The presentation is focused on two original unbiased estimation techniques which are suitable for 2D and 3D image analysis. The first method is focused on the unbiased estimation of correlation dimension which is based on the Fourier image of given point set and its averaged power spectrum over all rotations in the Hilbert space. The second method is focused on the unbiased estimation of Renyi...
The work focusses on a statistical analysis of fractal diffusion and the estimation of fractal dimensions. We begin by introducing diffusion over fractal sets as subdiffusive anomalous diffusion characterised by statistical moments and return probability. We present butterfly diffusion and the constrained convolution schema, innovative approaches for analysis and numerical modelling. The...
Berry curvature expresses the curvature of the reciprocal space, in a similar manner as magnetic field express curvature of the real space, resulting in a curved transport of electrons in solids. Therefore, Berry curvature is a key to describe various transport phenomena such as anomalous Hall effect, anomalous Nerst effect, orbital magnetization, topological insulators or electric...
