The EDI SIAM-IMA PhD Student Colloquium 2020

Location:

Bayes Centre, ICMS, Room 5.10

Schedule:

14:00-14:05 EDI SIAM-IMA Committee Welcome and introduction
14:05-14:25 Tim Espin A Brief Introduction to Spin Networks

What do matrices have to do with Knot Theory? One answer is provided by Spin Networks: a graphical representation of algebraic matrix calculations. In this talk we give a brief outline of some basic aspects of the theory, prove that Spin Networks satisfy the Reidemeister moves (a key axiom of Knot Theory), and give an overview of their wider context in Mathematical Physics.
14:25-14:45 Thomas Zacharis Applications of invariant manifold theory to singularly perturbed systems

The most general and sophisticated theorems concerning the persistence of invariant manifolds for finite-dimensional dynamical systems where obtained independently by Fenichel and Hirsch, Pugh and Shub in the 1970's. We briefly mention these theorems and introduce the concept of normal hyperbolicity. The theory provides a 'geometric' approach to the study of singularly perturbed systems. We also present generalizations of these results to infinite-dimensional systems.
14:45-15:05 Jonna Roden PDE-Constrained Optimization for Multiscale Particle Dynamics

There are many industrial and biological processes, such as beer brewing, nano-separation and bird flocking, which can be described by integro-PDEs. These PDEs define the dynamics of a particle density within a fluid bath, under the influence of diffusion, external forces and particle interactions, and often include complex, nonlocal boundary conditions.

A key challenge is to optimize these types of processes. For example, in nano-separation, it is of interest to determine the optimal inflow rate of particles (the control), which leads to high separation of the particles (the target), at a minimal financial cost. Mathematically, this requires tools from PDE-constrained optimization. A standard technique is to derive a system of optimality conditions and solve it numerically. Due to the nonlinear, nonlocal nature of the governing PDE and boundary conditions, the optimization of multiscale particle dynamics problems requires the development of new theoretical and numerical methods.

In this talk, I will present the system of nonlinear, nonlocal integro-PDEs that describe the optimality conditions for such an optimization problem. Furthermore, I will introduce a numerical method, which combines pseudospectral methods with a multiple shooting approach. This provides a tool for the fast and accurate solution of these optimality systems. Finally, some examples of future industrial applications will be given. This is joint work with Ben Goddard and John Pearson.
15:05-15:25 Xander O'Neill Modelling the transmission and persistence of African swine fever in wild boar in contrasting European scenarios

We present a mathematical model of the wild boar and African swine fever (ASF) system to explore the key mechanisms that drive infection transmission and disease persistence. Model results show that direct environmental transmission is a key mechanism that determines the severity of an infectious outbreak and that direct frequency dependent transmission and a chronic infective stage are key for the long-term persistence of the virus. We consider scenarios representative of Estonia and Spain and show that the increased degradation rate of carcasses in Spain, due to elevated temperature and abundant obligate scavengers, may reduce the severity of the infectious outbreak. The model is also used to assess disease control measures and suggests that a combination of culling and infected carcass removal can lead to the eradication of the virus without also eradicating the host population. Furthermore, early implementation of these control measures will reduce infection levels and, in some situations, prevent ASF from establishing in a population
15:25-15:45 Muzammil Hussain Rammay Calibration and prediction improvement of imperfect models
15:45-16:15
- coffee break -
16:15-16:35 Tatiana Filatova Stochastic modelling of gene expression

Gene expression in both prokaryotes and eukaryotes cells is fundamentally stochastic. A number of experimental and theoretical approaches have studied the mechanisms or RNA transcription to get the mechanistic understanding of every step of transcription process. Many studies show that every step of RNA transcription such as initiation, elongation, termination etc. plays an important role in the regulation of gene expression at different levels. For many organisms, single-cell experiments have shown that gene expression can be described by a simple three-stage model which represents the steps of RNA transcription by first-order biochemical reactions. This model has been extensively studied and it is widely adopted in the literature.

In this talk I will introduce a mathematical model of gene expression which focusses on transcription initiation and multi-step elongation process, which can be defined by a system of biochemical reactions. The stochastic dynamics of this system are described by a Chemical Master Equation (CME). Mathematically speaking CME is a system of linear ordinary differential equations (ODEs) that describes the time evolution of the probabilities of observing a specific state in the system. This stochastic model of gene expression exhibits dynamics on different timescales. Hence an asymptotic solution of the system in steady-state can be obtained by using the Singular Perturbation Theory (SPT). The analytical solution for RNA distribution and the limits when the mentioned model converges to the three-stage model will be presented.
16:35-16:55 Andres Barajas Paz Age Heaping in Population Data of Emerging Countries

Mortality analyses have commonly focused on countries represented in the Human Mortality Database that have good quality mortality data. This presentation will address the challenge that in many other countries population and deaths data can be somewhat unreliable. In many countries, for example, there is significant misreporting of age in both census and deaths data: referred to as 'age heaping'. The purpose of our research, is to develop mortality models for countries where their population data is affected by age heaping. We design a log-likelihood method for the two dimensional data, based on a parametric model with smooth period effects. We maximize the log-likelihood function and obtain improved exposures and death rates by reducing age heaping across all calendars years. We show empirical results for Mexican mortality to illustrate our approach. Finally, we will collaborate with HMD to see how their approach can be adapted to Mexican data for producing complete life table series, which is also relevant to international reinsurance.
16:55-17:15 Vadim Platonov Expansions in measure for Itô random fields

We present two Itô-Wentzell formulas on Wiener spaces for real-valued functional random field of semimartingale type depending on measures. Derivatives with respect to the measure components are understood in the sense of Lions.
17:15-17:35 Spyridoula Sklaveniti Discretization of the matrix AKNS scheme

In this talk we present space discretization of the matrix AKNS scheme. More precisely, we derive the matrix semi-discrete non-linear Schrödinger (DNLS) hierarchy as well as solutions associated to non-linear ODEs of this hierarchy via the dressing process.
17:35-17:55 Thomas Hodgson All Together Now! Flocking, Herding and Collective Behaviour in Nature

Everywhere we look in nature, things are interacting: from the simplest bacteria to the largest mammals. These interactions can produce behaviours far more complex than these individuals are capable of alone. In physics, systems of particles are generally well-understood — we know the rules. In biology, the picture is not so clear. How do animals interact? Do we have anything in common with ants? This talk aims to provide an introduction to some models of emergent behaviour and begin to answer some of these questions.