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2021-22

SPAAM Seminar Series

The Statistics, Probability, Analysis and Applied Mathematics (SPAAM) seminar series will take place on Thursdays between 3-4pm in room B3.02 and virtually on the SPAAM Microsoft Teams channel. It will host a variety of talks from PhD students involved in applied mathematics research at Warwick and invited guests from other institutions (see the bottom of this page for the talk abstracts!).

Each seminar will usually host two speakers (unless otherwise stated) with each talk taking around 15-20 minutes with 5-10 minutes of questions afterwards. Speakers and committee members will hang around for some time after the talks for social tea/coffee and further questions. Please do contact one of the committee if you would like to join and be added to the MS Teams channel. Note that these talks may be recorded for later viewing on our Youtube channelLink opens in a new window so do join with audio and video off if you don't wish to feature!

If you would like to give a talk this term, please contact Matthew Coates (matthew.coates@warwick.ac.uk) or Swetha Usha Lal (swetha.usha-lal@warwick.ac.uk) and we will find you a slot!

Current Talks (Term 3)
Date Talk 1 Talk 2
28th April 2022 (Week 1) TBC TBC
5th May 2022 (Week 2) Olayinka AjayiLink opens in a new window (MathSys) TBC
12th May 2022 (Week 3) TBC
19th May 2022 (Week 4) Melissa IacovidouLink opens in a new window (MathSys)
26th May 2022 (Week 5) Charlie HepburnLink opens in a new window (MathSys) Jack O'ConnorLink opens in a new window (MathSys)
2nd June 2022 (Week 6) Bank Holiday (no talks)
9th June 2022 (Week 7) Social Event
16th June 2022 (Week 8) Jakub TakacLink opens in a new window (Maths)  
23rd June 2022 (Week 9) Alex KayeLink opens in a new window (MathSys)  
30th June 2022 (Week 10) Zak Ogi-GittensLink opens in a new window (MathSys) Byron TzamariasLink opens in a new window (MathSys)

Week 2 - Graph Neural Network, lightweight for Video Representation Learning - Olayinka Ajayi (MathSys)

For Thursday's seminar, I will be discussing a paper related to my research, video representation learning using GNNs. The paper is titled "Learning Skeletal Graph Neural Networks for Hard 3D Pose Estimation" by Zeng et al.. The focus of my research is on human action recognition, which is discussed in later parts of the paper. Below is the abstract of the paper:

Various deep learning techniques have been proposed to solve the single-view 2D-to-3D pose estimation problem. While the average prediction accuracy has been improved significantly over the years, the performance on hard poses with depth ambiguity, self-occlusion, and complex or rare poses is still far from satisfactory. In this work, we target these hard poses and present a novel skeletal GNN learning solution. To be specific, we propose a hop-aware hierarchical channel-squeezing fusion layer to effectively extract relevant information from neighbouring nodes while suppressing undesired noises in GNN learning. In addition, we propose a temporal-aware dynamic graph construction procedure that is robust and effective for 3D pose estimation. Experimental results on the Human3.6M dataset show that our solution achieves 10.3% average prediction accuracy improvement and greatly improves on hard poses over state-of-the-art techniques. We further apply the proposed technique on the skeleton-based action recognition task and also achieve state-of-the-art performance.

Week 4 - Mathematical models of malaria: the effects of insecticide resistance and the importance of age-dependent mortality - Melissa Iacovidou (MathSys)

Abstract TBC.

Week 5 (Talk 1) - Offline Reinforcement Learning - Charlie Hepburn (MathSys)

Deep reinforcement learning (DRL) is the mechanism to infer an optimal decision-making policy using online interactions with a dynamic environment. The field has gained large success in highly complex domains such as Atari, chess and Go. These achievements are largely exclusive to closed-world environments where simulation is cheap. In the real world, there is an abundance of noisy data but collecting new data is both time-consuming and expensive. Offline DRL aims to learn solely from a fixed dataset, finding an optimal decision-making policy in noisy data without active online collection. This talk will overview DRL and describe the issues in the offline setting such as distributional shift. As well as briefly discussing some “solutions” to distributional shift and my current research in this area.

