We propose an algorithmic framework of a pluripotent structure evolving from a simple compact structure into diverse complex 3-D structures for designing the shape transformable, reconfigurable, and deployable structures and robots. Our algorithmic approach suggests a way of transforming a compact structure consisting of uniform building blocks into a large, desired 3-D shape. Analogous to the pluripotent stem cells that can grow into a preprogrammed shape according to coded information, which we call DNA, compactly stacked panels named the zygote structure can evolve into arbitrary 3-D structures by programming their connection path. Our stacking algorithm obtains this coded sequence by inversely stacking the voxelized surface of the desired structure into a tree. Applying the connection path obtained by the stacking algorithm, the compactly stacked panels named the zygote structure can be deployed into diverse large 3-D structures. We conceptually demonstrated our pluripotent evolving structure by energy releasing commercial spring hinges and thermally actuated shape memory alloy (SMA) hinges, respectively. We also show that the proposed concept enables the fabrication of large s
Understanding historical datasets, such as the England and Wales infant mortality data, for local government districts can provide valuable insights into our changing society. Such analyses can prove challenging in practice, due to frequent changes in the boundaries of local government districts for which records are collected. One solution adopted in the literature to overcome such practical challenges is to pre-process data using areal interpolation to render the units consistent over the time period of focus. However, such methods are prone to errors. In this paper we introduce a novel changepoint method to detect instances where interpolation performs poorly. We demonstrate the utility of our method on original data, and also demonstrate how correcting interpolation errors can affect the clustering of the infant mortality curves.
We propose a new method of determining regional and city boundaries based on the Valeriepieris circle, the smallest circle containing a given fraction of the data. By varying the fraction in the circle we can map complex spatial data to a simple model of concentric rings which we then fit to determine natural density cutoffs. We apply this method to population, occupation, economic and transport data from England and Wales, finding that the regions determined by this method affirm well known social facts such as the disproportionate wealth of London or the relative isolation of the North East and South West of England. We then show how different data sets give us different views of the same cities, providing insight into their development and dynamics.
This paper critically evaluates the HESA (Higher Education Statistics Agency) Data Report for the Employer Justified Retirement Age (EJRA) Review Group at the University of Cambridge (\cite{CambridgeHESA2024}), identifying significant methodological flaws and misinterpretations. Our analysis reveals issues such as unclear application of data filters, inconsistent variable treatment, and erroneous statistical conclusions. The Report suggests that the EJRA increased job creation rates at Cambridge, but we show Cambridge consistently had lower job creation rates for Established Academic Careers compared to other Russell Group universities, both before and after EJRA implementation in 2011, with no evidence for a significant change in this deficit post implementation. This suggests that EJRA is not a significant factor driving job creation rates. Since other universities without an EJRA exhibit higher job creation rates, this suggests job creation can be sustained without such a policy. We conclude that the EJRA did not achieve its intended goal of increasing opportunities for young academics and may have exacerbated existing disparities compared to other leading universities. We recom
Human Immunodeficiency Virus (HIV) has posed a major global health challenge for decades, and forecasting HIV diagnoses continues to be a critical area of research. However, capturing the complex spatial and temporal dependencies of HIV transmission remains challenging. Conventional Message Passing Neural Network (MPNN) models rely on a fixed binary adjacency matrix that only encodes geographic adjacency, which is unable to represent interactions between non-contiguous counties. Our study proposes a deep learning architecture Mobility-Aware Transformer-Message Passing Neural Network (MAT-MPNN) framework to predict county-level HIV diagnosis rates across California, Florida, and the New England region. The model combines temporal features extracted by a Transformer encoder with spatial relationships captured through a Mobility Graph Generator (MGG). The MGG improves conventional adjacency matrices by combining geographic and demographic information. Compared with the best-performing hybrid baseline, the Transformer MPNN model, MAT-MPNN reduced the Mean Squared Prediction Error (MSPE) by 27.9% in Florida, 39.1% in California, and 12.5% in New England, and improved the Predictive Mode
On October 19 and 20, 2023, the authors of this report convened in Cambridge, MA, to discuss the state of the database research field, its recent accomplishments and ongoing challenges, and future directions for research and community engagement. This gathering continues a long standing tradition in the database community, dating back to the late 1980s, in which researchers meet roughly every five years to produce a forward looking report. This report summarizes the key takeaways from our discussions. We begin with a retrospective on the academic, open source, and commercial successes of the community over the past five years. We then turn to future opportunities, with a focus on core data systems, particularly in the context of cloud computing and emerging hardware, as well as on the growing impact of data science, data governance, and generative AI. This document is not intended as an exhaustive survey of all technical challenges or industry innovations in the field. Rather, it reflects the perspectives of senior community members on the most pressing challenges and promising opportunities ahead.
