Verified Integration of ODEs and Flows Using Differential Algebraic Methods on High-Order Taylor Models

A method is developed that allows the verified integration of ODEs based on local modeling with high-order Taylor polynomials with remainder bound. The use of such Taylor models of order n allows convenient automated verified inclusion of functional dependencies with an accuracy that scales with the (n + 1)-st order of the domain and substantially reduces blow-up.Utilizing Schauder's fixed point theorem on certain suitable compact and convex sets of functions, we show how explicit nth order integrators can be developed that provide verified nth order inclusions of a solution of the ODE. The method can be used not only for the computation of solutions through a single initial condition, but also to establish the functional dependency between initial and final conditions, the so-called flow of the ODE. The latter can be used efficiently for a substantial reduction of the wrapping effect.Examples of the application of the method to conventional initial value problems as well as flows are given. The orders of the integration range up to twelve, and the verified inclusions of up to thirteen digits of accuracy have been demanded and obtained.     

Intermittent Hypoxia Increased the Expression of DBH and PNMT in Neuroblastoma Cells via MicroRNA-375-Mediated Mechanism

Sleep apnea syndrome (SAS), characterized by recurrent episodes of oxygen desaturation and reoxygenation (intermittent hypoxia (IH)), is a risk factor for hypertension and insulin resistance. We report a correlation between IH and insulin resistance/diabetes. However, the reason why hypertension is induced by IH is elusive. Here, we investigated the effect of IH on the expression of catecholamine-metabolizing enzymes using an in vitro IH system. Human and mouse neuroblastoma cells (NB-1 and Neuro-2a) were exposed to IH or normoxia for 24 h. Real-time RT-PCR revealed that IH significantly increased the mRNA levels of dopamine β-hydroxylase (DBH) and phenylethanolamine N-methyltransferase (PNMT) in both NB-1 and Neuro-2a. Western blot showed that the expression of DBH and PNMT in the NB-1 cells was significantly increased by IH. Reporter assays revealed that promoter activities of DBH and PNMT were not increased by IH. The miR-375 level of IH-treated cells was significantly decreased relative to that of normoxia-treated cells. The IH-induced up-regulation of DBH and PNMT was abolished by the introduction of the miR-375 mimic, but not by the control RNA. These results indicate that IH stress increases levels of DBH and PNMT via the inhibition of miR-375-mediated mRNA degradation, potentially playing a role in the emergence of hypertension in SAS patients.     

Elevated Alpha 1(I) to Alpha 2(I) Collagen Ratio in Dermal Fibroblasts Possibly Contributes to Fibrosis in Systemic Sclerosis

Systemic sclerosis (SSc) is characterized by excessive collagen deposition in the skin and internal organs. Activated fibroblasts are the key effector cells for the overproduction of type I collagen, which comprises the α1(I) and α2(I) chains encoded by COL1A1 and COL1A2, respectively. In this study, we examined the expression patterns of α1(I) and α2(I) collagen in SSc fibroblasts, as well as their co-regulation with each other. The relative expression ratio of COL1A1 to COL1A2 in SSc fibroblasts was significantly higher than that in control fibroblasts. The same result was observed for type I collagen protein levels, indicating that α2(I) collagen is more elevated than α2(I) collagen. Inhibition or overexpression of α1(I) collagen in control fibroblasts affected the α2(I) collagen levels, suggesting that α1(I) collagen might act as an upstream regulator of α2(I) collagen. The local injection of COL1A1 small interfering RNA in a bleomycin-induced SSc mouse model was found to attenuate skin fibrosis. Overall, our data indicate that α2(I) collagen is a potent regulator of type I collagen in SSc; further investigations of the overall regulatory mechanisms of type I collagen may help understand the aberrant collagen metabolism in SSc.     

Association of Ligamentum Flavum Hypertrophy with Adolescent Idiopathic Scoliosis Progression—Comparative Microarray Gene Expression Analysis

The role of the ligamentum flavum (LF) in the pathogenesis of adolescent idiopathic scoliosis (AIS) is not well understood. Using magnetic resonance imaging (MRI), we investigated the degrees of LF hypertrophy in 18 patients without scoliosis and on the convex and concave sides of the apex of the curvature in 22 patients with AIS. Next, gene expression was compared among neutral vertebral LF and LF on the convex and concave sides of the apex of the curvature in patients with AIS. Histological and microarray analyses of the LF were compared among neutral vertebrae (control) and the LF on the apex of the curvatures. The mean area of LF in the without scoliosis, apical concave, and convex with scoliosis groups was 10.5, 13.5, and 20.3 mm², respectively. There were significant differences among the three groups (p < 0.05). Histological analysis showed that the ratio of fibers (Collagen/Elastic) was significantly increased on the convex side compared to the concave side (p < 0.05). Microarray analysis showed that ERC2 and MAFB showed significantly increased gene expression on the convex side compared with those of the concave side and the neutral vertebral LF cells. These genes were significantly associated with increased expression of collagen by LF cells (p < 0.05). LF hypertrophy was identified in scoliosis patients, and the convex side was significantly more hypertrophic than that of the concave side. ERC2 and MAFB genes were associated with LF hypertrophy in patients with AIS. These phenomena are likely to be associated with the progression of scoliosis.     

