We examine the estimation of selectivities for range and spatial join queries in real spatial databases. As we have shown earlier [FK94], real point sets: (a) violate consistently the “uniformity” and “independence” assumptions, (b) can often be described as “fractals”, with non-integer (fractal) dimension. In this paper we show that, among the infinite family of fractal dimensions, the so call...

This study was concentrated on changes of complexity of EEG signals during the sleep onset process and the comparison of sleep onset with relaxation. The ability of two complexity measures correlation dimension D2 and fractal exponent γ to distinguish these slightly distinct states was examined. Both measures confirmed decreased complexity of EEG signals during sleep onset process, on the contr...

In this work we quantify the degree to which star-forming events are clumped. We apply a precise and accurate technique to calculate the correlation dimension Dc of the distribution of HII regions in a sample of disk galaxies. Our reliable results are distributed in the range 1.5 ∼< Dc ∼< 2.0. We get significant variations in the fractal dimension among galaxies, contrary to a universal picture...

It is known that the gas has a fractal structure in a wide range of spatial scales with a fractal dimension that seems to be a constant around Df ≃ 2.7. It is expected that stars forming from this fractal medium exhibit similar fractal patterns. Here we address this issue by quantifying the degree to which starforming events are clumped. We develop, test, and apply a precise and accurate techni...

We present a dimension analysis of a set of solar type I storms and type IV events with different kind of fine structures, recorded at the Trieste Astronomical Observatory. The signature of such types of solar radio events is highly structured in time. However, periodicities are rather seldom, and linear mode theory can provide only limited interpretation of the data. Therefore, we performed an...

We investigate the breaking of proper self similarity of attractors in the presence of intermittency. We show that this can lead to dramatically too small values of the numerically estimated correlation dimension D 2 , which we relate, in the case of type I intermittency, to universal scaling properties in the vicinity of the critical value of the control parameter. For spatially extended syste...

It has recently been observed that a stochastic (in nite degree of freedom) time series with a 1=f power spectrum can exhibit a nite correlation dimension, even for arbitrarily large data sets. [A. R. Osborne and A. Provenzale, Physica D 35, 357 (1989).] I will discuss the relevance of this observation to the practical estimation of dimension from a time series, and in particular I will argue t...