## UPCOMING RESEARCH SEMINAR

The history of inflation measurement
• Speaker: Jeff Ralph (RSS William Guy Lecturer for 2017-2018), Office of National Statistics
• Date/time: 22 June, 15:30-16:30
• Venue: Room 213, Babbage Building

• Room 213, Babbage Building

• Room 210, Rolle Building

• Room 2.13, South Cloisters Building, St Luke's Campus, University of Exeter

• Room 210, Rolle Building

## The Centre for Mathematical Sciences research seminars and events are listed below.

The four main seminar series are in applied mathematics, pure mathematics, statistics and theoretical physics. Visit the centre's webpages for the latest seminar updates and information.

22 June, 15:30-16:30 (Room 213, Babbage Building): The history of inflation measurement

• Speaker: Jeff Ralph (RSS William Guy Lecturer for 2017-2018), Office of National Statistics

The monthly consumer price inflation figures from the Office for National Statistics are among the most influential of all Official Statistics. They are used for a wide variety of important purposes from indicating the health of the economy to the adjustment of pensions and benefits. Behind the numbers sits a sophisticated methodology that has been developed over a long period of time. This talk looks at the development of these measures from their origins at the start of the 18th century to the current day. It will identify some of the visionary individuals who contributed to establishing the foundations, the dates when important changes were made and the social and political factors that drove the developments.

Seminar organiser: Dr Yinghui Wei (yinghui.wei@plymouth.ac.uk)

16 July, 14:00-15:00 (Room 210, Rolle Building): Xmeta: a comprehensive tool-box for advanced meta-analysis - meta-analysis, publication bias, and beyond

• Speaker: Yong Chen, University of Pennsylvania

Abstract: In this talk, Yong is going to introduce a web-platform that they have been developing over the last few years, known as ‘xmeta’, which aims to facilitate advanced comprehensive meta-analysis for applied investigators within and beyond the Perelman School of Medicine at University of Pennsylvania. The functionality of this platform includes implementation of various multivariate meta-analysis for continuous and/or binary outcomes in randomised controlled trials, meta-analysis of diagnostic tests with/without gold standard, as well as methods to identify and correct for publication biases or small study effects. In addition, Yong will also introduce the online-analysis feature, which allows applied investigators to conduct these analyses without programing by themselves. At the end, Yong will talk about the future direction of incorporating semi-automated text mining to speed up the systematic review process.

Seminar organiser: Dr Yinghui Wei (yinghui.wei@plymouth.ac.uk)

20 July, 14:00-15:00 (Room 2.13, South Cloisters Building, St Luke's Campus, University of Exeter): Methodological advances in evidence synthesis

• Speaker: Orestis Efthimiou, University of Bern

Abstract: Network meta-analysis (NMA) is an extension of the usual (pairwise) meta-analysis. It is a statistical tool for synthesizing evidence obtained from studies comparing multiple competing interventions for the same disease. In this lecture, we will go through some recent advances in the field. First, we will discuss a new model for the NMA of binary outcomes. This model generalises the well-known Mantel-Haenszel method, and can be especially valuable for the case of rare events, e.g. when synthesising data on mortality or serious adverse events. The method has been implemented in R in freely available, easy-to-use routines. Second, we will discuss models for including non-randomised studies in NMA. Non-randomised studies can reveal whether or not interventions are effective in real-life clinical practice and there is a growing interest in including such evidence in the decision-making process. Here we present and compare an array of alternative methods, and we apply some of the methods in previously published clinical examples. Finally, we will discuss methods for individual participant data network meta-analysis (IPD-NMA). IPD are considered the gold standard in evidence synthesis, and inclusion of IPD in NMA offers unique advantages, such as increase in precision, decrease in heterogeneity, as well as the capacity to individualise the treatment according to a patient’s characteristics. We showcase our methods using an example from depression.

Note: This is a joint RSS South West Local Group and Exeter Health Statistics event.

