Physical modelling meets machine learning: performing music with a virtual string ensemble

This dissertation describes a new method of computer performance of bowed string instruments (violin, viola, cello) using physical simulations and intelligent feedback control. Computer synthesis of music performed by bowed string instruments is a challenging problem. Unlike instruments whose notes originate with a single discrete excitation (e.g., piano, guitar, drum), bowed string instruments are controlled with a continuous stream of excitations (i.e. the bow scraping against the string). Most existing synthesis methods utilize recorded audio samples, which perform quite well for single-excitation instruments but not continuous-excitation instruments. This work improves the realism of synthesis of violin, viola, and cello sound by generating audio through modelling the physical behaviour of the instruments. A string's wave equation is decomposed into 40 modes of vibration, which can be acted upon by three forms of external force: A bow scraping against the string, a left-hand finger pressing down, and/or a right-hand finger plucking. The vibration of each string exerts force against the instrument bridge; these forces are summed and convolved with the instrument body impulse response to create the final audio output. In addition, right-hand haptic output is created from the force of the bow against the string. Physical constants from ten real instruments (five violins, two violas, and three cellos) were measured and used in these simulations. The physical modelling was implemented in a high-performance library capable of simulating audio on a desktop computer one hundred times faster than real-time. The program also generates animated video of the instruments being performed. To perform music with the physical models, a virtual musician interprets the musical score and generates actions which are then fed into the physical model. The resulting audio and haptic signals are examined with a support vector machine, which adjusts the bow force in order to establish and maintain a good timbre. This intelligent feedback control is trained with human input, but after the initial training is completed the virtual musician performs autonomously. A PID controller is used to adjust the position of the left-hand finger to correct any flaws in the pitch. Some performance parameters (initial bow force, force correction, and lifting factors) require an initial value for each string and musical dynamic; these are calibrated automatically using the previously-trained support vector machines. The timbre judgements are retained after each performance and are used to pre-emptively adjust bowing parameters to avoid or mitigate problematic timbre for future performances of the same music. The system is capable of playing sheet music with approximately the same ability level as a human music student after two years of training. Due to the number of instruments measured and the generality of the machine learning, music can be performed with ensembles of up to ten stringed instruments, each with a distinct timbre. This provides a baseline for future work in computer control and expressive music performance of virtual bowed string instruments

Changes in symptomatology, reinfection, and transmissibility associated with the SARS-CoV-2 variant B.1.1.7: an ecological study

Background The SARS-CoV-2 variant B.1.1.7 was first identified in December, 2020, in England. We aimed to investigate whether increases in the proportion of infections with this variant are associated with differences in symptoms or disease course, reinfection rates, or transmissibility. Methods We did an ecological study to examine the association between the regional proportion of infections with the SARS-CoV-2 B.1.1.7 variant and reported symptoms, disease course, rates of reinfection, and transmissibility. Data on types and duration of symptoms were obtained from longitudinal reports from users of the COVID Symptom Study app who reported a positive test for COVID-19 between Sept 28 and Dec 27, 2020 (during which the prevalence of B.1.1.7 increased most notably in parts of the UK). From this dataset, we also estimated the frequency of possible reinfection, defined as the presence of two reported positive tests separated by more than 90 days with a period of reporting no symptoms for more than 7 days before the second positive test. The proportion of SARS-CoV-2 infections with the B.1.1.7 variant across the UK was estimated with use of genomic data from the COVID-19 Genomics UK Consortium and data from Public Health England on spike-gene target failure (a non-specific indicator of the B.1.1.7 variant) in community cases in England. We used linear regression to examine the association between reported symptoms and proportion of B.1.1.7. We assessed the Spearman correlation between the proportion of B.1.1.7 cases and number of reinfections over time, and between the number of positive tests and reinfections. We estimated incidence for B.1.1.7 and previous variants, and compared the effective reproduction number, Rt, for the two incidence estimates. Findings From Sept 28 to Dec 27, 2020, positive COVID-19 tests were reported by 36 920 COVID Symptom Study app users whose region was known and who reported as healthy on app sign-up. We found no changes in reported symptoms or disease duration associated with B.1.1.7. For the same period, possible reinfections were identified in 249 (0·7% [95% CI 0·6–0·8]) of 36 509 app users who reported a positive swab test before Oct 1, 2020, but there was no evidence that the frequency of reinfections was higher for the B.1.1.7 variant than for pre-existing variants. Reinfection occurrences were more positively correlated with the overall regional rise in cases (Spearman correlation 0·56–0·69 for South East, London, and East of England) than with the regional increase in the proportion of infections with the B.1.1.7 variant (Spearman correlation 0·38–0·56 in the same regions), suggesting B.1.1.7 does not substantially alter the risk of reinfection. We found a multiplicative increase in the Rt of B.1.1.7 by a factor of 1·35 (95% CI 1·02–1·69) relative to pre-existing variants. However, Rt fell below 1 during regional and national lockdowns, even in regions with high proportions of infections with the B.1.1.7 variant. Interpretation The lack of change in symptoms identified in this study indicates that existing testing and surveillance infrastructure do not need to change specifically for the B.1.1.7 variant. In addition, given that there was no apparent increase in the reinfection rate, vaccines are likely to remain effective against the B.1.1.7 variant. Funding Zoe Global, Department of Health (UK), Wellcome Trust, Engineering and Physical Sciences Research Council (UK), National Institute for Health Research (UK), Medical Research Council (UK), Alzheimer's Society

