On a Convex Set with Nondifferentiable Metric Projection

A remarkable example of a nonempty closed convex set in the Euclidean plane for which the directional derivative of the metric projection mapping fails to exist was constructed by A. Shapiro. In this paper, we revisit and modify that construction to obtain a convex set with smooth boundary which possesses the same property

The unique ethical challenges of conducting research in the rehabilitation medicine population

BACKGROUND: The broad topic of research ethics is one which has been relatively well-investigated and discussed. Unique ethical issues have been identified for such populations as pediatrics, where the issues of consent and assent have received much attention, and obstetrics, with concerns such as the potential for research to cause harm to the fetus. However, little has been written about ethical concerns which are relatively unique to the population of patients seen by the practitioner of rehabilitation medicine. DISCUSSION: This paper reviews unique ethical concerns in conducting research in this population, including decision-making capacity, communication, the potential for subject overuse, the timing of recruitment, hope for a cure and therapeutic misconception and the nature of the health care provider-research subject relationship. SUMMARY: Researchers in the area of rehabilitation medicine should be aware of some of the unique ethical challenges posed by this patient population and should take steps to address any potential concerns in order to optimize subject safety and ensure that studies meet current ethical guidelines and standards

Growth characteristics in individuals with osteogenesis imperfecta in North America: results from a multicenter study.

PurposeOsteogenesis imperfecta (OI) predisposes people to recurrent fractures, bone deformities, and short stature. There is a lack of large-scale systematic studies that have investigated growth parameters in OI.MethodsUsing data from the Linked Clinical Research Centers, we compared height, growth velocity, weight, and body mass index (BMI) in 552 individuals with OI. Height, weight, and BMI were plotted on Centers for Disease Control and Prevention normative curves.ResultsIn children, the median z-scores for height in OI types I, III, and IV were -0.66, -6.91, and -2.79, respectively. Growth velocity was diminished in OI types III and IV. The median z-score for weight in children with OI type III was -4.55. The median z-scores for BMI in children with OI types I, III, and IV were 0.10, 0.91, and 0.67, respectively. Generalized linear model analyses demonstrated that the height z-score was positively correlated with the severity of the OI subtype (P < 0.001), age, bisphosphonate use, and rodding (P < 0.05).ConclusionFrom the largest cohort of individuals with OI, we provide median values for height, weight, and BMI z-scores that can aid the evaluation of overall growth in the clinic setting. This study is an important first step in the generation of OI-specific growth curves

Steady-state modulation of voltage-gated K+ channels in rat arterial smooth muscle by cyclic AMP-dependent protein kinase and protein phosphatase 2B

Voltage-gated potassium channels (Kv) are important regulators of membrane potential in vascular smooth muscle cells, which is integral to controlling intracellular Ca2+ concentration and regulating vascular tone. Previous work indicates that Kv channels can be modulated by receptor-driven alterations of cyclic AMP-dependent protein kinase (PKA) activity. Here, we demonstrate that Kv channel activity is maintained by tonic activity of PKA. Whole-cell recording was used to assess the effect of manipulating PKA signalling on Kv and ATP-dependent K+ channels of rat mesenteric artery smooth muscle cells. Application of PKA inhibitors, KT5720 or H89, caused a significant inhibition of Kv currents. Tonic PKA-mediated activation of Kv appears maximal as application of isoprenaline (a β-adrenoceptor agonist) or dibutyryl-cAMP failed to enhance Kv currents. We also show that this modulation of Kv by PKA can be reversed by protein phosphatase 2B/calcineurin (PP2B). PKA-dependent inhibition of Kv by KT5720 can be abrogated by pre-treatment with the PP2B inhibitor cyclosporin A, or inclusion of a PP2B auto-inhibitory peptide in the pipette solution. Finally, we demonstrate that tonic PKA-mediated modulation of Kv requires intact caveolae. Pre-treatment of the cells with methyl-β-cyclodextrin to deplete cellular cholesterol, or adding caveolin-scaffolding domain peptide to the pipette solution to disrupt caveolae-dependent signalling each attenuated PKA-mediated modulation of the Kv current. These findings highlight a novel, caveolae-dependent, tonic modulatory role of PKA on Kv channels providing new insight into mechanisms and the potential for pharmacological manipulation of vascular tone

Theorems on existence and global dynamics for the Einstein equations

This article is a guide to theorems on existence and global dynamics of solutions of the Einstein equations. It draws attention to open questions in the field. The local-in-time Cauchy problem, which is relatively well understood, is surveyed. Global results for solutions with various types of symmetry are discussed. A selection of results from Newtonian theory and special relativity that offer useful comparisons is presented. Treatments of global results in the case of small data and results on constructing spacetimes with prescribed singularity structure or late-time asymptotics are given. A conjectural picture of the asymptotic behaviour of general cosmological solutions of the Einstein equations is built up. Some miscellaneous topics connected with the main theme are collected in a separate section.Comment: Submitted to Living Reviews in Relativity, major update of Living Rev. Rel. 5 (2002)

