Derived A-infinity Algebras: Combinatorial models and obstruction theory

Let R be a commutative ring, and let A be a derived A_\infty-algebra over R with structure maps m_{ij} for all i\geq 0, j \geq 1. In this thesis we construct a collection of based topological spaces V_{ij} which give rise to the notion of a DA_\infty-space. The structure of these spaces gives new insight into the structure of a derived A_\infty-algebra. We study the cell structure of these spaces via a combinatorial model using partitioned trees. We will prove that the singular chain complex on a DA_\infty-space gives rise to a derived A_\infty-algebra. We go on to consider obstruction theories to the existence of the structure maps of a derived A_\infty-algebra. The bigrading on A leads to choices of the order in which we develop the derived A_\infty-structure. We give three different definitions of a “partial” derived A_\infty-structure and in light of these definitions provide two different obstruction theories to extend a dA´_{ij}-structure to a dA_{ij} structure, plus an obstruction theory to extend a dA_{r-1}-structure to a dA_{r+1}-structure. In each case, the obstruction lies in a particular class of the Hochschild cohomology of the homology of A

Substance use and Intimate Partner Abuse (IPA):A descriptive model of the pathways between substance use and IPA perpetration for men

Intimate partner abuse (IPA) is a pervasive public health and human rights issue disproportionately affecting women. There is a complex link between IPA and substance use; substance use can increase both the frequency and severity of IPA. Pathway models have been applied to explore heterogeneous trajectories into other behaviours and to identify areas for intervention. This approach has not previously been applied in the area of substance use and IPA. Inductive thematic analysis of 37 interviews with heterosexual men aged 28-52 who had reported previous IPA perpetration was conducted. Men were recruited from alcohol and drug services across two areas of England. Three groupings of pathways into substance use-related IPA were generated: 1) Rule Breaking Pathway (n = 11); 2) Entrenched Substance Use Pathway (n = 13); and 3) Relationship Insecurity Pathway (n = 13). Across the three groupings of pathways, the men's childhood and early experiences led to different journeys into SU-related IPA (abuse that was associated with intoxication, withdrawal, acquisition and substance use lifestyle). Each pathway presented differently with varying core features, for example core features of generalised violence, mental health or jealousy, and different predisposing background factors, including types and timing of childhood abuse and trauma. Adopting a pathways approach drawing on principles of equifinality and multifinality can improve understanding of heterogeneity in men who perpetrate IPA and use substances and propose treatment/intervention targets

Substance Use and Intimate Partner Abuse (IPA): A Descriptive Model of the Pathways Between Substance Use and IPA Perpetration for Men

Intimate partner abuse (IPA) is a pervasive public health and human rights issue disproportionately affecting women. There is a complex link between IPA and substance use; substance use can increase both the frequency and severity of IPA. Pathway models have been applied to explore heterogeneous trajectories into other behaviours and to identify areas for intervention. This approach has not previously been applied in the area of substance use and IPA. Inductive thematic analysis of 37 interviews with heterosexual men aged 28-52 who had reported previous IPA perpetration was conducted. Men were recruited from alcohol and drug services across two areas of England. Three groupings of pathways into substance use-related IPA were generated: 1) Rule Breaking Pathway (n = 11); 2) Entrenched Substance Use Pathway (n = 13); and 3) Relationship Insecurity Pathway (n = 13). Across the three groupings of pathways, the men's childhood and early experiences led to different journeys into SU-related IPA (abuse that was associated with intoxication, withdrawal, acquisition and substance use lifestyle). Each pathway presented differently with varying core features, for example core features of generalised violence, mental health or jealousy, and different predisposing background factors, including types and timing of childhood abuse and trauma. Adopting a pathways approach drawing on principles of equifinality and multifinality can improve understanding of heterogeneity in men who perpetrate IPA and use substances and propose treatment/intervention targets

The feasibility of delivering the ADVANCE digital intervention to reduce intimate partner abuse by men receiving substance use treatment:protocol for a non-randomised multi-centre feasibility study and embedded process evaluation

BACKGROUND: Compared to men in the general population, men in substance use treatment are more likely to perpetrate intimate partner abuse (IPA). The ADVANCE group intervention for men in substance use treatment is tailored to address substance use and IPA in an integrated way. In a feasibility trial pre-COVID, men who received the ADVANCE intervention via face-to-face group delivery showed reductions in IPA perpetration. Due to COVID-19, ADVANCE was adapted for remote digital delivery. METHODS/DESIGN: This mixed-methods non-randomised feasibility study, with a nested process evaluation, will explore the feasibility and acceptability of delivering the ADVANCE digital intervention to men in substance use treatment who have perpetrated IPA towards a female partner in the past year. Sixty men will be recruited from seven substance use treatment services in Great Britain. The ADVANCE digital intervention comprises a preparatory one-to-one session with a facilitator to set goals, develop a personal safety plan, and increase motivation and a preparatory online group to prepare men for taking part in the intervention. The core intervention comprises six fortnightly online group sessions and 12 weekly self-directed website sessions to recap and practise skills learned in the online group sessions. Each website session is followed by a one-to-one video/phone coaching session with a facilitator. Men will also receive their usual substance use treatment. Men’s female (ex) partners will be invited to provide outcome data and offered support from integrated safety services (ISS). Outcome measures for men and women will be sought post intervention (approximately 4 months post male baseline interview). Feasibility parameters to be estimated include eligibility, suitability, consent, recruitment, attendance, retention and follow-up rates. In-depth interviews or focus groups will explore the intervention’s acceptability to participants, facilitators and ISS workers. A secondary focus of the study will estimate pre-post-differences in outcome measures covering substance use, IPA, mental health, self-management, health and social care service use, criminal justice contacts and quality of life. DISCUSSION: Findings will inform the design of a multicentre randomised controlled trial evaluating the efficacy and cost-effectiveness of the ADVANCE digital intervention for reducing IPA. TRIAL REGISTRATION: The feasibility study was prospectively registered: ISRCTN66619273