Clearing and subword-clearing restarting automata are linguistically motivated models of automata. We investigate the problem of grammatical inference for such automata based on the given set of positive and negative samples. We show that it is possible to identify these models in the limit. In this way we can learn a large class of languages. On the other hand, we prove that the task of findin...

A direct search method for the class of problems considered by Lewis and Torczon [SIAM J. Optim., 12 (2002), pp. 1075-1089] is developed. Instead of using an augmented Lagrangian method, a simplicial approximation method to the feasible set is implicitly employed. This allows the points our algorithm considers to conveniently remain within an a priori specified distance of the feasible set. In ...

We introduce and study some concepts of sensitivity via Furstenberg families. A dynamical system X, f is F-sensitive if there exists a positive ε such that for every x ∈ X and every open neighborhood U of x there exists y ∈ U such that the pair x, y is not F-ε-asymptotic; that is, the time set {n : d f x , f y > ε} belongs to F, where F is a Furstenberg family. A dynamical system X, f is F1, F2...

We examine the behavior of positive bounded, localized solutions of semilinear parabolic equations ut = ∆u + f(u) on RN . Here f ∈ C1, f(0) = 0, and a localized solution refers to a solution u(x, t) which decays to 0 as x → ∞ uniformly with respect to t > 0. In all previously known examples, bounded, localized solutions are convergent or at least quasiconvergent in the sense that all their limi...