Finding appropriate parameter settings of parameterized algorithms or AI systems is an ubiquitous task in many practical applications. This task is usually tedious and time-consuming. To reduce human intervention, the study of methods for automated algorithm configuration has received increasing attention in recent years. In this article, we study the mesh adaptive direct search (MADS) method f...

The paper deals with the F-transform technique which was introduced as a method for an approximate representation of continuous functions which is appropriate for many applications. In the terminology of neural networks, the F-transform uses so called off-line (batch) learning. However, for certain applications an on-line (incremental) learning algorithm has to be implemented. We study the F-tr...

The structure and the properties of the eigenfunctions of the canonical integral transform are investigated. It is shown that a signal can be decomposed into a set of the orthogonal eigenfunctions of the generalized Fresnel transform. The property that the set contains a finite number of functions is obtained. The canonical integral transform, also known as the generalized Fresnel transform (GF...

A computational framework for the construction of solutions to linear homogenous partial differential equations (PDEs) with variable coefficients is developed in this paper. The considered class PDEs reads: ∂p∂t−∑j=0m∑r=0njajrtxr∂jp∂xj=0 F-operators are introduced and used transform original PDE into image PDE. Factorization solution rational exponential parts enables us construct analytic with...

Using Theorem 1 (or, rather, the analogous result for higher-dimensional Euclidean spaces) we deduce4' 6 THEOREM 2. Let D be any partial differential operator with constant coefficients, and let T be any distribution. Then we can find a distribution S such that DS = T. This result is also valid if D is a partial differential-difference operator with constant coefficients. Remark: We can also gi...

This paper investigates the relations between the least-squares approximation techniques and the Fuzzy Transform. Assuming that the function f : R → R underlying a discrete data set D := {(xi, f(xi))}i=1 has been computed with interpolating or least-squares constraints, we prove that the Discrete Fuzzy Transform of the sets {f(xi)}i=1 and {f(xi)}i=1 is the same. This result shows that the Discr...

Given a formal power series f(z) ∈ C[[z]] we define, for any positive integer r, its rth Witt transform, W (r) f , by W (r) f (z) = 1 r ∑ d|r μ(d)f(z d)r/d, where μ denotes the Möbius function. The Witt transform generalizes the necklace polynomials, M(α;n), that occur in the cyclotomic identity 1 1− αy = ∞