PGR talks

Since the release of Bitcoin in 2009, cryptocurrency markets have been quickly evolving with their market capitalisation reaching even $3 trillion U.S. dollars. These markets are seen as volatile, speculative, prone to manipulation and lacking intrinsic value. Therefore, regulators all over the world are trying to protect their investors by regulating or cracking down on cryptocurrencies at various levels of severity. The UK’s FCA ban on crypto derivatives for retail investors is only one example of such restrictions. Excluding a group of traders from the derivatives markets could have altered the information content of the prices. With cryptocurrencies being traded on many markets, it is crucial to know where the information incorporated into prices originates from, and whether it has been affected by the action. As a result, this talk will introduce the concept of price discovery together with the relevant literature. It will demonstrate more and less established methods for analysing it. Finally, it will reveal the leading Bitcoin markets from among four spot and two futures markets.

In this talk, I will first introduce the concept of financial contagion and explain why network analysis is crucial in modelling it, based on a literature review conducted through a systematic search of the topic. I will then focus on a case study of the recent 2023 banking crisis, particularly emphasising how the collapse of SVB (Silicon Valley Bank) changes the network dynamics of the US Tech Industry. We combine LASSOed VAR (Vector Autoregressive) and network analysis to examine both static and dynamic volatility risk contagion among 30 tech companies in the US before and after the SVB collapse. We found that the TCI (Total Connectedness Index) shows a downward trend, which indicates the contagion risk decreased after the SVB collapse. Furthermore, we discovered the density of the network dropped and highlighted the key player and the risk transmission path within this network. These results offer insights for different stakeholders to mitigate the risk associated with such failures.

In this talk, we consider the NP-hard problem of finding fixed-length paths in edge-weighted graphs. That is, we want to find a path (a sequence of vertices and edges where they can appear in the path at most once) in a network from one point to another where the total length of the path, in terms of the sum of its edge weights, is as close to possible as some prescribed length k. A particular application of interest is that of exercise. A street network can be conceptualised as a graph, where intersections and dead ends act as vertices, and roads as edges. Designing a workout route for activities like walking, running, or cycling, involves determining a path from a starting point to a destination within a specified number of steps, calories to be burned, or distance to cover. The selection of criteria, such as steps, calories, or distance, would define the weights assigned to the edges, making the task akin to identifying a path of a fixed length. Routing services are a feasible option for finding a solution, although they usually focus on routes with minimum length (weight) rather than a specific length.

Quantum computing is a research field which uses the study of quantum theory to do calculations. The motivation for expanding this area of study was first projected by physicist Richard Feynman, who found classical computers were not efficient enough to deal with the calculations he was producing through his own developments of quantum mechanics. My research focuses on the construction of algebras we use to work with particles in the systems which arise from quantum mechanics, with a view to advance topological quantum computing. In this talk, I will begin by introducing particle physics with the assumption of no prior knowledge, and endeavour to communicate the complex world of quantum physics in the most welcoming manner I can manage.

Successfully forecasting stock returns has a clear benefit for investors. However, there is significant debate about the effectiveness of signals commonly used for forecasting, and conventional economic theory suggests that opportunities to profit from forecasting are rare. Despite these considerations, publications have shown evidence that machine learning models perform well at this task. My current research aims to address this discrepancy. I am assessing a recently published novel machine-learning forecasting model to determine if the results hold up under scrutiny. This talk introduces the financial background of my research before diving into the methodology of assessing the predictive power and profitability of the forecasting model under investigation.

In many competitions a set of point assignments is used to determine a winner, with the winning candidate being the one with the highest score. When it comes to revealing the result to an audience, some competitions proceed by having a roll call where each voter announces their vote in turn. This is done for entertainment purposes, raising the question: Which ordering of the voters should be chosen to maximise the entertainment value of the roll call? In this talk, I present a formal definition for the Score Reveal Problem, some background on entertainment theory, and a framework of entertainment measures that can be used to find entertaining permutations.

In this talk, I will explore the stability of various geometric inequalities. To start, I will define what I mean by geometric inequalities. Then, I will explain the concept of stability in this context and how such a problem is framed mathematically. I will discuss some techniques used to analyse such stability questions and share some of my own results in this area.