Hospital admission and emergency care attendance risk for SARS-CoV-2 delta (B.1.617.2) compared with alpha (B.1.1.7) variants of concern: a cohort study

Background: The SARS-CoV-2 delta (B.1.617.2) variant was first detected in England in March, 2021. It has since rapidly become the predominant lineage, owing to high transmissibility. It is suspected that the delta variant is associated with more severe disease than the previously dominant alpha (B.1.1.7) variant. We aimed to characterise the severity of the delta variant compared with the alpha variant by determining the relative risk of hospital attendance outcomes. Methods: This cohort study was done among all patients with COVID-19 in England between March 29 and May 23, 2021, who were identified as being infected with either the alpha or delta SARS-CoV-2 variant through whole-genome sequencing. Individual-level data on these patients were linked to routine health-care datasets on vaccination, emergency care attendance, hospital admission, and mortality (data from Public Health England's Second Generation Surveillance System and COVID-19-associated deaths dataset; the National Immunisation Management System; and NHS Digital Secondary Uses Services and Emergency Care Data Set). The risk for hospital admission and emergency care attendance were compared between patients with sequencing-confirmed delta and alpha variants for the whole cohort and by vaccination status subgroups. Stratified Cox regression was used to adjust for age, sex, ethnicity, deprivation, recent international travel, area of residence, calendar week, and vaccination status. Findings: Individual-level data on 43 338 COVID-19-positive patients (8682 with the delta variant, 34 656 with the alpha variant; median age 31 years [IQR 17–43]) were included in our analysis. 196 (2·3%) patients with the delta variant versus 764 (2·2%) patients with the alpha variant were admitted to hospital within 14 days after the specimen was taken (adjusted hazard ratio [HR] 2·26 [95% CI 1·32–3·89]). 498 (5·7%) patients with the delta variant versus 1448 (4·2%) patients with the alpha variant were admitted to hospital or attended emergency care within 14 days (adjusted HR 1·45 [1·08–1·95]). Most patients were unvaccinated (32 078 [74·0%] across both groups). The HRs for vaccinated patients with the delta variant versus the alpha variant (adjusted HR for hospital admission 1·94 [95% CI 0·47–8·05] and for hospital admission or emergency care attendance 1·58 [0·69–3·61]) were similar to the HRs for unvaccinated patients (2·32 [1·29–4·16] and 1·43 [1·04–1·97]; p=0·82 for both) but the precision for the vaccinated subgroup was low. Interpretation: This large national study found a higher hospital admission or emergency care attendance risk for patients with COVID-19 infected with the delta variant compared with the alpha variant. Results suggest that outbreaks of the delta variant in unvaccinated populations might lead to a greater burden on health-care services than the alpha variant. Funding: Medical Research Council; UK Research and Innovation; Department of Health and Social Care; and National Institute for Health Research

Genomic assessment of quarantine measures to prevent SARS-CoV-2 importation and transmission

