Random subgraphs of finite graphs: I. The scaling window under the triangle condition

We study random subgraphs of an arbitrary finite connected transitive graph $\mathbb G$ obtained by independently deleting edges with probability $1-p$. Let $V$ be the number of vertices in $\mathbb G$, and let $\Omega$ be their degree. We define the critical threshold $p_c=p_c(\mathbb G,\lambda)$ to be the value of $p$ for which the expected cluster size of a fixed vertex attains the value $\lambda V^{1/3}$, where $\lambda$ is fixed and positive. We show that for any such model, there is a phase transition at $p_c$ analogous to the phase transition for the random graph, provided that a quantity called the triangle diagram is sufficiently small at the threshold $p_c$. In particular, we show that the largest cluster inside a scaling window of size |p-p_c|=\Theta(\cn^{-1}V^{-1/3}) is of size $\Theta(V^{2/3})$, while below this scaling window, it is much smaller, of order $O(\epsilon^{-2}\log(V\epsilon^3))$, with \epsilon=\cn(p_c-p). We also obtain an upper bound O(\cn(p-p_c)V) for the expected size of the largest cluster above the window. In addition, we define and analyze the percolation probability above the window and show that it is of order \Theta(\cn(p-p_c)). Among the models for which the triangle diagram is small enough to allow us to draw these conclusions are the random graph, the $n$-cube and certain Hamming cubes, as well as the spread-out $n$-dimensional torus for $n>6$

Preliminary comparison of 3.5-cm and 12.6-cm wavelength continuous wave observations of Mars

Radar observations of Mars at Goldstone in 1990 were conducted by transmitting pure sinusoidal signals at 3.5-cm wavelengths and receiving the Doppler-spread echoes from Mars at Earth. Radar transmissions were circularly polarized and the echoes recorded in two senses: depolarized and polarized. Latitudes of the subradar points are between 3.5 deg and 11.1 deg S; longitude coverage is discontinuous. The observed depolarized and polarized echo total cross-sections and their ratios for two wavelengths were compared and discussed

Suicide screening tools for use in adult offenders: a systematic review

Self-inflicted deaths in prisons in England and Wales, recently reported as the highest in over a decade, are a significant cause of mortality. A lack of guidelines surrounding the screening and identification of suicide risk of new prisoners along with a dearth of effective screening tools indicate the need for review. Our aims are to examine findings on the effectiveness of prison specific suicide screening tools used with adult prisoners. Papers were identified via systematic searches of databases, scanning grey literature, and reference checking. Included studies were published over the period between 2000–2016. PRISMA guidelines were followed. Studies were selected based on population – adult imprisoned offenders; intervention – suicide screening tool; comparators – participants screened vs. not screened outcome – suicide or attempted suicide. Data was extracted manually. A narrative synthesis presented the findings between different screening tools. Eight screening tools were critically appraised. Evidence suggested that the VISCI and Dutch screening tools are most effective in identifying those at risk and reducing suicide and/or self-harm behavior. Variance in methodological quality and associated factors indicate the need for further development of prospective studies to develop robust screening tools

Unobtrusive Maintenance: Temporal Complexity, Latent Category Control and the Stalled Emergence of the Cleantech Sector

© 2018 John Wiley & Sons Ltd and Society for the Advancement of Management Studies Disruptive innovation changes the basis of competition within an industry and poses substantial threats for market incumbents. While researchers have focused on whether incumbents can successfully adapt, we know little about how potentially disruptive innovation may be avoided. Studying clean technology in Canada, we examine incumbent resistance when potentially disruptive technologies are seen as socially beneficial. We identify actions taken by incumbents and other socio-technical regime actors to respond to the issue while simultaneously enacting legitimate stabilizing mechanisms within the regime’s institutional infrastructure. Specifically, temporal and resource-based actions led to temporal complexity for disruptive cleantech entrepreneurs, and evaluation structuring work led to latent control of the cleantech category, privileging incumbents and resulting in unobtrusive maintenance. Our findings contribute to the disruptive innovation and institutional theory literatures by showing how disruption may be stalled by the enactment of legitimate elements of the institutional infrastructure rather than direct institutional defence

