Convergence of the restricted Nelder-Mead algorithm in two dimensions

The Nelder-Mead algorithm, a longstanding direct search method for unconstrained optimization published in 1965, is designed to minimize a scalar-valued function f of n real variables using only function values, without any derivative information. Each Nelder-Mead iteration is associated with a nondegenerate simplex defined by n+1 vertices and their function values; a typical iteration produces a new simplex by replacing the worst vertex by a new point. Despite the method's widespread use, theoretical results have been limited: for strictly convex objective functions of one variable with bounded level sets, the algorithm always converges to the minimizer; for such functions of two variables, the diameter of the simplex converges to zero, but examples constructed by McKinnon show that the algorithm may converge to a nonminimizing point. This paper considers the restricted Nelder-Mead algorithm, a variant that does not allow expansion steps. In two dimensions we show that, for any nondegenerate starting simplex and any twice-continuously differentiable function with positive definite Hessian and bounded level sets, the algorithm always converges to the minimizer. The proof is based on treating the method as a discrete dynamical system, and relies on several techniques that are non-standard in convergence proofs for unconstrained optimization.Comment: 27 page

Pharmacist-led management of chronic pain in primary care:results from a randomised controlled exploratory trial

To compare the effectiveness of pharmacist medication review, with or without pharmacist prescribing, with standard care, for patients with chronic pain

Sex-dependent influence of endogenous estrogen in pulmonary hypertension

Rationale: The incidence of pulmonary arterial hypertension (PAH) is greater in women suggesting estrogens may play a role in the disease pathogenesis. Experimentally, in males exogenously administered estrogen can protect against PH; however in models that display female susceptibility estrogens may play a causative role. Objectives: To clarify the influence of endogenous estrogen and gender in PH and assess the therapeutic potential of a clinically available aromatase inhibitor. Methods: We interrogated the effect of reduced endogenous estrogen in males and females using the aromatase inhibitor, anastrozole, in two models of PH; the hypoxic mouse and Sugen 5416/hypoxic rat. We also determined the effects of gender on pulmonary expression of aromatase in these models and in lungs from PAH patients. Results: Anastrozole attenuated PH in both models studied, but only in females. To verify this effect was due to reduced estrogenic activity we confirmed that in hypoxic mice inhibition of estrogen receptor alpha also has a therapeutic effect specifically in females. Female rodent lung displays increased aromatase and decreased BMPR2 and Id1 expression compared to male. Anastrozole treatment reversed the impaired BMPR2 pathway in females. Increased aromatase expression was also detected in female human pulmonary artery smooth muscle cells compared to male. Conclusions: The unique phenotype of female pulmonary arteries facilitates the therapeutic effects of anastrozole in experimental PH confirming a role for endogenous estrogen in the disease pathogenesis in females and suggests aromatase inhibitors may have therapeutic potential

Service provision and barriers to care for homeless people with mental health problems across 14 European capital cities

This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited

Walk with Me: a protocol for a pilot RCT of a peer-led walking programme to increase physical activity in inactive older adults

Background: Levels of physical activity decline with age. Some of the most disadvantaged individuals in society, such as those from lower socio-economic position, are also the most inactive. Increasing physical activity levels, particularly among those most inactive, is a public health priority. Peer-led physical activity interventions may offer a model to increase physical activity in the older adult population. This study aims to test the feasibility of a peer-led, multicomponent physical activity intervention in socio-economically disadvantaged community dwelling older adults. Methods: The Medical Research Council framework for developing and evaluating complex interventions will be used to design and test the feasibility of a randomised controlled trial (RCT) of a multicomponent peer-led physical activity intervention. Data will be collected at baseline, immediately after the intervention (12 weeks) and 6 months after baseline measures. The pilot RCT will provide information on recruitment of peer mentors and participants and attrition rates, intervention fidelity, and data on the variability of the primary outcome (minutes of moderate to vigorous physical activity measured with an accelerometer). The pilot trail will also assess the acceptability of the intervention and identify potential resources needed to undertake a definitive study. Data analyses will be descriptive and include an evaluation of eligibility, recruitment, and retention rates. The findings will be used to estimate the sample size required for a definitive trial. A detailed process evaluation using qualitative and quantitative methods will be conducted with a variety of stakeholders to identify areas of success and necessary improvements. Discussion: This paper describes the protocol for the ‘Walk with Me’ pilot RCT which will provide the information necessary to inform the design and delivery of a fully powered trial should the Walk with Me intervention prove feasible

Prostaglandin E2 Regulates AMPA Receptor Phosphorylation and Promotes Membrane Insertion in Preoptic Area Neurons and Glia during Sexual Differentiation

Sexual differentiation of the rodent brain is dependent upon the organizing actions of the steroid hormone, estradiol. In the preoptic area, a brain region critical for the expression of adult reproductive behavior, there are twice as many dendritic spine synapses per unit length on newborn male neurons compared to female neurons and this sex difference correlates with the expression of adult male copulatory behavior. The sex difference in the POA is achieved via estradiol's upregulation of the membrane-derived lipid signaling molecule prostaglandin E2 (PGE2); PGE2 is necessary and sufficient to masculinize both dendritic spine density and adult sexual behavior in rats. We have previously shown that PGE2 activates EP2 and EP4 receptors which increases protein kinase A (PKA) activity and that masculinized dendritic spine density and sex behavior are both dependent upon PKA as well as activation of AMPA type glutamate receptors. In the current experiments, we build upon this signaling cascade by determining that PGE2 induces phosphorylation of the AMPA receptor subunit, GluR1, which leads to increased AMPA receptor insertion at the membrane. Treating female pups on the day of birth with PGE2 induced the phosphorylation of GluR1 at the PKA-sensitive site within 2 hours of treatment, an effect that was blocked by co-administration of the PKA/AKAP inhibitor, HT31 with PGE2. Brief treatment of mixed neuronal/glial POA cultures with PGE2 or the cAMP/PKA stimulator, forskolin, increased membrane associated GluR1 in both neurons and glia. We speculate that PGE2 induced increases in AMPA receptor associated with the membrane underlies our previously observed increase in dendritic spine density and is a critical component in the masculinization of rodent sex behavior

