Welcome to the 7th SAMBa Summer Conference, taking place Tuesday 11th and Wednesday 12th of July 2023.
The SAMBa conference is an opportunity for students to showcase their work to members of the department,
outside the department and at other Universities in a supportive environment. The work of SAMBa students
covers the entire spectrum of statistical applied mathematics: including projects in statistics,
probability, analysis, numerical analysis, mathematical biology, fluid dynamics, machine learning and
high-performance computing. The conference is organized by students and contains talks by SAMBa
students, external speakers, and students from other departments and institutions.
This website will be updated with conference details as they are confirmed, including speakers,
abstracts, registration forms, and the conference schedule.
The conference will be hosted in the Wolfson Lecture Theatre, 4 West room 1.7, the Mathematical Sciences
department of the University of Bath
Department of Mathematical Sciences,
University of Bath,
Claverton Down,
Bath, BA2 7AY,
United Kingdom
Below is the schedule for the conference. The list of speakers can be found below the timetable with
their titles and abstracts updated when they become available. Each session of talks is linked nominally
by theme, given to provide an idea of focus for the session.
Time
Tuesday (11th July)
Wednesday (12th July)
09:30
Arrivals and Registration
Arrivals
09:45
Welcome talk
10:00
Keynote Talk: Dr Aretha Teckentrup - Deep Gaussian processes: theory and
applications
Keynote Talk: Dr Thomas Woolley - The Turing bifurcation isn't (always) a
pitchfork
11:00
Break
Break
11:15
Timothy Peters, Andrei Sontag, Dan Miles
Christopher Dean, Shahzeb Noureen
12:15
Lunch
Lunch
13:15
Keynote Talk: Dr Perla Sousi - Speed of biased random walk on dynamical
percolation
Keynote Talk: Prof Oliver Jensen - Flow and transport in the human placenta
14:15
Lightning Talks
Conference Photo
14:45
Guannan Chen, Matthew Pawley, Marcel Stozir
Jenny Power, Pablo Arratia, Carmen van-de-l'Isle
15:45
Break
Break
16:00
Poster Sessions
Keynote Talk: Dr Tom Crawford - From Maths to YouTube - my journey in science
communication
17:00
Closing remarks and walk down to restaurant
KEYNOTE SPEAKERS
This section lists the confirmed speakers, and their titles and abstracts as they become available.
Tom Crawford
St Edmund Hall, University of Oxford
Title: From Maths to YouTube - my journey in science communication
Beginning in radio with the Naked Scientists, Dr Tom Crawford now runs a successful
YouTube channel (Tom Rocks Maths)
with video production listed as part of his job description at the University of Oxford.
In this talk, he will share details of his journey, and top-tips for carving out a
career in science communication.
Oliver Jensen
University of Manchester
Title: Flow and transport in the human placenta
The placenta provides a life-support system for a growing fetus, delivering nutrients
and removing waste products by bringing maternal and fetal blood into close proximity.
Mathematical modelling, alongside imaging, has an important role to play in
understanding how the placenta's function as an exchange organ is closely related to its
physical structure, which can be bewilderingly complex but which is compromised in
certain diseases. Two factors present particular modelling challenges: the lengthscales
over which transport and exchange processes take place range continuously over at least
four orders of magnitude; furthermore, there are high levels of spatial disorder within
individual organs. I will describe some of the techniques used to model flow and
transport across different scales, and recent attempts to integrate models with data
emerging from imaging and experiment.
Aretha Teckentrup
University of Edinburgh
Title: Deep Gaussian processes: theory and applications
Deep Gaussian processes have proved remarkably successful as a tool for various
statistical
inference and machine learning tasks. This success relates in part to the flexibility of
these processes and their ability to capture complex, non-stationary behaviours. In this
talk, we will introduce the general framework of deep Gaussian processes, in which many
examples can be constructed, and demonstrate their superiority in regression and
interpolation tasks. We will further discuss recent theoretical results which give
crucial
insight into the behaviour of the methodology as the number of layers or the number of
training points increases.
