Complex dynamics emerging in Rule 30 with majority memory

In cellular automata with memory, the unchanged maps of the conventional cellular automata are applied to cells endowed with memory of their past states in some specified interval. We implement Rule 30 automata with a majority memory and show that using the memory function we can transform quasi-chaotic dynamics of classical Rule 30 into domains of travelling structures with predictable behaviour. We analyse morphological complexity of the automata and classify dynamics of gliders (particles, self-localizations) in memory-enriched Rule 30. We provide formal ways of encoding and classifying glider dynamics using de Bruijn diagrams, soliton reactions and quasi-chemical representations

Fractional Powers of Non-Negative Operators in Fréchet Spaces

[EN] In the present paper the theory of fractional powers, which has been restricted to date to certain operators on Banach spaces, is generalized to certain particular operators in Frchet spaces. The main difficulty consists in the fact that neither the holomorphlc functional calculus nor the results on Banach algebras are available for bounded operators on Frchet spaces. All the basic properties which a good theory of fractional powers must fulfill are proved, except for the spectral relation,Martinez, C.; Sanz, M.; Calvo Roselló, V. (1989). Fractional Powers of Non-Negative Operators in Fréchet Spaces. International Journal of Mathematics and Mathematical Sciences. 12(2):309-320. http://hdl.handle.net/10251/19145630932012

Fractional Powers of Non-Negative Operators in Fréchet Spaces

[EN] In the present paper the theory of fractional powers, which has been restricted to date to certain operators on Banach spaces, is generalized to certain particular operators in Frchet spaces. The main difficulty consists in the fact that neither the holomorphlc functional calculus nor the results on Banach algebras are available for bounded operators on Frchet spaces. All the basic properties which a good theory of fractional powers must fulfill are proved, except for the spectral relation,Martinez, C.; Sanz, M.; Calvo Roselló, V. (1989). Fractional Powers of Non-Negative Operators in Fréchet Spaces. International Journal of Mathematics and Mathematical Sciences. 12(2):309-320. http://hdl.handle.net/10251/19145630932012

Detection of non-Gaussianity in the WMAP 1-year data using spherical wavelets

A non-Gaussian detection in the WMAP 1-year data is reported. The detection has been found in the combined Q-V-W map proposed by the WMAP team (Komatsu et al. 2003) after applying a wavelet technique based on the Spherical Mexican Hat Wavelet (SMHW). The skewness and the kurtosis of the SMHW coefficients are calculated at different scales. A non-Gaussian signal is detected at scales of the SMHW around 4 deg (size in the sky of around 10 deg). The right tail probability of the detection is approx. 0.4%. In addition, a study of Gaussianity is performed in each hemisphere. The northern hemisphere is compatible with Gaussianity, whereas the southern one deviates from Gaussianity with a right tail probability of approx. 0.1%. Systematics, foregrounds and uncertainties in the estimation of the cosmological parameters are carefully studied in order to identify the possible source of non-Gaussianity. The detected deviation from Gaussianity is not found to be caused by systematic effects: 1) each one of the Q, V and W receivers shows the same non-Gaussianity pattern, and 2) several combinations of the different receivers at each frequency band do not show this non-Gaussian pattern. Similarly, galactic foregrounds show a negligible contribution to the non-Gaussian detection: non-Gaussianity is detected in all the WMAP maps and no frequency dependence is observed. Moreover, the expected foreground contribution to the combined WMAP map was added to CMB Gaussian simulations showing a behaviour compatible with the Gaussian model. Influence of uncertainties in the CMB power spectrum estimation are also quantified. Hence, possible intrinsic temperature fluctuations (like secondary anisotropies and primordial features) can not be rejected as the source of this non-Gaussian detection.Comment: 33 pages, 14 figures. Revised to match version accepted for publication in Ap

Peaks in the Cosmic Microwave Background: flat versus open models

We present properties of the peaks (maxima) of the CMB anisotropies expected in flat and open CDM models. We obtain analytical expressions of several topological descriptors: mean number of maxima and the probability distribution of the gaussian curvature and the eccentricity of the peaks. These quantities are calculated as functions of the radiation power spectrum, assuming a gaussian distribution of temperature anisotropies. We present results for angular resolutions ranging from 5' to 20' (antenna FWHM), scales that are relevant for the MAP and COBRAS/SAMBA space missions and the ground-based interferometer experiments. Our analysis also includes the effects of noise. We find that the number of peaks can discriminate between standard CDM models, and that the gaussian curvature distribution provides a useful test for these various models, whereas the eccentricity distribution can not distinguish between them.Comment: 13 pages latex file using aasms4.sty + 3 tables + 2 postscript figures, to appear in ApJ (March 1997