Mitigation of SARS-CoV-2 transmission from international travel is a priority. We evaluated the effectiveness of travellers being required to quarantine for 14-days on return to England in Summer 2020. We identified 4,207 travel-related SARS-CoV-2 cases and their contacts, and identified 827 associated SARS-CoV-2 genomes. Overall, quarantine was associated with a lower rate of contacts, and the impact of quarantine was greatest in the 16–20 age-group. 186 SARS-CoV-2 genomes were sufficiently unique to identify travel-related clusters. Fewer genomically-linked cases were observed for index cases who returned from countries with quarantine requirement compared to countries with no quarantine requirement. This difference was explained by fewer importation events per identified genome for these cases, as opposed to fewer onward contacts per case. Overall, our study demonstrates that a 14-day quarantine period reduces, but does not completely eliminate, the onward transmission of imported cases, mainly by dissuading travel to countries with a quarantine requirement

Genomic epidemiology of SARS-CoV-2 in a UK university identifies dynamics of transmission

AbstractUnderstanding SARS-CoV-2 transmission in higher education settings is important to limit spread between students, and into at-risk populations. In this study, we sequenced 482 SARS-CoV-2 isolates from the University of Cambridge from 5 October to 6 December 2020. We perform a detailed phylogenetic comparison with 972 isolates from the surrounding community, complemented with epidemiological and contact tracing data, to determine transmission dynamics. We observe limited viral introductions into the university; the majority of student cases were linked to a single genetic cluster, likely following social gatherings at a venue outside the university. We identify considerable onward transmission associated with student accommodation and courses; this was effectively contained using local infection control measures and following a national lockdown. Transmission clusters were largely segregated within the university or the community. Our study highlights key determinants of SARS-CoV-2 transmission and effective interventions in a higher education setting that will inform public health policy during pandemics.</jats:p

Investigation of hospital discharge cases and SARS-CoV-2 introduction into Lothian care homes

Background The first epidemic wave of severe acute respiratory syndrome coronavirus-2 (SARS-CoV-2) in Scotland resulted in high case numbers and mortality in care homes. In Lothian, over one-third of care homes reported an outbreak, while there was limited testing of hospital patients discharged to care homes. Aim To investigate patients discharged from hospitals as a source of SARS-CoV-2 introduction into care homes during the first epidemic wave. Methods A clinical review was performed for all patients discharges from hospitals to care homes from 1st March 2020 to 31st May 2020. Episodes were ruled out based on coronavirus disease 2019 (COVID-19) test history, clinical assessment at discharge, whole-genome sequencing (WGS) data and an infectious period of 14 days. Clinical samples were processed for WGS, and consensus genomes generated were used for analysis using Cluster Investigation and Virus Epidemiological Tool software. Patient timelines were obtained using electronic hospital records. Findings In total, 787 patients discharged from hospitals to care homes were identified. Of these, 776 (99%) were ruled out for subsequent introduction of SARS-CoV-2 into care homes. However, for 10 episodes, the results were inconclusive as there was low genomic diversity in consensus genomes or no sequencing data were available. Only one discharge episode had a genomic, time and location link to positive cases during hospital admission, leading to 10 positive cases in their care home. Conclusion The majority of patients discharged from hospitals were ruled out for introduction of SARS-CoV-2 into care homes, highlighting the importance of screening all new admissions when faced with a novel emerging virus and no available vaccine

SARS-CoV-2 Omicron is an immune escape variant with an altered cell entry pathway

Vaccines based on the spike protein of SARS-CoV-2 are a cornerstone of the public health response to COVID-19. The emergence of hypermutated, increasingly transmissible variants of concern (VOCs) threaten this strategy. Omicron (B.1.1.529), the fifth VOC to be described, harbours multiple amino acid mutations in spike, half of which lie within the receptor-binding domain. Here we demonstrate substantial evasion of neutralization by Omicron BA.1 and BA.2 variants in vitro using sera from individuals vaccinated with ChAdOx1, BNT162b2 and mRNA-1273. These data were mirrored by a substantial reduction in real-world vaccine effectiveness that was partially restored by booster vaccination. The Omicron variants BA.1 and BA.2 did not induce cell syncytia in vitro and favoured a TMPRSS2-independent endosomal entry pathway, these phenotypes mapping to distinct regions of the spike protein. Impaired cell fusion was determined by the receptor-binding domain, while endosomal entry mapped to the S2 domain. Such marked changes in antigenicity and replicative biology may underlie the rapid global spread and altered pathogenicity of the Omicron variant

Taking the pulse of Earth's tropical forests using networks of highly distributed plots