Medication non-adherence is a global public health concern, especially among older adults. There is an opportunity for the robots to help the older adults with this problem. My PhD research is about exploring the potential for the social robots to help older adults with their medication management in their home settings. For this, I have conducted two studies. First to understand the perspective of older adults and their caregivers about keeping the robots in their home settings. Second to explore if the social robots will be acceptable by the older adults in the other cultural settings e.g., Global South. In this talk, I will provide a succinct overview of these studies and the future of robots in this area.

Algebraic geometry is the study of geometric objects which can (locally) be described as the zero locus of a collection of polynomials. One can make us of the algebra to determine whether or not two (or more) geometric objects intersect, but the algebra can actually tell us much more, for instance the multiplicity with which the objects intersect. In this talk, I will attempt to give a brief account of my research in this area and the history of intersection multiplicities.

Reproductive value is the relative expected number of offspring produced by an individual in its remaining lifetime. For time-homogeneous population models, there are two existing methods for obtaining the reproductive value function: Perron-Frobenius (PF) method and renewal method. The PF method proceeds by looking for an invariant function or an eigenvector and the renewal method proceeds by fixing a type (state of an individual) and counting the number of offspring collected there. Both methods fail for time inhomogeneous population models (those with time dependent parameters), therefore other methods are needed to compute the reproductive value in that case. Towards that goal, we present two new characterizations of this function: for a general class of critical age-structured population models, we show that the asymptotic ratio of the survival probabilities, from different initial states, is equal to the initial ratio of reproductive values, and that in relation to a specific coupling of the size-biased model, both are equal to the limit of the inverse ratio of total reproductive values.

To provide context and background, we also discuss two defining properties of reproductive value, namely time-invariance in deterministic models and the martingale property in stochastic models, for some commonly used models. These findings contribute to a deeper understanding of reproductive value functions and their implications in critical population models.

How and why a human factors cyber security specialist and artsy web developer found themselves researching low level technical industrial control systems security and learning to code in C++

A brief introduction into the areas of creativity, ✨open endedness✨, and whether computers can solve computers in the same way humans can.

Events that have a significant impact on an organisation or on the environment, and are usually rare, but as a consequence, data on events tends to be scarce. In this talk, we will try to tackle the challenge of events using AI.

This research talk offers a holistic exploration of d/Deaf accessibility in television and film. Shedding light on the unique perspectives and challenges faced by d/Deaf and hard of hearing individuals when consuming media. Delving into the limitations and nuances of captioning, highlighting the complexities in providing accurate and synchronized text as well as the role of sign language in making content accessible. This presentation also explores strategies for representing auditory information in a non-audiotory format, providing a more immersive experience for d/Deaf viewers. This talk aims to provide perspective on enhancing inclusivity in the realm of television and film.

Category theory is a powerful tool in mathematics, that can be used to describe many, and sometimes rather different, areas of mathematics in one universal language. In mathematical physics, there are many ways to relate quantum field theories to particular types of categories. My research focuses on how we can use objects in these categories (called algebras) to solve classification problems in the corresponding field theories. In this talk, I will explain the general approach to this problem, and talk through how this can be solved using network graphs in some simple cases.

Starting your PhD is an exciting time, filled with new experiences and opportunities, but casting yourself into the great unknown of postgraduate study can be daunting! Fortunately, you don’t have to do it alone; this talk, given by a group of PhD students in the later stages of their programmes, will share some of the knowledge and experience we have gained over the years, telling you the things we wish we knew when we were just starting. We will cover a wide range of topics, including admin, networking and conferences, important software and looking after your mental health.

This talk is open to students from both Maths and Computer Science, and we encourage the participation of students from all stages of study. This session will be informal, so we welcome discussion within the audience to ensure no question goes unanswered (except ‘When are you submitting your thesis?’).