Room temperature continuous-wave operation of GaInNAs/GaAs VCSELsgrown by chemical beam epitaxy with output power exceeding 1 mW

The authors present a near 1200 nm wavelength vertical-cavity surface-emitting laser (VCSEL) the active region of which is formed by GaInNAs/GaAs quantum wells grown by chemical beam epitaxy. Room temperature continuous-wave operation has been demonstrated with a high slope efficiency of 0.23 W/A, a high output power of over 1.0 mW, and a singlemode output power of 0.34 mW. The fabricated devices with different aperture sizes show low threshold currents of 1.2-2.1 mA and a record low threshold current density of 2.6 kA/cm² in GaInNAs VCSELs     

Evaluation of absorption of micro-droplets on paper for creation of paper-based microstructures

This study clarifies the absorption behavior of micro-droplets of water on treated paper to support the design of functional microstructures, such as electronics and micro-fluid channels, on paper. The period of time between when a micro-droplet of water ejected from an ink-jet head lands on the paper’s surface and its complete disappearance by absorption was defined as the micro-sizing degree (MSD), and an MSD measurement method was established. The MSD was evaluated using microscopic high-speed video images of the side view recorded every millisecond. Several grades of commercially available ink-jet paper media and laboratory sheets having different levels of water repellency prepared from a pulp and a sizing agent were examined. The MSD of commercial ink-jet papers, which are known to absorb water very quickly, was 3–6 ms. Weakly sized laboratory sheets exhibited a lower MSD of 2–3 ms. The absorption behavior was analyzed in terms of the capillary pressure with and without the Laplace pressure; the theoretical and experimental results agreed moderately well. The results indicated that the Laplace pressure cannot be neglected in the analysis. The MSD of a wet surface where a preceding micro-droplet had already landed was higher than that on a dry or partially wet surface, presumably because water remains inside pores for an unexpectedly long time.     

How to identify water from thickener aqueous solutions by touch

Water detection is one of the most crucial psychological processes for many animals. However, nobody knows the perception mechanism of water through our tactile sense. In the present study, we found that a characteristic frictional stimulus with large acceleration is one of the cues to differentiate water from water contaminated with thickener. When subjects applied small amounts of water to a glass plate, strong stick-slip phenomena with a friction force of 0.46 ± 0.30 N and a vertical force of 0.57 ± 0.36 N were observed at the skin surface, as shown in previous studies. Surprisingly, periodic shears with acceleration seven times greater than gravitational acceleration occurred during the application process. Finite-element analyses predicted that these strong stimuli could activate tactile receptors: Meissner''s corpuscle and Pacinians. When such stimuli were applied to the fingertips by an ultrasonic vibrator, a water-like tactile texture was perceived by some subjects, even though no liquid was present between the fingertip and the vibrator surface. These findings could potentially be applied in the following areas: materials science, information technology, medical treatment and entertainment.     

Uncooled InAs0.09Sb0.91 photoconductors with cutoff wave- length extended to 11.5 μm

Uncooled InAsSb photoconductors were fabricated. The photoconductors were based on InAs0.05Sb0.95 and InAs0.09Sb0.91 thick epilayers grown on InAs substrates by melt epitaxy (ME). Ge immersion lenses were set on the photoconductors. The cutoff wavelength of InAs0.09Sb0.91 detectors is obviously extended to 11.5 mm, and that of InAs0.05Sb0.95 detectors is 8.3 mm. At room temperature, the peak detectivity of Dλp at wavelength of 6.8 mm and modulation frequency of 1 200 Hz is 1.08×109 cm.Hz1/2.W-1 for InAs0.09Sb0.91 photoconductors, the detectivity D at wavelength of 9 mm is 7.56×108 cm.Hz1/2.W-1, and that at 11 mm is 3.92×108 cm.Hz1/2.W-1. The detectivity of InAs0.09Sb0.91 detectors at the wavelengths longer than 9 mm is about one order of magnitude higher than that of InAs0.05Sb0.95 detectors, which rises from the increase of arsenic (As) composition in InAs0.09Sb0.91 materials.