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This document presents the outcomes of a comprehensive survey conducted among early career researchers (ECRs) in academic particle physics. Running from September 24, 2022, to March 3, 2023, the survey gathered responses from 759 ECRs employed in 39 countries. The study aimed to gain insights into the career prospects and experiences of ECRs while also delving into diversity and sociological aspects within particle physics research. The survey results are presented in a manner consistent with the survey choices. The document offers insights for the particle physics community, and provides a set of recommendations for enhancing career prospects, fostering diversity, and addressing sociological dimensions within this field., Comment: Editors: Julia Allen, Kate\v{r}ina Jarkovsk\'a, Aleksandra Lelek, Holly Pacey, Guillaume Pietrzyk and G\'eraldine R\"auber

Protecting patient privacy in healthcare records is a top priority, and redaction is a commonly used method for obscuring directly identifiable information in text. Rule-based methods have been widely used, but their precision is often low causing over-redaction of text and frequently not being adaptable enough for non-standardised or unconventional structures of personal health information. Deep learning techniques have emerged as a promising solution, but implementing them in real-world environments poses challenges due to the differences in patient record structure and language across different departments, hospitals, and countries. In this study, we present AnonCAT, a transformer-based model and a blueprint on how deidentification models can be deployed in real-world healthcare. AnonCAT was trained through a process involving manually annotated redactions of real-world documents from three UK hospitals with different electronic health record systems and 3116 documents. The model achieved high performance in all three hospitals with a Recall of 0.99, 0.99 and 0.96. Our findings demonstrate the potential of deep learning techniques for improving the efficiency and accuracy of redaction in global healthcare data and highlight the importance of building workflows which not just use these models but are also able to continually fine-tune and audit the performance of these algorithms to ensure continuing effectiveness in real-world settings. This approach provides a blueprint for the real-world use of de-identifying algorithms through fine-tuning and localisation, the code together with tutorials is available on GitHub (https://github.com/CogStack/MedCAT).

The increasing adoption of natural language processing (NLP) models across industries has led to practitioners' need for machine learning systems to handle these models efficiently, from training to serving them in production. However, training, deploying, and updating multiple models can be complex, costly, and time-consuming, mainly when using transformer-based pre-trained language models. Multi-Task Learning (MTL) has emerged as a promising approach to improve efficiency and performance through joint training, rather than training separate models. Motivated by this, we first provide an overview of transformer-based MTL approaches in NLP. Then, we discuss the challenges and opportunities of using MTL approaches throughout typical ML lifecycle phases, specifically focusing on the challenges related to data engineering, model development, deployment, and monitoring phases. This survey focuses on transformer-based MTL architectures and, to the best of our knowledge, is novel in that it systematically analyses how transformer-based MTL in NLP fits into ML lifecycle phases. Furthermore, we motivate research on the connection between MTL and continual learning (CL), as this area remains unexplored. We believe it would be practical to have a model that can handle both MTL and CL, as this would make it easier to periodically re-train the model, update it due to distribution shifts, and add new capabilities to meet real-world requirements.

ESSnuSB is a design study for an experiment to measure the CP violation in the leptonic sector at the second neutrino oscillation maximum using a neutrino beam driven by the uniquely powerful ESS linear accelerator. The reduced impact of systematic errors on sensitivity at the second maximum allows for a very precise measurement of the CP violating parameter. This review describes the fundamental advantages of measurement at the 2nd maximum, the necessary upgrades to the ESS linac in order to produce a neutrino beam, the near and far detector complexes, the expected physics reach of the proposed ESSnuSB experiment, concluding with the near future developments aimed at the project realization., Comment: 19 pages, 12 figures; Final version after review by the Universe journal

