27 research outputs found
Curing basis-set convergence of wave-function theory using density-functional theory: a systematically improvable approach
The present work proposes to use density-functional theory (DFT) to correct
for the basis-set error of wave-function theory (WFT). One of the key ideas
developed here is to define a range-separation parameter which automatically
adapts to a given basis set. The derivation of the exact equations are based on
the Levy-Lieb formulation of DFT, which helps us to define a complementary
functional which corrects uniquely for the basis-set error of WFT. The coupling
of DFT and WFT is done through the definition of a real-space representation of
the electron-electron Coulomb operator projected in a one-particle basis set.
Such an effective interaction has the particularity to coincide with the exact
electron-electron interaction in the limit of a complete basis set, and to be
finite at the electron-electron coalescence point when the basis set is
incomplete. The non-diverging character of the effective interaction allows one
to define a mapping with the long-range interaction used in the context of
range-separated DFT and to design practical approximations for the unknown
complementary functional. Here, a local-density approximation is proposed for
both full-configuration-interaction (FCI) and selected
configuration-interaction approaches. Our theory is numerically tested to
compute total energies and ionization potentials for a series of atomic
systems. The results clearly show that the DFT correction drastically improves
the basis-set convergence of both the total energies and the energy
differences. For instance, a sub kcal/mol accuracy is obtained from the
aug-cc-pVTZ basis set with the method proposed here when an aug-cc-pV5Z basis
set barely reaches such a level of accuracy at the near FCI level
On the number of simple arrangements of five double pseudolines
We describe an incremental algorithm to enumerate the isomorphism classes of
double pseudoline arrangements. The correction of our algorithm is based on the
connectedness under mutations of the spaces of one-extensions of double
pseudoline arrangements, proved in this paper. Counting results derived from an
implementation of our algorithm are also reported.Comment: 24 pages, 16 figures, 6 table
Making maps of cosmic microwave background polarization for B-mode studies: The POLARBEAR example
Analysis of cosmic microwave background (CMB) datasets typically requires some filtering of the raw time-ordered data. For instance, in the context of ground-based observations, filtering is frequently used to minimize the impact of low frequency noise, atmospheric contributions and/or scan synchronous signals on the resulting maps. In this work we have explicitly constructed a general filtering operator, which can unambiguously remove any set of unwanted modes in the data, and then amend the map-making procedure in order to incorporate and correct for it. We show that such an approach is mathematically equivalent to the solution of a problem in which the sky signal and unwanted modes are estimated simultaneously and the latter are marginalized over. We investigated the conditions under which this amended map-making procedure can render an unbiased estimate of the sky signal in realistic circumstances. We then discuss the potential implications of these observations on the choice of map-making and power spectrum estimation approaches in the context of B-mode polarization studies. Specifically, we have studied the effects of time-domain filtering on the noise correlation structure in the map domain, as well as impact it may haveon the performance of the popular pseudo-spectrum estimators. We conclude that although maps produced by the proposed estimators arguably provide the most faithful representation of the sky possible given the data, they may not straightforwardly lead to the best constraints on the power spectra of the underlying sky signal and special care may need to be taken to ensure this is the case. By contrast, simplified map-makers which do not explicitly correct for time-domain filtering, but leave it to subsequent steps in the data analysis, may perform equally well and be easier and faster to implement. We focused on polarization-sensitive measurements targeting the B-mode component of the CMB signal and apply the proposed methods to realistic simulations based on characteristics of an actual CMB polarization experiment, POLARBEAR. Our analysis and conclusions are however more generally applicable. \ua9 ESO, 2017
Word-mappings of level 2
International audienceA sequence of natural numbers is said to have {\em level k}, for some natural integer , if it can be computed by a deterministic pushdown automaton of level ([Fratani-Sénizergues, APAL, 2006]). We show here that the sequences of level 2 are exactly the rational formal power series over one undeterminate. More generally, we study mappings {\em from words to words} and show that the following classes coincide:\\ - the mappings which are computable by deterministic pushdown automata of level \\ - the mappings which are solution of a system of catenative recurrence equations\\ - the mappings which are definable as a Lindenmayer system of type HDT0L.\\ We illustrate the usefulness of this characterization by proving three statements about formal power series, rational sets of homomorphisms and equations in words