What are the behavioural dynamics that emerge at the interface of emergency departments (EDs) and ambulance services? What is the impact of time-target policies, and how does it affect staff behaviour and patient well-being? This research focuses on building a queueing theoretic model to represent an ED that accepts two types of patients: ambulance patients and other patients. Consequently, a game theoretic model is presented to explore the behavioural gaming that takes place when three players (two EDs and an ambulance service) interact with each other. Evolutionary learning algorithms are used to explore the behaviours that emerge in such a scenario. In particular, the behaviour that naturally emerges from the game seems to be one that causes more blockage and includes less cooperation. Several ways to escape these learned inefficient behaviours are explored and discussed. The results of this research can be used to inform policy makers about the impact of time-target policies on the behaviour of EDs and ambulance services, and to suggest ways to improve the efficiency of the system.

Writing a talk is an experience common to all PhD students. It’s easy to sink hours into making the perfect slides, optimising the script and practising until you can rehearse it in your sleep, but is there a better way? A great minimalist philosopher once said `the more that you say, the less I know’ [1], leading us to consider an alternative, more simple strategy, showcased in this talk.

As if volunteering to give an additional talk wasn’t suffering enough, Josh and Tim have decided to add additional constraints to the typical seminar writing process: we won’t know what the talk is about until an hour before it happens. The objective of this talk is to explore good practice in fast, efficient and effective slide creation and presentation, but it could alternatively be a monumental dumpster fire, which should be entertaining. Either way, you should come to this talk, if not only to justify having biscuits afterwards.

References

[1] Willow, Taylor Swift, evermore, 2020

The use of machine learning (ML) in threat detection has gained significant attention in recent years due to its ability to improve the accuracy and speed of detecting malicious activities. However, the deployment of ML models on resource-constrained devices, such as IoT devices and microcontrollers, poses significant challenges due to the limited computational resources and energy constraints.

The potential for bringing security to these resource-constrained devices through the use of ML, which has traditionally been located only on a centralized device, is enormous. This traditional approach has led to a single point of failure and reliance on external devices for security, leading to large-scale botnets used for malicious attacks.

There are approximately 2 million people with sight loss in the UK, yet few people with low vision visit museums due to the inconsistent and incomplete strategies implemented to accommodate them. Existing accessibility solutions in museums focus on non-visual senses, and there is little technology to enhance the visual aspects of artworks for people with low vision. Image enhancement techniques can improve visual tasks, but it is unclear how effective they would be in museums and galleries. This presentation describes three focus groups conducted with 18 people with low vision from the UK who have experience viewing art in museums. The participants commented on visual problems in museums and gave suggestions for enhancing the visual aspects of artworks. The analysis identified several themes, including environmental challenges, the importance of colour and contrast, support from people and technology, appreciation for tactile options, and design considerations for Head Mounted Displays (HMDs) and Augmented Reality (AR) solutions. The presentation concludes by discussing how these findings can inform the design of HMDs for people with low vision in museums to enhance the visual aspects of artworks.

Following the disruption caused by COVID-19, the NHS is struggling with a backlog of patients and growing elective waiting lists, which is currently the case at Cardiff and Vale University Health Board. The Trauma & Orthopaedics specialty is especially under pressure with high demand for elective surgery driven by both the unprecedented backlog size and ageing population. I’ll present the key results of my systematic review into operational research methods applied to orthopaedic settings and treatments. I have further developed a discrete-event simulation that models patient flows through a holistic orthopaedic surgical pathway, enabling hospital staff to make more informed decisions on demand and capacity planning. Furthermore, I discuss plans to combine the discrete-event simulation with a system dynamics model to assess the inflows from Primary care and the community, and to incorporate into the simulation patient deterioration whilst on the waitlists.

Viscoelastic fluids are a type of Non-Newtonian fluid that deform according to elasticity as well as viscosity. They are ubiquitous in natural and engineering processes so being able to simulate them computationally is of high importance. In my talk I will take particular focus on multiphase flows, where we have two fluids (gaseous and viscoelastic) and define an interface between them. In addition, I will introduce the power of exploiting symmetry to obtain physically 3D results from 2D simulations. Using these broad aspects of computational fluid dynamics I will introduce my mathematical model for simulating these types of flows, with particular focus on rising gas bubble dynamics, where multiple interesting phenomena are presented.

