Abstract In this paper, multi-dimensional global optimization problems are considered, where the objective function is supposed to be Lipschitz continuous, multiextremal, and without a known analytic expression. Two different approximations of Peano-Hilbert curve applied reduce problem univariate one satisfying Hölder condition discussed. The first them, piecewise-linear approximation, broadly ...

In boosting-based object detectors, weak classifiers are often build on Haar-like features using conventional integral images. That approach leads to the utilization of simple rectangle-shaped structures which are only partial suitable for curved-shaped structures, as present in natural object classes such as faces. In this paper, we propose a new class of fractal features based on space-fillin...

Partial differential equations can be solved efficiently by adaptive multigrid methods on a parallel computer. We report on the concepts of hash-table storage techniques and space-filling curves to set up such a code. The hash-table storage requires substantial less amount of memory and is easier to code than tree data structures used in traditional adaptive multigrid codes, already for the seq...

A new method for generating pictures is presented and illustrated with examples. The idea is to generate a string of symbols using an L−system, and to interpret this string as a sequence of commands which control a "turtle". Suitable generalizations of the notions of the L−system and of a turtle are introduced. The resulting mathematical model can be used to create a variety of (finite approxim...

This paper is about a type of quantitative density closed geodesics and orthogeodesics on complete finite-area hyperbolic surfaces. The main results are upper bounds the length shortest geodesic doubly truncated orthogeodesic that $\varepsilon$-dense given compact set surface.

We study the non-Hermitian Hofstadter dynamics of a quantum particle with biased motion on a square lattice in the background of a magnetic field. We show that in quasimomentum space, the energy spectrum is an overlap of infinitely many inequivalent fractals. The energy levels in each fractal are space-filling curves with Hausdorff dimension 2. The band structure of the spectrum is similar to a...