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WELCOME & INFORMATION
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
Travel information for getting to the University of Bath campus can be found on the University of Bath Travel Advice page.
REGISTRATION
CONFERENCE SCHEDULE
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.
- Title: From Maths to YouTube - my journey in science communication
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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.
- Title: Flow and transport in the human placenta
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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.
- Title: Deep Gaussian processes: theory and applications
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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.
- Title: The Turing bifurcation isn't (always) a pitchfork
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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.
- Title: Speed of biased random walk on dynamical percolation
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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
- Title: High Accuracy Algorithms for Quantum Spin Dynamics and Control
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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.
- Title: Coexistence in the Chase-Escape Process: First Passage Percolation with Two Competing Types
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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.
- Title: A Brief Introduction to Physics-Informed Neural Networks and how to Solve Image Registration Problems with WarpPINN
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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.
- Title: Encouraging Sparsity and Similarity Across Multiple Covariate-Adjusted Gaussian Graphical Models
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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.
- Title: An Agent-Based Model for Cell Movement Incorporating Swapping Between Cells
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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.
- Title: Estimating the Probability of Very Rare Events
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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.
- Title: Mathematical Models of Engine Ice Crystal Icing
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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.
- Title: PDE Constrained Optimisation for Brachytherapy Radiation Treatments
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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.
- Title: Stochastic drift in discrete waves of nonlocally interacting particles
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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.
- Title: Coupling in the Data-Driven Newsvendor Model
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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.
- Title: The Symbiotic Contact Process on Trees
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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
- Fraser Waters: Minimal reaction schemes exhibiting Turing instabilities
ORGANISERS
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.
Wilfred Armfield
Aminat Yetunde Saula
