117 research outputs found
T. E. Harris's contributions to recurrent Markov processes and stochastic flows
This is a brief survey of T. E. Harris's work on recurrent Markov processes
and on stochastic flows, and of some more recent work in these fields.Comment: Published in at http://dx.doi.org/10.1214/10-AOP594 the Annals of
Probability (http://www.imstat.org/aop/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Renewal theory and computable convergence rates for geometrically ergodic Markov chains
We give computable bounds on the rate of convergence of the transition
probabilities to the stationary distribution for a certain class of
geometrically ergodic Markov chains. Our results are different from earlier
estimates of Meyn and Tweedie, and from estimates using coupling, although we
start from essentially the same assumptions of a drift condition toward a
``small set.'' The estimates show a noticeable improvement on existing results
if the Markov chain is reversible with respect to its stationary distribution,
and especially so if the chain is also positive. The method of proof uses the
first-entrance-last-exit decomposition, together with new quantitative versions
of a result of Kendall from discrete renewal theory.Comment: Published at http://dx.doi.org/10.1214/105051604000000710 in the
Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute
of Mathematical Statistics (http://www.imstat.org
Studies on the measurement and significance of androgens in saliva
Imperial Users onl
Lyapunov exponents and shear-induced chaos for a Hopf bifurcation with additive noise
This paper considers the effect of additive white noise on the normal form
for the supercritical Hopf bifurcation in 2 dimensions. The main results
involve the asymptotic behavior of the top Lyapunov exponent lambda associated
with this random dynamical system as one or more of the parameters in the
system tend to 0 or infinity. This enables the construction of a bifurcation
diagram in parameter space showing stable regions where lambda is negative
(implying synchronization) and unstable regions where lambda is positive
(implying chaotic behavior). The value of lambda depends strongly on the
shearing effect of the twist factor of the deterministic Hopf bifurcation. If
the twist factor is sufficiently small then lambda is negative regardless of
all the other parameters in the system. But when all the parameters except the
shear coefficient are fixed then lambda tends to infinity as the shear
coefficient tends to infinity.Comment: 47 pages, 3 figure
Uniform shrinking and expansion under isotropic Brownian flows
We study some finite time transport properties of isotropic Brownian flows.
Under a certain nondegeneracy condition on the potential spectral measure, we
prove that uniform shrinking or expansion of balls under the flow over some
bounded time interval can happen with positive probability. We also provide a
control theorem for isotropic Brownian flows with drift. Finally, we apply the
above results to show that under the nondegeneracy condition the length of a
rectifiable curve evolving in an isotropic Brownian flow with strictly negative
top Lyapunov exponent converges to zero as with positive
probability
A structured, blended learning program towards proficiency in epileptology: the launch of the ILAE Academy Level 2 Program
The ILAE Academy is the online learning platform of the International League Against Epilepsy (ILAE) and offers a structured educational program addressing the competency-based ILAE curriculum in epileptology. The platform was launched in July 2020 with a self-paced course portfolio of interactive e-learning modules addressing ILAE Level 1 learning objectives, defined as the entry level in epileptology. Using feedback questionnaires from completed Level 1 courses as well as sociodemographic and learning-related data obtained from 47 participants, we show that over 50% of learners have an entry level in epileptology and do not have access to on-site training and over 40% do not have access to on-site training. Most respondents found the case-based e-learning modules relevant to their practice needs, and the time for completion was regarded as viable for most, reiterating the value of an online self-paced training in the field. Participants who have successfully completed all compulsory e-learning material of the Level 1 program and received their final certificate will now be eligible to subscribe to the Level 2 program. The Level 2 program addressing the proficiency level of the ILAE curriculum of epileptology was launched on the ILAE Academy platform in May 2022. The Level 2 program will offer an evolving series of self-paced, interactive, case-based e-learning modules on diagnosis, treatment, and counseling of common as well as rare epilepsies at a higher level of care. An interactive online EEG and MRI reader was developed and is embedded into the course content to satisfy the demands of the learners. The hallmark of this level will be the blended learning with tutored online courses, e.g., the established VIREPA courses on EEG and the newly introduced VIREPA MRI program. Our distinguished faculty will hold live tutored online courses in small groups in various languages and continental time zones. Finally, the ILAE face-to-face curricular teaching courses at summer schools and congresses will represent another pillar of this advanced teaching level. The ILAE Academy will also provide Continuing Medical Education (CME) credits to support career planning in epileptology
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