The European Committee for Future Accelerators (ECFA) Early Career Researcher's (ECR) panel, which represents the interests of the ECR community to ECFA, officially began its activities in January 2021. In the first two years, the panel has defined its own internal structure, responded to ECFA requests for feedback, and launched its own initiatives to better understand and support the diverse interests of early career researchers. This report summarises the panel composition and structure, as well as the different activities the panel has been involved with during the first two years of its existence., Comment: Editors: Jan-Hendrik Arling, Emanuele Bagnaschi, Xabier Cid Vidal, Katherine Dunne, Viktoria Hinger, Armin Ilg, Henning Kirschenmann, Steven Schramm, Pawe{\l} Sznajder, Sarah Williams, Valentina Zaccolo

Background: Electronic Health Records hold detailed longitudinal information about each patient's health status and general clinical history, a large portion of which is stored within the unstructured text. Existing approaches focus mostly on structured data and a subset of single-domain outcomes. We explore how temporal modelling of patients from free text and structured data, using deep generative transformers can be used to forecast a wide range of future disorders, substances, procedures or findings. Methods: We present Foresight, a novel transformer-based pipeline that uses named entity recognition and linking tools to convert document text into structured, coded concepts, followed by providing probabilistic forecasts for future medical events such as disorders, substances, procedures and findings. We processed the entire free-text portion from three different hospital datasets totalling 811336 patients covering both physical and mental health. Findings: On tests in two UK hospitals (King's College Hospital, South London and Maudsley) and the US MIMIC-III dataset precision@10 0.68, 0.76 and 0.88 was achieved for forecasting the next disorder in a patient timeline, while precision@10 of 0.80, 0.81 and 0.91 was achieved for forecasting the next biomedical concept. Foresight was also validated on 34 synthetic patient timelines by five clinicians and achieved relevancy of 97% for the top forecasted candidate disorder. As a generative model, it can forecast follow-on biomedical concepts for as many steps as required. Interpretation: Foresight is a general-purpose model for biomedical concept modelling that can be used for real-world risk forecasting, virtual trials and clinical research to study the progression of disorders, simulate interventions and counterfactuals, and educational purposes.

Presently under construction in Lund, Sweden, the European Spallation Source (ESS) will be the world's brightest neutron source. As such, it has the potential for a particle physics program with a unique reach and which is complementary to that available at other facilities. This paper describes proposed particle physics activities for the ESS. These encompass the exploitation of both the neutrons and neutrinos produced at the ESS for high precision (sensitivity) measurements (searches)., Comment: 121 pages, updated version after referee comments

This conceptual design report provides a detailed account of the European Spallation Source neutrino Super Beam (ESS$\nu$SB) feasibility study. This facility has been proposed after the measurements reported in 2012 of a relatively large value of the neutrino mixing angle $\theta_{13}$, which raised the possibility of observing potential CP violation in the leptonic sector with conventional neutrino beams. The measured value of $\theta_{13}$ also privileges the $2^{nd}$ oscillation maximum for the discovery of CP violation instead of the more typically studied $1^{st}$ maximum. The sensitivity at this $2^{nd}$ oscillation maximum is about three times higher than at the $1^{st}$ one, which implies a reduced influence of systematic errors. Working at the $2^{nd}$ oscillation maximum requires a very intense neutrino beam with an appropriate energy. The world's most intense pulsed spallation neutron source, the European Spallation Source (ESS), will have a proton linac operating at 5\,MW power, 2\,GeV kinetic energy and 14~Hz repetition rate (3~ms pulse duration, 4\% duty cycle) for neutron production. In this design study it is proposed to double the repetition rate and compress the beam pulses to the level of microseconds in order to provide an additional 5~MW proton beam for neutrino production. The physics performance has been evaluated for such a neutrino super beam, in conjunction with a megaton-scale underground water Cherenkov neutrino detector installed at a distance of 360--550\,km from ESS. The ESS proton linac upgrades, the accumulator ring required for proton-pulse compression, the target station design and optimisation, the near and far detector complexes, and the physics potential of the facility are all described in this report. The ESS linac will be operational by 2025, at which point the implementation of upgrades for the neutrino facility could begin., Comment: 216 pages

