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We show that the stable module $\infty$-category of a finite group $G$ decomposes in three different ways as a limit of the stable module $\infty$-categories of certain subgroups of $G$. Analogously to Dwyer's terminology for homology decompositions, we call these the centraliser, normaliser, and subgroup decompositions. We construct centraliser and normaliser decompositions and extend the subgroup decomposition (constructed by Mathew) to more collections of subgroups. The key step in the proof is extending the stable module $\infty$-category to be defined for any $G$-space, then showing that this extension only depends on the $S$-equivariant homotopy type of a $G$-space. The methods used are not specific to the stable module $\infty$-category, so may also be applicable in other settings where an $\infty$-category depends functorially on $G$., 16 pages

Traumatic injury affects over 2.6 million U.S. adults annually and elevates risk for a number of negative health consequences. This includes substantial psychological harm, the most prominent being posttraumatic stress disorder (PTSD), with approximately 21% of traumatic injury survivors developing the disorder within the first year after injury. Posttraumatic stress disorder is associated with deficits in physical recovery, social functioning, and quality of life. Depression is diagnosed in approximately 6% in the year after injury and is also a predictor of poor quality of life. The American College of Surgeons Committee on Trauma suggests screening for and treatment of PTSD and depression, reflecting a growing awareness of the critical need to address patients' mental health needs after trauma. While some trauma centers have implemented screening and treatment or referral for treatment programs, the majority are evaluating how to best address this recommendation, and no standard approach for screening and treatment currently exists. Further, guidelines are not yet available with respect to resources that may be used to effectively screen and treat these disorders in trauma survivors, as well as who is going to bear the costs. The purpose of this review is: (1) to evaluate the current state of the literature regarding evidence-based screens for PTSD and depression in the hospitalized trauma patient and (2) summarize the literature to date regarding the treatments that have empirical support in treating PTSD and depression acutely after injury. This review also includes structural and funding information regarding existing postinjury mental health programs. Screening of injured patients and timely intervention to prevent or treat PTSD and depression could substantially improve health outcomes and improve quality of life for this high-risk population. LEVEL OF EVIDENCE: Review, level IV.

The Hanna Neumann conjecture gives a bound on the intersection of finitely generated subgroups of free groups. We explore a natural extension of this result, which turns out to be true only in the finite index case, and provide counterexamples for the general case. We also see that the graph-based method of generating random subgroups of free groups developed by Bassino, Nicaud and Weil is well-suited to generating subgroups with non-trivial intersections. The same method is then used to generate a counterexample to a similar conjecture of Guzman., Comment: 9 pages, 4 figures; added counterexample to a conjecture of Guzman

There is a rapid increase in the number of chaplains working in secondary schools within the UK, and their contributions to pastoral care are well documented and evidenced. Less explored are the chaplains’ contributions to school ethos and culture. Despite a chaplain’s impact upon school ethos and culture showing the potential for significant impact upon school communities, this is an area which is only addressed infrequently in school chaplaincy research. This aspect of a chaplain’s role needs further attention in order to fully explore and understand its impact and influence.\ud \ud This research utilises a case study approach and explores chaplaincy in six different school contexts across the spectrum of educational institutions. The role of the chaplain in relation to school ethos is uncovered, by hearing of the lived experience of students, staff and chaplains.\ud \ud This study identified a characteristic duality in the chaplain’s work, as they simultaneously ministered to both individuals and the whole of the school community. There were identified tensions and challenges as chaplains balanced their commitments to both the person and the institution. A series of ‘modes’ were identified to capture new language of how the chaplain interacts with the concept of school ethos, including times when the chaplain was perceived to have taken sole responsibility for this area of school life. The study used a bespoke theoretical framework to identify complex layers of ethos at work within school communities, and to understand the chaplain’s role as ‘translator’ between them.\ud \ud This study identified five distinctive features of chaplaincy that explained why the chaplain was able to make such important contributions to the work of embedding school ethos. These included the chaplain’s impartiality, relationships, peaceful presence, authority and their depth and embodiment.\ud \ud This research thereby demonstrates a way to frame and understand the chaplain’s under researched yet important contribution to this significant area of school life.