We study the properties of spectrum and eigenstates of the Google matrix of a directed network formed by the procedure calls in the Linux Kernel. Our results obtained for various versions of the Linux Kernel show that the spectrum is characterized by the fractal Weyl law established recently for systems of quantum chaotic scattering and the Perron-Frobenius operators of dynamical maps. The frac...

The soft fault diagnosis of nonlinear analog circuits is an important guarantee of the stable and reliable operation of electronic products. In view of the low accuracy and heavy computation load of current soft fault diagnosis methods for nonlinear analog circuits, this paper presents a soft fault diagnosis method for nonlinear analog circuits based on fractal theory. Analyzing the single-frac...

The border collision normal form is a continuous piecewise affine map of R n with applications in piecewise smooth bifurcation theory. We show that these maps have absolutely continuous invariant measures for an open set of parameter space and hence that the attractors have Haus-dorff (fractal) dimension n. If n = 2 the attractors have topological dimension two, i.e. they contain open sets, and...

We present a method to recover a fractal dimension of a multi-scale rough surface, the so-called correlation dimension, from the knowledge of the far-field scattered intensity. The results are validated by numerical experiments on Weierstrass-like surfaces.

This work demonstrates that the distance measuring the likelihood of the graphs of two functions, usually referred as Hausdor distance between functions and widely used in function approximation tasks and signal processing, can be calculated e ciently using grey scale morphological operations even in the case of noncontinuous (discrete as well as nondiscrete) functions. Also we have presented a...

We describe two dimensional DNA walks, and analyze their fractal properties. We show results for the complete genome of S. cerevisiae. We find that the mean square deviation of the walks is superdifussive, corresponding to a fractal structure of dimension lower than two. Furthermore, the coding part of the genome seems to have smaller fractal dimension, and longer correlations, than noncoding p...

2014 The propagation of a front (we use the model of a forest fire) in a bidimensional random lattice is studied for several different types of interactions. We obtain the corresponding critical concentrations and critical exponents calculated by means of the finite size scaling conjecture. These exponents are expressed in terms of the fractal dimension of the infinite cluster and of the spread...

This thesis combines computability theory and various notions of fractal dimension, mainly Hausdorff dimension. An algorithmic approach to Hausdorff measures makes it possible to define the Hausdorff dimension of individual points instead of sets in a metric space. This idea was first realized by Lutz (2000b). Working in the Cantor space 2ω of all infinite binary sequences, we study the theory ...

A brain computer interface (BCI) enables direct communication between a brain and a computer translating brain activity into computer commands usi ng preprocessing, feature extraction and classification operations. Feature extraction is crucial as it has a substantial effect on the classification accuracy and speed. While fractal dimension has been successfully used in various domains to charac...