Tropical forests are the most diverse and productive ecosystems on Earth. While better understanding of these forests is critical for our collective future, until quite recently efforts to measure and monitor them have been largely disconnected. Networking is essential to discover the answers to questions that transcend borders and the horizons of funding agencies. Here we show how a global community is responding to the challenges of tropical ecosystem research with diverse teams measuring forests tree-by-tree in thousands of long-term plots. We review the major scientific discoveries of this work and show how this process is changing tropical forest science. Our core approach involves linking long-term grassroots initiatives with standardized protocols and data management to generate robust scaled-up results. By connecting tropical researchers and elevating their status, our Social Research Network model recognises the key role of the data originator in scientific discovery. Conceived in 1999 with RAINFOR (South America), our permanent plot networks have been adapted to Africa (AfriTRON) and Southeast Asia (T-FORCES) and widely emulated worldwide. Now these multiple initiatives are integrated via ForestPlots.net cyber-infrastructure, linking colleagues from 54 countries across 24 plot networks. Collectively these are transforming understanding of tropical forests and their biospheric role. Together we have discovered how, where and why forest carbon and biodiversity are responding to climate change, and how they feedback on it. This long-term pan-tropical collaboration has revealed a large long-term carbon sink and its trends, as well as making clear which drivers are most important, which forest processes are affected, where they are changing, what the lags are, and the likely future responses of tropical forests as the climate continues to change. By leveraging a remarkably old technology, plot networks are sparking a very modern revolution in tropical forest science. In the future, humanity can benefit greatly by nurturing the grassroots communities now collectively capable of generating unique, long-term understanding of Earth's most precious forests. Resumen Los bosques tropicales son los ecosistemas más diversos y productivos del mundo y entender su funcionamiento es crítico para nuestro futuro colectivo. Sin embargo, hasta hace muy poco, los esfuerzos para medirlos y monitorearlos han estado muy desconectados. El trabajo en redes es esencial para descubrir las respuestas a preguntas que trascienden las fronteras y los plazos de las agencias de financiamiento. Aquí mostramos cómo una comunidad global está respondiendo a los desafíos de la investigación en ecosistemas tropicales a través de diversos equipos realizando mediciones árbol por árbol en miles de parcelas permanentes de largo plazo. Revisamos los descubrimientos más importantes de este trabajo y discutimos cómo este proceso está cambiando la ciencia relacionada a los bosques tropicales. El enfoque central de nuestro esfuerzo implica la conexión de iniciativas locales de largo plazo con protocolos estandarizados y manejo de datos para producir resultados que se puedan trasladar a múltiples escalas. Conectando investigadores tropicales, elevando su posición y estatus, nuestro modelo de Red Social de Investigación reconoce el rol fundamental que tienen, para el descubrimiento científico, quienes generan o producen los datos. Concebida en 1999 con RAINFOR (Suramérica), nuestras redes de parcelas permanentes han sido adaptadas en África (AfriTRON) y el sureste asiático (T-FORCES) y ampliamente replicadas en el mundo. Actualmente todas estas iniciativas están integradas a través de la ciber-infraestructura de ForestPlots.net, conectando colegas de 54 países en 24 redes diferentes de parcelas. Colectivamente, estas redes están transformando nuestro conocimiento sobre los bosques tropicales y el rol de éstos en la biósfera. Juntos hemos descubierto cómo, dónde y porqué el carbono y la biodiversidad de los bosques tropicales está respondiendo al cambio climático y cómo se retroalimentan. Esta colaboración pan-tropical de largo plazo ha expuesto un gran sumidero de carbono y sus tendencias, mostrando claramente cuáles son los factores más importantes, qué procesos se ven afectados, dónde ocurren los cambios, los tiempos de reacción y las probables respuestas futuras mientras el clima continúa cambiando. Apalancando lo que realmente es una tecnología antigua, las redes de parcelas están generando una verdadera y moderna revolución en la ciencia tropical. En el futuro, la humanidad puede beneficiarse enormemente si se