A time-varying empirical spectral process indexed by classes of functions is defined for locally stationary time series. We derive weak convergence in a function space, and prove a maximal exponential inequality and a Glivenko–Cantelli-type convergence result. The results use conditions based on the metric entropy of the index class. In contrast to related earlier work, no Gaussian assumption i...

Azobenzene photoalignment materials are highly effective for liquid crystal alignment with high sensitivity and rewritability. A strong relationship between relative humidity and the alignment quality of a thin layer of azobenzenesulfonic dye has been investigated, where the photoinduced phase retardation, order parameter, and anchoring strength of the alignment layer are influenced dramaticall...

In 1968, Orevkov presented proofs of conservativity of classical over intuitionistic and minimal predicate logic with equality for seven classes of sequents, what are known as Glivenko classes. The proofs of these results, important in the literature on the constructive content of classical theories, have remained somehow cryptic. In this paper, direct proofs for more general extensions are giv...

We study learnability in the online learning model. We define several complexity measures which capture the difficulty of learning in a sequential manner. Among these measures are analogues of Rademacher complexity, covering numbers and fat shattering dimension from statistical learning theory. Relationship among these complexity measures, their connection to online learning, and tools for boun...

We obtain the strong law of large numbers, Glivenko-Cantelli theorem, central limit functional theorem for various Bayesian nonparametric priors which include stick-breaking process with general weights, two-parameter Poisson-Dirichlet process, normalized inverse Gaussian generalized gamma and Dirichlet process. For we introduce two conditions such that hold. Except in case since finite dimensi...