This article addresses the concept of authenticity, a characteristic of late modern Western culture. This characteristic is viewed by some as an ideal and by others as a root of the problems inherent within Western culture. After discussing various viewpoints, the author supports the idea that authenticity should not be totally accepted or rejected and sets forth a proposal based on the so-call...

We study the order in Grammatical Inference algorithms, and its influence on the polynomial (with respect to the data) identification of languages. This work is motivated by recent results on the polynomial convergence of data-driven grammatical inference algorithms. In this paper, we prove a sufficient condition that assures the existence of a characteristic sample whose size is polynomial wit...

For X a separable metric space define p(X) to be the smallest cardinality of a subset Z of X which is not a relative γset in X, i.e., there exists an ω-cover of X with no γ-subcover of Z. We give a characterization of p(2) and p(ω) in terms of definable free filters on ω which is related to the pseudo-intersection number p. We show that for every uncountable standard analytic space X that eithe...

The translative intersection formula of integral geometry yields an expression for the mean Euler characteristic a stationary random closed set intersected with fixed observation window. We formulate this result in setting sets positive reach and using flag measures which yield curvature as marginals. As application, we consider excursion fields $C^{1,1}$ realizations, particular, Gaussian fiel...