nutren y cultivan comunidades de investigadores de base, actualmente con la capacidad de generar información única y de largo plazo para entender los que probablemente son los bosques más preciados de la tierra. Resumo Florestas tropicais são os ecossistemas mais diversos e produtivos da Terra. Embora uma boa compreensão destas florestas seja crucial para o nosso futuro coletivo, até muito recentemente os esforços de medições e monitoramento foram amplamente desconexos. É essencial formarmos redes para obtermos respostas que transcendem fronteiras e horizontes de agências financiadoras. Neste estudo nós mostramos como uma comunidade global está respondendo aos desafios da pesquisa de ecossistemas tropicais, com equipes diversas medindo florestas, árvore por árvore, em milhares de parcelas monitoradas à longo prazo. Nós revisamos as maiores descobertas científicas deste trabalho, e mostramos também como este processo está mudando a ciência de florestas tropicais. Nossa abordagem principal envolve unir iniciativas de base a protocolos padronizados e gerenciamento de dados a fim de gerar resultados robustos em escalas ampliadas. Ao conectar pesquisadores tropicais e elevar seus status, nosso modelo de Rede de Pesquisa Social reconhece o papel-chave do produtor dos dados na descoberta científica. Concebida em 1999 com o RAINFOR (América do Sul), nossa rede de parcelas permanentes foi adaptada para África (AfriTRON) e Sudeste asiático (T-FORCES), e tem sido extensamente reproduzida em todo o mundo. Agora estas múltiplas iniciativas estão integradas através de uma infraestrutura cibernética do ForestPlots.net, conectando colegas de 54 países de 24 redes de parcelas. Estas iniciativas estão transformando coletivamente o entendimento das florestas tropicais e seus papéis na biosfera. Juntos nós descobrimos como, onde e por que o carbono e a biodiversidade da floresta estão respondendo às mudanças climáticas, e seus efeitos de retroalimentação. Esta duradoura colaboração pantropical revelou um grande sumidouro de carbono persistente e suas tendências, assim como tem evidenciado quais direcionadores são mais importantes, quais processos florestais são mais afetados, onde eles estão mudando, seus atrasos no tempo de resposta, e as prováveis respostas das florestas tropicais conforme o clima continua a mudar. Dessa forma, aproveitando uma notável tecnologia antiga, redes de parcelas acendem faíscas de uma moderna revolução na ciência das florestas tropicais. No futuro a humanidade pode se beneficiar incentivando estas comunidades basais que agora são coletivamente capazes de gerar conhecimentos únicos e duradouros sobre as florestas mais preciosas da Terra. Résume Les forêts tropicales sont les écosystèmes les plus diversifiés et les plus productifs de la planète. Si une meilleure compréhension de ces forêts est essentielle pour notre avenir collectif, jusqu'à tout récemment, les efforts déployés pour les mesurer et les surveiller ont été largement déconnectés. La mise en réseau est essentielle pour découvrir les réponses à des questions qui dépassent les frontières et les horizons des organismes de financement. Nous montrons ici comment une communauté mondiale relève les défis de la recherche sur les écosystèmes tropicaux avec diverses équipes qui mesurent les forêts arbre après arbre dans de milliers de parcelles permanentes. Nous passons en revue les principales découvertes scientifiques de ces travaux et montrons comment ce processus modifie la science des forêts tropicales. Notre approche principale consiste à relier les initiatives de base à long terme à des protocoles standardisés et une gestion de données afin de générer des résultats solides à grande échelle. En reliant les chercheurs tropicaux et en élevant leur statut, notre modèle de réseau de recherche sociale reconnaît le rôle clé de l'auteur des données dans la découverte scientifique. Conçus en 1999 avec RAINFOR (Amérique du Sud), nos réseaux de parcelles permanentes ont été adaptés à l'Afrique (AfriTRON) et à l'Asie du Sud-Est (T-FORCES) et largement imités dans le monde entier. Ces multiples initiatives sont désormais intégrées via l'infrastructure ForestPlots.net, qui relie des collègues de 54 pays à travers 24 réseaux de parcelles. Ensemble, elles transforment la compréhension des forêts tropicales et de leur rôle biosphérique. Ensemble, nous avons découvert comment, où et pourquoi le carbone forestier et la biodiversité réagissent au changement climatique, et comment ils y réagissent. Cette collaboration pan-tropicale à long terme a révélé un important puits de carbone à long terme et ses tendances, tout en mettant