An easy proof of Jensen's theorem on the uniqueness of infinity harmonic functions

We present a new, easy, and elementary proof of Jensen's Theorem on the uniqueness of infinity harmonic functions. The idea is to pass to a finite difference equation by taking maximums and minimums over small balls.Comment: 4 pages; comments added, proof simplifie

Novel DNA methylation profiles associated with key gene regulation and transcription pathways in blood and placenta of growth-restricted neonates

BB/H012494/1/ Biotechnology and Biological Sciences Research Counci

Magnetic and thermodynamic properties of Sr_{2}LaFe_{3}O_{9}

Using a Dirac-Heisenberg Hamiltonian with biquadratic exchange interactions, we study the effect of iron disproportionation on the magnetic ordering, and describe the first-order magnetic transition occurring in the perovskite Sr_{2}LaFe_{3}O_{9}. Upon fitting the experimental data, we give an estimate of the exchange integrals for the antiferromagntic and ferromagnetic interactions, in agreement with previous works on kindered compounds. Spin-wave theory yields a magnon spectrum with a gapless antiferromagnetic mode together with two gapped ferromagnetic ones.Comment: 8 pages of RevTex, 5 figures (available upon request), submitted to J. Mag. Mag. Ma

Convexity criteria and uniqueness of absolutely minimizing functions

We show that absolutely minimizing functions relative to a convex Hamiltonian $H:\mathbb{R}^n \to \mathbb{R}$ are uniquely determined by their boundary values under minimal assumptions on $H.$ Along the way, we extend the known equivalences between comparison with cones, convexity criteria, and absolutely minimizing properties, to this generality. These results perfect a long development in the uniqueness/existence theory of the archetypal problem of the calculus of variations in $L^\infty.$Comment: 34 page

Analytic Conditions for Energy Neutrality in Uniformly-Formed Wireless Sensor Networks

Future deployments of wireless sensor network (WSN) infrastructures for environmental or event monitoring are expected to be equipped with energy harvesters (e.g. piezoelectric, thermal, photovoltaic) in order to substantially increase their autonomy. In this paper we derive conditions for energy neutrality, i.e. perpetual energy autonomy per sensor node, by balancing the node's expected energy consumption with its expected energy harvesting capability. Our analysis assumes a uniformly-formed WSN, i.e. a network comprising identical transmitter sensor nodes and identical receiver/relay sensor nodes with a balanced cluster-tree topology. The proposed framework is parametric to: (i) the duty cycle for the network activation; (ii) the number of nodes in the same tier of the cluster-tree topology; (iii) the consumption rate of the receiver node(s) that collect (and possibly relay) data along with their own; (iv) the marginal probability density function (PDF) characterizing the data transmission rate per node; (v) the expected amount of energy harvested by each node. Based on our analysis, we obtain the number of nodes leading to the minimumenergy harvestingrequirement for each tier of the WSN cluster-tree topology. We also derive closed-form expressions for the difference in the minimum energy harvesting requirements between four transmission rate PDFs in function of the WSN parameters. Our analytic results are validated via experiments using TelosB sensor nodes and an energy measurement testbed. Our framework is useful for feasibility studies on energy harvesting technologies in WSNs and for optimizing the operational settings of hierarchical WSN-based monitoring infrastructures prior to time-consuming testing and deployment within the application environment

Parallaxes of Five L Dwarfs with a Robotic Telescope

We report the parallax and proper motion of five L dwarfs obtained with observations from the robotic Liverpool Telescope. Our derived proper motions are consistent with published values and have considerably smaller errors. Based on our spectral type versus absolute magnitude diagram, we do not find any evidence for binaries among our sampleor, at least no comparable mass binaries. Their space velocities locate them within the thin disk, and based on the model comparisons, they have solar-like abundances. For all five objects, we derived effective temperature, luminosity, radius, gravity, and mass from an evolutionary model (CBA00) and our measured parallax; moreover, we derived their effective temperature by integrating observed optical and near-infrared spectra and model spectra (BSH06 or BT-Dusty) at longer wavelengths to obtain bolometric flux using the classical Stefan-Boltzmann law. Generally, the three temperatures for one object derived using two different methods with three models are consistent, although at lower temperature (e.g., for L4) the differences among the three temperatures are slightly larger than those at higher temperature (e.g., for L1).Peer reviewe

