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Fragment screening using X-ray crystallography can yield rich structural data to help guide the optimization of low-molecular-weight compounds into more potent binders. Fragment merging, whereby substructural motifs from partially overlapping fragments are incorporated into a single larger compound, represents a potentially powerful and efficient approach for increasing potency. Searching commercial catalogues provides one useful way to quickly and cheaply identify follow-up compounds for purchase and further screening, and circumvents the challenge of synthetic accessibility. The Fragment Network is a graph database that provides a novel way to explore the chemical space surrounding fragment hits. We use an iteration of the database containing >120 million catalogue compounds to find fragment merges for four XChem fragment screening campaigns. Retrieved molecules were filtered using a pipeline of 2D and 3D filters and contrasted against a traditional fingerprint-based similarity search. The two search techniques were found to have complementary results, identifying merges in different regions of chemical space. Both techniques were able to identify merges that are predicted to replicate the interactions made by the parent fragments. This work demonstrates the use of the Fragment Network to increase the yield of fragment merges beyond that of a classical catalogue search, thus increasing the likelihood of finding promising follow-up compounds. We present a pipeline that is able to systematically exploit all known fragment hits by performing large-scale enumeration of all possible fragment pairs for merging.

This review covers emerging biosensors for SARS-CoV-2 detection together with a review of the biochemical and clinical assays that are in use in hospitals and clinical laboratories. We discuss the gap in bridging the current practice of testing laboratories with nucleic acid amplification methods, and the robustness of assays the laboratories seek, and what emerging SARS-CoV-2 sensors have currently addressed in the literature. Together with the established nucleic acid and biochemical tests, we review emerging technology and antibody tests to determine the effectiveness of vaccines on individuals.

We report two children with molecularly confirmed mitochondrial disease mimicking Neuromyelitis Optica Spectrum Disorder (NMOSD). The first patient presented at the age of 15 months with acute deterioration following a pyrexial illness with clinical features localising to the brainstem and spinal cord. The second patient presented at 5 years with acute bilateral visual loss. In both cases, MOG and AQP4 antibodies were negative. Both patients died within a year of symptoms onset from respiratory failure. Arriving at an early genetic diagnosis is important for redirection of care and avoiding potentially harmful immunosuppressant therapies.

Purpose To date there has been limited research on the impact of the COVID-19 pandemic on autistic people. This study aims to present the results of a survey of autistic people (n = 51) conducted by a UK specialist autism team. Design/methodology/approach A cross-sectional online survey. Findings A total of 72% respondents reported either some or significant deterioration in mental health during the pandemic. The issues that caused most negative impact were uncertainty over what will happen next and disruption of normal routine. Respondents reported a variety of coping strategies to help them through the pandemic. Originality/value To date there has been little research looking specifically at the impact of the COVID-19 pandemic on autistic people. This paper adds weight to the evidence that the pandemic has had a particularly severe impact on autistic adults and includes useful information on potential coping strategies for this population.

We introduce a neural architecture for navigation in novel environments. Our proposed architecture learns to map from first-person views and plans a sequence of actions towards goals in the environment. The Cognitive Mapper and Planner (CMP) is based on two key ideas: (a) a unified joint architecture for mapping and planning, such that the mapping is driven by the needs of the task, and (b) a spatial memory with the ability to plan given an incomplete set of observations about the world. CMP constructs a top-down belief map of the world and applies a differentiable neural net planner to produce the next action at each time step. The accumulated belief of the world enables the agent to track visited regions of the environment. We train and test CMP on navigation problems in simulation environments derived from scans of real world buildings. Our experiments demonstrate that CMP outperforms alternate learning-based architectures, as well as, classical mapping and path planning approaches in many cases. Furthermore, it naturally extends to semantically specified goals, such as “going to a chair”. We also deploy CMP on physical robots in indoor environments, where it achieves reasonable performance, even though it is trained entirely in simulation.

The COVID-19 pandemic changed continuous positive airway pressure (CPAP) setup pathways. We evaluated patients commenced on CPAP in 2019 (prepandemic) and 2020 (post-first UK wave). Face-to-face (F2F) setup numbers, with CPAP turned on, decreased from 613 patients (98.9%) in 2019, to 6 (1.1%) in 2020. In 2020, setups were F2F without CPAP turned on (403 (71.1%)), or remote (158 (27.9%)). Prepandemic median CPAP usage at first follow-up was 5.4 (2.7–6.9) hours/night and fell by 0.9 hours/night (95% CI 0.5 to 1.2, p

This chapter defines probability measures and probability spaces in a general context, as a case of the concepts introduced in Chapter 3. The axioms of probability are explained, and the important concepts of conditional probability and independence are introduced and linked to the role of product spaces and product measures.

This chapter reviews the theory of weak convergence in metric spaces. Topics include Skorokhod’s representation theorem, the metrization of spaces of measures, and the concept of tightness of probability measures. The key relation is shown between weak convergence and uniform tightness. Considering the space C of continuous functions in particular, the functional central limit theorem is proved for martingales, together with extensions to the multivariate case.

In this chapter, the first approach is made to establishing the convergence of scaled random sums, considering independent sequences. The classic Lindeberg–Lévy, Khinchine, Lindeberg–Feller, and Liapunov theorems are proved. The main focus is on the treatment of heterogeneous summands, applying the Lindeberg condition, and extensions are given to allow trending (growing or shrinking) variances. The final sections review cases of the central limit theorem under non-standard conditions and α-stable convergence.

The modes of convergence introduced in Chapter 12 are studied in detail. Conditions for almost‐sure convergence are derived via the Borel–Cantelli lemma. Convergence in probability is contrasted, and then a number of results for convergence of transformed series are given. Convergence in LP‐norm is introduced as a sufficient condition for convergence in probability. Examples are given, and the chapter concludes with a preliminary look at the laws of large numbers.

This chapter introduces and illustrates the concept of a metric (distance measure), and the definition of a metric space. Open, closed, and compact sets are discussed in a general context, and the concepts of separability and completeness introduced. It goes on to look at mappings on metric spaces, examines the important case of function spaces, and treats the Arzelà–Ascoli theorem.

This chapter lays the foundations for functional limit theory, considering the case of general metric spaces from a topological standpoint. The issues of separability and measurability and techniques for assigning measures in metric spaces are then discussed, developing tools to replace the methods of characteristic functions and the inversion theorem used for real sequences. The key cases of function spaces are studied and in particular the case C of continuous functions on the unit interval. Weiner measure (Brownian motion) is defined as the leading case of a measure on C.

Specializing the concepts of Chapter 7 to the case of real variables, this chapter introduces distribution functions, discrete and continuous distributions, and describes examples such as the binomial, uniform, Gaussian, Cauchy, and gamma distributions. It then treats multivariate distributions and the concept of independence.