Magnetism, FeS colloids, and Origins of Life

A number of features of living systems: reversible interactions and weak bonds underlying motor-dynamics; gel-sol transitions; cellular connected fractal organization; asymmetry in interactions and organization; quantum coherent phenomena; to name some, can have a natural accounting via $physical$ interactions, which we therefore seek to incorporate by expanding the horizons of `chemistry-only' approaches to the origins of life. It is suggested that the magnetic 'face' of the minerals from the inorganic world, recognized to have played a pivotal role in initiating Life, may throw light on some of these issues. A magnetic environment in the form of rocks in the Hadean Ocean could have enabled the accretion and therefore an ordered confinement of super-paramagnetic colloids within a structured phase. A moderate H-field can help magnetic nano-particles to not only overcome thermal fluctuations but also harness them. Such controlled dynamics brings in the possibility of accessing quantum effects, which together with frustrations in magnetic ordering and hysteresis (a natural mechanism for a primitive memory) could throw light on the birth of biological information which, as Abel argues, requires a combination of order and complexity. This scenario gains strength from observations of scale-free framboidal forms of the greigite mineral, with a magnetic basis of assembly. And greigite's metabolic potential plays a key role in the mound scenario of Russell and coworkers-an expansion of which is suggested for including magnetism.Comment: 42 pages, 5 figures, to be published in A.R. Memorial volume, Ed Krishnaswami Alladi, Springer 201

On the effects of mechanical stress of biological membranes in modeling of swelling dynamics of biological systems

We highlight mechanical stretching and bending of membranes and the importance of membrane deformations in the analysis of swelling dynamics of biological systems, including cells and subcellular organelles. Membrane deformation upon swelling generates tensile stress and internal pressure, contributing to volume changes in biological systems. Therefore, in addition to physical (internal/external) and chemical factors, mechanical properties of the membranes should be considered in modeling analysis of cellular swelling. Here we describe an approach that considers mechanical properties of the membranes in the analysis of swelling dynamics of biological systems. This approach includes membrane bending and stretching deformations into the model, producing a more realistic description of swelling. We also discuss the effects of membrane stretching on swelling dynamics. We report that additional pressure generated by membrane bending is negligible, compared to pressures generated by membrane stretching, when both membrane surface area and volume are variable parameters. Note that bending deformations are reversible, while stretching deformation may be irreversible, leading to membrane disruption when they exceed a certain threshold level. Therefore, bending deformations need only be considered in reversible physiological swelling, whereas stretching deformations should also be considered in pathological irreversible swelling. Thus, the currently proposed approach may be used to develop a detailed biophysical model describing the transition from physiological to pathological swelling mode.National Aeronautics & Space Administration (NASA):80NSSC19M0049; PR Space Grant (NASA):NNX15AI11Hinfo:eu-repo/semantics/publishedVersio

Parental knowledge of paediatric vaccination

This is an Open Access article distributed under the terms of the Creative Commons Attribution Licens

Augmentation of osteochondral repair with hyperbaric oxygenation: a rabbit study

<p>Abstract</p> <p>Background</p> <p>Current treatments for osteochondral injuries often result in suboptimal healing. We hypothesized that the combination of hyperbaric oxygen (HBO) and fibrin would be superior to either method alone in treating full-thickness osteochondral defects.</p> <p>Methods</p> <p>Osteochondral repair was evaluated in 4 treatment groups (control, fibrin, HBO, and HBO+fibrin groups) at 2-12 weeks after surgical injury. Forty adult male New Zealand white rabbits underwent arthrotomy and osteochondral surgery on both knees. Two osteochondral defects were created in each femoral condyle, one in a weight-bearing area and the other in a non-weight-bearing area. An exogenous fibrin clot was placed in each defect in the right knee. Left knee defects were left empty. Half of the rabbits then underwent hyperbaric oxygen therapy. The defects in the 4 treatment groups were then examined histologically at 2, 4, 6, 8, and 12 weeks after surgery.</p> <p>Results</p> <p>The HBO+fibrin group showed more rapid and more uniform repair than the control and fibrin only groups, but was not significantly different from the group receiving HBO alone. In the 2 HBO groups, organized repair and good integration with adjacent cartilage were seen at 8 weeks; complete regeneration was observed at 12 weeks.</p> <p>Conclusions</p> <p>HBO significantly accelerated the repair of osteochondral defects in this rabbit model; however, the addition of fibrin produced no further improvement.</p