In this paper we investigate special types of Lukasiewicz filters. We show their connection to crisp filters. Further, we introduce the notion of Lukasiewicz ideal as a set-function which is in some sense complementary to Lukasiewicz filters.

Abstract: A new regression method based on convex correcting procedures over sets of predictors is developed. In contrast to previously developed approach based on minimization of generalized error, the proposed one utilies correcting procedures of maximal correlation with the target value. In the proposed approach a concept of a set of predictors irreducible against target functional is used w...

We study the problem of learning a kernel which minimizes a regularization error functional such as that used in regularization networks or support vector machines. We consider this problem when the kernel is in the convex hull of basic kernels, for example, Gaussian kernels which are continuously parameterized by a compact set. We show that there always exists an optimal kernel which is the co...

A unified approach is taken for deriving new generalization data dependent bounds for several classes of algorithms explored in the existing literature by different approaches. This unified approach is based on an extension of Vapnik’s inequality for VC classes of sets to random classes of sets that is, classes depending on the random data, invariant under permutation of the data and possessing...

It is proved that every doubly stochastic quantum channel that is properly averaged with the completely depolarizing channel can be written as a convex combination of unitary channels. As a consequence, we find that the collection of channels expressible as convex combinations of unitary channels has non-zero Borel measure within the space of doubly stochastic channels.

We propose an abstract definition of convex spaces as sets where one can take convex combinations in a consistent way. A priori, a convex space is an algebra over a finitary version of the Giry monad. We identify the corresponding Lawvere theory as the category from [Fri09] and use the results obtained there to extract a concrete definition of convex space in terms of a family of binary operati...

Abstract. The author here wish to further study the new concept of analytic and univalent functions normalized with f(ω) and f ′(ω) − 1 = 0 introduced by Kanas and Ronning in 1999 which was later also investigated in 2005 by Acu and Owa. The author in this paper obtain coefficient estimates, distortion theorems, convex linear combinations, and radii of ω-closeto-convex, ω − starlikeness and ω −...

We present coloring-based algorithms for tree augmentation and use them to construct convex combinations of 2-edge-connected subgraphs. This classic tool has been applied previously the problem, but our illustrate its flexibility, which – in coordination with choice spanning can be used obtain various properties (e.g., 2-vertex connectivity) that are useful applications. these coloring design a...