High gain feedback,tolerance, and stabilization of linear systems

The problem of stabilizing linear continuous-time systems is revisited with the objective of investigating the tolerance allowed in the implementation of stabilizing feedback controllers. It is shown that, for high gain feedback, this tolerance can be described by a cone in the feedback parameter space, called the “tolerance cone”. The tolerance cone describes fractional (percentage) errors the feedback controller can tolerate without jeopardizing the internal stability of the controlled system. The larger the vertex angle of this cone, the more tolerance is available when implementing the controller. The vertex angle of the tolerance cone is determined by the proximity to singularity of a certain matrix derived from the controlled system.     

Generalization ability of folding networks

The information theoretical learnability of folding networks, a very successful approach capable of dealing with tree structured inputs, is examined. We find bounds on the VC, pseudo-, and fat shattering dimension of folding networks with various activation functions. As a consequence, valid generalization of folding networks can be guaranteed. However, distribution independent bounds on the generalization error cannot exist in principle. We propose two approaches which take the specific distribution into account and allow us to derive explicit bounds on the deviation of the empirical error from the real error of a learning algorithm. The first approach requires the probability of large trees to be limited a priori and the second approach deals with situations where the maximum input height in a concrete learning example is restricted     

Sabbatical leave: Who gains and how much?

A rigorous quasi-experiment tested the ameliorative effects of a sabbatical leave, a special case of respite from routine work. We hypothesized that (a) respite increases resource level and well-being and (b) individual differences and respite features moderate respite effects. A sample of 129 faculty members on sabbatical and 129 matched controls completed measures of resource gain, resource loss, and well-being before, during, and after the sabbatical. Among the sabbatees, resource loss declined and resource gain and well-being rose during the sabbatical. The comparison group showed no change. Moderation analysis revealed that those who reported higher respite self-efficacy and greater control, were more detached, had a more positive sabbatical experience, and spent their sabbatical outside their home country enjoyed more enhanced well-being than others. (PsycINFO Database Record (c) 2010 APA, all rights reserved)