In line with Valuing People Now: A New Three-year Strategy for People With Learning Disabilities (Department of Health, 2009), this article details a service evaluation for a learning disability-child and adolescent mental health service (LD-CAMHS) in Chesterfield, North Derbyshire. The aim of the project was to produce a set of quality standards in order to ensure service users' needs are met. Semi-structured interviews were conducted with seven children between the ages of 11 and 17 years, with moderate to severe learning disabilities. Four themes were derived from a thematic analysis; the experience of the service, communication, impact of the work carried out, and difficulties encountered. It was recommended that staff working within the service should ensure communication is at a level appropriate for the client; offer a welcoming approach; provide an open approach; and offer a reasonable choice of location. This article provides suggestions for how other LD-CAMHS teams could use these standards for their own purposes.

Specifying time-dependent correlation matrices is a problem that occurs in several important areas of finance and risk management. The goal of this work is to tackle this problem by applying techniques of geometric integration in financial mathematics, i.e., to combine two fields of numerical mathematics that have not been studied yet jointly. Based on isospectral flows we create valid time-dependent correlation matrices, so called correlation flows, by solving a stochastic differential equation (SDE) that evolves in the special orthogonal group. Since the geometric structure of the special orthogonal group needs to be preserved we use stochastic Lie group integrators to solve this SDE. An application example is presented to illustrate this novel methodology.

In this paper we present a general procedure for designing higher strong order methods for linear Itô stochastic differential equations on matrix Lie groups and illustrate this strategy with two novel schemes that have a strong convergence order of 1.5. Based on the Runge–Kutta–Munthe–Kaas (RKMK) method for ordinary differential equations on Lie groups, we present a stochastic version of this scheme and derive a condition such that the stochastic RKMK has the same strong convergence order as the underlying stochastic Runge–Kutta method. Further, we show how our higher order schemes can be applied in a mechanical engineering as well as in a financial mathematics setting.

Dear Readers, Unfortunately, the original article was published without ORCID NUMBERs. This has since been corrected.

In this paper, we introduce a novel methodology to model rating transitions with a stochastic process. To introduce stochastic processes, whose values are valid rating matrices, we noticed the geometric properties of stochastic matrices and its link to matrix Lie groups. We give a gentle introduction to this topic and demonstrate how Itô-SDEs in R will generate the desired model for rating transitions.To calibrate the rating model to historical data, we use a Deep-Neural-Network (DNN) called TimeGAN to learn the features of a time series of historical rating matrices. Then, we use this DNN to generate synthetic rating transition matrices. Afterwards, we fit the moments of the generated rating matrices and the rating process at specific time points, which results in a good fit.After calibration, we discuss the quality of the calibrated rating transition process by examining some properties that a time series of rating matrices should satisfy, and we will see that this geometric approach works very well.