In this Snowmass 2021 white paper, we summarise the Conceptual Design of the European Spallation Source neutrino Super Beam (ESSvSB) experiment and its synergies with the possible future muon based facilities, e.g. a Low Energy nuSTORM and the Muon Collider. The ESSvSB will benefit from the high power, 5 MW, of the European Spallation Source (ESS) LINAC in Lund-Sweden to produce the world most intense neutrino beam, enabling measurements to be made at the second oscillation maximum. Assuming a ten-year exposure, physics simulations show that the CP-invariance violation can be established with a significance of 5 sigma over more than 70% of all values of delta CP and with an error in the measurement of the delta CP angle of less than 8 degree for all values of delta CP. However, several technological and physics challenges must be further studied before achieving a final Technical Design. Measuring at the 2nd oscillation maximum necessitates a very intense neutrino beam with the appropriate energy. For this, the ESS proton beam LINAC, which is designed to produce the world's most intense neutron beam, will need to be upgraded to 10 MW power, 2.5 GeV energy and 28 Hz beam pulse repetition rate. An accumulator ring will be required for the compression of the ESS LINAC beam pulse from 2.86 ms to 1.3 mus. A high power target station facility will be needed to produce a well-focused intense (super) mu-neutrino beam. The physics performance of that neutrino Super Beam in conjunction with a megaton underground Water Cherenkov neutrino far detector installed at a distance of either 360 km or 540 km from the ESS, the baseline, has been evaluated., Comment: contribution to Snowmass 2021

We report the design, operation and performance of a high-resolution, low-latency, bunch-by-bunch feedback system for nano-beam stabilisation. The system employs novel, ultra-low quality-factor cavity beam position monitors (BPMs), a two-stage analogue signal down-mixing system, and a digital signal processing and feedback board incorporating an FPGA. The FPGA firmware allows for the real-time integration of up to fifteen samples of the BPM waveforms within a measured latency of 232 ns. We show that this real-time sample integration improves significantly the beam position resolution and, consequently, the feedback performance. The best demonstrated real-time beam position resolution was 19 nm, which, as far as we are aware, is the best real-time resolution achieved in any operating BPM system. The feedback was operated in two complementary modes to stabilise the vertical position of the ultra-small beam produced at the focal point of the ATF2 beamline at KEK. In single-BPM feedback mode, beam stabilisation to 50$\pm$5 nm was demonstrated. In two-BPM feedback mode, beam stabilisation to 41$\pm$4 nm was achieved.

The data available in Electronic Health Records (EHRs) provides the opportunity to transform care, and the best way to provide better care for one patient is through learning from the data available on all other patients. Temporal modelling of a patient's medical history, which takes into account the sequence of past events, can be used to predict future events such as a diagnosis of a new disorder or complication of a previous or existing disorder. While most prediction approaches use mostly the structured data in EHRs or a subset of single-domain predictions and outcomes, we present MedGPT a novel transformer-based pipeline that uses Named Entity Recognition and Linking tools (i.e. MedCAT) to structure and organize the free text portion of EHRs and anticipate a range of future medical events (initially disorders). Since a large portion of EHR data is in text form, such an approach benefits from a granular and detailed view of a patient while introducing modest additional noise. MedGPT effectively deals with the noise and the added granularity, and achieves a precision of 0.344, 0.552 and 0.640 (vs LSTM 0.329, 0.538 and 0.633) when predicting the top 1, 3 and 5 candidate future disorders on real world hospital data from King's College Hospital, London, UK (\textasciitilde600k patients). We also show that our model captures medical knowledge by testing it on an experimental medical multiple choice question answering task, and by examining the attentional focus of the model using gradient-based saliency methods., Comment: 6 pages, 2 figures, 3 tables

The European Committee for Future Accelerators (ECFA) Early-Career Researchers (ECR) Panel was invited by the ECFA Detector R&D Roadmap conveners to collect feedback from the European ECR community. A working group within the ECFA ECR panel held a Townhall Meeting to get first input, and then designed and broadly circulated a detailed survey to gather feedback from the larger ECR community. A total of 473 responses to this survey were received, providing a useful overview of the experiences of ECRs in instrumentation training and related topics. This report summarises the feedback received, and is intended to serve as an input to the ECFA Detector R&D Roadmap process., Comment: Editors: Jan-Hendrik Arling, Katherine Dunne, Armin Ilg, Adri\'an Irles, Predrag Milenovic, Steven Schramm, Mariana Shopova, and Sarah Williams

