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Thomas Ward

Publications and source records attributed to Thomas Ward.

At least 19 recordsLinked to original sources
arXiv2025

Local structure of classical sequences, regular sequences, and dynamics

We introduce the notions of local realizability at a prime and algebraic realizability of an integer sequence. After discussing this notion in general we consider it for the Euler numbers, the Bernoulli denominators, and the Bernoulli numerators. This gives, for example, a dynamical characterization of the Bernoulli regular primes. Algebraic realizability of the Bernoulli denominators is shown at every prime, giving a different perspective on the great diversity of congruences satisfied by this sequence. We show that the sequence of Euler numbers cannot be realized on a nilpotent group, which may explain why it is less hospitable to congruence hunting.

math.NT↗
arXiv2024

Best practices for estimating and reporting epidemiological delay distributions of infectious diseases using public health surveillance and healthcare data

Epidemiological delays, such as incubation periods, serial intervals, and hospital lengths of stay, are among key quantities in infectious disease epidemiology that inform public health policy and clinical practice. This information is used to inform mathematical and statistical models, which in turn can inform control strategies. There are three main challenges that make delay distributions difficult to estimate. First, the data are commonly censored (e.g., symptom onset may only be reported by date instead of the exact time of day). Second, delays are often right truncated when being estimated in real time (not all events that have occurred have been observed yet). Third, during a rapidly growing or declining outbreak, overrepresentation or underrepresentation, respectively, of recently infected cases in the data can lead to bias in estimates. Studies that estimate delays rarely address all these factors and sometimes report several estimates using different combinations of adjustments, which can lead to conflicting answers and confusion about which estimates are most accurate. In this work, we formulate a checklist of best practices for estimating and reporting epidemiological delays with a focus on the incubation period and serial interval. We also propose strategies for handling common biases and identify areas where more work is needed. Our recommendations can help improve the robustness and utility of reported estimates and provide guidance for the evaluation of estimates for downstream use in transmission models or other analyses.

stat.ME↗
arXiv2024

Patrick Moss 25/10/1947--17/3/2024

Patrick Moss (1947--2024) had two distinct lives as a mathematician. The first was as a ring theorist in the late 1970s, in which he worked with Ginn and Lenagan as a student. After a long career as an inspirational mathematics teacher, Patrick completed a doctorate under my supervision in 2003. This led to a second mathematical life in arithmetic dynamics almost forty years after his first period of research. This is a short obituary of his remarkable contributions, several of which have stimulated further research.

math.HO↗
arXiv2023

Dark Matter Interpretation of Neutron Multiplicity Anomalies

Subterrestrial neutron spectra show weak but consistent anomalies at multiplicities ~100 and above [1-3]. The data of the available measurements are of low statistical significance [4] but indicate an excess of events not correlated with the muon flux. The origin of the anomalies remains ambiguous but could be a signature of WIMP annihilation-like interaction with a Pb target. In this paper, we outline a model consistent with this hypothesis, the extended Standard Model (SM) approach called the Radiation Gauge Model (RGM) [5]. The RGM identifies scalar neutrino-antineutrino wave function components of WIMP Dark Matter (DM) responsible for the weak interaction leading to annihilation with ordinary matter. The model assigns neutrino-nucleon(target) charged current (CC) transitions to the observed anomalies. If the existence of the anomalies is confirmed and the model interpretation is positively verified, this will be the first terrestrial indirect detection of DM.

hep-ph↗
arXiv2023

Influenza Hospitalisations in England during the 2022/23 Season: do different data sources drive divergence in modelled waves? A comparison of surveillance and administrative data

Accurate and representative data is vital for precisely reporting the impact of influenza in healthcare systems. Northern hemisphere winter 2022/23 experienced the most substantial influenza wave since the COVID-19 pandemic began in 2020. Simultaneously, new data streams become available within health services because of the pandemic. Comparing these data, surveillance and administrative, supports the accurate monitoring of population level disease trends. We analysed admissions rates per capita from four different collection mechanisms covering National Health Service hospital Trusts in England over the winter 2022/23 wave. We adjust for difference in reporting and extracted key epidemic characteristics including the maximum admission rate, peak timing, cumulative season admissions and growth rates by fitting generalised additive models at national and regional levels. By modelling the admission rates per capita across surveillance and administrative data systems we show that different data measuring the epidemic produce different estimates of key quantities. Nationally and in most regions the data correspond well for the maximum admission rate, date of peak and growth rate, however, in subnational analysis discrepancies in estimates arose, particularly for the cumulative admission rate. This research shows that the choice of data used to measure seasonal influenza epidemics can influence analysis substantially at sub-national levels. For the admission rate per capita there is comparability in the sentinel surveillance approach (which has other important functions), rapid situational reports, operational databases and time lagged administrative data giving assurance in their combined value. Utilising multiple sources of data aids understanding of the impact of seasonal influenza epidemics in the population.