Seminar organiser: Dr Yinghui Wei (yinghui.wei@plymouth.ac.uk)

23 July, 14:00-15:00 (venue: Room 210, Rolle Building): N-of-1 Trials for Making Personalised Treatment Decisions with Personalised Designs Using Self-Collected Data

• Speaker: Christopher Schmid, Brown University

Abstract: N-of-1 trials hold great promise for enabling participants to create personalised protocols to make personalised treatment decisions. Fundamentally, N-of-1 trials are single-participant multiple-crossover studies for determining the relative comparative effectiveness of two or more treatments for one individual. An individual selects treatments and outcomes of interest, carries out the trial, and then makes a final treatment decision with or without a clinician based on results of the trial. Established in a clinical environment, an N-of-1 practice provides data on multiple trials from different participants. Such data can be combined using meta-analytic techniques to inform both individual and population treatment effects. When participants undertake trials with different treatments, the data form a treatment network and suggest use of network meta-analysis methods. This talk will discuss ongoing and completed clinical research projects using N-of-1 trials for chronic pain, atrial fibrillation, inflammatory bowel disease, fibromyalgia and attention deficit hyperactivity disorder. Several of these trials collect data from participants using mobile devices. I will describe design, data collection and analytic challenges as well as unique aspects deriving from use of the N-of-1 design and mobile data collection for personalised decision-making. Challenges involve defining treatments, presenting results, assessing model assumptions and combining information from multiple participants to provide a better estimate of each individual’s effect than from his or her own data alone.

Seminar organiser: Dr Yinghui Wei (yinghui.wei@plymouth.ac.uk)

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Today's events

## Previous Research Seminars - 2018

Wednesday 17 January: Acoustic-gravity waves, theory and applications

Abstract: Acoustic–gravity waves (AGWs) are compression-type waves generated as a response to a sudden change in the water pressure, e.g. due to nonlinear interaction of surface waves, submarine earthquakes, landslides, falling meteorites and objects impacting the sea surface. AGWs can travel at near the speed of sound in water (ca. 1500 m/s), but can also penetrate through the sea-floor surface amplifying their speed, which turns them into excellent precursors. “Acoustic–gravity waves” is an emerging field that is rapidly gaining popularity among the scientific community, as it finds broad utility in physical oceanography, marine biology, geophysics, water engineering, and quantum analogues. This talk is an overview on AGWs, with emphasis on recent developments, current challenges, and future directions.

Wednesday 31 January: The Dawn of FIMP Dark Matter

• Speaker: Tommi Tenkanen, QMUL

Abstract: Tommi will present an overview of scenarios where the observed Dark Matter (DM) abundance consists of Feebly Interacting Massive Particles (FIMPs), produced non-thermally by the so-called “freeze-in” mechanism. In contrast to the usual freeze-out scenario, frozen-in FIMP DM interacts very weakly with particles in the visible sector and never attained thermal equilibrium with them in the early Universe. This makes frozen-in DM very difficult but not impossible to test. In this talk Tommi will present the freeze-in mechanism and its variations previously considered in the literature, compare them to the standard DM freeze-out scenario, discuss several aspects of model building, and pay particular attention to observational properties of such feebly interacting DM.

Wednesday 21 February: Smoothed Particles Hydrodynamics Modelling in Free Surface Single Phase Flows

• Speaker: Ruaa Wana, Plymouth

Abstract: Smoothed Particle Hydrodynamics (SPH) is a meshfree, Lagrangian, particle method. It is particularly well suited to simulating flow problems that have large deformations or contain free surfaces. This talk will discuss the SPH single phase simulations of a dam break flow and a tsunami wave generated by a fault rupture.

Wednesday 21 February: Recent results from LHCb

Abstract: The LHCb experiment at CERN has collected an unprecedented data set in beauty and charm decays. The resulting precision measurements are sensitive to physics at mass scales far beyond the “energy frontier”, i.e. the highest collision energies achievable in colliders. Recent results indicate that these data are beginning to challenge the SM of particle physics. This seminar will summarise recent LHCb results, with focus on precision measurements of Charge-Parity violation and rare decays.

Wednesday 28 February: Charge Propagation

• Speaker: David McMullan, Plymouth

Abstract: Charge propagation is surprisingly difficult to describe in quantum field theory. Even in the abelian theory, where the spectre of confinement is avoided, the persistent interaction of the electron with its environment leads to deep theoretical problems. There is, though, an exactly solvable model of an electron in a plane wave background (the so called Volkov solution) that provides an attractive arena for testing ideas related to the more general propagation problem. David will review some of the recent results we have derived concerning charges propagating in an elliptical class of backgrounds, and outline how to incorporate loop corrections. Some of the lessons learnt from this will be discussed in the context of the more general problems that arise when charges propagate.

