4,863 research outputs found
Basic Singular Spectrum Analysis and Forecasting with R
Singular Spectrum Analysis (SSA) as a tool for analysis and forecasting of
time series is considered. The main features of the Rssa package, which
implements the SSA algorithms and methodology in R, are described and examples
of its use are presented. Analysis, forecasting and parameter estimation are
demonstrated by means of case study with an accompanying code in R
Cyclic Interference Alignment and Cancellation in 3-User X-Networks with Minimal Backhaul
We consider the problem of Cyclic Interference Alignment (IA) on the 3-user
X-network and show that it is infeasible to exactly achieve the upper bound of
degrees of freedom for the lower bound of n=5
signalling dimensions and K=3 user-pairs. This infeasibility goes beyond the
problem of common eigenvectors in invariant subspaces within spatial IA.
In order to gain non-asymptotic feasibility with minimal intervention, we
first investigate an alignment strategy that enables IA by feedforwarding a
subset of messages with minimal rate. In a second step, we replace the proposed
feedforward strategy by an analogous Cyclic Interference Alignment and
Cancellation scheme with a backhaul network on the receiver side and also by a
dual Cyclic Interference Neutralization scheme with a backhaul network on the
transmitter side.Comment: 8 pages, short version submitted to ISIT 201
A Jeziorski-Monkhorst fully uncontracted Multi-Reference perturbative treatment I: principles, second-order versions and tests on ground state potential energy curves
The present paper introduces a new multi-reference perturbation approach
developed at second order, based on a Jeziorsky-Mokhorst expansion using
individual Slater determinants as perturbers. Thanks to this choice of
perturbers, an effective Hamiltonian may be built, allowing for the dressing of
the Hamiltonian matrix within the reference space, assumed here to be a CAS-CI.
Such a formulation accounts then for the coupling between the static and
dynamic correlation effects. With our new definition of zeroth-order energies,
these two approaches are strictly size-extensive provided that local orbitals
are used, as numerically illustrated here and formally demonstrated in the
appendix. Also, the present formalism allows for the factorization of all
double excitation operators, just as in internally contracted approaches,
strongly reducing the computational cost of these two approaches with respect
to other determinant-based perturbation theories. The accuracy of these methods
has been investigated on ground-state potential curves up to full dissociation
limits for a set of six molecules involving single, double and triple bond
breaking. The spectroscopic constants obtained with the present methods are
found to be in very good agreement with the full configuration interaction
(FCI) results. As the present formalism does not use any parameter or
numerically unstable operation, the curves obtained with the two methods are
smooth all along the dissociation path.Comment: 4 figures, 18 page
Beyond the traditional Line-of-Sight approach of cosmological angular statistics
We present a new efficient method to compute the angular power spectra of
large-scale structure observables that circumvents the numerical integration
over Bessel functions, expanding on a recently proposed algorithm based on
FFTlog. This new approach has better convergence properties. The method is
explicitly implemented in the CLASS code for the case of number count
's (including redshift-space distortions, weak lensing, and all other
relativistic corrections) and cosmic shear 's. In both cases our
approach speeds up the calculation of the exact 's (without the Limber
approximation) by a factor of order 400 at a fixed precision target of 0.1%.Comment: 40 pages, 6 figures; v2: one reference adde
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