q-bio.PE↗
arXiv2023

A Model for Circuit Execution Runtime And Its Implications for Quantum Kernels At Practical Data Set Sizes

Quantum machine learning (QML) is a fast-growing discipline within quantum computing. One popular QML algorithm, quantum kernel estimation, uses quantum circuits to estimate a similarity measure (kernel) between two classical feature vectors. Given a set of such circuits, we give a heuristic, predictive model for the total circuit execution time required, based on a recently-introduced measure of the speed of quantum computers. In doing so, we also introduce the notion of an "effective number of quantum volume layers of a circuit", which may be of independent interest. We validate the performance of this model using synthetic and real data by comparing the model's predictions to empirical runtime data collected from IBM Quantum computers through the use of the Qiskit Runtime service. At current speeds of today's quantum computers, our model predicts data sets consisting of on the order of hundreds of feature vectors can be processed in order a few hours. For a large-data workflow, our model's predictions for runtime imply further improvements in the speed of circuit execution -- as well as the algorithm itself -- are necessary.

quant-ph↗
arXiv2023

Real-time COVID-19 hospital admissions forecasting with leading indicators and ensemble methods in England

Hospitalisations from COVID-19 with Omicron sub-lineages have put a sustained pressure on the English healthcare system. Understanding the expected healthcare demand enables more effective and timely planning from public health. We collect syndromic surveillance sources, which include online search data, NHS 111 telephonic and online triages. Incorporating this data we explore generalised additive models, generalised linear mixed-models, penalised generalised linear models and model ensemble methods to forecast over a two-week forecast horizon at an NHS Trust level. Furthermore, we showcase how model combinations improve forecast scoring through a mean ensemble, weighted ensemble, and ensemble by regression. Validated over multiple Omicron waves, at different spatial scales, we show that leading indicators can improve performance of forecasting models, particularly at epidemic changepoints. Using a variety of scoring rules, we show that ensemble approaches outperformed all individual models, providing higher performance at a 21-day window than the corresponding individual models at 14-days. We introduce a modelling structure used by public health officials in England in 2022 to inform NHS healthcare strategy and policy decision making. This paper explores the significance of ensemble methods to improve forecasting performance and how novel syndromic surveillance can be practically applied in epidemic forecasting.

stat.AP↗
arXiv2023

Understanding the leading indicators of hospital admissions from COVID-19 across successive waves in the UK

Following the UK Government's Living with COVID-19 Strategy and the end of universal testing, hospital admissions are an increasingly important measure of COVID-19 pandemic pressure. Understanding leading indicators of admissions at National Health Service (NHS) Trust, regional and national geographies help health services plan capacity needs and prepare for ongoing pressures. We explored the spatio-temporal relationships of leading indicators of hospital pressure across successive waves of SARS-CoV-2 incidence in England. This includes an analysis of internet search volume values from Google Trends, NHS triage calls and online queries, the NHS COVID-19 App, lateral flow devices and the ZOE App. Data sources were analysed for their feasibility as leading indicators using linear and non-linear methods; granger causality, cross correlations and dynamic time warping at fine spatial scales. Consistent temporal and spatial relationships were found for some of the leading indicators assessed across resurgent waves of COVID-19. Google Trends and NHS queries consistently led admissions in over 70% of Trusts, with lead times ranging from 5-20 days, whereas an inconsistent relationship was found for the ZOE app, NHS COVID-19 App, and rapid testing, that diminished with granularity, showing limited autocorrelation of leads between -7 to 7 days. This work shows that novel syndromic surveillance data has utility for understanding the expected hospital burden at fine spatial scales. The analysis shows at low level geographies that some surveillance sources can predict hospital admissions, though care must be taken in relying on the lead times and consistency between waves.

stat.AP↗
arXiv2023

Forecasting influenza hospital admissions within English sub-regions using hierarchical generalised additive models