Thursday 8 March: Rigidity and global rigidity of graphs

• Speaker: Bernd Schulze, Lancaster

Abstract: Rigidity theory is concerned with the rigidity and flexibility analysis of bar-joint frameworks and related constraint systems of geometric objects. This area has a rich history which can be traced back to classical work of Euler, Cauchy and Maxwell on the rigidity of polyhedra and skeletal frames. Since Laman’s celebrated result from 1970 (which provided the first combinatorial characterisation of generic rigid bar-joint frameworks in the plane), rigidity theory has received steadily increasing attention and it is now a highly diverse and thriving research area with many practical applications. Bernd will give an introduction to rigidity theory, concentrating on results and problems for bar-joint frameworks, but also describing how these have been extended to some other types of frameworks. Moreover, Bernd will summarise some recent progress in the rigidity analysis of symmetric frameworks.

Tuesday 20 March: Implementation of a Lattice Boltzmann Method for Multiphase Flows with High Density and Viscosity Ratios

• Speaker: Norjan Jumaa, Plymouth

Abstract: We present a Lattice Boltzmann Method (LBM) for multiphase flows with high viscosity and density ratios. Following Banari et al. (2014), the motion of the interface between fluids is modelled by solving the Cahn-Hilliard (CH) equation with LBM. Incompressibility of the velocity fields in each phase is imposed by using a pressure correction scheme. We use a unified LBM approach with separate formulations for the phase field, the pressure-less Navies-Stokes (NS) equations and the pressure Poisson equation required for correction of the velocity field. The implementation has been verified for various test cases. Here, we present results for some complex flow problems including two dimensional single and multiple mode Rayleigh-Taylor Instability (RTI). Also, we present the evolution of the height of a standing wave for both high and low viscosity and density ratios.

Wednesday 21 March: Multi-state models for observed and latent cognitive function in the older population

• Speaker: Ardo van den Hout, Department of Statistical Science, University College London

Abstract: Due to the ageing population there is a growing interest in the statistical modelling of cognitive function in old age. When analysing longitudinal data on ageing, lost to follow-up because of death cannot be ignored. One option is to model survival and change of cognitive function jointly by specifying submodels for the two processes and linking these models by individual-specific random effects. Another option – and the topic of this seminar – is to use a continuous-time multi-state survival model where a series of living states is defined by the level of cognitive function and an additional dead state is included. This multi-state approach is quite general and can be used in many other applications in biostatistics, social statistics, and demography.

The seminar will start with introducing the continuous-time multi-state survival model by discussing model specification and maximum likelihood estimation. The second part will present an extension of current methods: a hidden Markov model for modelling bivariate cognitive function. The methods will be illustrated by using longitudinal data from a UK survey of the older population.

Wednesday 21 March: Accuracy and Stability of Virtual Source Method for Numerical Simulations of Nonlinear Water Waves

• Speaker: Omar Al-Tameemi, Plymouth

Abstract: The Virtual Source Method (VSM) is based upon the integral equations derived by using Green’s identity with Laplace’s equation for the velocity potential. The velocity potential within the fluid domain is completely determined by the potential on a virtual boundary located above the fluid, avoiding the need to evaluate the singular integrals normally associated with integral equation methods. This talk will present numerical simulations of non-linear standing waves and sloshing problems using VSM. We will discuss stability and convergence of the method as well as looking at global and energy and volume conservation.

Wednesday 21 March: Simulating dipole wall collisions with slip boundaries by using moment-based boundary conditions for lattice Boltzmann method

• Speaker: Seemaa Mohammed, Plymouth

Abstract: The accuracy of moment-based boundary conditions for no slip and slip walls in the lattice Boltzmann method is examined numerically by using dipole wall collision for both normal and oblique cases. To do that hydrodynamic moments impose to the boundary instead of the distribution functions. For accurate results a two relaxation time (TRT) model are used with moment boundary conditions. An excellent agreement with a benchmark data is obtained and the results are obtained to converge with second order accuracy.

Wednesday 25 April: Integrability of Relativistic Dynamical Systems

• Speaker: Tom Heinzl, Plymouth

Abstract: Tom will give a brief overview of our recent studies of relativistic dynamical systems. These are described by the Newton-Einstein-Lorentz equation generalising F = ma in the presence of external (electromagnetic) forces. Tom will explain how space-time and conformal symmetries may be employed to find conserved quantities that lead to integrability. In quite a few cases, the number of these quantities is surprisingly large implying super-integrability. This feature is somewhat ‘exotic’ due to its rare occurrence. For instance, by Bertrand’s theorem, in classical mechanics it only holds for the Kepler problem (with its Laplace-Runge-Lenz vector) and the harmonic oscillator. Using our generalised setting we have been able to extend this list significantly.