The effect of morphine upon DNA methylation in ten regions of the rat brain

Morphine is one of the most effective analgesics in medicine. However, its use is associated with the development of tolerance and dependence. Recent studies demonstrating epigenetic changes in the brain after exposure to opiates have provided insight into mechanisms possibly underlying addiction. In this study, we sought to identify epigenetic changes in ten regions of the rat brain following acute and chronic morphine exposure. We analyzed DNA methylation of six nuclear-encoded genes implicated in brain function (Bdnf, Comt, Il1b, Il6, Nr3c1 and Tnf) and three mitochondrially-encoded genes (Mtco1, Mtco2 and Mtco3), and measured global 5-methylcytosine (5-mc) and 5-hydroxymethylcytosine (5-hmc) levels. We observed differential methylation of Bdnf and Il6 in the pons, Nr3c1 in the cerebellum, and Il1b in the hippocampus in response to acute morphine exposure (all p<0.05). Chronic exposure was associated with differential methylation of Bdnf and Comt in the pons, Nr3c1 in the hippocampus and Il1b in the medulla oblongata (all p<0.05). Global 5-mc levels significantly decreased in the superior colliculus following both acute and chronic morphine exposure, and increased in the hypothalamus following chronic exposure. Chronic exposure was also associated with significantly increased global 5-hmc levels in the cerebral cortex, hippocampus and hypothalamus, but significantly decreased in the midbrain. Our results demonstrate, for the first time, highly localized epigenetic changes in the rat brain following acute and chronic morphine exposure. Further work is required to elucidate the potential role of these changes in the formation of tolerance and dependence

Mixed Matrix Carbon Molecular Sieve and Alumina (CMS-Al₂O₃) Membranes

This work shows mixed matrix inorganic membranes prepared by the vacuum-assisted impregnation method, where phenolic resin precursors filled the pore of a-alumina substrates. Upon carbonisation, the phenolic resin decomposed into several fragments derived from the backbone of the resin matrix. The final stages of decomposition (>650 degrees C) led to a formation of carbon molecular sieve (CMS) structures, reaching the lowest average pore sizes of similar to 5 angstrom at carbonisation temperatures of 700 degrees C. The combination of vacuum-assisted impregnation and carbonisation led to the formation of mixed matrix of CMS and a-alumina particles (CMS-Al2O3) in a single membrane. These membranes were tested for pervaporative desalination and gave very high water fluxes of up to 25 kg m(-2) h(-1) for seawater (NaCl 3.5 wt%) at 75 degrees C. Salt rejection was also very high varying between 93-99% depending on temperature and feed salt concentration. Interestingly, the water fluxes remained almost constant and were not affected as feed salt concentration increased from 0.3, 1 and 3.5 wt%

Ruthenium atomically dispersed in carbon outperforms platinum toward hydrogen evolution in alkaline media.

Hydrogen evolution reaction is an important process in electrochemical energy technologies. Herein, ruthenium and nitrogen codoped carbon nanowires are prepared as effective hydrogen evolution catalysts. The catalytic performance is markedly better than that of commercial platinum catalyst, with an overpotential of only -12 mV to reach the current density of 10 mV cm-2 in 1 M KOH and -47 mV in 0.1 M KOH. Comparisons with control experiments suggest that the remarkable activity is mainly ascribed to individual ruthenium atoms embedded within the carbon matrix, with minimal contributions from ruthenium nanoparticles. Consistent results are obtained in first-principles calculations, where RuCxNy moieties are found to show a much lower hydrogen binding energy than ruthenium nanoparticles, and a lower kinetic barrier for water dissociation than platinum. Among these, RuC2N2 stands out as the most active catalytic center, where both ruthenium and adjacent carbon atoms are the possible active sites