The space-clamped Hodgkin-Huxley system with random synaptic input: inhibition of spiking by weak noise and analysis with moment equations

We consider a classical space-clamped Hodgkin-Huxley model neuron stimulated by synaptic excitation and inhibition with conductances represented by Ornstein-Uhlenbeck processes. Using numerical solutions of the stochastic model system obtained by an Euler method, it is found that with excitation only there is a critical value of the steady state excitatory conductance for repetitive spiking without noise and for values of the conductance near the critical value small noise has a powerfully inhibitory effect. For a given level of inhibition there is also a critical value of the steady state excitatory conductance for repetitive firing and it is demonstrated that noise either in the excitatory or inhibitory processes or both can powerfully inhibit spiking. Furthermore, near the critical value, inverse stochastic resonance was observed when noise was present only in the inhibitory input process. The system of 27 coupled deterministic differential equations for the approximate first and second order moments of the 6-dimensional model is derived. The moment differential equations are solved using Runge-Kutta methods and the solutions are compared with the results obtained by simulation for various sets of parameters including some with conductances obtained by experiment on pyramidal cells of rat prefrontal cortex. The mean and variance obtained from simulation are in good agreement when there is spiking induced by strong stimulation and relatively small noise or when the voltage is fluctuating at subthreshold levels. In the occasional spike mode sometimes exhibited by spinal motoneurons and cortical pyramidal cells the assunptions underlying the moment equation approach are not satisfied

Virtual Enriching Operators

We construct bounded linear operators that map $H^1$ conforming Lagrange finite element spaces to $H^2$ conforming virtual element spaces in two and three dimensions. These operators are useful for the analysis of nonstandard finite element methods

Virtual Element Methods on Meshes with Small Edges or Faces

We consider a model Poisson problem in $\R^d$ ($d=2,3$) and establish error estimates for virtual element methods on polygonal or polyhedral meshes that can contain small edges ($d=2$) or small faces ($d=3$).Comment: 36 page

Optical properties of carbon grains: Influence on dynamical models of AGB stars

For amorphous carbon several laboratory extinction data are available, which show quite a wide range of differences due to the structural complexity of this material. We have calculated self-consistent dynamic models of circumstellar dust-shells around carbon-rich asymptotic giant branch stars, based on a number of these data sets. The structure and the wind properties of the dynamical models are directly influenced by the different types of amorphous carbon. In our test models the mass loss is not severely dependent on the difference in the optical properties of the dust, but the influence on the degree of condensation and the final outflow velocity is considerable. Furthermore, the spectral energy distributions and colours resulting from the different data show a much wider spread than the variations within the models due to the variability of the star. Silicon carbide was also considered in the radiative transfer calculations to test its influence on the spectral energy distribution.Comment: 12 pages, 6 figures. To appear in A&

Leveraging Employer Practices in Global Regulatory Frameworks to Improve Employment Outcomes for People with Disabilities

Work is an important part of life, providing both economic security and a forum to contribute one’s talents and skills to society, thereby anchoring the individual in a social role. However, access to work is not equally available to people with disabilities globally. Regulatory environments that prohibit discrimination and support vocational training and educational opportunities constitute a critical first step toward economic independence. However, they have not proven sufficient in themselves. In this article, we aim to infuse deeper consideration of employer practice and demand-side policy reforms into global policy discussions of the right to work for people with disabilities. We begin by documenting the employment and economic disparities existing for people with disabilities globally, followed by a description of the international, regional, and local regulatory contexts aiming to improve labor market outcomes for people with disabilities. Next, we examine how policies can leverage employer interests to further address inequalities. We discuss employer policies and practices demonstrated in the research to facilitate recruitment, hiring, career development, retention, and meaningful workplace inclusion. The goal of the article is to synthesize existing international literature on employment rights for people with disabilities with the employer perspective

A Robust Solver for a Second Order Mixed Finite Element Method for the Cahn-Hilliard Equation

We develop a robust solver for a second order mixed finite element splitting scheme for the Cahn-Hilliard equation. This work is an extension of our previous work in which we developed a robust solver for a first order mixed finite element splitting scheme for the Cahn-Hilliard equaion. The key ingredient of the solver is a preconditioned minimal residual algorithm (with a multigrid preconditioner) whose performance is independent of the spacial mesh size and the time step size for a given interfacial width parameter. The dependence on the interfacial width parameter is also mild.Comment: 17 pages, 3 figures, 4 tables. arXiv admin note: substantial text overlap with arXiv:1709.0400