Wednesday 25 April: Double copy on plane wave backgrounds

Abstract: Double copy is a method for constructing (perturbatively) scattering amplitudes in gravity from scattering amplitudes in gauge theory, and even has a catchy slogan: Gravity = (Gauge theory)^2. Despite is many uses, the status of double copy as a fundamental feature of perturbative field theories is poorly understood. In this talk Tim will describe how the robustness of double copy can be tested by considering the simplest scattering amplitudes on plane wave backgrounds. This makes use of several tools familiar from the study of QED in strong background fields. Despite various subtleties introduced by the non-trivial scattering background, it is clear that a notion of double copy does indeed exist.

Wednesday 25 April: Trust in Numbers

• Speaker: Professor Sir David Spiegelhalter, President of the Royal Statistical Society for 2017-18

Abstract: Those who value quantitative and scientific evidence are faced with claims both of a reproducibility crisis in scientific publication, and of a post-truth society abounding in fake news and alternative facts. Both issues are of vital importance to statisticians, and both are deeply concerned with trust in expertise. By considering the ‘pipelines’ through which scientific and political evidence is propagated, David will consider possible ways of improving both the trustworthiness of the statistical evidence being communicated, and the ability of audiences to assess the quality and reliability of what they are being told. There will also be cheap laughs at numerous examples of disastrous communication of statistics in the media.

Wednesday 2 May: Guiding laser-produced fast electrons using super-strong magnetic fields

• Speaker: Kate Lancaster, York

Abstract: Currently we are able produce with laser plasma interactions some of the most extreme conditions on earth. When ultra-intense lasers are focused on to solid material, the fields associated with the laser are so strong that electrons can easily escape the atoms in the material. Absorption of the laser pulse results in the generation of a population of relativistic electrons, with currents on the order of Mega Amps. The physics associated with how the electrons are produced and subsequently transported in plasma is complex and proves challenging to diagnose and study. Importantly, these fast electrons are the driver for much of the subsequent physics during these interactions including generation of energetic particles/ photon sources, unique atomic physics states such as hollow atoms, hydrodynamic phenomena, production of warm / hot dense matter relevant to stellar interiors, heating of matter relevant to alternative laser driven fusion schemes such as fast ignition, and conditions relevant for understanding of nuclear astrophysics in the most extreme objects in our universe.

This talk will illustrate some of the experiments happening on petawatt-class lasers concerning how to control important fast electron beam parameters (such as divergence) using novel structured targets. Alex Robinson et al first proposed using targets incorporating a resistivity gradient to confine fast electrons. At the material interface of a high resistivity feature, e.g. a wire, surrounded by a lower resistivity material a strong magnetic field is generated which confines electrons to areas of higher resistivity and higher current density. In this talk experiments using targets with novel silicon embedded features created by Scitech Precision Ltd using MEMS technology will be presented. A novel duel channel front surface imaging system was created in order to enable both pre-shot alignment and on-shot focal spot position, information critical for performing these types of complex experiments.

Wednesday 9 May: Searching for dark matter with the LUX and LUX-ZEPLIN direct detection experiments

• Speaker: Jim Dobson, UCL

Abstract: For the past decade liquid xenon time-projection chambers (TPCs) hidden deep underground have led the race to make a first direct detection of dark matter here on Earth. In this talk Jim will present the final results from the recently completed Large Underground Xenon (LUX) experiment as well as the status and physics reach of its successor, the 40 times as massive LUX-ZEPLIN experiment currently being constructed and due to start data taking in 2020.

Wednesday 16 May: Progress on the connection between spectral embedding and network models used by the probability, statistics and machine-learning communities

• Speaker: Patrick Rubin-Delanchy, University of Bristol

Abstract: In this talk, Patrick gives theoretical and methodological results, based on work spanning Johns Hopkins, the Heilbronn Institute for Mathematical Research, Imperial and Bristol, regarding the connection between various graph spectral methods and commonly used network models which are popular in the probability, statistics and machine-learning communities. An attractive feature of the results is that they lead to very simple take-home messages for network data analysis: a) when using spectral embedding, consider eigenvectors from both ends of the spectrum; b) when implementing spectral clustering, use Gaussian mixture models, not k-means; c) when interpreting spectral embedding, think of “mixtures of behaviour” rather than “distance”. Results are illustrated with cyber-security applications.

