Taylor's Theorem for Functionals on BMO with Application to BMO Local Minimizers

In this note two results are established for energy functionals that are given by the integral of $W(\mathbf x,\nabla \mathbf u(\mathbf x))$ over $\Omega \subset\mathbb{R}^n$ with $\nabla \mathbf u \in BMO(\Omega;{\mathbb R}^{N\times n})$, the space of functions of Bounded Mean Oscillation of John & Nirenberg. A version of Taylor's theorem is first shown to be valid provided the integrand $W$ has polynomial growth. This result is then used to demonstrate that, for the Dirichlet, Neumann, and mixed problems, every Lipschitz-continuous solution of the corresponding Euler-Lagrange equations at which the second variation of the energy is uniformly positive is a strict local minimizer of the energy in $W^{1,BMO}(\Omega;\mathbb{R}^N)$, the subspace of the Sobolev space $W^{1,1}(\Omega;\mathbb{R}^N)$ for which the weak derivative $\nabla\mathbf u \in BMO(\Omega;{\mathbb R}^{N\times n})$.Comment: 8 page

Applications of Partial Supersymmetry

I examine quantum mechanical Hamiltonians with partial supersymmetry, and explore two main applications. First, I analyze a theory with a logarithmic spectrum, and show how to use partial supersymmetry to reveal the underlying structure of this theory. This method reveals an intriguing equivalence between two formulations of this theory, one of which is one-dimensional, and the other of which is infinite-dimensional. Second, I demonstrate the use of partial supersymmetry as a tool to obtain the asymptotic energy levels in non-relativistic quantum mechanics in an exceptionally easy way. In the end, I discuss possible extensions of this work, including the possible connections between partial supersymmetry and renormalization group arguments.Comment: 11 pages, harvmac, no figures; typo corrected in identifying info on title pag

ImpRess: an Implementation Readiness checklist developed using a systematic review of randomised controlled trials assessing cognitive stimulation for dementia

Background Research reporting results of clinical trials, psychosocial or technological interventions frequently omit critical details needed to inform implementation in practice. The aim of this article is to develop an Implementation Readiness (ImpRess) checklist, that includes criteria deemed useful in measuring readiness for implementation and apply it to trials of cognitive stimulation in dementia, providing a systematic review of their readiness for widespread implementation. Methods Five electronic databases were searched. After initial screening of papers, two reviewers assessed quality and scored the included studies based on the ImpRess checklist specifically developed for this review. Results Twenty studies met the inclusion criteria. As determined by the ImpRess checklist, scores ranged from 11 to 29 out of 52. According to the checklist the most comprehensive and ready to implement version of cognitive stimulation was Cognitive Stimulation Therapy. Conclusions Reports of interventions rarely include consideration of implementation in practice. Contrary to the growing number of reporting guidelines, crucial items within the ImpRess checklist have been frequently overlooked. This study was able to show that the ImpRess checklist was feasible in practice and reliable. The checklist may be useful in evaluating readiness for implementation for other manualised interventions

Is Virtual Cognitive Stimulation Therapy the Future for People with Dementia? An Audit of UK NHS Memory Clinics During the COVID-19 Pandemic

Access to psychosocial interventions for people with dementia, such as Cognitive Stimulation Therapy (CST), has been restricted during the COVID-19 pandemic. Some services have shifted to provision via videoconferencing, but the prevalence of this is unknown. This audit aimed to understand provision of virtual CST (vCST) within National Health Service (NHS) memory clinics throughout the UK and Channel Islands and investigate plans for ongoing CST provision. A cross-sectional survey was circulated to NHS memory clinics, which included closed and open-ended questions to generate quantitative and qualitative data. Thirty-three memory clinics responded to the survey. During the pandemic, 55% of respondents offered vCST, whereas 45% offered no CST. Of those offering vCST, 80% plan to continue with a hybrid model of separate face-to-face and vCST groups, whilst 20% intend to deliver face-to-face CST only. Reported positive aspects of vCST were participant and staff enjoyment, perceived improved digital confidence in participants, and improved accessibility for those who cannot attend face-to-face groups. Negative aspects related to digital poverty, limited digital literacy, support needed from carers, the impact of sensory impairment on engagement, and staff time commitment. Virtual CST has been a feasible alternative to face-to-face services during the pandemic but should not completely replace in-person groups. A hybrid approach would increase accessibility for all. Future research should explore efficacy of vCST and seek to understand patterns of exclusion from such digital interventions

Development of an Evidence-based Extended Programme of Maintenance Cognitive Stimulation Therapy (CST) for People with Dementia