In this paper, we present the physics performance of the ESSnuSB experiment in the standard three flavor scenario using the updated neutrino flux calculated specifically for the ESSnuSB configuration and updated migration matrices for the far detector. Taking conservative systematic uncertainties corresponding to a normalization error of $5\%$ for signal and $10\%$ for background, we find that there is $10\sigma$ $(13\sigma)$ CP violation discovery sensitivity for the baseline option of 540 km (360 km) at $\delta_{\rm CP} = \pm 90^\circ$. The corresponding fraction of $\delta_{\rm CP}$ for which CP violation can be discovered at more than $5 \sigma$ is $70\%$. Regarding CP precision measurements, the $1\sigma$ error associated with $\delta_{\rm CP} = 0^\circ$ is around $5^\circ$ and with $\delta_{\rm CP} = -90^\circ$ is around $14^\circ$ $(7^\circ)$ for the baseline option of 540 km (360 km). For hierarchy sensitivity, one can have $3\sigma$ sensitivity for 540 km baseline except $\delta_{\rm CP} = \pm 90^\circ$ and $5\sigma$ sensitivity for 360 km baseline for all values of $\delta_{\rm CP}$. The octant of $\theta_{23}$ can be determined at $3 \sigma$ for the values of: $\theta_{23} > 51^\circ$ ($\theta_{23} < 42^\circ$ and $\theta_{23} > 49^\circ$) for baseline of 540 km (360 km). Regarding measurement precision of the atmospheric mixing parameters, the allowed values at $3 \sigma$ are: $40^\circ < \theta_{23} < 52^\circ$ ($42^\circ < \theta_{23} < 51.5^\circ$) and $2.485 \times 10^{-3}$ eV$^2 < \Delta m^2_{31} < 2.545 \times 10^{-3}$ eV$^2$ ($2.49 \times 10^{-3}$ eV$^2 < \Delta m^2_{31} < 2.54 \times 10^{-3}$ eV$^2$) for the baseline of 540 km (360 km)., Comment: 13 pages, 8 figures, 3 tables. Changes: Text updated, this is a published version

Negative hydrogen ions are often used for injecting protons from linacs to storage rings via charge-exchange injection. In this process, the two electrons are stripped by a foil or laser to produce protons which can be merged with an existing beam without significantly affecting its dynamics, allowing high intensities of protons to be accumulated. However, this capability comes with the drawback that the outer electron of an H$^-$ ion has a low binding energy and can easily be stripped away prior to injection. This paper addresses the following stripping mechanisms: interactions with residual gas in the beam pipe, blackbody radiation from accelerator components, and electromagnetic fields from accelerator optics (Lorentz-force stripping) and particles within the bunch itself (intrabeam stripping); with a discussion on how to avoid excessive activation from stripped H$^0$ particles and protons. We also demonstrate that the proportion of stripped H$^0$ colliding with a nearby beam pipe or machine-element walls presents only roughly 10\% of those lost in stripping; the remaining stripped particles traverse to the end of a linac or local straight section, which may relax the limits for allowable stripping-based beam loss in H$^-$ accelerators., Comment: 7 pages

The ability to perform accurate prognosis of patients is crucial for proactive clinical decision making, informed resource management and personalised care. Existing outcome prediction models suffer from a low recall of infrequent positive outcomes. We present a highly-scalable and robust machine learning framework to automatically predict adversity represented by mortality and ICU admission from time-series vital signs and laboratory results obtained within the first 24 hours of hospital admission. The stacked platform comprises two components: a) an unsupervised LSTM Autoencoder that learns an optimal representation of the time-series, using it to differentiate the less frequent patterns which conclude with an adverse event from the majority patterns that do not, and b) a gradient boosting model, which relies on the constructed representation to refine prediction, incorporating static features of demographics, admission details and clinical summaries. The model is used to assess a patient's risk of adversity over time and provides visual justifications of its prediction based on the patient's static features and dynamic signals. Results of three case studies for predicting mortality and ICU admission show that the model outperforms all existing outcome prediction models, achieving PR-AUC of 0.891 (95$%$ CI: 0.878 - 0.969) in predicting mortality in ICU and general ward settings and 0.908 (95$%$ CI: 0.870-0.935) in predicting ICU admission., Comment: 14 pages