Background: Seasonal influenza causes a substantial burden on healthcare services over the winter period when these systems are already under pressure. Policies during the COVID-19 pandemic supressed the transmission of season influenza, making the timing and magnitude of a potential resurgence difficult to predict. Methods: We developed a hierarchical generalised additive model (GAM) for the short-term forecasting of hospital admissions with a positive test for the influenza virus sub-regionally across England. The model incorporates a multi-level structure of spatio-temporal splines, weekly seasonality, and spatial correlation. Using multiple performance metrics including interval score, coverage, bias, and median absolute error, the predictive performance is evaluated for the 2022/23 seasonal wave. Performance is measured against an autoregressive integrated moving average (ARIMA) time series model. Results: The GAM method outperformed the ARIMA model across scoring rules at both high and low-level geographies, and across the different phases of the epidemic wave including the turning point. The performance of the GAM with a 14-day forecast horizon was comparable in error to the ARIMA at 7 days. The performance of the GAM is found to be most sensitive to the flexibility of the smoothing function that measures the national epidemic trend. Interpretation: This study introduces a novel approach to short-term forecasting of hospital admissions with influenza using hierarchical, spatial, and temporal components. The model is data-driven and practical to deploy using information realistically available at time of prediction, addressing key limitations of epidemic forecasting approaches. This model was used across the winter for healthcare operational planning by the UK Health Security Agency and the National Health Service in England.

stat.AP↗
arXiv2023

Nowcasting the 2022 mpox outbreak in England

In May 2022, a cluster of mpox cases were detected in the UK that could not be traced to recent travel history from an endemic region. Over the coming months, the outbreak grew, with over 3000 total cases reported in the UK, and similar outbreaks occurring worldwide. These outbreaks appeared linked to sexual contact networks between gay, bisexual and other men who have sex with men. Following the COVID-19 pandemic, local health systems were strained, and therefore effective surveillance for mpox was essential for managing public health policy. However, the mpox outbreak in the UK was characterised by substantial delays in the reporting of the symptom onset date and specimen collection date for confirmed positive cases. These delays led to substantial backfilling in the epidemic curve, making it challenging to interpret the epidemic trajectory in real-time. Many nowcasting models exist to tackle this challenge in epidemiological data, but these lacked sufficient flexibility. We have developed a novel nowcasting model using generalised additive models to correct the mpox epidemic curve in England, and provide real-time characteristics of the state of the epidemic, including the real-time growth rate. This model benefited from close collaboration with individuals involved in collecting and processing the data, enabling temporal changes in the reporting structure to be built into the model, which improved the robustness of the nowcasts generated.

q-bio.PE↗
arXiv2021

Test of Nuclear Decay Rate Variation due to an Antineutrino Flux

Unexplained variations of the decay rate for weak interaction decays such as $\beta^{\pm}$-decay, electron capture, as well as strong interaction $\alpha$-decay have been reported. Some researcher interpreted these variations as caused by an unexplained fundamental interaction. The purpose of the paper is to review decay rate parameter variations experiments and place them into a common comparable context and to make decay parameter measurements at the level of 10$^{-5}$ in the presences of an antineutrino flux, $\sim 3 \times10^{12}$ $\overline{\nu} \, cm^{-2} \, sec^{-1}$, 6.5 meters from the High Flux Isotope Reactor(HFIR) reactor core having an on-off cycle time of $\sim$30 days. Two weak interaction decays, one via electron capture and the other via $\beta^-$ decay were selected because the final state and the time reverse state each contain a neutrino and anti-neutrino, covering arguments that the anti-neutrino flux may interact differently or not at all in one of the cases. The experiment searched for variation of the $^{54}_{25}$Mn, e$^-$ capture and $^{137}_{~55}$Cs, $\beta^-$ decay rate parameters. The measured variation in the decay rate parameters are found to be $\delta \lambda/ \lambda = (0.034\pm 1.38)\times 10^{-5}$ for $^{54}_{25}$Mn and $\delta \lambda/ \lambda = (0.67\pm 1.56)\times 10^{-5}$ for $^{137}_{~55}$Cs. These results are consistent with no measurable decay rate parameter variation due to an antineutrino flux, yielding a $68\%$ confidence level upper limit sensitivity for $^{54}_{25}$Mn, $\delta \lambda/ \lambda \leq 1.31\times10^{-5}$ or $\sigma \leq 1.29\times10^{-25}\,cm^{2}$ in cross section and for $^{137}_{~55}$Cs, $\delta \lambda/ \lambda \leq 2.23\times10^{-5}$ or $\sigma \leq 5.69\times10^{-27}\,cm^{2}$. These null or no observable effect measurements places cross-section upper limits $\sim 10^{4}$ times more sensitive than past experiments.

nucl-ex↗
arXiv2020

Aggregating Long-Term Context for Learning Laparoscopic and Robot-Assisted Surgical Workflows