Week 5 (Talk 2) - Zero-knowledge distribution testing - Jack O'Connor (MathSys)

Zero-knowledge proofs are an exciting and very interesting area of study, with many applications focused on online privacy and distributed computing. I will introduce the notion of a zero-knowledge proof (which can be quite slippery at a conceptual level) and the broader idea of an interactive proof, wherein two parties send messages back and forth, one aiming to convince the other of the truth of some statement. These are extremely powerful notions and can be used to prove a wide class of statements. Further, I will discuss my recent work in applying zero-knowledge to distribution testing, where the aim is to prove statements about some unseen distribution, and demonstrate an interesting protocol for achieving this.

Week 8 - Typical behaviour of 1-Lipschitz maps on rectifiable sets - Jakub Takac (Maths)

A set E in a metric space X is called n-rectifiable, if it can be covered, up to set of Hn-measure zero, with Lipschitz images of subsets of Rn. It is called n-purely unrectifiable, if none of its nonzero Hn-measure subsets are rectifiable. We study properties of rectifiable and purely unrectifiable sets E by considering spaces of 1-Lipschitz functions and studying their images. We mainly study rectifiable sets and answer the following question. When is there some ∆ > 0 such that for a typical f as above, one has Hn(f(E)) ≥ ∆.

Week 9 - Modelling vector-borne disease epidemic risks using forward climate projections - Alex Kaye (MathSys)

The effects of climate change are numerous, the obvious being a change in global temperature and with this local climate. Mosquitoes are picky about what climate they inhabit, they like a specific temperature range; not too hot or cold, and they like a specific rainfall range; enough so that breeding sites are available but not so much that larvae are washed away. With a changing climate, mosquito populations will vary globally and will consequently alter their ability to transmit diseases such as dengue, Zika and chikungunya. Using predictions of future climates from the Community Earth System Model we aim to estimate the risk posed by dengue at various spatial locations.

Week 10 (Talk 1) - Modelling the Bird-Flu Outbreak in the UK (2021-22) - Zak Gittins (MathSys)

TBC.

Week 10 (Talk 2) - Optimal control theory on cancer chemotherapy - Byron Tzamarias (MathSys)

The circadian clock, a biochemical oscillator that is synchronized to the day-night cycle, regulates cell division throughout the human body in addition to many other processes. Cancer cells lose the ability to synchronize, or have reduced synchronization, with the diurnal rhythm and follow shifted, perturbed or even arrhythmic cell cycles.

In cancer therapy, drugs that eliminate dividing cells are commonly used. The timing of drug administration, as well as the drug dosage, is crucial for treatment efficacy. In this talk, we will focus on applying optimal control theory to determine efficient therapy strategies, with the aim of minimizing the cancer cell population, whilst limiting the damage to healthy dividing cell. Future directions will also be discussed, namely the development of a payoff formulation, where the efficacy of treatments, is calibrated by evaluating the expected lifetime of a patient, weighted over possible cancer/future outcomes. The advantage of such a payoff is that its parameters have direct physical interpretations and hence can be potentially used in the development of personalized treatments.

Previous Talks (Term 2)
Date Talk 1 Talk 2
13th January 2022 (Week 1) Yijie ZhouLink opens in a new window (MathSys)  
20th January 2022 (Week 2) Abi ColemanLink opens in a new window (MathSys)  
27th January 2022 (Week 3) Social event - board games in the maths common room!
3rd February 2022 (Week 4) Francesca BasiniLink opens in a new window (MathSys) Connah JohnsonLink opens in a new window (MathSys)
10th February 2022 (Week 5) Social event - board games in the maths common room!
17th February 2022 (Week 6) Talk: Publishing papers (Dr Ed BrambleyLink opens in a new window)
24th February 2022 (Week 7) Social event - board games in the maths common room!
3rd March 2022 (Week 8) Kamran PentlandLink opens in a new window (MathSys)
10th March 2022 (Week 9) Andrew RoutLink opens in a new window (Maths) Haoran NiLink opens in a new window (MathSys)
17th March 2022 (Week 10) Melissa IacovidouLink opens in a new window (MathSys)  

