Existence, Uniqueness, and Stability Analysis of Impulsive Neural Networks with Mixed Time Delays

We study a class of impulsive neural networks with mixed time delays and generalized activation functions. The mixed delays include time-varying transmission delay, bounded time-varying distributed delay, and discrete constant delay in the leakage term. By using the contraction mapping theorem, we obtain a sufficient condition to guarantee the global existence and uniqueness of the solution for the addressed neural networks. In addition, a delay-independent sufficient condition for existence of an equilibrium point and some delay-dependent sufficient conditions for stability are derived, respectively, by using topological degree theory and Lyapunov-Krasovskii functional method. The presented results require neither the boundedness, monotonicity, and differentiability of the activation functions nor the differentiability (even differential boundedness) of time-varying delays. Moreover, the proposed stability criteria are given in terms of linear matrix inequalities (LMI), which can be conveniently checked by the MATLAB toolbox. Finally, an example is given to show the effectiveness and less conservativeness of the obtained results

Reducibility for a Class of Almost-Periodic Differential Equations with Degenerate Equilibrium Point under Small Almost-Periodic Perturbations

This paper focuses on almost-periodic time-dependent perturbations of an almost-periodic differential equation near the degenerate equilibrium point. Using the KAM method, the perturbed equation can be reduced to a suitable normal form with zero as equilibrium point by an affine almost-periodic transformation. Hence, for the equation we can obtain a small almost-periodic solution

Study of an Arctic blowing snow-induced bromine explosion event in Ny-Ålesund, Svalbard

Bromine explosion events (BEEs) are important processes that influence the atmospheric oxidation capacity, especially in the polar troposphere during spring. Although sea ice surface is thought to be a significant bromine source, bromine release mechanisms remain unclear. High-resolution ground-based observations of reactive bromine, such as BrO, are important for assessing the potential impacts on tropospheric ozone and evaluating chemical models. However, previous model studies paid little attention to Svalbard, which is surrounded by both open ocean and sea ice. In this paper, we present continuous BrO slant column densities and vertical column densities derived by Multi-Axis Differential Optical Absorption Spectroscopy deployed at Ny-Ålesund (78.92°N, 11.93°E) in March 2017. We focused on one BEE in mid-March, during which the vertical column densities of BrO surged from 4.26 × 1013 molecular cm−2 to the peak at 1.23 × 1014 molecular cm−2 on March 17, surface ozone depleted from a background level of 46.25 parts per billion by volume (ppbv) to 13.9 ppbv. This case study indicates that the BEE was strongly associated with blowing snow induced by the cyclone systems that approached Svalbard from March 14 to 18. By considering meteorological conditions, sea ice coverage, and airmass trajectory history, we demonstrate that sea salt aerosols (SSAs) from blowing snow on sea ice, rather than from open ocean, are attributed to the occurrence of this BEE. Model results from a parallelized-tropospheric offline model of chemistry and transport (p-TOMCAT) indicate that this BEE was mainly triggered by a blowing snow event associated with a low-pressure cyclone system. The concentration of blowing-snow-sourced SSAs surged to peak when the airmass pass across the sea-ice-covered area under high wind speed, which is a critical factor in the process of bromine explosion observed in Ny-Ålesund. Due to the coarse resolution, the possible delayed timing of bromine release from SSA and the model-data discrepancies still exist

Asprellcosides B of Ilex asprella Inhibits Influenza A Virus Infection by Blocking the Hemagglutinin- Mediated Membrane Fusion

Ilex asprella is routinely used in China as a traditional medicinal herb to treat influenza (Flu). However, its specific antiviral activity and underlying molecular mechanism have not yet been determined. In this study, we sought to determine the antiviral activity and mechanism of Asprellcosides B, an active component extracted from Ilex asprella, and used against the influenza A virus cell culture. We also performed a computer-assisted structural modeling analysis and carried out surface plasmon resonance (SPR) experiments in the hope of determining the viral target of Asprellcosides B. Results from our studies show that Asprellcosides B reduced virus replication by up to 63% with an IC50 of about 9 μM. It also decreased the low pH-induced and virus-mediated hemolysis by 71% in vitro. Molecular docking simulation analysis suggested a possible binding of Asprellcosides B to the hemagglutinin (HA), which was confirmed by a surface plasmon resonance (SPR) assay. Altogether, our findings demonstrate that Asprellcosides B inhibits the influenza A virus, through a specific binding to the HA, resulting in the blockade of the HA-mediated membrane fusion

Safety and Immunogenicity of H5N1 Influenza Vaccine Based on Baculovirus Surface Display System of Bombyx mori