These lecture notes cover the Standard Model (SM) course for Part III of the Cambridge Mathematical Tripos, taught during the years 2020-2023. The course comprised 25 lectures and 4 example classes. Following a brief historical introduction, the SM is constructed from first principles. We begin by demonstrating that essentially only particles with spin/helicity $0, \frac{1}{2}, 1, \frac{3}{2}, 2$ can describe matter and interactions, using spacetime symmetries, soft theorems, gauge redundancies, Ward identities, and perturbative unitarity. The remaining freedom lies in the choice of the Yang-Mills gauge group and matter representations. Effective field theories (EFTs) are a central theme throughout the course, with the 4-Fermi interactions and chiral perturbation theory serving as key examples. Both gravity and the SM itself are treated as EFTs, specifically as the SMEFT (Standard Model Effective Field Theory). Key phenomenological aspects of the SM are covered, including the Higgs mechanism, Yukawa couplings, the CKM matrix, the GIM mechanism, neutrino oscillations, running couplings, and asymptotic freedom. The discussion of anomalies and their non-trivial cancellations in the SM
This chapter examines the challenges of the revised opt out system and the secondary use of health data in England. The analysis of this data could be very valuable for science and medical treatment as well as for the discovery of new drugs. For this reason, the UK government established the care.data program in 2013. The aim of the project was to build a central nationwide database for research and policy planning. However, the processing of personal data was planned without proper public engagement. Research has suggested that IT companies, such as in the Google DeepMind deal case, had access to other kinds of sensitive data and failed to comply with data protection law. Since May 2018, the government has launched the national data opt out system with the hope of regaining public trust. Nevertheless, there are no evidence of significant changes in the ND opt out, compared to the previous opt out system. Neither in the use of secondary data, nor in the choices that patients can make. The only notorious difference seems to be in the way that these options are communicated and framed to the patients. Most importantly, according to the new ND opt out, the type 1 opt out option, which
This paper builds and extends on the authors' previous work related to the algorithmic tool, Cylindrical Algebraic Decomposition (CAD), and one of its core applications, Real Quantifier Elimination (QE). These topics are at the heart of symbolic computation and were first implemented in computer algebra systems decades ago, but have recently received renewed interest as part of the ongoing development of SMT solvers for non-linear real arithmetic. First, we consider the use of iterated univariate resultants in traditional CAD, and how this leads to inefficiencies, especially in the case of an input with multiple equational constraints. We reproduce the workshop paper [Davenport and England, 2023], adding important clarifications to our suggestions first made there to make use of multivariate resultants in the projection phase of CAD. We then consider an alternative approach to this problem first documented in [McCallum and Brown, 2009] which redefines the actual object under construction, albeit only in the case of two equational constraints. We correct an unhelpful typo and provide a proof missing from that paper. We finish by revising the topic of how to deal with SMT or Real QE
There has been an increasing number of applications of machine learning to the field of Computer Algebra in recent years, including to the prominent sub-field of Symbolic Integration. However, machine learning models require an abundance of data for them to be successful and there exist few benchmarks on the scale required. While methods to generate new data already exist, they are flawed in several ways which may lead to bias in machine learning models trained upon them. In this paper, we describe how to use the Risch Algorithm for symbolic integration to create a dataset of elementary integrable expressions. Further, we show that data generated this way alleviates some of the flaws found in earlier methods.
In England, it is anecdotally remarked that the number of Greggs bakeries to be found in a town is a reliable measure of the area's 'Northern-ness'. Conversely, a commercial competitor to Greggs in the baked goods and sandwiches market, Pret-a-Manger, is reputed to be popular in more 'southern' areas of England. Using a Support Vector Machine and an Artificial Neural Network (ANN) Regression Model, the relative geographical distributions of Greggs and Pret have been utilised for the first time to quantify the North-South divide in England. The calculated dividing lines were each compared to another line, based on Gross Domestic Household Income (GDHI). The lines match remarkably well, and we conclude that this is likely because much of England's wealth is concentrated in London, as are most of England's Pret-a-Manger shops. Further studies were conducted based on the relative geographical distributions of popular supermarkets Morrisons and Waitrose, which are also considered to have a North-South association. This analysis yields different results. For all metrics, the North-South dividing line passes close to the M1 Watford Gap services. As a common British idiom, this location is
The increased integration of variable renewable generation into the power systems, along with the phase-out of fossil-based power stations, necessitate procuring more flexibility from the demand sectors. The electrification of the residential heat sector is an option to decarbonise the heat sector in the United Kingdom. The inherent flexibility that is available in the residential heat sector, in the form of the thermal inertia of buildings, is expected to play an important role in supporting the critical task of short-term balancing of electricity supply and demand. This paper proposes a method for characterising the locally aggregated flexibility envelope from the electrified residential heat sector, considering the most influential factors including outdoor and indoor temperature, thermal mass and heat loss of dwellings. Applying the method to England and Wales as a case study, demonstrated a significant potential for a temporary reduction of electricity demand for heating even during cold weather. Total electricity demand reductions of approximately 25 GW to 85 GW were shown to be achievable for the outdoor temperature of 10 degreeC and -5 degreeC, respectively. Improving the e
