3,978 research outputs found
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
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