An X chromosome-wide association study in autism families identifies TBL1X as a novel autism spectrum disorder candidate gene in males

<p>Abstract</p> <p>Background</p> <p>Autism spectrum disorder (ASD) is a complex neurodevelopmental disorder with a strong genetic component. The skewed prevalence toward males and evidence suggestive of linkage to the X chromosome in some studies suggest the presence of X-linked susceptibility genes in people with ASD.</p> <p>Methods</p> <p>We analyzed genome-wide association study (GWAS) data on the X chromosome in three independent autism GWAS data sets: two family data sets and one case-control data set. We performed meta- and joint analyses on the combined family and case-control data sets. In addition to the meta- and joint analyses, we performed replication analysis by using the two family data sets as a discovery data set and the case-control data set as a validation data set.</p> <p>Results</p> <p>One SNP, rs17321050, in the transducin β-like 1X-linked (<it>TBL1X</it>) gene [OMIM:300196] showed chromosome-wide significance in the meta-analysis (<it>P </it>value = 4.86 × 10^-6) and joint analysis (<it>P </it>value = 4.53 × 10^-6) in males. The SNP was also close to the replication threshold of 0.0025 in the discovery data set (<it>P </it>= 5.89 × 10^-3) and passed the replication threshold in the validation data set (<it>P </it>= 2.56 × 10^-4). Two other SNPs in the same gene in linkage disequilibrium with rs17321050 also showed significance close to the chromosome-wide threshold in the meta-analysis.</p> <p>Conclusions</p> <p><it>TBL1X </it>is in the Wnt signaling pathway, which has previously been implicated as having a role in autism. Deletions in the Xp22.2 to Xp22.3 region containing <it>TBL1X </it>and surrounding genes are associated with several genetic syndromes that include intellectual disability and autistic features. Our results, based on meta-analysis, joint analysis and replication analysis, suggest that <it>TBL1X </it>may play a role in ASD risk.</p

Peer-led walking programme to increase physical activity in inactive 60- to 70-year-olds: Walk with Me pilot RCT

Background Levels of physical activity decline with age. Some of the most disadvantaged individuals in society, such as those with a lower rather than a higher socioeconomic position, are also the most inactive. Peer-led physical activity interventions may offer a model to increase physical activity in these older adults and thus help reduce associated health inequalities. This study aims to develop and test the feasibility of a peer-led, multicomponent physical activity intervention in socioeconomically disadvantaged community-dwelling older adults. Objectives The study aimed to develop a peer-led intervention through a rapid review of previous peer-led interventions and interviews with members of the target population. A proposed protocol to evaluate its effectiveness was tested in a pilot randomised controlled trial (RCT). Design A rapid review of the literature and the pilot study informed the intervention design; a pilot RCT included a process evaluation of intervention delivery. Setting Socioeconomically disadvantaged communities in the South Eastern Health and Social Care Trust and the Northern Health and Social Care Trust in Northern Ireland. Participants Fifty adults aged 60–70 years, with low levels of physical activity, living in socioeconomically disadvantaged communities, recruited though community organisations and general practices. Interventions ‘Walk with Me’ is a 12-week peer-led walking intervention based on social cognitive theory. Participants met weekly with peer mentors. During the initial period (weeks 1–4), each intervention group participant wore a pedometer and set weekly step goals with their mentor’s support. During weeks 5–8 participants and mentors met regularly to walk and discuss step goals and barriers to increasing physical activity. In the final phase (weeks 9–12), participants and mentors continued to set step goals and planned activities to maintain their activity levels beyond the intervention period. The control group received only an information booklet on active ageing. Main outcome measures Rates of recruitment, retention of participants and completeness of the primary outcome [moderate- and vigorous-intensity physical activity measured using an ActiGraph GT3X+ accelerometer (ActiGraph, LLC, Pensacola, FL, USA) at baseline, 12 weeks (post intervention) and 6 months]; acceptability assessed through interviews with participants and mentors. Results The study planned to recruit 60 participants. In fact, 50 eligible individuals participated, of whom 66% (33/50) were female and 80% (40/50) were recruited from general practices. At 6 months, 86% (43/50) attended for review, 93% (40/43) of whom returned valid accelerometer data. Intervention fidelity was assessed by using weekly step diaries, which were completed by both mentors and participants for all 12 weeks, and checklists for the level of delivery of intervention components, which was high for the first 3 weeks (range 49–83%). However, the rate of return of checklists by both mentors and participants diminished thereafter. Outcome data indicate that a sample size of 214 is required for a definitive trial. Limitations The sample was predominantly female and somewhat active. Conclusions The ‘Walk with Me’ intervention is acceptable to a socioeconomically disadvantaged community of older adults and a definitive RCT to evaluate its effectiveness is feasible. Some modifications are required to ensure fidelity of intervention delivery is optimised. Future research needs to identify methods to recruit males and less active older adults into physical activity interventions