Search results for "correlation dimension"
showing 4 items of 24 documents
Linear inverse filtering improves spatial separation of nonlinear brain dynamics: a simulation study.
2000
We examined topographic variations in nonlinear measures based on scalp voltages, which were generated by two simulated current dipoles each placed in a different hemisphere of a spherical volume conductor (three-shell model). Dipole dynamics were that of a three-torus and the x-component of the Lorenz-system and scalp voltage were calculated for a configuration of 29 electrode positions. Although estimates for correlation dimension D2 and Lyapunov exponent L1 were close to the theoretical values for the original time series, the simulated scalp voltage data showed almost no topographic resolution of dipole positions. In order to enhance topographic differentiation, we constructed linear in…
Fractal Aspects of Galaxy Clustering
2008
In the past decade, the mathematical concept of fractal has exerted a great influence in a large variety of scientific disciplines. It is very common to find recent papers on the application of fractals to different fields in Physics, Chemistry, Biology, etc. The success of the fractal geometry in the description of many systems is due to the fact that deep insights into very simple objects show how fractal measures are more natural for their study.
Searching for the scale of homogeneity
1998
We introduce a statistical quantity, known as the $K$ function, related to the integral of the two--point correlation function. It gives us straightforward information about the scale where clustering dominates and the scale at which homogeneity is reached. We evaluate the correlation dimension, $D_2$, as the local slope of the log--log plot of the $K$ function. We apply this statistic to several stochastic point fields, to three numerical simulations describing the distribution of clusters and finally to real galaxy redshift surveys. Four different galaxy catalogues have been analysed using this technique: the Center for Astrophysics I, the Perseus--Pisces redshift surveys (these two lying…
Correlation dimension and affinity of AE data and bicolored noise
1993
This paper is concerned with the general question of the dynamics of the magnetosphere. In general, to solve the dynamics of the magnetosphere one has to solve magnetohydrodynamic equations with some appropriate set of boundary conditions. This results in a very complex solution, which gives indications of being chaotic. The question of the chaotic nature of the magnetospheric dynamics has been addressed by various authors by looking at the correlation dimension of the auroral electrojet index. There has been disagreement on the outcome of such experiments, so the authors report on a detailed analysis of the auroral electrojet index time series. They find a correlation dimension of 3.4. For…