Electronic health records (EHR) contain large volumes of unstructured text, requiring the application of Information Extraction (IE) technologies to enable clinical analysis. We present the open-source Medical Concept Annotation Toolkit (MedCAT) that provides: a) a novel self-supervised machine learning algorithm for extracting concepts using any concept vocabulary including UMLS/SNOMED-CT; b) a feature-rich annotation interface for customising and training IE models; and c) integrations to the broader CogStack ecosystem for vendor-agnostic health system deployment. We show improved performance in extracting UMLS concepts from open datasets (F1:0.448-0.738 vs 0.429-0.650). Further real-world validation demonstrates SNOMED-CT extraction at 3 large London hospitals with self-supervised training over ~8.8B words from ~17M clinical records and further fine-tuning with ~6K clinician annotated examples. We show strong transferability (F1 > 0.94) between hospitals, datasets, and concept types indicating cross-domain EHR-agnostic utility for accelerated clinical and research use cases., Comment: Preprint: 27 Pages, 3 Figures

We study corners and fundamental corners of the irreducible representations of the groups G=Spin(n,1) that are not elementary, i.e. that are equivalent to subquotients of reducible nonunitary principal series representations. For even n we obtain results in a way analogous to the results in [10] for the groups SU(n,1). Especially, we again get a bijection between the nonelementary part $\hat{G}^0$ of the unitary dual $\hat{G}$ and the unitary dual $\hat{K}.$ In the case of odd n we get a bijection between $\hat{G}^0$ and a tru subset of $\hat{K}.$

The Compact Linear Collider (CLIC) targets a nanometre beam size at the collision point. Realising this beam size requires the generation and transport of ultra-low emittance beams. Dynamic imperfections can deflect the colliding beams, leading to a collision with a relative offset. They can also degrade the emittance of each beam. Both of these effects can significantly impact the luminosity of CLIC. In this paper, we examine a newly considered dynamic imperfection: stray magnetic fields. Measurements of stray magnetic fields in the Large Hadron Collider tunnel are presented and used to develop a statistical model that can be used to realistically generate stray magnetic fields in simulations. The model is used in integrated simulations of CLIC at 380GeV including mitigation systems for stray magnetic fields to evaluate their impact on luminosity.

There is an increasing need to shield beams and accelerator elements from stray magnetic fields. The application of magnetic shielding in linear colliders is discussed. The shielding performance of soft iron and mu-metal is measured for magnetic fields of varying amplitude and frequency. Special attention is given to characterise the shielding performance for very small-amplitude magnetic fields.

The Compact Linear Collider is one of the two main European options for a collider in a post Large Hadron Collider era. This is a linear $e^+e^-$ collider with three centre-of-mass energy stages: 380 GeV, 1.5 TeV and 3 TeV. The luminosity performance of the first stage at 380 GeV is presented including the impact of static and dynamic imperfections. These calculations are performed with fully realistic tracking simulations from the exit of the damping rings to the interaction point and including beam-beam effects in the collisions. A luminosity of $4.3\times10^{34}\,\text{cm}^{-2}\text{s}^{-1}$ can be achieved with a perfect collider, which is almost three times the nominal luminosity target of $1.5\times10^{34}\,\text{cm}^{-2}\text{s}^{-1}$. In simulations with static imperfections, a luminosity of $2.35\times10^{34}\,\text{cm}^{-2}\text{s}^{-1}$ or greater is achieved by 90% of randomly misaligned colliders. Expressed as a percentage of the nominal luminosity target, this is a surplus of approximately 57%. Including the impact of ground motion, a luminosity surplus of 53% or greater can be expected for 90% of colliders. The average expected luminosity is $2.8\times10^{34}~\text{cm}^{-2}\text{s}^{-1}$, which is almost twice the nominal luminosity target.