Wide-band variable transversal phase-shifter

We present a novel broadband phase-shifter based on a transversal filter configuration. This approach allows flexible control of the amplitude response while providing continuous variation of a linear phase slope. Numerical examples, both ideal and using practical RF components are presented and practical challenges in realising the phase-shifter are identified

The development of the Slade–Pais Expectations of Childbirth Scale (SPECS) *

Objective: To develop a valid and reliable English language-based scale to measure pregnant women’s expectations of childbirth. Background: During pregnancy, most women think about their forthcoming childbirth, and develop expectations of how they think this experience will be. Women with adverse expectations of childbirth have been found to have more negative actual experiences. Measuring expectations is therefore important. Existing measures are limited in their established psychometric properties. Methods: Items were generated from semi-structured interviews with 18 pregnant women to explore their expectations of their forthcoming childbirth. Content analysis was used to analyse interview data and scale items were developed using the constructs extracted. A population sample of 148 pregnant women completed the initial 85-item version of the Slade–Pais Expectations of Childbirth Scale (SPECS) and the State Trait Anxiety Inventory. Results: Principal components analysis of the SPECS identified six underlying components labelled ‘coping and robustness to pain’, ‘staff and service responsive to needs’, ‘fear’, ‘out of control and embarrassed’, ‘perceptions of partner’s coping’ and ‘positive anticipation of birth’. Items with poor psychometric properties were excluded. A final 50-item version of the SPECS showed acceptable internal reliability and good content and construct validity. Conclusion: The SPECS shows promising psychometric robustness for use both as a research and clinical tool. It can be used as a total score, as a shortened scale focussed only on expectations of self, or as a series of subscales covering all domains

Demographic and clinical characteristics of 1092 consecutive police custody mental health referrals

The 43 police forces in England and Wales have made over 13 million arrests in the last decade. Yet despite this high volume criminal justice system activity, and evidence of substantial health morbidity across the criminal justice pathway, mental health services in police custody have so far only been developed in patches, and the literature in this area is limited. Referrals (n=1092) to a pilot mental health service operating across two police stations in a London borough were examined over an 18-month period in 2012/13. The referred group had high levels of mental health and substance misuse problems (including acute mental illness, intoxication and withdrawal), self-harm, suicide risk and vulnerability, with some important gender differences. Although this work has limitations, the findings are broadly consistent with the small existing literature and they confirm the need for services that are sufficiently resourced to meet the presenting needs

Suicide ideation amongst people referred for mental health assessment in police custody

Purpose The purpose of this paper is to examine the prevalence of suicide ideation amongst a group of people who had been arrested and taken into police custody, and were then referred to a mental health service operating in the police stations. Design/methodology/approach A referred sample of 888 cases were collected over an 18-month period during 2012/2013. Clinical assessments were conducted using a template in which background information was collected (including information about their previous clinical history, substance misuse, alleged offence, any pre-identified diagnoses, and the response of the service) as part of the standard operating procedure of the service. Data were analysed using a statistical software package. Findings In total, 16.2 per cent (n=144) reported suicide ideation, with women being more likely to report than men. In total, 82.6 per cent of the suicide ideation sample reported a history of self-harm or a suicide attempt. Suicide ideation was also associated with certain diagnostic categories (depression, post-traumatic stress disorder and personality disorder), a history of contact with mental health services, and recent (within 24 hours) consumption of alcohol or drugs. Originality/value This evaluation adds to the limited literature in this area by describing a large sample from a real clinical service. It provides information that can assist with future service designs and it offers support for calls for a standardised health screening process, better safety arrangements for those who have recently used alcohol or drugs (within 24 hours) and integrated service delivery across healthcare domains (i.e. physical healthcare, substance use, and mental health)