Thomas Woolley
Cardiff University
Title: The Turing bifurcation isn't (always) a pitchfork
Turing's theory of morphogenesis is one of the most widely used, well known and most
successful theories for understanding pattern formation. It has been extended in a vast
number of different directions, such as: adding larger numbers of morphogens; including
domain growth and adding noise. However, is the base theory well understood? One of the
first facts that you learn after using linear analysis to derive the Turing bifurcation
point is that nonlinear analysis tells us that the point is pitchfork (subcritical, or
supercritical) in nature. Although true on rectilinear domains with Neumann boundary
conditions, my work shows this is not generally the case and, thus, we must be careful
when generalising our results.
Perla Sousi
Emmanuel College, University of Cambridge
Title: Speed of biased random walk on dynamical percolation
We study the speed of a biased random walk on dynamical percolation on Z^d as a function
of the bias. While in dimension one, the speed is easily seen to be monotone increasing,
we show that in higher dimensions this fails and some new phenomena occur. This is joint
work with Sebastian Andres, Nina Gantert and Dominik Schmid.
STUDENT SPEAKERS
Guannan Chen
Title: High Accuracy Algorithms for Quantum Spin Dynamics and Control
The development of effective algorithms for computing dynamics and optimal control of
many-body two-level quantum systems such as spin systems under the presence of
time-dependent Hamiltonians is crucial for many quantum technologies. The recently
proposed QOALA algorithm highlights a need for high-order integrators in these
applications. We develop fourth-order Magnus-based algorithms for simulating many-body
systems under the presence of highly-oscillatory time-dependent pulses. These algorithms
can be efficiently implemented on classical as well as quantum computers. These
integrators achieve high accuracy despite taking large time-steps, which corresponds to
faster computation on classical computers and shorter circuit depths on quantum
computers, making our algorithm a suitable candidate for near-term quantum computers.
The favourable properties of these numerical algorithms for quantum spin dynamics and
control are achieved by exploiting certain Lie algebraic properties for eliminating
commutators appearing in a fourth-order Magnus expansion, the utilisation of extremely
inexpensive analytical Lie derivatives for computation of gradients and Hessians, and
the preservation of nested integrals in the Magnus expansion which allows arbitrarily
accurate resolution of highly-oscillatory pulses.
Christopher Dean
Title: Coexistence in the Chase-Escape Process: First Passage Percolation with Two
Competing Types
Chase-escape is an interacting particle system on graphs. The model has seen recent
interest due to its wide number of applications, such as, modelling predator-prey
dynamics, and modelling the spread of computer malware. In the model, vertices can be in
one of three states, blank, red, or green. Green vertices evolve as first passage
percolation on blank vertices with rate lambda. Red vertices evolve on green
vertices as first passage percolation with rate 1. For infinite graphs, if one takes
lambda large enough, it is possible for green to outrun red and survive
forever. In
this talk, I will discuss this phenomenon for several infinite graphs.
Pablo Arratia Lopez
Title: A Brief Introduction to Physics-Informed Neural Networks and how to Solve
Image Registration Problems with WarpPINN
In this talk, I will introduce the idea of Physics-Informed Neural Networks (PINNs) and
the related Deep-Ritz Method, two novel approaches where the deep learning machinery is
employed for solving Partial Differential Equations, PDE-Constrained Optimization
Problems and Inverse Problems with physical constraints.
The application I will show is in cardiac imaging, where the goal is to determine the
deformation field of the heart during the cardiac cycle from magnetic resonance images.
Solving this inverse problem is very useful since allows for assessing cardiac diseases
from non-invasive measurements (a quite challenging task). To solve this problem, we
propose WarpPINN, a physics-informed neural network designed to solve image registration
problems with a hyper-elastic regularizer. The network aims to approximate the
deformation field, then, it takes as input a point in the domain of the reference frame
and some time t, and outputs the new position of the point at the time t. The
physics-informed part comes from the nearly incompressible behavior of the heart during
the cardiac cycle: we want the determinant of the jacobian of the transformation to be
close to 1.
Dan Miles
Title: Encouraging Sparsity and Similarity Across Multiple Covariate-Adjusted
Gaussian Graphical Models
Across various applications, many data sets are high-dimensional in nature,
characterised by an inherent graphical structure, amongst other linear relationships.
