are hard to analyse. Here, we present a simple basic interaction model of the same Rho GTPase protein in three-dimensional geometries, taking into account the different spatial compartmentalisation through the maturing theory of coupled bulk-surface semilinear parabolic equations.

In this work the bulk-surface model is a substantial extension of the wave pinning model first proposed by Mori et al (2008, Biophys J.). To understand the theoretical behavior of the model, we carry out detailed asymptotic and local perturbation analysis, which helps to find parameter regions in which polarisation occurs. The geometry effects are naturally taken into account and with the emergent property that polarisation regions become bigger when a cell increases its surface. This last result is particularly meaningful since surface increase typical occurs during cell migration. To provide validation and confirmation of the theoretical results, we proposed and implemented a corresponding bulk-surface finite element method which we use to solve the system of coupled bulk-surface reaction-diffusion equations. Simulation results are shown over simple and more complex three-dimensional geometries and the pattern generation mechanism is in line with theoretical predictions.

Using Boolean Modelling and Natural Language Processing to unveils patterns of antimicrobial resistance

  • Marie Zepeda Mendoza (Microbiology and Infection, University of Birmingham
  • Thursday 06 February 2020, 12:00
  • Biosciences 301

My main research methods are computational modelling and data science. The talk has two parts. First, I will talk about a study we just completed of the use of Boolean modelling on the virulence network of the opportunistic pathogen Pseudomonas aeruginosa. Treatment of P. aeruginosa infections often fail due to its antibiotic resistance mechanisms, thus novel strategies aim at targeting virulence factors instead of growth-related features. Although the elements of the virulence networks of P. aeruginosa have been identified, how they interact and influence the overall virulence regulation is unclear. We reconstructed the signalling and transcriptional regulatory networks of 12 acute and 8 chronic virulence factors, and the 4 quorum sensing systems of P. aeruginosa, and analysed them with Boolean modelling techniques. Then, I will talk about my ongoing study on the use of natural language processing techniques for the unveiling of patterns of the spread of antimicrobial resistance in pathogenic microbes by analysing the text from all the public research epidemiology papers to date.

Turing instability, localised patterns and plant cell polarity formation

  • Alan Champneys, University of Bristo
  • Wednesday 05 February 2020, 14:00
  • Engineering ENG-G29

In this talk I shall describe recent work inspired by problems in cell biology, namely how the dynamics of small G-proteins underlies polarity formation. Their dynamics is such that their active membrane-bound form diffuses more slowly. Hence you might expect Turing patterns. Yet how do cells form backs and fronts or single isolated patches? In understanding these questions we shall show that the key is to identify the parameter region where Turing bifurcations are sub-critical. What emerges is a unified 2-parameter bifurcation diagram containing pinned fronts, localised spots, localised patterns. This diagram appears in many canonical models such as Schnakenberg and Brusselator, as well as biologically more realistic systems. A link is also found between theories of semi-strong interaction asymptotics and so-called homoclinic snaking. I will close with some remarks about relevance to root hair formation and pavement cells to the importance of sub-criticality in biology.

Total variation of the normal as a prior in geometric inverse problems

  • Roland Herzog, TU Chemnit
  • Wednesday 29 January 2020, 13:00
  • Physics West 103

The total variation (TV) is an important regularizing seminorm in inverse problems.We consider geometric inverse problems, where the shape is among the unknowns.The notion of total variation of the surface normal will be defined and considered as a prior for this class of problems.We also address a suitable numerical scheme to deal with the non-smoothness arising from the TV of the normal and present numerical results.

Strategies for Multilevel Monte Carlo

  • Kody Law, University of Manchester
  • Thursday 30 January 2020, 12:00
  • Biosciences 301

This talk will concern the problem of inference when the posterior measure involves continuous models which require approximation before inference can be performed. Typically one cannot sample from the posterior distribution directly, but can at best only evaluate it, up to a normalizing constant. Therefore one must resort to computationally-intensive inference algorithms in order to construct estimators. These algorithms are typically of Monte Carlo type, and include for example Markov chain Monte Carlo, importance samplers, and sequential Monte Carlo samplers. The multilevel Monte Carlo method provides a way of optimally balancing discretization and sampling error on a hierarchy of approximation levels, such that cost is optimized. Recently this method has been applied to computationally intensive inference. This non-trivial task can be achieved in a variety of ways. This talk will review 3 primary strategies which have been successfully employed to achieve optimal (or canonical) convergence rates – in other words faster convergence than i.i.d. sampling at the finest discretization level. Some of the specific resulting algorithms, and applications, will also be presented.

The role of surfactants on the interfacial stability of multilayer channel flows

  • Anna Kalogirou, University of Nottingham
  • Thursday 23 January 2020, 12:00
  • Biosciences 301 

The linear and nonlinear stability of a two-layer surfactant-laden flow in a channel is examined using asymptotic modelling and direct numerical simulations (DNS). The surfactant molecules exist in one of the fluids only but they can get adsorbed at the interface or form micellar aggregates when their concentration is beyond a critical value. A mathematical model is formulated, consisting of governing equations for the hydrodynamics and appropriate transport equations for the surfactant concentration at the interface, the concentration of monomers in the bulk fluid and the micelle concentration. A primary objective of this study is to investigate the effect of surfactants on the stability of the interface, and in particular surfactants in high concentrations and above the critical micelle concentration. Interfacial instabilities are induced due to the acting forces of gravity and inertia, as well as the action of Marangoni forces generated as a result of the dependence of surface tension on the interfacial surfactant concentration. An asymptotic model is also derived in the long-wave approximation, comprising a system of highly nonlinear PDEs describing the evolution of the interface as well as interfacial, bulk and micelle surfactant concentrations. The identified linear instabilities are followed into the nonlinear regime by carrying out numerical computations of the model system as well as DNS . The underlying physical mechanism responsible for the formation of interfacial waves will be discussed, together with the complex flow dynamics (typical nonlinear phenomena associated with interfacial flows include travelling waves, solitary pulses, quasi-periodic and chaotic dynamics).

Title to be confirmed

  • Veronica Grieneisen, Cardiff University
  • Thursday 16 January 2020, 12:00
  • Biosciences 301

Abstract not available

Find out more

There is a complete list of talks in the Applied Mathematics Seminar on talks@bham.