25 research outputs found
A mathematical framework for critical transitions: normal forms, variance and applications
Critical transitions occur in a wide variety of applications including
mathematical biology, climate change, human physiology and economics. Therefore
it is highly desirable to find early-warning signs. We show that it is possible
to classify critical transitions by using bifurcation theory and normal forms
in the singular limit. Based on this elementary classification, we analyze
stochastic fluctuations and calculate scaling laws of the variance of
stochastic sample paths near critical transitions for fast subsystem
bifurcations up to codimension two. The theory is applied to several models:
the Stommel-Cessi box model for the thermohaline circulation from geoscience,
an epidemic-spreading model on an adaptive network, an activator-inhibitor
switch from systems biology, a predator-prey system from ecology and to the
Euler buckling problem from classical mechanics. For the Stommel-Cessi model we
compare different detrending techniques to calculate early-warning signs. In
the epidemics model we show that link densities could be better variables for
prediction than population densities. The activator-inhibitor switch
demonstrates effects in three time-scale systems and points out that excitable
cells and molecular units have information for subthreshold prediction. In the
predator-prey model explosive population growth near a codimension two
bifurcation is investigated and we show that early-warnings from normal forms
can be misleading in this context. In the biomechanical model we demonstrate
that early-warning signs for buckling depend crucially on the control strategy
near the instability which illustrates the effect of multiplicative noise.Comment: minor corrections to previous versio
Novel outcome measures for clinical trials in cystic fibrosis
Cystic fibrosis (CF) is a common inherited condition caused by mutations in the gene encoding the CF transmembrane regulator protein. With increased understanding of the molecular mechanisms underlying CF and the development of new therapies there comes the need to develop new outcome measures to assess the disease, its progression and response to treatment. As there are limitations to the current endpoints accepted for regulatory purposes, a workshop to discuss novel endpoints for clinical trials in CF was held in Anaheim, California in November 2011. The pros and cons of novel outcome measures with potential utility for evaluation of novel treatments in CF were critically evaluated. The highlights of the 2011 workshop and subsequent advances in technologies and techniques that could be used to inform the development of clinical trial endpoints are summarized in this review