These are often represented through a Markovian conditional dependence graph upon a
sparse adjacency matrix, where sparsity describes many zero (insignificant) off-diagonal
elements. Traditional likelihood approaches, relying on arbitrarily large sample sizes,
do not account for sparsity well, thus requiring some form of heuristic or penalty. A
multivariate Gaussian graphical model is a standard choice for continuous data, where a
LASSO one-norm penalty can be employed to shrink the off-diagonal precision matrix
elements. However, a complication arises when the distribution is derived from sparse
covariates, and further, there may be multiple instances of the model, in the form of
adjacent samples, each having their own parameter set. A Fused-LASSO-like penalty is
desired to encourage parameter similarity across such adjacent samples, utilising the
conditional covariate dependence structure as a regression. Fortunately, through a novel
block-matrix formulation, it is shown that the conditional model can be transformed and
penalised through a generalisation of the LASSO one-norm penalty (aptly named the
Generalised LASSO). Results show that the prescribed optimisation offers accurate
shrinkage for varying dimensionality and finite sample size, but increasing this also
demonstrates asymptotic consistency. This presentation aims to outline the theoretical
underpinning behind this novel regression approach, the computational implementation,
and results from simulations undertaken.
Shahzeb Raja Noureen
Title: An Agent-Based Model for Cell Movement Incorporating Swapping Between Cells
Cell migration is frequently modeled using on-lattice agent-based models (ABMs) that
employ the excluded volume interaction. However, cells are also capable of exhibiting
more complex cell-cell interactions, such as adhesion, repulsion, pulling, pushing, and
swapping. Although the first four of these have already been incorporated into
mathematical models for cell migration, swapping has not been well studied in this
context. In this talk, we present an ABM for cell movement in which an active agent can
“swap” its position with another agent in its neighborhood with a given swapping
probability.
Matthew Pawley
Title: Estimating the Probability of Very Rare Events
What is the probability that all stocks in a financial portfolio crash at the same time?
What is the probability that record-breaking temperatures are observed simultaneously at
all locations in a region? These are challenging problems to answer due to the rareness
of the events of interest. This talk will outline a strategy for estimating such
probabilities and, in doing so, provide an overview of various concepts and tools from
extreme value theory.
Timothy Peters
Title: Mathematical Models of Engine Ice Crystal Icing
In the last decade, ice crystal accretion on the interior surfaces of aircraft engines
has been studied. Existing knowledge on the mechanism of ice crystal build-up within the
hot engine core is still limited, although some models have been recently developed. In
this talk, we discuss the derivation and study of a multi-phase mathematical model of
ice and water accretion over a flat plate, subject to a combination of flow and
ice/water flux conditions above the plate. The spatial variation and movement of the
initial water layer is modelled using thin-film equations, which are then coupled with a
transient heat transfer model in order to determine the onset of ice formation. The
effects of the moving- and non-uniform film shapes on the initial formation of the ice
layer, are considered.
Jenny Power
Title: PDE Constrained Optimisation for Brachytherapy Radiation Treatments
Brachytherapy is a cancer treatment where radioactive seeds are surgically implanted
directly onto the tumour and slowly emit radiation, killing the tumour from the inside.
An essential aspect of the radiotherapy treatment process is the planning stage.
Clinicians carefully create treatment plans to ensure the radiation is directed at the
tumour, and not at the healthy tissue as if this is damaged it could cause further
health complications. However, for brachytherapy, clinicians do not have a mechanism to
develop treatment plans. My research seeks to solve this problem mathematically. The
challenge lies in positioning the sources such that the tumour is exposed to the
critical dose, but the healthy tissue is not exposed to excessive radiation. This
problem is formulated as a PDE-constrained optimisation problem. The PDE constraint is
given by a diffusion approximation to the Boltzmann transport equation. A prescribed
dose is assigned to the tumour region such that when the objective function is
minimised, the dose in the tumour matches the prescribed dose and the dose outside of
the tumour is minimised. This problem is solved numerically using a Galerkin finite
element method.