Wednesday 23 May: Flexible inference for continuous-time models of wildlife movement

• Speaker: Paul Blackwell, University of Sheffield

The majority of statistical models of animal movement are formulated in discrete time, modelling separately each 'step' from one location (e.g. GPS fix) to the next. This can make it difficult to deal with missing or unequally-spaced observations, to compare studies with different time scales, or to interpret results biologically. In reality, animals exist and move in continuous time, and Paul will describe some switching diffusion models that try to capture some of the complexities of real behaviour in continuous time. Computational cost is an increasingly important issue in fitting movement models, and Paul will talk about some algorithms that allow exact inference for such models, even in the presence of spatial heterogeneity, borrowing ideas from Hidden Markov Models and Kalman Filtering. An increasingly important area of application is collective movement, where we model the locations of simultaneously-tracked animals as they interact; Paul will discuss some recent developments in modelling and computation for this situation.

Some of this work is joint with Mu Niu (University of Plymouth) and a number of recent or current research students at the University of Sheffield.

Wednesday 23 May: Analytical estimates of proton acceleration in laser-produced turbulent plasma

• Speaker: Konstantin Beyer (Oxford)

Abstract: With the advent of high power laser facilities new opportunities for scaled laboratory experiments of astrophysical processes have become available. Here we show that experiments at National Ignition Facility (NIF) laser have reached the condition where second order Fermi acceleration can be directly investigated with the available diagnostics. This requires measuring the diffusion of 3 MeV protons produced within a turbulent plasma. Since Fermi acceleration is essentially a biased diffusion process and using existing solutions, we show that a significant broadening of the initial proton distribution is expected for those particles existing the plasma.

Thursday 31 May: Symplectic geometry of the moduli space of framed Higgs bundles

• Speaker: Marina Logares, University of Plymouth

Abstract: Let X be a compact Riemann surface and D an effective divisor on X. The moduli space of D-twisted stable Higgs bundles on X is known to have a holomorphic Poisson structure which is in fact symplectic if and only if D is the zero divisor. We prove that this moduli space admits a natural enhancement to a holomorphic symplectic manifold. This is based on joint work in collaboration with I Biswas and A Peón-Nieto.

Wednesday 6 June: Research students using statistics mini-symposium

The influence of external peer reviewers on funding decisions in grant applications in NIHR

• Speaker: Lexy Sorrell, University of Plymouth

Abstract: The National Institute of Health Research (NIHR) is a large, long established national funder of health research, aiming to select applications for research funding which are of the highest quality and address important health issues, providing evidence for policy and practice. However, this selection process is time consuming and costly in terms of human resources: the NIHR staff, external reviewers and board members. This study is part of the wider ‘Push the Pace’ project aiming to reduce the time for research to get from ‘bench to beside’, which is currently averaging 10 years in the NIHR research pathway. We use the external reviewers’ scores along with reviewer and application characteristics to investigate the influence of external peer reviewers on the funding decisions made by the board, how many reviewers are needed to review an application; and the relative value of peer review scores from different kinds of reviewers.

Sonification: The Aesthetics of Listening to Data

• Speaker: Nuria Bonet Filella, University of Plymouth

Abstract: Sonification is ‘the use of non-speech audio to convey information’; in other words, the aural display of data (as opposed to visual). It can be a superior approach for the understanding of data, where their visual interpretation is difficult. Sonification has mainly been used for scientific purposes (for example Geiger counter, EEG monitor or heart rate monitor) but composers are showing increasing interest in the method.

Musical aesthetics are crucial to sonification. In order to be effective in transmitting data, a sonification must be clear, appropriate to the data, and aesthetically pleasing to the listener. Many examples are ‘typically unpleasant and lacking any natural connection to the data represented’. Scientists might not have the musical knowledge to create a good sonification; composers might not have the scientific knowledge to deal with the data musically. Therefore, the production of sonification has strongly increased in recent years but their quality has not.

Nuria has approached sonification from a compositional point of view in order to establish an aesthetic framework for aural display. Through a portfolio of sonifications and theoretical work, Nuria has explored the practical aspects of listening to data, whether for scientists or composers.

Friday 8 June: Thick subcategories of discrete derived categories

Speaker: Nathan Broomhead, University of Plymouth

Abstract: Nathan will explain some work, in which he describes the lattices of thick subcategories of discrete derived categories. This is done using certain generating collections of exceptional and sphere-like objects related to non-crossing configurations of arcs in a geometric model.