Multiple choice exams are widely used to assess candidates across a diverse range of domains and tasks. To moderate question quality, newly proposed questions often pass through pre-test evaluation stages before being deployed into real-world exams. Currently, this evaluation process is manually intensive, which can lead to time lags in the question development cycle. Streamlining this process via automation can significantly enhance efficiency, however, there's a current lack of datasets with adequate pre-test analysis information. In this paper we analyse a subset of the public Cambridge Multiple-Choice Questions Reading Database released by Cambridge University Press & Assessment; a multiple-choice comprehension dataset of questions at different target levels, with corresponding candidate selection distributions. We introduce the task of candidate distribution matching, propose several evaluation metrics for the task, and demonstrate that automatic systems trained on RACE++ can be leveraged as baselines for our task. We further demonstrate that these automatic systems can be used for practical pre-test evaluation tasks such as detecting underperforming distractors, where our
In this work, we propose HyperPose, which utilizes hyper-networks in absolute camera pose regressors. The inherent appearance variations in natural scenes, attributable to environmental conditions, perspective, and lighting, induce a significant domain disparity between the training and test datasets. This disparity degrades the precision of contemporary localization networks. To mitigate this, we advocate for incorporating hypernetworks into single-scene and multiscene camera pose regression models. During inference, the hypernetwork dynamically computes adaptive weights for the localization regression heads based on the particular input image, effectively narrowing the domain gap. Using indoor and outdoor datasets, we evaluate the HyperPose methodology across multiple established absolute pose regression architectures. We also introduce and share the Extended Cambridge Landmarks (ECL), a novel localization dataset, based on the Cambridge Landmarks dataset, showing it in multiple seasons with significantly varying appearance conditions. Our empirical experiments demonstrate that HyperPose yields notable performance enhancements for single- and multi-scene architectures. We have ma
We introduce the Cambridge Law Corpus (CLC), a dataset for legal AI research. It consists of over 250 000 court cases from the UK. Most cases are from the 21st century, but the corpus includes cases as old as the 16th century. This paper presents the first release of the corpus, containing the raw text and meta-data. Together with the corpus, we provide annotations on case outcomes for 638 cases, done by legal experts. Using our annotated data, we have trained and evaluated case outcome extraction with GPT-3, GPT-4 and RoBERTa models to provide benchmarks. We include an extensive legal and ethical discussion to address the potentially sensitive nature of this material. As a consequence, the corpus will only be released for research purposes under certain restrictions.
We propose a new approach to identifying geographical clustering and hotspots of inequality from decadal census data. We use diffusion mapping to study the 181,408 Output Areas in England and Wales, which allows us to decompose the feature structures of countries in the census data space. Additionally, we develop a new localization metric inspired by statistical physics to uncover the importance of minority groups in London. The results of our study can be applied to other census-like data constructions that include spatial localization and differentiation from low degrees of freedom. This new approach can help us better understand the patterns of social deprivation and segregation across the country and aid in the development of policies to address these issues.
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-
Cylindrical Algebraic Decomposition (CAD) by projection and lifting requires many iterated univariate resultants. It has been observed that these often factor, but to date this has not been used to optimise implementations of CAD. We continue the investigation into such factorisations, writing in the specific context of SC-Square.
The prevalence of dementia is set to explode throughout the 21st century. This trend has already started in developed countries and will continue to place heavy pressures on both public health and social care services across the world. No cure for dementia is likely within the foreseeable future, however, medical research highlights the potential to diminish the risk of dementia onset. Over one-third of dementia cases may be preventable if certain risk factors are addressed at the individual, clinical, and population level. This research further explores these modifiable risk factors and quantifies areal risk through the use of a composite index. The index operates at National Health Service Clinical Commission Group level to assess spatial differences across England. Clear spatial patterns are observed between the north and south of the country, and between London and the remainder of the country. The framework adopted in this research provides a firm foundation upon which similar indices could be produced, potentially at finer spatial resolutions, incorporating more informed local knowledge and data on relevant dementia risk factors.
The COVID-19 pandemic has had high mortality rates in the elderly and frail worldwide, particularly in care homes. This is driven by the difficulty of isolating care homes from the wider community, the large population sizes within care facilities (relative to typical households), and the age/frailty of the residents. To quantify the mortality risk posed by disease, the case fatality risk (CFR) is an important tool. This quantifies the proportion of cases that result in death. Throughout the pandemic, CFR amongst care home residents in England has been monitored closely. To estimate CFR, we apply both novel and existing methods to data on deaths in care homes, collected by Public Health England and the Care Quality Commission. We compare these different methods, evaluating their relative strengths and weaknesses. Using these methods, we estimate temporal trends in the instantaneous CFR (at both daily and weekly resolutions) and the overall CFR across the whole of England, and dis-aggregated at regional level. We also investigate how the CFR varies based on age and on the type of care required, dis-aggregating by whether care homes include nursing staff and by age of residents. This