4,243 research outputs found
The Fractal Dimension of Projected Clouds
The interstellar medium seems to have an underlying fractal structure which
can be characterized through its fractal dimension. However, interstellar
clouds are observed as projected two-dimensional images, and the projection of
a tri-dimensional fractal distorts its measured properties. Here we use
simulated fractal clouds to study the relationship between the tri-dimensional
fractal dimension (D_f) of modeled clouds and the dimension resulting from
their projected images. We analyze different fractal dimension estimators: the
correlation and mass dimensions of the clouds, and the perimeter-based
dimension of their boundaries (D_per). We find the functional forms relating
D_f with the projected fractal dimensions, as well as the dependence on the
image resolution, which allow to estimatethe "real" D_f value of a cloud from
its projection. The application of these results to Orion A indicates in a
self-consistent way that 2.5 < D_f < 2.7 for this molecular cloud, a value
higher than the result D_per+1 = 2.3 some times assumed in literature for
interstellar clouds.Comment: 27 pages, 13 figures, 1 table. Accepted for publication in ApJ. Minor
change
On Hilberg's Law and Its Links with Guiraud's Law
Hilberg (1990) supposed that finite-order excess entropy of a random human
text is proportional to the square root of the text length. Assuming that
Hilberg's hypothesis is true, we derive Guiraud's law, which states that the
number of word types in a text is greater than proportional to the square root
of the text length. Our derivation is based on some mathematical conjecture in
coding theory and on several experiments suggesting that words can be defined
approximately as the nonterminals of the shortest context-free grammar for the
text. Such operational definition of words can be applied even to texts
deprived of spaces, which do not allow for Mandelbrot's ``intermittent
silence'' explanation of Zipf's and Guiraud's laws. In contrast to
Mandelbrot's, our model assumes some probabilistic long-memory effects in human
narration and might be capable of explaining Menzerath's law.Comment: To appear in Journal of Quantitative Linguistic
The Hurst Exponent of Fermi GRBs
Using a wavelet decomposition technique, we have extracted the Hurst exponent
for a sample of 46 long and 22 short Gamma-ray bursts (GRBs) detected by the
Gamma-ray Burst Monitor (GBM) aboard the Fermi satellite. This exponent is a
scaling parameter that provides a measure of long-range behavior in a time
series. The mean Hurst exponent for the short GRBs is significantly smaller
than that for the long GRBs. The separation may serve as an unbiased criterion
for distinguishing short and long GRBs.Comment: Accepted for publication in Monthly Notices of the Royal Astronomical
Societ
Mainstream parallel array programming on cell
We present the E] compiler and runtime library for the âFâ subset of
the Fortran 95 programming language. âFâ provides first-class support for arrays,
allowing E] to implicitly evaluate array expressions in parallel using the SPU coprocessors
of the Cell Broadband Engine. We present performance results from
four benchmarks that all demonstrate absolute speedups over equivalent âCâ or
Fortran versions running on the PPU host processor. A significant benefit of this
straightforward approach is that a serial implementation of any code is always
available, providing code longevity, and a familiar development paradigm
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