Text classification tasks which aim at harvesting and/or organizing information from electronic health records are pivotal to support clinical and translational research. However these present specific challenges compared to other classification tasks, notably due to the particular nature of the medical lexicon and language used in clinical records. Recent advances in embedding methods have shown promising results for several clinical tasks, yet there is no exhaustive comparison of such approaches with other commonly used word representations and classification models. In this work, we analyse the impact of various word representations, text pre-processing and classification algorithms on the performance of four different text classification tasks. The results show that traditional approaches, when tailored to the specific language and structure of the text inherent to the classification task, can achieve or exceed the performance of more recent ones based on contextual embeddings such as BERT.

Multimorbidity research in mental health services requires data from physical health conditions which is traditionally limited in mental health care electronic health records. In this study, we aimed to extract data from physical health conditions from clinical notes using SemEHR. Data was extracted from Clinical Record Interactive Search (CRIS) system at South London and Maudsley Biomedical Research Centre (SLaM BRC) and the cohort consisted of all individuals who had received a primary or secondary diagnosis of severe mental illness between 2007 and 2018. Three pairs of annotators annotated 2403 documents with an average Cohen's Kappa of 0.757. Results show that the NLP performance varies across different diseases areas (F1 0.601 - 0.954) suggesting that the language patterns or terminologies of different condition groups entail different technical challenges to the same NLP task., Comment: 4 pages, 2 tables

Biomedical documents such as Electronic Health Records (EHRs) contain a large amount of information in an unstructured format. The data in EHRs is a hugely valuable resource documenting clinical narratives and decisions, but whilst the text can be easily understood by human doctors it is challenging to use in research and clinical applications. To uncover the potential of biomedical documents we need to extract and structure the information they contain. The task at hand is Named Entity Recognition and Linking (NER+L). The number of entities, ambiguity of words, overlapping and nesting make the biomedical area significantly more difficult than many others. To overcome these difficulties, we have developed the Medical Concept Annotation Tool (MedCAT), an open-source unsupervised approach to NER+L. MedCAT uses unsupervised machine learning to disambiguate entities. It was validated on MIMIC-III (a freely accessible critical care database) and MedMentions (Biomedical papers annotated with mentions from the Unified Medical Language System). In case of NER+L, the comparison with existing tools shows that MedCAT improves the previous best with only unsupervised learning (F1=0.848 vs 0.691 for disease detection; F1=0.710 vs. 0.222 for general concept detection). A qualitative analysis of the vector embeddings learnt by MedCAT shows that it captures latent medical knowledge available in EHRs (MIMIC-III). Unsupervised learning can improve the performance of large scale entity extraction, but it has some limitations when working with only a couple of entities and a small dataset. In that case options are supervised learning or active learning, both of which are supported in MedCAT via the MedCATtrainer extension. Our approach can detect and link millions of different biomedical concepts with state-of-the-art performance, whilst being lightweight, fast and easy to use., Comment: Preprint, 25 pages, 5 figures and 4 tables

We present MedCATTrainer an interface for building, improving and customising a given Named Entity Recognition and Linking (NER+L) model for biomedical domain text. NER+L is often used as a first step in deriving value from clinical text. Collecting labelled data for training models is difficult due to the need for specialist domain knowledge. MedCATTrainer offers an interactive web-interface to inspect and improve recognised entities from an underlying NER+L model via active learning. Secondary use of data for clinical research often has task and context specific criteria. MedCATTrainer provides a further interface to define and collect supervised learning training data for researcher specific use cases. Initial results suggest our approach allows for efficient and accurate collection of research use case specific training data.