Analyzing surgical workflow is crucial for surgical assistance robots to understand surgeries. With the understanding of the complete surgical workflow, the robots are able to assist the surgeons in intra-operative events, such as by giving a warning when the surgeon is entering specific keys or high-risk phases. Deep learning techniques have recently been widely applied to recognizing surgical workflows. Many of the existing temporal neural network models are limited in their capability to handle long-term dependencies in the data, instead, relying upon the strong performance of the underlying per-frame visual models. We propose a new temporal network structure that leverages task-specific network representation to collect long-term sufficient statistics that are propagated by a sufficient statistics model (SSM). We implement our approach within an LSTM backbone for the task of surgical phase recognition and explore several choices for propagated statistics. We demonstrate superior results over existing and novel state-of-the-art segmentation techniques on two laparoscopic cholecystectomy datasets: the publicly available Cholec80 dataset and MGH100, a novel dataset with more challenging and clinically meaningful segment labels.

cs.CV↗
arXiv2018

Mixing, wine, and serendipity

Mixing for measure-preserving group actions is a fundamental notion in ergodic theory, with different phenomena arising for different acting groups. In 1993, Klaus Schmidt and Tom Ward proved that 2-mixing implies mixing of all orders for actions by commuting automorphisms of connected groups. Tom Ward explains how he became interested in this problem, and describes how a chance encounter with a paper on a seemingly unrelated problem in number theory played a key role.

math.DS↗
arXiv2018

Dynamics on abelian varieties in positive characteristic

We study periodic points for endomorphisms $\sigma$ of abelian varieties $A$ over algebraically closed fields of positive characteristic $p$. We show that the dynamical zeta function $\zeta_\sigma$ of $\sigma$ is either rational or transcendental, the first case happening precisely when $\sigma^n-1$ is a separable isogeny for all $n$. We call this condition very inseparability and show it is equivalent to the action of $\sigma$ on the local $p$-torsion group scheme being nilpotent. The "false" zeta function $D_\sigma$, in which the number of fixed points of $\sigma^n$ is replaced by the degree of $\sigma^n-1$, is always a rational function. Let $1/\Lambda$ denote its largest real pole and assume no other pole or zero has the same absolute value. Then, using a general dichotomy result for power series proven by Royals and Ward in the appendix, we find that $\zeta_\sigma(z)$ has a natural boundary at $|z|=1/\Lambda$ when $\sigma$ is not very inseparable. We introduce and study tame dynamics, ignoring orbits whose order is divisible by $p$. We construct a tame zeta function $\zeta^*_{\sigma}$ that is always algebraic, and such that $\zeta_\sigma$ factors into an infinite product of tame zeta functions. We briefly discuss functional equations. Finally, we study the length distribution of orbits and tame orbits. Orbits of very inseparable endomorphisms distribute like those of Axiom A systems with entropy $\log \Lambda$, but the orbit length distribution of not very inseparable endomorphisms is more erratic and similar to $S$-integer dynamical systems. We provide an expression for the prime orbit counting function in which the error term displays a power saving depending on the largest real part of a zero of $D_\sigma(\Lambda^{-s})$.

math.NT↗
arXiv2015

The dynamical zeta function for commuting automorphisms of zero-dimensional groups

For a $\mathbb{Z}^d$-action $\alpha$ by commuting homeomorphisms of a compact metric space, Lind introduced a dynamical zeta function that generalizes the dynamical zeta function of a single transformation. In this article, we investigate this function when $\alpha$ is generated by continuous automorphisms of a compact abelian zero-dimensional group. We address Lind's conjecture concerning the existence of a natural boundary for the zeta function and prove this for two significant classes of actions, including both zero entropy and positive entropy examples. The finer structure of the periodic point counting function is also examined and, in the zero entropy case, we show how this may be severely restricted for subgroups of prime index in $\mathbb{Z}^d$. We also consider a related open problem concerning the appearance of a natural boundary for the dynamical zeta function of a single automorphism, giving further weight to the Polya-Carlson dichotomy proposed by Bell and the authors.

math.DS↗
arXiv2014

Directional uniformities, periodic points, and entropy

Dynamical systems generated by $d\ge2$ commuting homeomorphisms (topological $\mathbb{Z}^d$-actions) contain within them structures on many scales, and in particular contain many actions of $\mathbb{Z}^k$ for $1\le k\le d$. Familiar dynamical invariants for homeomorphisms, like entropy and periodic point data, become more complex and permit multiple definitions. We briefly survey some of these and other related invariants in the setting of algebraic $\mathbb{Z}^d$-actions, showing how, even in settings where the natural entropy as a $\mathbb{Z}^d$-action vanishes, a powerful theory of directional entropy and periodic points can be built. An underlying theme is uniformity in dynamical invariants as the direction changes, and the connection between this theory and problems in number theory; we explore this for several invariants. We also highlight Fried's notion of average entropy and its connection to uniformities in growth properties, and prove a new relationship between this entropy and periodic point growth in this setting.

math.DS↗