In this talk I will be your guide through the wonderful world of category theory, cohomology theories, and characteristic classes. My research has been focused on a certain map of spaces called the Weyl map which can be defined for any Lie group as it is dependent on something known as a maximal torus but we will deal only with the family of special unitary groups, and how it is transformed by composition with a map derived from exponential functors, functors from the category of isomorphism classes of vector spaces to itself that turn the direct sum into the tensor product, hence the name.

From any strict symmetric monoidal category (examples of which include the skeleton of the source and target categories of an exponential functor) one may construct a cohomology theory. Both of our categories result in cohomology theories that are closely related to K-theory where we can decompose the class of the Weyl map into easy to digest chunks, and then we can use a certain characteristic class to build natural transformations of cohomology theories that take our exotic cohomology theories back into the far more manageable ordinary cohomology with rational coefficients.

Bonus Round: An introductory talk on an important result in homological algebra. Short exact sequences induce long exact sequences of homology groups via two applications of the Snake Lemma.

In high-dimensional spaces, classical statistical methods often break down for theoretical reasons such as matrix non-invertibility or ill-conditioning. A standard approach to resolving this issue is to reduce the dimension (p) of the data by projecting it onto a d-dimensional (d < p) manifold in some optimal way. Principal Components Analysis (PCA), for example, seeks the subspace spanned by the first d normalised eigenvectors of the covariance matrix of the variables (the matrix whose ijth entry is given by the covariance of the i^th and j^th variables). It is optimal in the sense that the i^th normalised eigenvector maximises the variance of the dot product of some normalised vector with the random variable corresponding to the data, subject to the normalised vector being orthogonal to the previous solutions to the optimisation problem. In a regression context, PCA is often applied to the predictor variable X (which takes values in R^p) before then using the components of its projection in regression for some response variable Y (taking values in R) which we are interested in predicting. The fundamental issue with such an approach, and other unsupervised dimension reduction procedures such as t-SNE and Locally Linear Embedding, is that the components are not guaranteed to retain the predictive power for Y that X has (because Y is not used in the derivation). It is natural then to devise supervised dimension reduction methods, using both X and Y, which have this desired property. The purpose of this talk is to overview a framework, called Sufficient Dimension Reduction (SDR), for a class of such methods. The talk will cover the basic concepts when X is multivariate and Y is univariate, it will cover two of the earlier techniques for this situation which seek linear subspaces, and - time permitting - it will cover a modern measure-theoretic definition of SDR which allows for X and Y to be more general objects and which allows for nonlinear approaches. If, after that, time still permits then there will be a discussion of SDR methods, including one of my own, which are capable of handling when a categorical predictor W is present in addition to X.

Developing biological systems can self-organise to produce complex, diverse and robust patterns of cellular behaviour from relatively simple rules, with examples in animal coat patterns and limb generation during embryo development. In this talk, I will introduce the general concepts of modelling pattern formation in mathematical biology. Then motivated by mammary tissue development, I will discuss how graphs can be used to model pattern formation in systems with distinct cellular identity and polarity (anisotropic cell-cell communication). Using these graphical methods combined with imaging data, we will assess how local tissue geometry influences the amount of polarity required to maintain patterns needed for the healthy development of breast tissue. No knowledge of cellular biology is assumed!

Ageing is one of the most common and well-known risk factors for most chronic diseases, putting an increasing pressure on healthcare resources. We have utilised a variety of predictive modelling techniques, including classification and regression trees, to determine homogeneous clusters of patient attributes. By incorporating the associated length of stay distributions into deterministic and two-stage stochastic models, we provide novel insights for capacity planning of hospital beds and staffing requirements. This talk will discuss a case study of frail and elderly patients attending hospitals within South East Wales. This approach highlights how applying two healthcare analytical paradigms can be useful for decision makers to capture the stochastic nature of healthcare and make more robust strategic planning decisions.

Kernel matrices appear in a variety of machine learning problems, such as kernel support vector machines and kernel principal component analysis. In large-scale problems, it is often too computationally expensive to diagonalise these matrices, so in practice, low-rank approximations are desirable. We describe the Nyström method for low-rank approximations of SPSD matrices, and discuss efficient sequential sampling strategies based on the notion of squared-kernel discrepancy.