Wednesday 13 June: Probabilistic Regression Analysis of Extreme Events in Energy Sectors with Either Massive or Small Data

• Speaker: Keming Yu, Brunel University

Abstract: Buried pipelines and wind turbine are important devices to convert or transfer energy. Buried pipelines are vulnerable to the threat of corrosion. Of interest is an estimate of the probability when or where an affected pipeline is likely to fail from the extreme growth of a corrosion defect. Wind turbine monitoring uses acoustic emission signal detection of damage processes in the structure. Peak signals are something under the concern of the industry. Of interest is an estimate of the probability of a signal beyond a threshold. Many factors involved need to be taken into consideration when building a probabilistic model for these extreme events. But some classical regression models such as the logistic regression whose response is a binary variable seems inefﬁcient for an observable continuous-response. Furthermore, the probit regression may face either massive data to process or small size to apply, depending on different cases. Whatever the case, estimation accuracy with the support of sound statistical theory and computational algorithm is expected. This talk will introduce a novel inference of probit regression for extreme events to cope with either massive streaming or small size data and show that this objective may be achievable.

## Previous Research Seminars - 2017

Friday 23 June: Society and Teenagers: How statistics reveal the changes in young peoples lives through the last century

• Speaker: Jeff Ralph, RSS William Guy Lecturer for 2017-18

Abstract: Young people born in the year 2000 in the UK are more likely to be called Megan or Jack than Mary or John, had a life expectancy at birth of over 75 years and about half will go on to higher education. How was this different a hundred years ago? Official statistics tell the story of how our lives have developed over a century of dramatic change. Statisticians have played a key role in tracking and understanding these developments. I will talk about the statistics behind the measurement of our daily lives. For example, how a basket of goods is used to represent the way people spend their money and what the items in the basket tell us about changes in society and technology. The talk will also discuss the measurement of poverty and its development over time into more than just an indicator of having enough food to eat. Jeff will include examples of what life was like for teenagers through the last century as revealed by the rich source of official statistics.

Monday 26 June: Compositeness beyond the Standard Model

• Speaker: Barry Dillon, Plymouth

Abstract: One of the leading motivations in the search for new physics at the LHC is the idea of `naturalness’. As it stands, the current Standard Model (SM) of particle physics is deemed unnatural due the unexplained smallness of the Higgs boson mass, and due to the unexplained hierarchical nature of the Yukawa couplings. A promising explanation of these features is that the SM Higgs is composite, and that its fermions are partially-composite. Much like in QCD, this model predicts a plethora of new composite states with masses near the confinement scale. However the absence of any new physics detection at the LHC puts stringent constraints on the current models. In this talk we will discuss the Minimal Composite Higgs Model (MCHM) and how 5D holographic techniques can be used as calculational tools to derive predictions. We will then present results from a study of the top-partner spectrum in the holographic MCHM (1510.08482), and phenomenological bounds on heavy spin-2 composite states using the latest LHC results (1603.09550).

Wednesday 28 June: Hodge Polynomials of moduli spaces

Abstract: In this talk we consider how to use Mixed Hodge Theory to compute the Hodge polynomial of some moduli spaces of interest in Geometry and Physics. This is work in progress with M. Logares from the University of Plymouth.

Friday 30 June: Simultaneous Confidence Bands in Linear Regression

• Speaker: Yang Han, University of Exeter

Abstract: Construction of simultaneous confidence bands for a percentile line has been considered by several authors. However only conservative symmetric bands, which use critical constants over the whole covariate range are available in the literature. Our new methods allow the construction of exact symmetric bands for a percentile line over a finite interval of the covariate. The exact symmetric bands can be substantially narrower than the corresponding conservative symmetric bands. Several exact symmetric confidence bands are compared under the average band-width criterion. Furthermore, new asymmetric confidence bands for a percentile line are proposed. They are uniformly (and can be very substantially) narrower than the corresponding exact symmetric bands. Therefore, asymmetric bands should always be used under the average band-width criterion. The proposed methods are illustrated with a real example of a drug stability study.

Many modern medicines are targeted therapies, targeting specific pathways. A biomarker that is informative of how sick a patient in the targeted pathway is could be sufficiently predictive of the effect on the patients to allow such medicine to be personalized. Baseline HbA1c for diabetic patients is an example of such potential biomarkers. If a candidate biomarker is continuously valued, it is typically dichotomized to classify patients into target (marker-positive) and non-target (marker-negative) subgroups. The question, for each potential cut-point, is therefore whether the drug has sufficient efficacy in the overall population, or only in the marker-positive patients, or neither. This question can be fully answered by providing simultaneous confidence intervals on the effect of the drug on the marker-positive patients, on the marker-negative patients, and on their mixture. To confidently decide whether a continuously-valued biomarker is useful for targeting patients, such simultaneous confidence intervals need to be further adjusted for the multiplicity of searching through all possible cut-point values. This presentation gives, for continuously-valued outcome measures such as reduction in HbA1c for Type II Diabetes, a neat method providing exact (fully) multiplicity-adjusted simultaneously confidence intervals. An app is also available, which conveniently implements the method we propose.

