We consider a system where the arrivals form a Poisson process and the required service times of the requests are exponentially distributed. According to the generalized processor sharing discipline, each request in the system receives a fraction of the capacity of one processor which depends on the actual number of requests in the system. We derive systems of ordinary differential equations fo...

Many people who are mobility impaired are, for a variety of reasons, incapable of using an ordinary wheelchair. In some instances, a power wheelchair also cannot be used, usually because of the difficulty the person has in controlling it (often due to additional disabilities). This paper describes two low-cost robotic wheelchair prototypes that assist the operator of the chair in avoiding obsta...

Many people who are mobility impaired are, for a variety of reasons, incapable of using an ordinary wheelchair. In some instances, a power wheelchair also cannot be used, usually because of the difficulty the person has in controlling it (often due to additional disabilities). This paper describes two lowcost robotic wheelchair prototypes that assist the operator of the chair in avoiding obstac...

People often attribute poor performance to having bad days. Given that cognitive aging leads to lower average levels of performance and more moment-to-moment variability, one might expect that older adults should show greater day-to-day variability and be more likely to experience bad days than younger adults. However, both researchers and ordinary people typically sample only one performance p...

Over the last two decades, there has been an increasing awareness of, and interest in, the use of spatial moment techniques to provide insight into a range of biological and ecological processes. Models that incorporate spatial moments can be viewed as extensions of mean-field models. These mean-field models often consist of systems of classical ordinary differential equations and partial diffe...

It is known that Heston’s stochastic volatility model exhibits moment explosion, and that the critical moment s+ can be obtained by solving (numerically) a simple equation. This yields a leading order expansion for the implied volatility at large strikes: σBS(k, T ) T ∼ Ψ(s+ − 1) × k (Roger Lee’s moment formula). Motivated by recent “tail-wing” refinements of this moment formula, we first deriv...

Slow earthquakes have been hypothesized to be compound events, i.e. comprised of both an ordinary earthquake and a smooth moment-release transient of longer duration. Low-frequency normal-mode based studies which support the compound event hypothesis have suggested that low-frequency source-spectra of some slow earthquakes require that the slow-component initiated before the fast component. We ...

This work introduces a Gaussian variational mean-field approximation for inference in dynamical systems which can be modeled by ordinary stochastic differential equations. This new approach allows one to express the variational free energy as a functional of the marginal moments of the approximating Gaussian process. A restriction of the moment equations to piecewise polynomial functions, over ...

We consider ordinary and conditional first passage times in a general birth–death process. Under existence conditions, we derive closed-form expressions for the kth order moment of the defined random variables, k ≥ 1. We also give an explicit condition for a birth–death process to be ergodic degree 3. Based on the obtained results, we analyze some applications for Markovian queueing systems. In...