Week 1 (Talk 1) - Trophic analysis on input output datasets: From food chain to economics network - Yijie Zhou (MathSys)

This study aims to understand the position of economic sectors and regional supplier-buyer relationships between countries by studying the flow of goods within the production network built from the World Input-Output Table. We use the newly improved version of trophic levels and related concept trophic incoherence to investigate the flow structure of the production network. We present the trophic structures of different scales and their time evolution. In addition, understanding the cycles structure within the network helps the study of economic growth and shock propagation. Further using the trophic levels, we decompose the original network into the circular flow and potential flow. The Circular flow extracts the cycle structure from the original network. With the circular part, we find important economic clusters using flow-based community detection techniques.

Week 2 (Talk 1) - Modelling the Spread of Disease in Bees - Abi Coleman (MathSys)

Varroa destructor is a pervasive mite which is capable of decimating bee populations. Varroa has spread across the world to everywhere European Honeybees are kept except Australia, through the importation of infected equipment or plants. As Varroa is so pervasive, understanding how it spreads is key to its control. In this talk, we'll explore a method for modelling the spread of varroa and fitting the model to the available data as well as the problems that arise from this.

Week 4 (Talk 1) - Improving the Linear Noise Approximation method with applications in developmental biology - Francesca Basini (MathSys)

With the increase in complexity and size of data related to embryonic development, the need for mathematical methods able to describe these phenomena is becoming more and more urgent. We focus on new mathematical approaches that simplify the study of complex developmental processes by formalizing Waddington's landscape metaphor into a rigorous mathematical framework. Making use of catastrophe theory, we select the best qualitative model for the differentiation of stem cells into their fates, i.e. their cell types. In the talk, we will discuss the problems encountered when fitting the stochastic version of the system to real data and suggest a method, based on the Linear Noise Approximation, to overcome them.

Week 4 (Talk 2) - Modelling environmental-metabolic feedback in spatially distributed bio-films - Connah Johnson (MathSys)

Biofilms are ubiquitous in medical settings. They can contain multiple distinct bacterial strains which complicate the task of tackling infections. Additionally, excretion of protective enzymes by bacteria within biofilms can inhibit the effects of anti-bacterials, providing regions wherein resistant strains may proliferate. It has been shown that within biofilms cross feeding between different cell types or species can support strains who would otherwise starve under substrate removal. These findings show that building a better understanding of biofilms and the dynamics within them will pay dividends in understanding bacterial infections. We seek to understand biofilm systems through mathematical modelling using our hybrid modelling platform ChemChaste. ChemChaste has been developed with the aim of modelling realistic chemical dynamics and the chemical interactions between cells via their microenvironment. Here, biofilms are modelled through coupling multiple reaction-diffusion systems to a population of individual cell agents. The cells each have their own metabolic models encoding different cell types. They can interact through the excretion and uptake of chemicals in the shared film environment. The spatial distribution of these cells and their behaviours is investigated under a range of metabolic processes and phenomena. Therein providing insights into the complex dynamics that may suggest clinical applications.

Week 6 (Public talk) - The paper mill: a short tour of scientific journal publication - Dr Ed BrambleyLink opens in a new window

Ed is a researcher who has published some papers. He is also on the editorial board of the journal "Wave Motion". In this informal talk, he will give a brief tour of the paper mill, attempting to cover:
- Writing a journal paper
- Choosing a journal
- The path from submission to publication
- Writing reviews
- Responding to referees
- What to do when a paper is rejected
- What to do when a paper is accepted
- Paying for publications

Week 8 - GParareal: a time-parallel ODE solver using Gaussian process emulation - Kamran Pentland (MathSys)

