33,547 research outputs found
Coupling the neural and physical dynamics in rhythmic movements
A pair of coupled oscillators simulating a central pattern generator (CPG) interacting with a pendular limb were numerically integrated. The CPG was represented as a van der Pol oscillator and the pendular limb was modeled as a linearized, hybrid spring-pendulum system. The CPG oscillator drove the pendular limb while the pendular limb modulated the frequency of the CPG. Three results were observed. First, sensory feedback influenced the oscillation frequency of the coupled system. The oscillation frequency was lower in the absence of sensory feedback. Moreover, if the muscle gain was decreased, thereby decreasing the oscillation amplitude of the pendular limb and indirectly lowering the effect of sensory feedback, the oscillation frequency decreased monotonically. This is consistent with experimental data (Williamson and Roberts 1986). Second, the CPG output usually led the angular displacement of the pendular limb by a phase of 90° regardless of the length of the limb. Third, the frequency of the coupled system tuned itself to the resonant frequency of the pendular limb. Also, the frequency of the coupled system was highly resistant to changes in the endogenous frequency of the CPG. The results of these simulations support the view that motor behavior emerges from the interaction of the neural dynamics of the nervous system and the physical dynamics of the periphery
The Controversy of Vaccinations
Recently vaccination has become a controversial topic. There is a growing number of people who believe that vaccines carry great health risks to patients and therefore refuse to be vaccinated or to vaccinate their children. This ill-informed view of immunizations is beginning to cause serious problems in the United States as growing numbers of disease cases are being seen. A closer look into the science of vaccines and the benefits they have brought, clearly show that not only do vaccines carry very little risk to patients, but they are responsible for the eradication and reduction of multiple debilitating diseases
On the half-Cauchy prior for a global scale parameter
This paper argues that the half-Cauchy distribution should replace the
inverse-Gamma distribution as a default prior for a top-level scale parameter
in Bayesian hierarchical models, at least for cases where a proper prior is
necessary. Our arguments involve a blend of Bayesian and frequentist reasoning,
and are intended to complement the original case made by Gelman (2006) in
support of the folded-t family of priors. First, we generalize the half-Cauchy
prior to the wider class of hypergeometric inverted-beta priors. We derive
expressions for posterior moments and marginal densities when these priors are
used for a top-level normal variance in a Bayesian hierarchical model. We go on
to prove a proposition that, together with the results for moments and
marginals, allows us to characterize the frequentist risk of the Bayes
estimators under all global-shrinkage priors in the class. These theoretical
results, in turn, allow us to study the frequentist properties of the
half-Cauchy prior versus a wide class of alternatives. The half-Cauchy occupies
a sensible 'middle ground' within this class: it performs very well near the
origin, but does not lead to drastic compromises in other parts of the
parameter space. This provides an alternative, classical justification for the
repeated, routine use of this prior. We also consider situations where the
underlying mean vector is sparse, where we argue that the usual conjugate
choice of an inverse-gamma prior is particularly inappropriate, and can lead to
highly distorted posterior inferences. Finally, we briefly summarize some open
issues in the specification of default priors for scale terms in hierarchical
models
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