In a previous talk, I discussed a type of Neural Network called a Concept Bottleneck Model (CBM) which first maps raw input(s) to a vector of human-defined concepts, before using this vector to predict a final classification. With this model we may expect concepts to map to distinct regions of the input but, as shown, that was not the case. Today’s talk will be an updated look at CBMs and how we can train the model to work as we intend, with concepts predicted based on the presence or non-presence of them in an input image.

The talk will start with a recap of the previous talk before moving on to our recent developments and ending with a live demo. Knowledge of the previous talk is not required to understand this talk.

Algebraic geometry is the study of geometric objects which can (locally) be described as the zero locus of a collection of polynomials. One can make us of the algebra to determine whether or not two (or more) geometric objects intersect, but the algebra can actually tell us much more, for instance the multiplicity with which the objects intersect. In this talk, I will attempt to give a brief account of my research in this area and the history of intersection multiplicities.

Starting your PhD is an exciting time, filled with new experiences and opportunities, but casting yourself into the great unknown of postgraduate study can be daunting! Fortunately, you don’t have to do it alone; this talk, given by a group of PhD students in the later stages of their programmes, will share some of the knowledge and experience we have gained over the years, telling you the things we wish we knew when we were just starting. We will cover a wide range of topics, including admin, networking and conferences, important software and looking after your mental health.

This talk is open to students from both Maths and Computer Science, and we encourage the participation of students from all stages of study. This session will be informal, so we welcome discussion within the audience to ensure no question goes unanswered (except ‘When are you submitting your thesis?’).

In many elections or competitions, a set of voters will either rank a set of candidates from best to worst or will give scores to some of the candidates, with the winner then being the candidate that gets the highest total number of points. When it comes to revealing the result after all votes have been cast, some competitions proceed by having a roll-call of all the voters in which each announces their votes. This is often done for entertainment purposes (e.g., the Eurovision Song Contest), raising the question: Which ordering of voters should be chosen to maximise the entertainment value of the roll-call?

Extreme events, such as environmental hazards, network failure, extreme price movements, disease outbreaks, can have a severe impact on the stability of our environment, infrastructure, health and economic systems and affect our personal lives in many ways. Typically these are rare events in data. Lots of situations require a better understanding of the likely nature of future extreme events (e.g. frequency and magnitude), which informs adaptation, mitigation and critical safety measures. Statistical analysis for these events is highly non-standard and difficult; however some theoretically-backed principles known under the term extreme value theory (EVT) have arisen to guide the tail extrapolation from data closest to the risky regions of interest. In this talk, I will give an introduction to basic ideas at the heart of EVT and point out some of the challenges in dependence modelling that we aim to address.

With humans and machines working ever closer together additional capabilities are required to aid the integration of the separate agents to make the overall team more productive. Humans are known to build mental models of their environment but current neural network solutions are not guaranteed to learn human-understandable solutions to tasks and due to their “black box” nature a human may face difficulties building an accurate mental model of the agent possibly resulting in unjustified trust. This talk will discuss a type of model which aims at improving human-machine interaction and if it can aid a human to create a mental model of the neural network based agent.

Multiphase flows are ubiquitous in nature and understanding their dynamics is crucial in many natural and industrial scenarios. The level set method, invented in 1988 by Osher and Sethian provides a way of simulating two-phase flow by implicitly defining an interface as the zero-contour of a signed distance function. We will discuss why it is so beneficial to define fluid interfaces implicitly, how the level-set function is transported in a velocity field and how we can maintain the desirable properties of the signed distance function during advection. We will also describe the application of the level set method to my research area, the modelling of rising gas bubbles in viscoelastic fluids, and the phenomena associated with them. These include the trailing cusp shape, negative wake velocity field and velocity jump discontinuity

Dominating sets can be used in many applications of graph theory as a means to reach every vertex as efficiently as possible. Usually, we only try to minimize the size of such a set, but if every vertex also has an associated weight, or cost, what methods can we use to optimize a dominating set both in terms of size and weight?