en évidence les facteurs les plus importants, les processus forestiers qui sont affectés, les endroits où ils changent, les décalages et les réactions futures probables des forêts tropicales à mesure que le climat continue de changer. En tirant parti d'une technologie remarquablement ancienne, les réseaux de parcelles déclenchent une révolution très moderne dans la science des forêts tropicales. À l'avenir, l'humanité pourra grandement bénéficier du soutien des communautés de base qui sont maintenant collectivement capables de générer une compréhension unique et à long terme des forêts les plus précieuses de la Terre. Abstrak Hutan tropika adalah di antara ekosistem yang paling produktif dan mempunyai kepelbagaian biodiversiti yang tinggi di seluruh dunia. Walaupun pemahaman mengenai hutan tropika amat penting untuk masa depan kita, usaha-usaha untuk mengkaji dan mengawas hutah-hutan tersebut baru sekarang menjadi lebih diperhubungkan. Perangkaian adalah sangat penting untuk mencari jawapan kepada soalan-soalan yang menjangkaui sempadan dan batasan agensi pendanaan. Di sini kami menunjukkan bagaimana sebuah komuniti global bertindak balas terhadap cabaran penyelidikan ekosistem tropika melalui penglibatan pelbagai kumpulan yang mengukur hutan secara pokok demi pokok dalam beribu-ribu plot jangka panjang. Kami meninjau semula penemuan saintifik utama daripada kerja ini dan menunjukkan bagaimana proses ini sedang mengubah bidang sains hutan tropika. Teras pendekatan kami memberi tumpuan terhadap penghubungan inisiatif akar umbi jangka panjang dengan protokol standar serta pengurusan data untuk mendapatkan hasil skala besar yang kukuh. Dengan menghubungkan penyelidik-penyelidik tropika dan meningkatkan status mereka, model Rangkaian Penyelidikan Sosial kami mengiktiraf kepentingan peranan pengasas data dalam penemuan saintifik. Bermula dengan pengasasan RAINFOR (Amerika Selatan) pada tahun 1999, rangkaian-rangkaian plot kekal kami kemudian disesuaikan untuk Afrika (AfriTRON) dan Asia Tenggara (T-FORCES) dan selanjutnya telah banyak dicontohi di seluruh dunia. Kini, inisiatif-inisiatif tersebut disepadukan melalui infrastruktur siber ForestPlots.net yang menghubungkan rakan sekerja dari 54 negara di 24 buah rangkaian plot. Secara kolektif, rangkaian ini sedang mengubah pemahaman tentang hutan tropika dan peranannya dalam biosfera. Kami telah bekerjasama untuk menemukan bagaimana, di mana dan mengapa karbon serta biodiversiti hutan bertindak balas terhadap perubahan iklim dan juga bagaimana mereka saling bermaklum balas. Kolaborasi pan-tropika jangka panjang ini telah mendedahkan sebuah sinki karbon jangka panjang serta arah alirannya dan juga menjelaskan pemandu-pemandu perubahan yang terpenting, di mana dan bagaimana proses hutan terjejas, masa susul yang ada dan kemungkinan tindakbalas hutan tropika pada perubahan iklim secara berterusan di masa depan. Dengan memanfaatkan pendekatan lama, rangkaian plot sedang menyalakan revolusi yang amat moden dalam sains hutan tropika. Pada masa akan datang, manusia sejagat akan banyak mendapat manfaat jika memupuk komuniti-komuniti akar umbi yang kini berkemampuan secara kolektif menghasilkan pemahaman unik dan jangka panjang mengenai hutan-hutan yang paling berharga di dunia

Genomic reconstruction of the SARS-CoV-2 epidemic in England.

The evolution of the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) virus leads to new variants that warrant timely epidemiological characterization. Here we use the dense genomic surveillance data generated by the COVID-19 Genomics UK Consortium to reconstruct the dynamics of 71 different lineages in each of 315 English local authorities between September 2020 and June 2021. This analysis reveals a series of subepidemics that peaked in early autumn 2020, followed by a jump in transmissibility of the B.1.1.7/Alpha lineage. The Alpha variant grew when other lineages declined during the second national lockdown and regionally tiered restrictions between November and December 2020. A third more stringent national lockdown suppressed the Alpha variant and eliminated nearly all other lineages in early 2021. Yet a series of variants (most of which contained the spike E484K mutation) defied these trends and persisted at moderately increasing proportions. However, by accounting for sustained introductions, we found that the transmissibility of these variants is unlikely to have exceeded the transmissibility of the Alpha variant. Finally, B.1.617.2/Delta was repeatedly introduced in England and grew rapidly in early summer 2021, constituting approximately 98% of sampled SARS-CoV-2 genomes on 26 June 2021