K-means clustering is widely used for exploratory data analysis. While its dependence on initialisation is well-known, it is common practice to assume that the partition with lowest sum-of-squares (SSQ) total i.e. within cluster variance, is both reproducible under repeated initialisations and also the closest that k-means can provide to true structure, when applied to synthetic data. We show that this is generally the case for small numbers of clusters, but for values of k that are still of theoretical and practical interest, similar values of SSQ can correspond to markedly different cluster partitions. This paper extends stability measures previously presented in the context of finding optimal values of cluster number, into a component of a 2-d map of the local minima found by the k-means algorithm, from which not only can values of k be identified for further analysis but, more importantly, it is made clear whether the best SSQ is a suitable solution or whether obtaining a consistently good partition requires further application of the stability index. The proposed method is illustrated by application to five synthetic datasets replicating a real world breast cancer dataset with varying data density, and a large bioinformatics dataset.

Proteases of human pathogens are becoming increasingly important drug targets, hence it is necessary to understand their substrate specificity and to interpret this knowledge in practically useful ways. New methods are being developed that produce large amounts of cleavage information for individual proteases and some have been applied to extract cleavage rules from data. However, the hitherto proposed methods for extracting rules have been neither easy to understand nor very accurate. To be practically useful, cleavage rules should be accurate, compact, and expressed in an easily understandable way.

Management of nightlife in UK cities focuses on creating safe places for individuals to drink. Little is known about intoxication levels as measuring total alcohol consumption on nights out is complicated by early evening interviews missing subsequent consumption and later interviews risking individuals being too drunk to recall consumption or participate at all. Here we assess mixed survey and modelling techniques as a methodological approach to examining these issues. Interviews with a cross sectional sample of nightlife patrons (n = 214) recruited at different locations in three cities established alcohol consumption patterns up to the point of interview, self-assessed drunkenness and intended drinking patterns throughout the remaining night out. Researchers observed individuals' behaviours to independently assess drunkenness. Breath alcohol tests and general linear modelling were used to model blood alcohol levels at participants' expected time of leaving nightlife settings. At interview 49.53% of individuals regarded themselves as drunk and 79.43% intended to consume more alcohol before returning home, with around one in ten individuals (15.38% males; 4.35% females) intending to consume >40 units (equal to 400 mls of pure alcohol). Self-assessed drunkenness, researcher observed measures of sobriety and blood alcohol levels all correlated well. Modelled estimates for blood alcohol at time of going home suggested that 71.68% of males would be over 0.15%BAC (gms alcohol/100 mls blood). Higher blood alcohol levels were related to drinking later into the night. UK nightlife has used substantive health and judicial resources with the aim of creating safer and later drinking environments. Survey and modelling techniques together can help characterise the condition of drinkers when using and leaving these settings. Here such methods identified patrons as routinely getting drunk, with risks of drunkenness increasing over later nights. Without preventing drunkenness and sales to intoxicated individuals, extended drinking hours can simply act as havens for drunks. A public health approach to nightlife is needed to better understand and take into account the chronic effects of drunkenness, the damages arising after drunk individuals leave city centres and the costs of people avoiding drunken city centres at night.

In the UK, the 2009/10 winter was characterised by sustained low temperatures; grit stocks became depleted and surfaces left untreated. We describe the relationship between temperature and emergency hospital admissions for falls on snow and ice in England, identify the age and gender of those most likely to be admitted, and estimate the inpatient costs of these admissions during the 2009/10 winter.

Suicide is a major public health issue and a leading cause of death among children and young people (CYP) worldwide. There is strong evidence linking adverse childhood experiences (ACEs) to an increased risk of suicidal behaviours in adults, but there is limited understanding regarding ACEs and suicidal crises in CYP. This study aims to examine the ACEs associated with CYP presenting at Emergency Departments for suicidal crises, and specifically the factors associated with repeat attendances. This is a case series study of CYP (aged 8–16) experiencing suicidal crisis who presented in a paediatric Emergency Department in England between March 2019 and March 2021 (n = 240). The dataset was subjected to conditional independence graphical analysis. Results revealed a significant association between suicidal crisis and several ACEs. Specifically, evidence of clusters of ACE variables suggests two distinct groups of CYP associated with experiencing a suicidal crisis: those experiencing “household risk” and those experiencing “parental risk”. Female sex, history of self-harm, mental health difficulties, and previous input from mental health services were also associated with repeat hospital attendances. Findings have implications for early identification of and intervention with children who may be at a heightened risk for ACEs and associated suicidal crises.

Withdrawal assessment in critically ill children is complicated by the reliance on non-specific behaviours and compounded when the child's typical behaviours are unknown. The existing approach to withdrawal assessment assumes that nurses elicit the parents' view of the child's behaviours. This qualitative study explored parents' perspectives of their child's withdrawal and preferences for involvement and participation in withdrawal assessment. Parents of eleven children were interviewed after their child had completed sedation weaning during recovery from critical illness. Data were analysed using thematic analysis. A large children's hospital in the Northwest of England. Parents experienced varying degrees of partnership in the context of withdrawal assessment and identified information deficits which contributed to their distress of parenting a child with withdrawal syndrome. Most parents were eager to participate in withdrawal assessment and reported instances where their knowledge enabled a personalised interpretation of their child's behaviours. Reflecting on the reciprocal nature of the information deficits resulted in the development of a model for nurse-parent collaboration in withdrawal assessment. Facilitating nurse-parent collaboration in withdrawal assessment may have reciprocal benefits by moderating parental stress and aiding the assessment and management of withdrawal syndrome.