We consider the fractal von Neumann entropy associated with the fractal distribution function and we obtain for some universal classes h of fractons their entropies. We obtain also for each of these classes a fractal-deformed Heisenberg algebra. This one takes into account the braid group structure of these objects which live in two-dimensional multiply connected space. PACS numbers: 05.30.-d; ...

Dynamical systems in nature exhibit selfsimilar fractal fluctuations and the corresponding power spectra follow inverse power law form signifying long-range space-time correlations identified as self-organized criticality. The physics of selforganized criticality is not yet identified. The Gaussian probability distribution used widely for analysis and description of large data sets underestimat...

Dynamical systems in nature exhibit self-similar fractal space-time fluctuations on all scales indicating long-range correlations and therefore the statistical normal distribution with implicit assumption of independence, fixed mean and standard deviation cannot be used for description and quantification of fractal data sets. The author has developed a general systems theory based on classical ...

We analyse the Las Campanas Redshift Survey using the integrated conditional density (or density of neighbors) in volume-limited subsamples up to unprecedented scales (200 Mpc/h) in order to determine without ambiguity the behavior of the density field. We find that the survey is well described by a fractal up to 20-30 Mpc/h, but flattens toward homogeneity at larger scales. Although the data a...

A new framework is presented for saliency based analysis of naturally complex scenes. In this framework, the fluctuation of local scale shift and the diversity of subtle chromatic scattering are extracted as the environmental saliency: viewer specific visualization of sign patterns to be associated with landmark objects. Being guided by the probability distribution of the scale shift, the scene...

For underground mining and construction, it is important to obtain a discontinuities’ model of rocks for simulations to evaluate rock stability around the working space and fluid flow in these rocks. We have developed a method using the fractal property of acoustic emission (AE) source distribution to construct a feasible crack distribution model. We confirmed the usefulness of the model throug...

The low-frequency eigenmodes of a fractal drum are studied through experimental observation of the acoustical resonances of a fractal-shaped liquid crystal film. The resonance frequencies agree with the numerical predictions for the Laplacian eigenvalues in the fractal domain with Dirichlet boundary conditions. The amplitude distribution of the modes is detected by scanning the excitation posit...

Context. Cosmic voids are observed in the distribution of galaxies and, to some extent, in the dark matter distribution. If these distributions have fractal geometry, it must be reflected in the geometry of voids; in particular, we expect scaling sizes of voids. However, this scaling is not well demonstrated in galaxy surveys yet. Aims. Our objective is to understand the geometry of cosmic void...