These kernels combine the benefits of two other important classes of kernels: the homogeneous additive kernels (e.g. the χ2 kernel) and the RBF kernels (e.g. the exponential kernel). However, large scale problems require machine learning techniques of at most linear complexity and these are usually limited to linear kernels. Recently, Maji and Berg [2] and Vedaldi and Zisserman [4] proposed exp...

We discuss the proof of a version of the maximum principle with state space constraints for data with very weak regularity properties, using the classical method of packets of needle variations (PNVs), as in Pontryagin’s book, but coupling it with a nonclassical theory of multivalued differentials, the so-called “generalized differential quotients” (GDQs). The key technical point of our argumen...

Digital maps are used, for example, in car navigation systems and web-based map services. As digital data, digital maps are easy to update, duplicate, and distribute. At the same time, illegal duplication and distribution or forgery of the maps is also easy. This paper proposes a digital watermarking algorithm for vector digital maps as a method to counter such abuses of the maps. A watermark b...

Abstract We establish a sufficient condition for continuous map, acting on compact metric space, to have Baire residual set of points exhibiting historic behavior (also known as irregular points). This criterion applies, instance, minimal and non-uniquely ergodic map; maps preserving two distinct probability measures with full support; non-trivial homoclinic classes; some non-uniformly expandin...