Sequential numerical methods for integrating initial value problems (IVPs) can be prohibitively expensive when high numerical accuracy is required over the entire interval of integration. One remedy is to integrate in a parallel fashion, "predicting" the solution serially using a cheap (coarse) solver and "correcting" these values using an expensive (fine) solver that runs in parallel on a number of temporal subintervals. In this work, we propose a time-parallel algorithm (GParareal) that solves IVPs by modelling the correction term, i.e. the difference between fine and coarse solutions, using a Gaussian process emulator. This approach compares favourably with the classic parareal algorithm and we demonstrate, on a number of IVPs, that GParareal can converge in fewer iterations than parareal, leading to an increase in parallel speed-up. GParareal also manages to locate solutions to certain IVPs where parareal fails and has the additional advantage of being able to use archives of legacy solutions, e.g. solutions from prior runs of the IVP for different initial conditions, to further accelerate convergence of the method - something that existing time-parallel methods do not do.

Week 9 (Talk 1) - Probabilistic approaches to Well-Posedness of PDEs - Andrew Rout (Maths)

In general, PDEs are well-posed for high regularity initial data, and ill-posed for sufficiently rough data. A natural question is, given a random piece of initial data, what is the probability that a problem will have a solution? We explore this problem by summarising the construction of Gibbs measures for the 1D nonlinear Schrödinger equation given in Jean Bourgain’s 1994 paper “Periodic Nonlinear Schrödinger Equation and Invariant Measures.”

Week 9 (Talk 2) - Demystifying k-th Nearest Neighbor Estimators - Haoran Ni (MathSys)

The Mutual Information (MI) between two random variables measures the reduction in uncertainty of one random quantity due to information obtained from the other. It is an important information-theoretic concept, closely related to Entropy, that plays a role in many applications, including decision trees in machine learning, independent component analysis (ICA), gene detection and expression, link prediction, topic discovery, image registration, feature selection and transformations, and channel capacity.

Previous Talks (Term 1)
Date Talk 1 Talk 2
21st October 2021 (Week 3) Yiming MaLink opens in a new window (MathSys) Jimmy McKendrickLink opens in a new window (MathSys)
28th October 2021 (Week 4) Rafal SzlendakLink opens in a new window (Maths)
4th November 2021 (Week 5) Social event
11th November 2021 (Week 6) Jack BaraLink opens in a new window (MathSys) Charlie PilgrimLink opens in a new window (MathSys)
18th November 2021 (Week 7) Matthew CoatesLink opens in a new window (MASDOC)
25th November 2021 (Week 8) Giorgos VasdekisLink opens in a new window (Stats)
2nd December 2021 (Week 9) Social event
9th December 2021 (Week 10) David ItkinLink opens in a new window (Carnegie Mellon) Matthew KingLink opens in a new window (MASDOC)

Week 3 (Talk 1) - Introduction to MobileNets - Yiming Ma (MathSys)

Convolutional neural networks have been prosperous for years in the field of computer vision. However, most of them achieve better performance by leveraging extremely complex architectures. Although leaderboards might have been swept by hundreds of this type of models, none of them has real application values – they cannot be implemented in mobile devices due to their gigantic sizes. Thus, studying efficient models is of crucial importance. In this talk, the family of MobileNets, which are both accurate and lightweight, will be introduced.

Week 3 (Talk 2) - Modelling the Seasonality in Lassa Fever Cases in Nigeria  - Jimmy McKendrick (MathSys)

Recent Lassa Fever epidemics in Nigeria have been following a seasonal pattern in cases. Using vector models, and Approximate Bayesian Computation I attempt to discern what the seasonal drivers of the disease are.

