Mentally disordered young offenders in transition from child and adolescent to adult mental health services across England and Wales

This paper provides an overview of transitions across forensic child and adolescent mental health services in England and Wales. The aim of this paper is to delineate the national secure services system for young people in contact with the youth justice system. This paper reviews findings from the existing literature of transitions across forensic child and adolescent mental health services, drawing attention to present facilitators and barriers to optimal transition. We examine the infrastructure of current services and highlight gaps between child and adult service continuity and evaluate the impact of poor transitions on young offenders’ mental health and wellbeing. Young offenders experience a broad range of difficulties, from the multiple interfaces with the legal system, untreated mental health problems, and poor transition to adult services. Barriers such as long waiting lists, lack of coordination between services and lack of transition preparation impede significantly smooth transitions. We need to develop, test and evaluate models of transitional care that improve mental health and wellbeing of this group. Mapping young offenders’ care pathway will help to understand their needs and also to impact current policy and practice. Key workers in forensic services should facilitate the transition process by developing sustainable relationships with the young person and creating a safe clinical environment. Transition of care from forensic child and adolescent mental health services is a neglected area. This paper attempts to highlight the nature and magnitude of the problems at the transition interface in a forensic context

Entanglement on linked boundaries in Chern-Simons theory with generic gauge groups

We study the entanglement for a state on linked torus boundaries in $3d$ Chern-Simons theory with a generic gauge group and present the asymptotic bounds of R\'enyi entropy at two different limits: (i) large Chern-Simons coupling $k$, and (ii) large rank $r$ of the gauge group. These results show that the R\'enyi entropies cannot diverge faster than $\ln k$ and $\ln r$, respectively. We focus on torus links $T(2,2n)$ with topological linking number $n$. The R\'enyi entropy for these links shows a periodic structure in $n$ and vanishes whenever $n = 0 \text{ (mod } \textsf{p})$, where the integer $\textsf{p}$ is a function of coupling $k$ and rank $r$. We highlight that the refined Chern-Simons link invariants can remove such a periodic structure in $n$.Comment: 31 pages, 5 figure

Eigenvalue hypothesis for multi-strand braids

Computing polynomial form of the colored HOMFLY-PT for non-arborescent knots obtained from three or more strand braids is still an open problem. One of the efficient methods suggested for the three-strand braids relies on the eigenvalue hypothesis which uses the Yang-Baxter equation to express the answer through the eigenvalues of the ${\cal R}$-matrix. In this paper, we generalize the hypothesis to higher number of strands in the braid where commuting relations of non-neighbouring $\mathcal{R}$ matrices are also incorporated. By solving these equations, we determine the explicit form for $\mathcal{R}$-matrices and the inclusive Racah matrices in terms of braiding eigenvalues (for matrices of size up to 6 by 6). For comparison, we briefly discuss the highest weight method for four-strand braids carrying fundamental and symmetric rank two $SU_q(N)$ representation. Specifically, we present all the inclusive Racah matrices for representation $[2]$ and compare with the matrices obtained from eigenvalue hypothesis.Comment: 23 page