Determination of the threshold of the break-up of invariant tori in a class of three frequency Hamiltonian systems

We consider a class of Hamiltonians with three degrees of freedom that can be mapped into quasi-periodically driven pendulums. The purpose of this paper is to determine the threshold of the break-up of invariant tori with a specific frequency vector. We apply two techniques: the frequency map analysis and renormalization-group methods. The renormalization transformation acting on a Hamiltonian is a canonical change of coordinates which is a combination of a partial elimination of the irrelevant modes of the Hamiltonian and a rescaling of phase space around the considered torus. We give numerical evidence that the critical coupling at which the renormalization transformation starts to diverge is the same as the value given by the frequency map analysis for the break-up of invariant tori. Furthermore, we obtain by these methods numerical values of the threshold of the break-up of the last invariant torus.Comment: 18 pages, 4 figure

A Preliminary Study Looking at the Use of Mindful Compassion and Cannabis Suppositories for Anodyspareunia among Men Who Have Sex with Men (MSM)

Research on the use of cannabis rectal suppositories for analgesia is limited. Few trials have evaluated the combined use of mindfulness and cannabis suppositories for anodyspareunia in men who have sex with men (MSM). This preliminary study, including a randomised control trial (RCT) and content analysis, assessed the effectiveness of an online mindful-compassion and cannabis suppository intervention among 52 British MSM (aged 18–50) who predominantly identified as bottoms (recipients of anal sex). Participants were randomly allocated to one of four groups based on whether they were using cannabis suppositories: adjunct cannabis suppository and mindful-compassion (CSMF), cannabis suppository only (CS), mindful compassion only (MF) and care as usual/control (CAU). Assessments measuring mindful compassion, sexual functioning, sexual self-efficacy, well-being, and anodyspareunia levels were completed at weeks 0, 4, and 12. Anodyspareunia levels were lower in the CSMF group compared to the other groups (CS/MF/CAU), p = 0.031. Feedback revealed that participants felt mindful compassion potentiated the effects of cannabis suppositories during sexual intimacy, reducing pain and enhancing sexual self-efficacy, sexual functioning, and well-being. This preliminary study warrants larger-scale investigation to establish the role of cannabis suppositories and mindful compassion in reducing anodyspareunia

Low Dose of Bisphosphonate Enhances Sclerostin Antibody‐Induced Trabecular Bone Mass Gains in Brtl/+ Osteogenesis Imperfecta Mouse Model

Osteogenesis imperfecta (OI) is a genetic disorder characterized by altered bone quality and imbalanced bone remodeling, leading to skeletal fractures that are most prominent during childhood. Treatments for OI have focused on restoring pediatric bone density and architecture to recover functional strength and consequently reduce fragility. Though antiresorptive agents like bisphosphonates (BPs) are currently the most common intervention for the treatment of OI, a number of studies have shown efficacy of sclerostin antibody (SclAb) in inducing gains in bone mass and reducing fragility in OI mouse models. In this study, the effects of the concurrent use of BP and SclAb were evaluated during bone growth in a mouse harboring an OI‐causing Gly→Cys mutation on col1a1. A single dose of antiresorptive BP facilitated the anabolic action of SclAb by increasing availability of surfaces for new bone formation via retention of primary trabeculae that would otherwise be remodeled. Chronic effects of concurrent administration of BP and SclAb revealed that accumulating cycles conferred synergistic gains in trabecular mass and vertebral stiffness, suggesting a distinct advantage of both therapies combined. Cortical gains in mass and strength occurred through SclAb alone, independent of presence of BP. In conclusion, these preclinical results support the scientific hypothesis that minimal antiresorptive treatment can amplify the effects of SclAb during early stages of skeletal growth to further improve bone structure and rigidity, a beneficial outcome for children with OI. © 2018 American Society for Bone and Mineral Research.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/144688/1/jbmr3421.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/144688/2/jbmr3421_am.pd