Stability guarantee is the most important issue in designing variable recursive digital filters since unstable variable filters cannot be applied in signal processing applications.
For systems that involve only two variables, an unstable focus provides a necessary condition for Hopf bifurcation and a stable limit cycle.
By contrast, from a scientific point of view, these differences are not surprising, since it is well known that the multiple regression analysis used for studying the relationship between A1C and glucose values at different times is an unstable model when explanatory variables, i.e., the glucose values in the present example, are intercorrelated.
To circumvent the risk of an overfitted model, which can arise when there are excess potential explanatory variables, as is often the case with biomarkers, we have used bootstrap sampling to refine the models by excluding variables with an unstable form or those that are unreliably included as necessary for prediction.
The basis of the model is a hidden variable that has an unstable fixed point (threshold).
In humans, an unstable plaque ruptures, leading to a variable degree of staggered occlusion caused by clot formation over the ulcerated plaque, and showering debris into the bloodstream, which leads to an inflammatory response and distal embolization.
BIC penalizes the number of variables to avoid an unstable or over-fitting model [ 31].
What the team did find was that tinkering with any of one of these three variables could make a stable bicycle unridable, and an unstable one ridable.
If pressure drop, rather than flow rates, is fixed, one observes an unstable regime between stable "strong" and "coarse" foam regimes; in the unstable regime ∇p is nonuniform in space or variable in time.
This is an unstable situation.
