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

E-cadherin mediates adherens junction organization through protein kinase C

Cultured human keratinocytes maintained in 30 μM Ca2+ do not form adherens junctions; however, when the extracellular Ca2+ concentration is raised to 1 mM, adherens junctions form very rapidly. The formation of a junction involves the coordinate organization of intracellular and extracellular components. Cadherins have been shown to mediate this coordinate organization. In this report we show that E-cadherin organizes the various junctional components by signalling through protein kinase C

Interpersonal discrimination and depressive symptomatology: examination of several personality-related characteristics as potential confounders in a racial/ethnic heterogeneous adult sample

Background Research suggests that reports of interpersonal discrimination result in poor mental health. Because personality characteristics may either confound or mediate the link between these reports and mental health, there is a need to disentangle its role in order to better understand the nature of discrimination-mental health association. We examined whether hostility, anger repression and expression, pessimism, optimism, and self-esteem served as confounders in the association between perceived interpersonal discrimination and CESD-based depressive symptoms in a race/ethnic heterogeneous probability-based sample of community-dwelling adults. Methods We employed a series of ordinary least squares regression analyses to examine the potential confounding effect of hostility, anger repression and expression, pessimism, optimism, and self-esteem between interpersonal discrimination and depressive symptoms. Results Hostility, anger repression, pessimism and self-esteem were significant as possible confounders of the relationship between interpersonal discrimination and depressive symptoms, together accounting for approximately 38% of the total association (beta: 0.1892, p \u3c 0.001). However, interpersonal discrimination remained a positive predictor of depressive symptoms (beta: 0.1176, p \u3c 0.001). Conclusion As one of the first empirical attempts to examine the potential confounding role of personality characteristics in the association between reports of interpersonal discrimination and mental health, our results suggest that personality-related characteristics may serve as potential confounders. Nevertheless, our results also suggest that, net of these characteristics, reports of interpersonal discrimination are associated with poor mental health

A Study of the Ascorbic Acid Content of the Diet Commonly Prescribed for Patients with Gastric Ulcers

Author Institution: The Ohio State University Hospital and the Department of Agricultural Chemistry, The Ohio State University, Columbus, Ohi

Oakleaf: an S locus-linked mutation of Primula vulgaris that affects leaf and flower development

•In Primula vulgaris outcrossing is promoted through reciprocal herkogamy with insect-mediated cross-pollination between pin and thrum form flowers. Development of heteromorphic flowers is coordinated by genes at the S locus. To underpin construction of a genetic map facilitating isolation of these S locus genes, we have characterised Oakleaf, a novel S locus-linked mutant phenotype. •We combine phenotypic observation of flower and leaf development, with classical genetic analysis and next-generation sequencing to address the molecular basis of Oakleaf. •Oakleaf is a dominant mutation that affects both leaf and flower development; plants produce distinctive lobed leaves, with occasional ectopic meristems on the veins. This phenotype is reminiscent of overexpression of Class I KNOX-homeodomain transcription factors. We describe the structure and expression of all eight P. vulgaris PvKNOX genes in both wild-type and Oakleaf plants, and present comparative transcriptome analysis of leaves and flowers from Oakleaf and wild-type plants. •Oakleaf provides a new phenotypic marker for genetic analysis of the Primula S locus. We show that none of the Class I PvKNOX genes are strongly upregulated in Oakleaf leaves and flowers, and identify cohorts of 507 upregulated and 314 downregulated genes in the Oakleaf mutant

Effect of Oral Iron Repletion on Exercise Capacity in Patients With Heart Failure With Reduced Ejection Fraction and Iron Deficiency: The IRONOUT HF Randomized Clinical Trial.

Importance: Iron deficiency is present in approximately 50% of patients with heart failure with reduced left ventricular ejection fraction (HFrEF) and is an independent predictor of reduced functional capacity and mortality. However, the efficacy of inexpensive readily available oral iron supplementation in heart failure is unknown. Objective: To test whether therapy with oral iron improves peak exercise capacity in patients with HFrEF and iron deficiency. Design, Setting, and Participants: Phase 2, double-blind, placebo-controlled randomized clinical trial of patients with HFrEF ( Interventions: Oral iron polysaccharide (n = 111) or placebo (n = 114), 150 mg twice daily for 16 weeks. Main Outcomes and Measures: The primary end point was a change in peak oxygen uptake (V̇o2) from baseline to 16 weeks. Secondary end points were change in 6-minute walk distance, plasma N-terminal pro-B-type natriuretic peptide (NT-proBNP) levels, and health status as assessed by Kansas City Cardiomyopathy Questionnaire (KCCQ, range 0-100, higher scores reflect better quality of life). Results: Among 225 randomized participants (median age, 63 years; 36% women) 203 completed the study. The median baseline peak V̇o2 was 1196 mL/min (interquartile range [IQR], 887-1448 mL/min) in the oral iron group and 1167 mL/min (IQR, 887-1449 mL/min) in the placebo group. The primary end point, change in peak V̇o2 at 16 weeks, did not significantly differ between the oral iron and placebo groups (+23 mL/min vs -2 mL/min; difference, 21 mL/min [95% CI, -34 to +76 mL/min]; P = .46). Similarly, at 16 weeks, there were no significant differences between treatment groups in changes in 6-minute walk distance (-13 m; 95% CI, -32 to 6 m), NT-proBNP levels (159; 95% CI, -280 to 599 pg/mL), or KCCQ score (1; 95% CI, -2.4 to 4.4), all P \u3e .05. Conclusions and Relevance: Among participants with HFrEF with iron deficiency, high-dose oral iron did not improve exercise capacity over 16 weeks. These results do not support use of oral iron supplementation in patients with HFrEF. Trial Registration: clinicaltrials.gov Identifier: NCT02188784

Focus, Vol. 1 No. 1

A literary magazine of student writing published by the Department of English of Stephen F. Austin State College.https://scholarworks.sfasu.edu/focus/1000/thumbnail.jp

The path to universal health coverage in five African and Asian countries: examining the association between insurance status and health-care use

Despite major efforts to achieve universal health coverage (UHC), progress has lagged in many African and Asian countries. A key strategy pursued by many countries is the use of health insurance to increase access and affordability. However, evidence on insurance coverage and on the association between insurance and UHC is mixed. We analysed nationally representative cross-sectional data collected between 2022 and 2023 in Ethiopia, Kenya, South Africa, India, and Laos. We described public and private insurance coverage by sociodemographic factors and used logistic regression to examine the associations between insurance status and seven health-care use outcomes. Health insurance coverage ranged from 25% in India to 100% in Laos. The share of private insurance ranged from 1% in Ethiopia to 13% in South Africa. Relative to the population with private insurance, the uninsured population had reduced odds of health-care use (adjusted odds ratio 0·68, 95% CI 0·50–0·94), cardiovascular examinations (0·63, 0·47–0·85), eye and dental examinations (0·54, 0·42–0·70), and ability to get or afford care (0·64, 0·48–0·86); private insurance was not associated with unmet need, mental health care, and cancer screening. Relative to private insurance, public insurance was associated with reduced odds of health-care use (0·60, 0·43–0·82), mental health care (0·50, 0·31–0·80), cardiovascular examinations (0·62, 0·46–0·84), and eye and dental examinations (0·50, 0·38–0·65). Results were highly heterogeneous across countries. Public health insurance appears to be only weakly associated with access to health services in the countries studied. Further research is needed to improve understanding of these associations and to identify the most effective financing strategies to achieve UHC