Wednesday 27 September: A Multivariate Mixture Model for Responses to Rating Questions allowing for Uncertainty

• Speaker: Sabrina Giordano, University of Calabria

Abstract: This talk proposes a multivariate model for ordinal rating responses, allowing for uncertainty in answering. In responding to rating questions, an individual may give answers either according to his/her knowledge (feeling) or to his/her level of indecision (uncertainty). Since ignoring this uncertainty may lead to misleading results, we define the joint distribution of the ordinal responses via a mixture of components, characterised by uncertainty in answering to a subset of variables. A marginal approach is proposed to parameterise the models and the effectiveness of the model is attested through an application to real data and supported by a Monte Carlo study. Uncertain people can be assumed to give an answer at random, by assigning equal probability to every category in the scale (Uniform distribution), but in most cases, wavering respondents tend to use only a small number of the available rating scale options: someone may skip extreme values, optimists may overvalue their feelings and pessimists may underrate them, someone else can take shelter in the middle category. The proposed approach aims to model adequately the distribution of responses, given with uncertainty, according to these different behaviours, by U-shaped, bell shaped, symmetric and skewed distributions. Moreover, since the proposed models are based on some restrictive assumptions which assure identifiability, the true distribution is not necessarily in the model we are using. For this reason, testing procedures for comparing competitive models will be dealt with by avoiding the assumption of correct specification of the models.

Wednesday 11 October: Hochschild cohomology of dg categories, derived centers and spectral sequences

• Speaker: Frank Neumann, Leicester

Abstract: The Hochschild cohomology of a differential graded algebra or more generally of a differential graded category admits a natural map to the graded center of its derived category: the characteristic homomorphism. We interpret it as an edge homomorphism in a spectral sequence. This gives a conceptual explanation of the possible failure of the characteristic homomorphism to be injective or surjective, answering a question by Bernstein and Drinfeld. To illustrate this, we will discuss several examples from algebra, geometry and topology, like coherent sheaves over algebraic curves, cohomology of free loop spaces and string topology. This is joint work with Markus Szymik (NTNU Trondheim).

Wednesday 11 October: New Approaches in Science Communication at the CERN Media Lab

• Speaker: Joao Pequenao, CERN Media Lab

Abstract: As the world’s largest Particle Physics Laboratory, CERN is often in the media spotlight. Physics results from the last few years and the high profile of the organisation increased the public interest in its the nature, operations and outcome. In order to connect with the public in an efficient and enticing way, a special team was created to conceive and implement educational resources using state-of-the-art technology and novel approaches to difficult scientific communication problems.

The CERN Media Lab team produces interactive installations which have been featured in venues all over the planet, is helping several Science Centres conceive their new exhibits, helped dramatically change the perception of CERN to its visitors and on the way contributed to the education and entertainment of many people all over the globe. In this presentation we will have a peek into the technology developed, the projects, the context and scope, and hint about what will come in the future.

Wednesday 1 November: On particle trajectories for Stokes’ edge waves

• Speaker: Raphael Stuhlmeier, Plymouth

Abstract: The matter of particle motion beneath water waves is one of the most natural of questions; it is immediately clear from observations that water particles do not generally travel with the speed of the waveform, but the exact character of their motion in different types of waves has been the matter of much investigation. We treat the particle motion in Stokes’ linear edge wave, which propagates along a uniformly sloping beach: a three-dimensional wave with variation in the cross-shore and long-shore directions. Using analogies between the exact, rotational solution developed by Gerstner and linear water wave theory, and an appropriate rotation of the coordinate frame, we show that there is no particle motion in the direction orthogonal to the sloping beach. Some applications to weakly nonlinear edge waves, as well as modern results by Constantin, Ehrnström, and Villari on particle paths will also be discussed.

Wednesday 15 November: Duality in Topological Quantum Field Theories

Abstract: In this talk, we will study Topological Quantum Field Theories (TQFT for short) as powerful tools for understanding and computing topological invariants. We will review some of the categorical machinery needed, like monoidal categories, and their physical inspiration as models for path integrals. Focusing on the case of surfaces, we will characterize 2d TQFT in purely algebraic terms as Frobenius algebras. As these low dimensional cases show, the monoidality of these constructions imposes very strong duality restrictions on the theory, which lie in the germ of Baez and Dolan’s cobordism hypothesis. Finally, we will explain how these difficulties can be overcome by considering lax monoidal TQFT and almost TQFT and how they can be used for explicit computations of topological invariants.