Avian influenza virus (H5N1) has caused serious infections in human beings. This virus has the potential to emerge as a pandemic threat in humans. Effective vaccines against H5N1 virus are needed. A recombinant Bombyx mori baculovirus, Bmg64HA, was constructed for the expression of HA protein of H5N1 influenza virus displaying on the viral envelope surface. The HA protein accounted for approximately 3% of the total viral proteins in silkworm pupae infected with the recombinant virus. Using a series of separation and purification methods, pure Bmgp64HA virus was isolated from these silkworm pupae bioreactors. Aluminum hydroxide adjuvant was used for an H5N1 influenza vaccine. Immunization with this vaccine at doses of 2 mg/kg and 0.67 mg/kg was carried out to induce the production of neutralizing antibodies, which protected monkeys against influenza virus infection. At these doses, the vaccine induced 1:40 antibody titers in 50% and 67% of the monkeys, respectively. The results of safety evaluation indicated that the vaccine did not cause any toxicity at the dosage as large as 3.2 mg/kg in cynomolgus monkeys and 1.6 mg/kg in mice. The results of dose safety evaluation of vaccine indicated that the safe dose of the vaccine were higher than 0.375 mg/kg in rats and 3.2 mg/kg in cynomolgus monkeys. Our work showed the vaccine may be a candidate for a highly effective, cheap, and safe influenza vaccine for use in humans

The Human Serum Metabolome

Continuing improvements in analytical technology along with an increased interest in performing comprehensive, quantitative metabolic profiling, is leading to increased interest pressures within the metabolomics community to develop centralized metabolite reference resources for certain clinically important biofluids, such as cerebrospinal fluid, urine and blood. As part of an ongoing effort to systematically characterize the human metabolome through the Human Metabolome Project, we have undertaken the task of characterizing the human serum metabolome. In doing so, we have combined targeted and non-targeted NMR, GC-MS and LC-MS methods with computer-aided literature mining to identify and quantify a comprehensive, if not absolutely complete, set of metabolites commonly detected and quantified (with today's technology) in the human serum metabolome. Our use of multiple metabolomics platforms and technologies allowed us to substantially enhance the level of metabolome coverage while critically assessing the relative strengths and weaknesses of these platforms or technologies. Tables containing the complete set of 4229 confirmed and highly probable human serum compounds, their concentrations, related literature references and links to their known disease associations are freely available at http://www.serummetabolome.ca

Existence, Uniqueness, and Stability Analysis of Impulsive Neural Networks with Mixed Time Delays

We study a class of impulsive neural networks with mixed time delays and generalized activation functions. The mixed delays include time-varying transmission delay, bounded time-varying distributed delay, and discrete constant delay in the leakage term. By using the contraction mapping theorem, we obtain a sufficient condition to guarantee the global existence and uniqueness of the solution for the addressed neural networks. In addition, a delay-independent sufficient condition for existence of an equilibrium point and some delay-dependent sufficient conditions for stability are derived, respectively, by using topological degree theory and Lyapunov-Krasovskii functional method. The presented results require neither the boundedness, monotonicity, and differentiability of the activation functions nor the differentiability (even differential boundedness) of time-varying delays. Moreover, the proposed stability criteria are given in terms of linear matrix inequalities (LMI), which can be conveniently checked by the MATLAB toolbox. Finally, an example is given to show the effectiveness and less conservativeness of the obtained results

Quasi-periodic solutions of nonlinear beam equations with quintic quasi-periodic nonlinearities

In this article, we consider the one-dimensional nonlinear beam equations with quasi-periodic quintic nonlinearities $$u_{tt}+u_{xxxx}+(B+ \varepsilon\phi(t))u^5=0$$ under periodic boundary conditions, where B is a positive constant, $\varepsilon$ is a small positive parameter, $\phi(t)$ is a real analytic quasi-periodic function in t with frequency vector $\omega=(\omega_1,\omega_2,\dots,\omega_m)$. It is proved that the above equation admits many quasi-periodic solutions by KAM theory and partial Birkhoff normal form

Boundedness of Solutions for a Class of Sublinear Reversible Oscillators with Periodic Forcing

We study the boundedness of all solutions for the following differential equation x′′+f(x)x′+(B+εe(t))|x|α-1x=p(t), where f(x),  p(t) are odd functions, e(t) is an even function, e(t),  p(t) are smooth 1-periodic functions, B is a nonzero constant, and ε is a small parameter. A sufficient and necessary condition for the boundedness of all solutions of the above equation is established. Moreover, the existence of Aubry-Mather sets is obtained as well

Analytic Solutions of a Functional Equation for Invariant Curves

AbstractAn iterative functional equation is deduced by C. T. Ng and W. Zhang (1997, J. Differ. Equations Appl.3, 147–168) from the problem of invariant curves. In this paper, its analytic solutions are discussed by locally reducing the equation to another functional equation without iteration and by constructing solutions in uniformly convergent power series for the latter equation