My thesis stems from a simple question: given the set {0,1,2,…,N-1}, can you find two other sets, A and B, such that you have A+B={0,1,2,…,N-1} so that each term occurs only once each? Indeed, you can! (If you couldn’t, my thesis would be fairly short for sure) A few natural questions might be; can you find 3 sets that sum to make this set? Can you find 10 sets? What connects these sets? Can you do subtraction? All shall be revealed in this talk!

Can Linked Data Observatory be developed to answer questions and predict events to support bioscience/wildlife research studies and conservation activities in-the-wild? Approaches to tackling poaching with Apps, Internet of Things, and humans in the loop.

In this talk I will define the braid group and discuss its relevance to topological quantum computing. I then discuss a deformation of the Braid group called the BMW algebra and represent this using R-matrices (matrices that satisfy the Yang-Baxter equation). I go on to generalise the constant restrictions of this representation to develop a class of matrices dubbed the “contractive R-matrices”. Finally, time-permitting I will briefly delve into properties & examples of these contractive R-matrices.

A computation model to predict well-being trade-off choices.

Do YOU think that democracy and free thought is being torn to pieces by the rise of extremism on the internet? Then this talk is for you!

We will look at what political bias is and whether it’s inherently bad, as well as how modern NLP techniques can help us to determine political bias in news content, and how we can put this bias rating into context to provide readers with methods to evaluate and contextualise their information.

We will also take a look at how to make machine learning models like this useable by the general public, using Flask APIs and React.

This talk will give a brief overview of how to make an awesome package in python, starting with how to create a basic package and how to make it publicly available and then extending it to make it awesome. Making a package awesome refers to adding documentation, tests, and automation to the package. These are powerful concepts that can be extended to projects beyond python.

The creation of synthetic data is increasingly important in a range of applications for example to increase dataset volume or to anonymise sensitive datasets. However, missing data in datasets is common, and is an issue for data analysis as calculations cannot be performed with missing data. There is thus a need for data synthesis methods capable of using datasets with missing data.

To achieve this, we propose a novel Generative Adversarial Model, or GAN algorithm, that creates synthetic data from datasets with missing values …..

Group theory is the mathematical study of symmetry and is ubiquitous across the entire spectrum of mathematics. Simple groups play a similar role in group theory to prime numbers in the integers, they form a kind of “building block” that every group is made from. Classifying finite simple groups was a titanic effort undertaken in the 20th century, whose completion took hundreds of authors, over 10,000 pages worth of proof, and forms one of the greatest mathematical achievements of the last hundred years.
I will give a brief overview of group theory and define simple groups, in order to state the classification theorem and give a short history of the proof. Out of the classification theorem arises the Monster, the largest sporadic finite simple group, whose study I will also discuss.

Differential Dynamic Microscopy (DDM) is a recent advance on previous Dynamic Light Scattering (DLS) techniques designed to extract statistical motility parameters from objects suspended in fluids. DDM is emerging at the forefront of statistical image analysis for a variety of problems, characterising Brownian motion, bacterial motility and Spermatozoa movement with high accuracy, and is robust to a many of the issues that arise in image processing such as noise and problematic parameter initialisation.

However, DDM is limited in its scope by its reliance on key assumptions about system dynamics being ergodic and isotropic. These assumptions are, in practice, frequently violated, occasionally without the user being aware of such deviation from the assumed underlying behaviour. In this talk, I will give a very gentle introduction to the mathematics behind DDM, and discuss a few cases I have encountered in which DDM requires some adaption or additional consideration before it can be applied. This talk aims to be accessible to both mathematician and computer scientist.

Briefly, I will explain what is topology and why it is being used in neuroscience, crystallography, molecular biology and more. Then I will introduce some python libraries that are ready for analyzing different kinds of datasets, ranging from signals to images and low dimensional point clouds. We will briefly review the whole TDA pipeline: starting from raw data, going through topological summaries and outcome interpretation. Ahead of the talk, I will be sending a jupyter notebook with examples using the library scikit-tda.py. If time permits I will go over spectral sequences and their use in distributing persistent homology computations. In particular, I will present some examples using permaviss.py which computes topological summaries through the use of the Mayer-Vietoris spectral sequence.

