We demonstrate how the Hölder regularity of a given signal is a lower bound for the Grassberger-Procaccia correlation dimension of strange attractors PACS numbers : 05.45D,47.52 It is known from the celebrated work by Lorenz [1] that even low-dimensional deterministic dynamical systems may exhibit chaotic behavior. In the context of turbulence in fluid dynamics, Ruelle and Takens [2] have shown...

We present an algorithm for the efficient and reliable computation of the Grassberger-Procaccia correlation dimension in cases where the correlation integral is constructed using all pairs of points. This algorithm is explicitly designed for modem super-scalar processors. 0 Published by Elsevier Science B.V. PACS: 89.80. + h; 05.45. + b

In real systems like EEG the chaos is very difficult to prove or exclude. The scepticism against finite dimension estimates is understandable. It is hard to believe that a complicated system as the brain, which is continually interacting with many other complex systems, should manifest as deterministic low-dimensional dynamics. Predominantly, it is a manifestation of a mixture of noise, some cy...

Dimension reduction is helpful and often necessary in exploring nonlinear or nonparametric regression structures with a large number of predictors. We consider using the canonical variables from the design space whose correlations with a spline basis in the response space are significant. The method can be viewed as a variant of sliced inverse regression (SIR) with simple slicing replaced by Bs...