Using a result linking convexity and irreducibility of matrix sets it is shown that the generalized spectral radius of a compact set of matrices is a strictly increasing function of the set in a very natural sense. As an application some consequences of this property in the area of time-varying stability radii are discussed. In particular, using the implicit function theorem sufficient conditio...

Recently, Bilu and Linial [6] formalized an implicit assumption often made when choosing a clustering objective: that the optimum clustering to the objective should be preserved under small multiplicative perturbations to distances between points. Balcan and Liang [4] generalized this to a relaxed notion where the optimal clustering after perturbation is allowed to change slightly. In this pape...

On the basis of a conceptualization of implicit self-esteem as the implicit attitude toward the self, it was predicted that implicit self-esteem could be enhanced by subliminal evaluative conditioning. In 5 experiments, participants were repeatedly presented with trials in which the word I was paired with positive trait terms. Relative to control conditions, this procedure enhanced implicit sel...

We discuss a differential equations treatment of the implicit functions problem. Our approach allows a precise and complete description of the solution, of continuity and differentiability properties. The critical case is also considered. The investigation is devoted to dimension two and three, but extensions to higher dimension are possible. MSC: 26B10, 34A12, 53A05. keywords: implicit functio...