General motivation: This study investigates a continuous-time Markov process dubbed as the linear birth-death process with catastrophic extinction (B-D-C process). The primary motivation is to consider the B-D-C process as an auxiliary model for a more complex stochastic model that simulates the spread of different strains of Gyrodactylus parasites over the external surfaces of the host. Here, the B-D-C process is used to refine the summary statistics of a novel Approximate Bayesian Computation (ABC) in calibrating the multi-dimensional stochastic model based on estimates of the B-D-C model. The simulation of the B-D-C process using a τ-leaping algorithm also provides additional insights on how to accelerate the simulation of the sophisticated stochastic model by proposing a good error threshold based on the trade-off between simulation accuracy and computational speed.

Specific aims: In this current study, we derive the analytical transition function of the B-D-C process. The derived transition function is further validated analytically using mathematical induction and is numerically validated based on Monte Carlo estimation. Additionally, we estimate the B-D-C model parameters by comparing different estimation methods (Maximum likelihood estimation, generalized method of moments and embedded Galton-Watson approach) based on three different in silico simulation experiments where parasite population size is large, moderate or low. The bias, variance, and mean square error of the parameter estimates and the estimation methods’ computational times are compared. Finally, we develop and compare two different hybrid τ-leaping algorithm based on leap-size selection methods proposed by Gillespie (2001) and Gillespie and Petzold (2003), respectively, to accelerate the simulation of the B-D-C process. We propose a good error threshold by exploring the trade-off between simulation accuracy and computational speed of the three different in silico simulation experiments where parasite numbers are high (Case 1), moderate (Case 2) or low (Case 3). The differences between the two τ-leaping methods are the leap-size selection procedure (which is proportional to the simulation error bound) and their respective leap conditions.

Evolutionary game theory (EGT) combines principles of game theory, evolution, and dynamical systems to interpret the interactions of biological agents. There are several basic components to EGT. Game agents and their strategies, the fitness of different strategies relative to the population, and a process that governs evolution. In this talk I will give an introduction to EGT and present how it can be used to study the evolution of human cooperation.

The concept of entropy is one of the most basic and important in natural science and information theory. It remains a commonly used measure of uncertainty or the measure of disorder. I’ve tried to make this accessible about how to use entropy in Statistic. That’s why, in today talks, we provide the proof of L^2 consistency for the k-th nearest neighbour distance estimator of the Renyi entropy for an arbitrary fixed k≥1. We construct the non-parametric test of goodness-of-fit for a class of introduced multivariate Student – t distributions based on a maximum entropy principle. The theoretical results are followed by numerical studies on simulated samples.

We begin with the braid group, explaining its motivations in picture form, looking at its more rigorous definition, and seeing its applications in both mathematics and quantum computing. We then discuss the Yang-Baxter equation, tensor products, and R-matrices. We then draw similarities between these R-matrices and the generators of the braid group, and use this to build a representation of braid group. If there’s time, we’ll discuss the BMW algebra, which is an extension of the braid group, and I’ll give a glimpse of my work in constructing an R-matrix representation of the algebra.

As the year draws to a close, join me as I rant about my favourite shapes. From the many centres of the humble triangle to the interesting world of Archimedean polychora! This talk will attempt to cover a multitude of topics focussed on regular polygons (of which there are ℚ+ many!) and the regular (to some degree) structure one can induce in higher dimensions from them. I will be discussing the 75 uniform polyhedra (plus the infinite families thereof) and the 59 stellations of the icosahedron, two families with only two points of intersection that nonetheless give me an excellent segue into the fourth dimension! Spheres and Euclidean planes are one thing, but we will also attempt to toe the waters into tessellations of the hyperbolic two and three dimensional planes with a particular focus on some families and their relation to Archimedean solids and tillings.

