13,998 research outputs found
Penalized estimation in large-scale generalized linear array models
Large-scale generalized linear array models (GLAMs) can be challenging to
fit. Computation and storage of its tensor product design matrix can be
impossible due to time and memory constraints, and previously considered design
matrix free algorithms do not scale well with the dimension of the parameter
vector. A new design matrix free algorithm is proposed for computing the
penalized maximum likelihood estimate for GLAMs, which, in particular, handles
nondifferentiable penalty functions. The proposed algorithm is implemented and
available via the R package \verb+glamlasso+. It combines several ideas --
previously considered separately -- to obtain sparse estimates while at the
same time efficiently exploiting the GLAM structure. In this paper the
convergence of the algorithm is treated and the performance of its
implementation is investigated and compared to that of \verb+glmnet+ on
simulated as well as real data. It is shown that the computation time fo
On the Numerical Study of the Complexity and Fractal Dimension of CMB Anisotropies
We consider the problem of numerical computation of the Kolmogorov complexity
and the fractal dimension of the anisotropy spots of Cosmic Microwave
Background (CMB) radiation. Namely, we describe an algorithm of estimation of
the complexity of spots given by certain pixel configuration on a grid and
represent the results of computations for a series of structures of different
complexity. Thus, we demonstrate the calculability of such an abstract
descriptor as the Kolmogorov complexity for CMB digitized maps. The correlation
of complexity of the anisotropy spots with their fractal dimension is revealed
as well. This technique can be especially important while analyzing the data of
the forthcoming space experiments.Comment: LATEX, 3 figure
ArtDeco: A beam deconvolution code for absolute CMB measurements
We present a method for beam deconvolution for cosmic microwave background
(CMB) anisotropy measurements. The code takes as input the time-ordered data,
along with the corresponding detector pointings and known beam shapes, and
produces as output the harmonic a_Tlm, a_Elm, and a_Blm coefficients of the
observed sky. From these one can further construct temperature and Q and U
polarisation maps. The method is applicable to absolute CMB measurements with
wide sky coverage, and is independent of the scanning strategy. We test the
code with extensive simulations, mimicking the resolution and data volume of
Planck 30GHz and 70GHz channels, but with exaggerated beam asymmetry. We apply
it to multipoles up to l=1700 and examine the results in both pixel space and
harmonic space. We also test the method also in presence of white noise.Comment: 15 page
Application of the MEGNO technique to the dynamics of Jovian irregular satellites
We apply the MEGNO (Mean Exponential Growth of Nearby Orbits) technique to
the dynamics of Jovian irregular satellites. We demonstrate the efficiency of
applying the MEGNO indicator to generate a mapping of relevant phase-space
regions occupied by observed jovian irregular satellites. The construction of
MEGNO maps of the Jovian phase-space region within its Hill-sphere is addressed
and the obtained results are compared with previous studies regarding the
dynamical stability of irregular satellites. Since this is the first time the
MEGNO technique is applied to study the dynamics of irregular satellites we
provide a review of the MEGNO theory. We consider the elliptic restricted
three-body problem in which Jupiter is orbited by a massless test satellite
subject to solar gravitational perturbations. The equations of motion of the
system are integrated numerically and the MEGNO indicator computed from the
systems variational equations. An unprecedented large set of initial conditions
are studied to generate the MEGNO maps. The chaotic nature of initial
conditions are demonstrated by studying a quasi-periodic orbit and a chaotic
orbit. As a result we establish the existence of several high-order mean-motion
resonances detected for retrograde orbits along with other interesting
dynamical features. The computed MEGNO maps allows to qualitatively
differentiate between chaotic and quasi-periodic regions of the irregular
satellite phase-space given only a relatively short integration time. By
comparing with previous published results we can establish a correlation
between chaotic regions and corresponding regions of orbital instability.Comment: 15 pages, 13 figures, 2 tables, submitted to MNRA
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