Wednesday 15 November: Fast as Lightning: Supercomputers, solvers and software for Weather and Climate models

• Speaker: Chris Maynard, Met Office

Wednesday 22 November: Quantisation of Hodge structures of representation varieties

Abstract: Given a complex algebraic group $G$ and a compact manifold $M$, the set of representations $\rho: \pi_1(M) \to G$ has a natural algebraic structure, the so-called representation variety. In this talk, we will show how the mixed Hodge structures of these varieties can be encoded in a lax monoidal TQFT via a general quantisation procedure by means of Saito’s mixed Hodge modules theory. This strategy recovers the stratification technique developed by Logares, Muñoz and Newstead and offers a new framework in which mirror symmetry conjectures for $E$-polynomials can be addressed. Joint work with M Logares and V Muñoz.

Wednesday 29 November: Calabi-Yau Volumes and Reflexive Polytopes

• Speaker: Yang-Hui He, City, University of London

Abstract: We study various geometrical quantities for Calabi-Yau varieties realised as cones over Gorenstein Fano varieties, obtained as toric varieties from reflexive polytopes in various dimensions. Focus is made on reflexive polytopes up to dimension 4 and the minimised volumes of the Sasaki-Einstein base of the corresponding Calabi-Yau cone are calculated. By doing so, we conjecture new bounds for the Sasaki-Einstein volume with respect to various topological quantities of the corresponding toric varieties. We give interpretations about these volume bounds in the context of string theory. This is based on joint work with Rak-Kyeong Seong and Shing-Tung Yau.

Monday 4 December: A Reduced Tensor Product of Braided Fusion Categories containing a Symmetric Fusion Category

• Speaker: Thomas Wasserman, University of Oxford

Abstract: In this talk Thomas will construct a reduced tensor product of braided fusion categories containing a symmetric fusion category $\mathcal{A}$. This tensor product takes into account the relative braiding with respect to objects of $\mathcal{A}$ in these braided fusion categories. The resulting category is again a braided fusion category containing $\mathcal{A}$. This tensor product is inspired by the tensor product of $G$-equivariant once-extended three-dimensional quantum field theories, for a finite group $G$. To define this reduced tensor product, we equip the Drinfeld centre $\mathcal{Z}(\mathcal{A})$ of the symmetric fusion category $\mathcal{A}$ with an unusual tensor product, making $\mathcal{Z}(\mathcal{A})$ into a 2-fold monoidal category. Using this 2-fold structure, we introduce a new type of category enriched over the Drinfeld centre to capture the braiding behaviour with respect to $\mathcal{A}$ in the braided fusion categories, and use this encoding to define the reduced tensor product.

Wednesday 6 December: Gauge-invariant observables in perturbative quantum gravity

• Speaker: Markus Fröb, York

Abstract: It is well known that the diffeomorphism invariance of gravitational theories makes it impossible to define local and gauge-invariant observables in perturbative (quantum) gravity, except at linear order. While in flat space one can study the S-Matrix, which is a gauge-invariant global observable, no analogue exists in a general curved space. Relational observables (i.e., the value of one field at the point where a second field has a prescribed value) are natural candidates for observables in (quantum) gravity, but they are not local when constructed around flat space or around a cosmological (FLRW) background spacetime due to the high symmetry of the latter. We present two different approaches to this problem: a) correlation functions at fixed geodesic distance, and b) a construction of invariant coordinates, for which explicit and fully renormalised results for one-graviton-loop corrections to two-point functions and coupling constants have been obtained.

Wednesday 13 December: The birational geometry of moduli spaces via Bridgeland stability

• Speaker: Barbara Bolognese, Sheffield

Abstract: In 2006, Tom Bridgeland introduced the notion of stability conditions for objects in an arbitrary triangulated category. The original motivation came from Mirror Symmetry, as this was the generalization of the notion of stability for D-branes fathered by Michael Douglas. Soon afterwards, a whole stream of results flourished around Bridgeland’s original idea, and Bridgeland stability conditions had been seen to find applications in geometric representation theory and in binational geometry. In our talk, we will see how wall-crossing phenomena arising from the structure of the set of stability conditions on an algebraic surface give a new powerful machinery to study and, in some cases, to completely describe the binational geometry of certain moduli spaces of sheaves on the given algebraic surface. In a joint work with Huizenga, Lin, Riedl, Schmidt, Woolf and Zhao, we will apply this machinery to a very special moduli space of sheaves, called Hilbert scheme of points, to progress towards a description of its binational geometry via its Nef cone.

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