Filtered Noise Can Mimic Low-Dimensional Chaotic Attractors

This contribution presents four results. First, calculations indicate that when examined by the Grassberger-Procaccia algorithm alone, filtered noise can mimic low-dimensional chaotic attractors. Given the ubiquity Of signal filtering in experimental investigations, this is potentially important. Second, a criterion is derived which provides an estimate of the minimum data accuracy needed to resolve the dimension of an attractor. Third, it is shown that a criterion derived by Eckmann and Ruelle [Physica D 56, 185 (1992)] to estimate the minimum number of data points required in a Grassberger-Procaccia calculation can be used to provide a further check on these dimension estimates. Fourth, it is shown that surrogate data techniques recently published by Theiler and his colleagues [in Nonlinear Modeling and Forecasting, edited by M. Casdagli and S. Eubanks (Addison Wesley, Reading, MA, 1992)] can successfully distinguish between linearly correlated noise and nonlinear structure. These results, and most particularly the first, indicate that Grassberger-Procaccia results must be interpreted with far greater circumspection than has previously been the case, and that the algorithm should be used in combination with additional procedures such as calculations with surrogate data. When filtered signals are examined by this algorithm alone, a finite noninteger value of D2 is consistent with low-dimensional chaotic behavior, but it is certainly not a definitive diagnostic of chaos

Filtered Noise Can Mimic Low-Dimensional Chaotic Attractors

This contribution presents four results. First, calculations indicate that when examined by the Grassberger-Procaccia algorithm alone, filtered noise can mimic low-dimensional chaotic attractors. Given the ubiquity Of signal filtering in experimental investigations, this is potentially important. Second, a criterion is derived which provides an estimate of the minimum data accuracy needed to resolve the dimension of an attractor. Third, it is shown that a criterion derived by Eckmann and Ruelle [Physica D 56, 185 (1992)] to estimate the minimum number of data points required in a Grassberger-Procaccia calculation can be used to provide a further check on these dimension estimates. Fourth, it is shown that surrogate data techniques recently published by Theiler and his colleagues [in Nonlinear Modeling and Forecasting, edited by M. Casdagli and S. Eubanks (Addison Wesley, Reading, MA, 1992)] can successfully distinguish between linearly correlated noise and nonlinear structure. These results, and most particularly the first, indicate that Grassberger-Procaccia results must be interpreted with far greater circumspection than has previously been the case, and that the algorithm should be used in combination with additional procedures such as calculations with surrogate data. When filtered signals are examined by this algorithm alone, a finite noninteger value of D2 is consistent with low-dimensional chaotic behavior, but it is certainly not a definitive diagnostic of chaos

Filtered Noise Can Mimic Low-Dimensional Chaotic Attractors

This contribution presents four results. First, calculations indicate that when examined by the Grassberger-Procaccia algorithm alone, filtered noise can mimic low-dimensional chaotic attractors. Given the ubiquity Of signal filtering in experimental investigations, this is potentially important. Second, a criterion is derived which provides an estimate of the minimum data accuracy needed to resolve the dimension of an attractor. Third, it is shown that a criterion derived by Eckmann and Ruelle [Physica D 56, 185 (1992)] to estimate the minimum number of data points required in a Grassberger-Procaccia calculation can be used to provide a further check on these dimension estimates. Fourth, it is shown that surrogate data techniques recently published by Theiler and his colleagues [in Nonlinear Modeling and Forecasting, edited by M. Casdagli and S. Eubanks (Addison Wesley, Reading, MA, 1992)] can successfully distinguish between linearly correlated noise and nonlinear structure. These results, and most particularly the first, indicate that Grassberger-Procaccia results must be interpreted with far greater circumspection than has previously been the case, and that the algorithm should be used in combination with additional procedures such as calculations with surrogate data. When filtered signals are examined by this algorithm alone, a finite noninteger value of D2 is consistent with low-dimensional chaotic behavior, but it is certainly not a definitive diagnostic of chaos

K+ and K- production in heavy-ion collisions at SIS-energies

The production and the propagation of K+ and of K- mesons in heavy-ion collisions at beam energies of 1 to 2 AGeV have systematically been investigated with the Kaon Spectrometer KaoS at the SIS at the GSI. The ratio of the K+ production excitation function for Au+Au and for C+C reactions increases with decreasing beam energy, which is expected for a soft nuclear equation-of-state. At 1.5 AGeV a comprehensive study of the K+ and of the K- emission as a function of the size of the collision system, of the collision centrality, of the kaon energy, and of the polar emission angle has been performed. The K-/K+ ratio is found to be nearly constant as a function of the collision centrality. The spectral slopes and the polar emission patterns are different for K- and for K+. These observations indicate that K+ mesons decouple earlier from the reaction zone than K- mesons.Comment: invited talk given at the SQM2003 conference in Atlantic Beach, USA (March 2003), to be published in Journal of Physics G, 10pages, 7 figure

Partial Wave Analysis of the Reaction p(3.5GeV)+p→pK+Λp(3.5 GeV)+p \to pK^+\Lambda to Search for the "ppK−ppK^-" Bound State

Employing the Bonn-Gatchina partial wave analysis framework (PWA), we have analyzed HADES data of the reaction $p(3.5GeV)+p\to pK^{+}\Lambda$. This reaction might contain information about the kaonic cluster "$ppK^-$" via its decay into $p\Lambda$. Due to interference effects in our coherent description of the data, a hypothetical $\overline{K}NN$ (or, specifically "$ppK^-$") cluster signal must not necessarily show up as a pronounced feature (e.g. a peak) in an invariant mass spectra like $p\Lambda$. Our PWA analysis includes a variety of resonant and non-resonant intermediate states and delivers a good description of our data (various angular distributions and two-hadron invariant mass spectra) without a contribution of a $\overline{K}NN$ cluster. At a confidence level of CL$_{s}$=95\% such a cluster can not contribute more than 2-12\% to the total cross section with a $pK^{+}\Lambda$ final state, which translates into a production cross-section between 0.7 $\mu b$ and 4.2 $\mu b$, respectively. The range of the upper limit depends on the assumed cluster mass, width and production process.Comment: 7 Pages, 5 Figure