Week 4 - Permutation Compressors for Provably Faster Distributed Nonconvex Optimisation - Rafal Szlendak (Maths)

We study the MARINA method of Goerbunov et al., (2020) – the currentstate-of-the-art distributed non-convex optimization method in terms of theoretical communication complexity. Theoretical superiority of this method canbe largely attributed to two sources: the use of a carefully engineered biased stochastic gradient estimator, which leads to a reduction in the number of communication rounds, and the reliance on independent stochastic communication compression operators, which leads to a reduction in the number of transmitted bits within each communication round. In this paper we i) extend the theory of MARINA to support a much wider class of potentially correlated compressors, extending the reach of the method beyond the classical independent compressors setting, ii) show that a new quantity, for which we coin the name Hessian variance, allows us to significantly refine the original analysis of MARINA without any additional assumptions, and iii) identify a special class of correlated com-pressors based on the idea of random permutations, for which we coin the term PermK, the use of which leads to O(√n) (resp. O(1 +d/√n)) improvement in the theoretical communication complexity of MARINA in the low Hessian variance regime when d≥n (resp. d≤n), where n is the number of workers and d is the number of parameters describing the model we are learning. We corroborate our theoretical results with carefully engineered synthetic experiments with minimizing the average of nonconvex quadratics, and on autoencoder training with the MNIST dataset.

Week 6 (Talk 1) - Cooperation in Dynamic Networks - Jack Bara (MathSys)

To tackle large (global) issues such as climate change requires cooperation at multiple scales, from individuals choosing to recycle to international trade. When agents act negatively, they may be punished by mutual defection or unilaterally burning bridges. In my talk I will give some insights and results on cooperative games occurring on dynamic networks; namely what networks tend to form from the coevolutionary process and the importance of timescales.

Week 6 (Talk 2) - Information foraging in the attention economy drives the rising entropy of English - Charlie Pilgrim (MathSys)

Over the past 200 years there have been continual advances in communications technology, characterised by increasing ease of access to ever more abundant sources of information. In the face of this abundance, people choose which information to consume and which to ignore. Media producers need attention to survive and so must adapt to this selective pressure, creating a feedback process of co-evolution similar to that seen in many ecosystems. Here, we explore a model that describes this dynamic, and show how the model outcomes agree with empirical evidence of rising word entropy in English.

Week 7 - Constructing Reduced Order Models of the Lithium Ion Cell - Matthew Coates (MASDOC)

The modelling of rechargeable battery cells, and in particular lithium ion cells, is of increasing industrial importance due to increased demand for products like electric vehicles and increased need for systems for energy storage. Key to the efficient operation of such batteries is effective modelling, in particular there is a need for reduced order models, relatively simple models of the cell that can be used to perform calculations in real time. We review some methods of constructing such real time models, and discuss questions of accuracy and improvement.

Week 8 - Piecewise Deterministic Markov Chain Monte Carlo and the Speed Up Zig-Zag sampler - Giorgos Vasdekis (Stats)

Piecewise Deterministic Markov Processes (PDMPs) have recently drawn the attention of the Markov Chain Monte Carlo (MCMC) community. The main reason is that these processes have a natural notion of momentum, which sometimes leads to better exploration of the state space and faster mixing. In the first half of this talk, we will give an introduction on how one can use these processes in MCMC. We will introduce the state of the art PDMP algorithms and we will present some interesting properties they have that can make them useful tools in computational Bayesian statistics. In the second half of this talk, we will introduce a new PDMP algorithm called the Speed Up Zig-Zag sampler, we will study its properties and explain why it can be efficiently used to target heavy tailed distributions.

Week 10 (Talk 1) - Growth Optimization in Stochastic Portfolio Theory - David Itkin (Carnegie Mellon)

Stochastic Portfolio Theory is a framework introduced by R. Fernholz to study equity markets. In this talk we will examine an investors growth optimization problem in this framework and develop a tractable setup for it. An emphasis will be placed on our recent results in robust finance and in open markets (i.e. one where the investor is constrained to invest in high capitalization stocks). Possible future research directions will be discussed as well. This is based on joint work with Martin Larsson.

Week 10 (Talk 2) - Duct acoustics and using branch cuts to hide singularities - Matthew King (MASDOC)

In duct acoustics the sound field can be described as the sum of pole residues from a Fourier Inversion. Often ignored however is a branch cut. In this talk I will be discussing how this branch cut arises, how it can be treated within the Fourier Inversion, and observations that can be made about the validity of not including its contribution. Further, it will be observed that this branch cut can interact with poles and how this may be of importance to the wider field of study.