Previous experimental studies have explored the infrapopulation dynamics of Gyrodactylus turnbulli and G. bullatarudis ectoparasites on their fish host, Poecilia reticulata. Here, we used advanced statistics and mathematical models to address three important biological questions in relation to parasite microhabitat preference, host survival and parasite virulence based on existing empirical data. Firstly, although the respective caudal and rostral preferences of these species on the host are well reported, it is unknown whether this is consistent over time and across different fish stocks. We confirm that the captive-bred G. turnbulli and wild G. bullatarudis strains preferred the caudal and rostral regions respectively across different fish stocks; however, the wild G. turnbulli strain changed microhabitat preference over time. Hence, the microhabitat preference of gyrodactylids is host and time-dependent. Secondly, we improve on previous estimates of survival probabilities by using a multi-state Markov model that generalises the standard survival model. The multi-state model reveals that the mean time for fish to remain infected with any parasite strain before either fighting off their infection or dying is between 6 and 14 days. Fish that remain infected for a longer period had a higher chance of recovering than fish whose infection lasted for a shorter period. We show that the probability of host recovery is higher among Ornamental guppy population compared to the Trinidadian fish stocks irrespective of the type of infection, size, or sex of fish; and infected fish are more likely to die than recover at any time. We reveal that large male fish are more likely to die than small or medium-sized male or female fish of any size across the different guppy populations. Finally, we quantify and compare the virulence of three parasite strains across different fish stocks and sexes, by estimating both rates of host mortality and host recovery over time from the fitted multi-state model. We show that parasite-related mortalities are host, sex and time-dependent; whereas the size of fish is confirmed to be the key determinant of host infection loss such that large fish are less likely to clear off their infection as compared to smaller fish. The Markov model will be further expanded to include spatial information and other relevant information about parasite fecundity, age, parasite microhabitat preference, parasite mortality, parasite mobility and host immune response in a future study.

Abstract games, such as Chess and Go, have been played for 100s of years. Grand Champions are often hailed as geniuses of logical thinking and the games are signifiers for strategy and problem solving abilities. So through attempting to solve these games, with computers and computations, we uncover the depth of their complexities; giving us an insight into how deep the games really go.

Decision making processes are mostly dependent on the availability of data from sources which can be extracted information. Availability of data without any missing values that lead to get significant results and to meet the needs of scientific research. Moreover, the incomplete record lead to biased results in statistical methods and affect the quality measurements significantly. Meteorological time series in this study contain missing data. Thus, we are faced to the problem of imputing missing values before running statistical procedures on the time series. This study illustrates a variety of advanced methods to handle missing data and filling gaps. By choosing the proper imputing technique depends on the structure of time series concerned which are Singular Spectrum Analysis by using Iterative approach and regression methods and regression with lagging. These methods candidate solutions to the obstacle of missing data imputation that can often get reasonable results for addressing missing data.

Our PGR talk series will be kicked off by Ambrose Law, who will be speaking about topics related to his research. The talk will be held at 2pm, and will be followed by PGR Tea at 3. Please come along to support Ambrose, and to hear more about his fascinating work! If you would like to attend, please contact Elizabeth Williams to get the Zoom link.

Many fields of mathematics are born from simple but potent questions. The study of Sum Systems comes from such; given a natural number n, can you find two sets such that by taking every combinations of sums between elements of the two sets you get each value 0, 1, 2,…, n uniquely? This talk will be an introduction to the field of Sum Systems, some of their inheritance properties, and will discuss how deep the patterns go. This is a Number Theory based talk but can be enjoyed by any area of mathematics.

With the new term, we will be bringing back Wednesday PGR talks! These talks are given by PhD students, to PhD students, about anything mathematically motivated. This can be something to do with your research, or just something interesting you’d like to share with the PGR community. Previous talks have varied from introductions to a research field, specific topics from recent student published works, to the science of star wars and the mathematics of story telling. We have also received talks from outside of the mathematics department, which is a great opportunity to get some constructive feedback on mathematical ideas you’re using in your work from some friendly postgrad students.

PGR talks are given every two weeks on a Wednesday at 2pm, followed by ‘Tea at 3’ where we gather informally for a chat over some tea, coffee, biscuits and cake.

As we can’t meet in person, the SIAM community will pay to have biscuits sent to you if you give a talk!

If you would like to give a talk, please email Elizabeth Williams.