Andrei Sontag
Title: Stochastic drift in discrete waves of nonlocally interacting particles
Many processes of interest in biology such as the modelling of migration, information
dynamics in epidemics, and Muller's ratchet — the irreversible accumulation of
deleterious mutations in an evolving population — can be modelled as a stochastic $N$
particle system undergoing second-order nonlocal interactions on a lattice. Strikingly,
the average of numerous numerical simulations of the stochastic model is observed to
deviate significantly from its corresponding deterministic solution, even for large
population sizes. In this talk, based on our recent work [1], I will show that the
disagreement between deterministic and stochastic solutions stems from finite-size
effects that change the propagation speed and cause the position of the stochastic wave
to fluctuate. These effects are shown to decay anomalously as $(ln N)^{-2}$ and $(ln
N)^{-3}$, respectively—much slower than the usual $N^{-1/2}$ factor. Our results suggest
that the accumulation of deleterious mutations in a Muller's ratchet and the loss of
awareness in a population may occur much faster than predicted by the corresponding
deterministic models. The general applicability of our model suggests that this
unexpected scaling could be important in a wide range of real-world applications.
[1] A. S., T. R., C. A. Y. Physical Review E, vol. 107, no. 1. American Physical Society
(APS), Jan. 18, 2023. doi: 10.1103/physreve.107.014128.
Marcel Stozir
Title: Coupling in the Data-Driven Newsvendor Model
In the Newsvendor Problem a retailer can only observe the number of sales up to the
inventory level but cannot observe any excess demand. This results in a data set of
censored samples of the random demand variable. Based on this data set the decision
maker must make an inventory decision about the inventory level available in the next
period which, in turn, sets the censoring level for the next sample of the demand.
Hence, through her inventory decisions the decision maker directly influences the
quality of new information obtained from interactions with the environment. She is urged
to learn about the unknown distribution of the demand to make more informed decision in
the future but is discouraged from paying too much for additional information. This is
known as the exploration-exploitation trade-off.
In this talk, I will introduce the so-called critical fractile process which is used to
indicate the evolution of the knowledge of the decision maker about the underlying
demand distribution. I will show that we can infer about the location of the critical
fractile from the position of a biased one-dimensional random walk. Based on this
coupling I will derive the asymptotic empirical distribution the decision maker will
learn in case she always chooses the optimal decision based on the available data set at
the time.
Carmen van-de-l'Isle
Title: The Symbiotic Contact Process on Trees
The symbiotic contact process can be thought of as a two type generalisation of the
contact process which can be used to model the spread of two symbiotic diseases. Each
site can either be infected with type A, type B, both, or neither. Infections of either
type at a given site occur at a rate of lambda multiplied by the number of neighbours
infected by that type. Recoveries of either type at a given site occur at rate 1 if only
one type is present, or at a lower rate mu if both types are present, hence the
symbiotic name. Both the contact process and the symbiotic contact process have two
critical infection rates on a Galton-Watson tree, one determining weak survival, and the
other strong survival. Here, weak survival refers to the event where at least one A
infection and at least one B infection is present at all times. Strong survival is the
event that the root of the tree is infected with both A and B infections at the same
time infinitely often. In this talk, I will prove that for small values of mu the weak
critical infection rate for the symbiotic model is strictly smaller than the critical
rate for the contact process. I will also discuss the more complicated case of strong
survival for both processes.
POSTER SESSION
SAMBa abounds in good work and interesting topics, hence, to cram as much of our work as possible into
the two days of this conference, at the end of the first day there will be a poster session. Most of the
creators of the posters will be standing near their posters during this session to answer questions and
explain nuances. The following posters have already been confirmed:
Cecilie Andersen: Exponential Asymptotics for the Saffman-Taylor Problem in a Wedge
Abby Barlow: Epidemiological Dynamics in Neighbourhoods of Households
Sonny Medina Jimenez: Excursions from Hyperplanes for the Alpha-Stable Process
Mehar Motala: Williams' Path Decomposition for Real Self-Similar Markov Processes
Allen Paul: Diffeomorphic Statistical Shape Models
Kat Phillips: Drop Impact: Modelling a Lubrication Air Layer and Surface Waves in Droplet
Rebound Dynamics
Mohammad Sadegh Salehi: Inexact Algorithms for Bilevel Learning
Seb Scott: On Optimal Regularisation Parameters via Bilevel Learning
Jonty Sewell: Analysis of Vorticity Fronts
Beth Stokes: Density Dependent Diffusion in Reaction-Diffusion Systems
The 2023 SAMBa conference is being organised by three SAMBa Cohort 8 PhD students. If you have any
questions, please feel free to contact any of us using the information below.