58,686 research outputs found
How well can we measure and understand foregrounds with 21 cm experiments?
Before it becomes a sensitive probe of the Epoch of Reionization, the Dark
Ages, and fundamental physics, 21 cm tomography must successfully contend with
the issue of foreground contamination. Broadband foreground sources are
expected to be roughly four orders of magnitude larger than any cosmological
signals, so precise foreground models will be necessary. Such foreground models
often contain a large number of parameters, reflecting the complicated physics
that governs foreground sources. In this paper, we concentrate on spectral
modeling (neglecting, for instance, bright point source removal from spatial
maps) and show that 21 cm tomography experiments will likely not be able to
measure these parameters without large degeneracies, simply because the
foreground spectra are so featureless and generic. However, we show that this
is also an advantage, because it means that the foregrounds can be
characterized to a high degree of accuracy once a small number of parameters
(likely three or four, depending on one's instrumental specifications) are
measured. This provides a simple understanding for why 21 cm foreground
subtraction schemes are able to remove most of the contaminants by suppressing
just a small handful of simple spectral forms. In addition, this suggests that
the foreground modeling process should be relatively simple and will likely not
be an impediment to the foreground subtraction schemes that are necessary for a
successful 21 cm tomography experiment.Comment: 15 pages, 9 figures, 2 tables; Replaced with accepted MNRAS version
(slight quantitative changes to plots and tables, no changes to any
conclusions
A new class of wavelet networks for nonlinear system identification
A new class of wavelet networks (WNs) is proposed for nonlinear system identification. In the new networks, the model structure for a high-dimensional system is chosen to be a superimposition of a number of functions with fewer variables. By expanding each function using truncated wavelet decompositions, the multivariate nonlinear networks can be converted into linear-in-the-parameter regressions, which can be solved using least-squares type methods. An efficient model term selection approach based upon a forward orthogonal least squares (OLS) algorithm and the error reduction ratio (ERR) is applied to solve the linear-in-the-parameters problem in the present study. The main advantage of the new WN is that it exploits the attractive features of multiscale wavelet decompositions and the capability of traditional neural networks. By adopting the analysis of variance (ANOVA) expansion, WNs can now handle nonlinear identification problems in high dimensions
On the clustering phase transition in self-gravitating N-body systems
The thermodynamic behaviour of self-gravitating -body systems has been
worked out by borrowing a standard method from Molecular Dynamics: the time
averages of suitable quantities are numerically computed along the dynamical
trajectories to yield thermodynamic observables. The link between dynamics and
thermodynamics is made in the microcanonical ensemble of statistical mechanics.
The dynamics of self-gravitating -body systems has been computed using two
different kinds of regularization of the newtonian interaction: the usual
softening and a truncation of the Fourier expansion series of the two-body
potential. particles of equal masses are constrained in a finite three
dimensional volume. Through the computation of basic thermodynamic observables
and of the equation of state in the plane, new evidence is given of the
existence of a second order phase transition from a homogeneous phase to a
clustered phase. This corresponds to a crossover from a polytrope of index
, i.e. , to a perfect gas law , as is shown by
the isoenergetic curves on the plane. The dynamical-microcanonical
averages are compared to their corresponding canonical ensemble averages,
obtained through standard Monte Carlo computations. A major disagreement is
found, because the canonical ensemble seems to have completely lost any
information about the phase transition. The microcanonical ensemble appears as
the only reliable statistical framework to tackle self-gravitating systems.
Finally, our results -- obtained in a ``microscopic'' framework -- are compared
with some existing theoretical predictions -- obtained in a ``macroscopic''
(thermodynamic) framework: qualitative and quantitative agreement is found,
with an interesting exception.Comment: 19 pages, 20 figure
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