Psychosocial interventions for dementia have often been developed without a sound theoretical, empirical and clinical basis, and most evaluations of these interventions have had serious methodological limitations. This highlights the need to link intervention development with evaluation and design issues during the early stages of phase 1 or development of an intervention. Best practice is to develop interventions systematically, using the best available evidence and appropriate theory. This study focuses on the developmental stage of the Medical Research Council (MRC) guidelines (2008) to develop an evidence-based Maintenance Cognitive Stimulation Therapy (MCST) programme for dementia. The intervention was developed based on a mixed methods approach, using evidence obtained from the Cochrane review of Cognitive Stimulation for dementia followed by a Delphi consultation process with key stake-holders. Four techniques were used: (1) Cochrane review of cognitive stimulation for dementia, (2) a consultation with key stake holders using a Delphi Consensus Process (including an expert consensus conference), (3) focus groups with the target population and (4) a Delphi survey. These techniques were used to complete the theoretical preclinical and phase I modelling of the MRC framework for developing the MCST intervention for dementia. It was feasible and effective to use a systematic development process to produce successive modifications of the draft manual for an evidence based maintenance CST programme for dementia. Close involvement of users and carers ensured that the manual was well targeted on the preferences and abilities of people with dementia. The final Maintenance CST programme and manual is currently being tested as part of a large multicentre, randomised controlled trial

Expanding the Description of Spaceflight Effects beyond Bone Mineral Density [BMD]: Trabecular Bone Score [TBS] in ISS Astronauts

Dual-energy x-ray absorptiometry [DXA] is the widely-applied bone densitometry method used to diagnose osteoporosis in a terrestrial population known to be at risk for age-related bone loss. This medical test, which measures areal bone mineral density [aBMD] of clinically-relevant skeletal sites (e.g., hip and spine), helps the clinician to identify which persons, among postmenopausal women and men older than 50 years, are at high risk for low trauma or fragility fractures and might require an intervention. The most recognized osteoporotic fragility fracture is the vertebral compression fracture which can lead to kyphosis or hunched backs typically seen in the elderly. DXA measurement of BMD however is recognized to be insufficient as a sole index for assessing fracture risk. DXA's limitation may be related to its inability to monitor changes in structural parameters, such as trabecular vs. cortical bone volumes, bone geometry or trabecular microarchitecture. Hence, in order to understand risks to human health and performance due to space exposure, NASA needs to expand its measurements of bone to include other contributors to skeletal integrity. To this aim, the Bone and Mineral Lab conducted a pilot study for a novel measurement of bone microarchitecture that can be obtained by retrospective analysis of DXA scans. Trabecular Bone Score (TBS) assesses changes to trabecular microarchitecture by measuring the grey color "texture" information extracted from DXA images of the lumbar spine. An analysis of TBS in 51 ISS astronauts was conducted to assess if TBS could detect 1) an effect of spaceflight and 2) a response to countermeasures independent of DXA BMD. In addition, changes in trunk body lean tissue mass and in trunk body fat tissue mass were also evaluated to explore an association between body composition, as impacted by ARED exercise, and bone microarchitecture. The pilot analysis of 51 astronaut scans of the lumbar spine suggests that, following an ISS mission, DXA BMD and TBS are detecting different effects of ARED exercise and of ARED + Bisphosphonate on the lumbar spine of astronauts. There is emerging evidence associating reduced TBS with terrestrial metabolic bone disorders where a TBS 1.350 is associated with "normal." However, it is not possible to conclude how the spaceflight-induced changes in TBS increase risk for vertebral fractures in the astronaut or if changes in body composition of the trunk region could be an indirect method of assessing exercise effect on bone microarchitecture. More importantly, this pilot analysis demonstrates a new, minimal risk approach for monitoring changes to vertebral bone microarchitecture. This method could help assess the combined skeletal effects of spaceflight with the effects of aging in the astronaut after return to Earth

A lean neck mass clinic model: Adding value to care

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/115945/1/lary25535.pd

Stable periodic waves in coupled Kuramoto-Sivashinsky - Korteweg-de Vries equations

Periodic waves are investigated in a system composed of a Kuramoto-Sivashinsky - Korteweg-de Vries (KS-KdV) equation, which is linearly coupled to an extra linear dissipative equation. The model describes, e.g., a two-layer liquid film flowing down an inclined plane. It has been recently shown that the system supports stable solitary pulses. We demonstrate that a perturbation analysis, based on the balance equation for the field momentum, predicts the existence of stable cnoidal waves (CnWs) in the same system. It is found that the mean value U of the wave field u in the main subsystem, but not the mean value of the extra field, affects the stability of the periodic waves. Three different areas can be distinguished inside the stability region in the parameter plane (L,U), where L is the wave's period. In these areas, stable are, respectively, CnWs with positive velocity, constant solutions, and CnWs with negative velocity. Multistability, i.e., the coexistence of several attractors, including the waves with several maxima per period, appears at large value of L. The analytical predictions are completely confirmed by direct simulations. Stable waves are also found numerically in the limit of vanishing dispersion, when the KS-KdV equation goes over into the KS one.Comment: a latex text file and 16 eps files with figures. Journal of the Physical Society of Japan, in pres