A high-resolution, intratrain position feedback system has been developed to achieve and maintain collisions at the proposed future electron-positron International Linear Collider (ILC). A prototype has been commissioned and tested with a beam in the extraction line of the Accelerator Test Facility at the High Energy Accelerator Research Organization in Japan. It consists of a stripline beam position monitor (BPM) with analogue signal-processing electronics, a custom digital board to perform the feedback calculation, and a stripline kicker driven by a high-current amplifier. The closed-loop feedback latency is 148 ns. For a three-bunch train with 154 ns bunch spacing, the feedback system has been used to stabilize the third bunch to 450 nm. The kicker response is linear, and the feedback performance is maintained, over a correction range of over $\pm$60 {\mu}m. The propagation of the correction has been confirmed by using an independent stripline BPM located downstream of the feedback system. The system has been demonstrated to meet the BPM resolution, beam kick, and latency requirements for the ILC.

The Compact Linear Collider (CLIC) is a TeV-scale high-luminosity linear $e^+e^-$ collider under development at CERN. Following the CLIC conceptual design published in 2012, this report provides an overview of the CLIC project, its current status, and future developments. It presents the CLIC physics potential and reports on design, technology, and implementation aspects of the accelerator and the detector. CLIC is foreseen to be built and operated in stages, at centre-of-mass energies of 380 GeV, 1.5 TeV and 3 TeV, respectively. CLIC uses a two-beam acceleration scheme, in which 12 GHz accelerating structures are powered via a high-current drive beam. For the first stage, an alternative with X-band klystron powering is also considered. CLIC accelerator optimisation, technical developments and system tests have resulted in an increased energy efficiency (power around 170 MW) for the 380 GeV stage, together with a reduced cost estimate at the level of 6 billion CHF. The detector concept has been refined using improved software tools. Significant progress has been made on detector technology developments for the tracking and calorimetry systems. A wide range of CLIC physics studies has been conducted, both through full detector simulations and parametric studies, together providing a broad overview of the CLIC physics potential. Each of the three energy stages adds cornerstones of the full CLIC physics programme, such as Higgs width and couplings, top-quark properties, Higgs self-coupling, direct searches, and many precision electroweak measurements. The interpretation of the combined results gives crucial and accurate insight into new physics, largely complementary to LHC and HL-LHC. The construction of the first CLIC energy stage could start by 2026. First beams would be available by 2035, marking the beginning of a broad CLIC physics programme spanning 25-30 years., Comment: 112 pages, 59 figures; published as CERN Yellow Report Monograph Vol. 2/2018; corresponding editors: Philip N. Burrows, Nuria Catalan Lasheras, Lucie Linssen, Marko Petri\v{c}, Aidan Robson, Daniel Schulte, Eva Sicking, Steinar Stapnes

Let $G$ be the adjoint group of a real simple Lie algebra $\mathfrak{g}_0$ equal either $\mathfrak{s}\mathfrak{u}(n,1)$ or $\mathfrak{s}\mathfrak{o}(n,1),$ $K$ its maximal compact subgroup, ${\cal U}(\mathfrak{g})$ the universal enveloping algebra of the complexification $\mathfrak{g}$ of $\mathfrak{g}_0$ and ${\cal U}(\mathfrak{g})^K$ its subalgebra of $K-$invariant elements. By a result of F. Knopp [3] ${\cal U}(\mathfrak{g})$ is free as a ${\cal U}(\mathfrak{g})^K-$module, so there exists a $K-$submodule $E$ of ${\cal U}(\mathfrak{g})$ such that the multiplication defines an isomorphism of $K-$modules ${\cal U}(\mathfrak{g})^K\otimes E\longrightarrow{\cal U}(\mathfrak{g}).$ We prove that $E$ is equivalent to the regular representation of $K,$ i.e. that the multiplicity of every $\delta\in\hat{K}$ in $E$ equals its dimension. As a consequence we get that for any finitedimensional complex $K-$module $V$ the space $({\cal U}(\mathfrak{g})\otimes V)^K$ of $K-$invariants is free ${\cal U}(\mathfrak{g})^K-$module of rank $\dim\,V.$