36 research outputs found
Sur les facteurs des suites de sturm
RĂ©sumĂ©Cet article a pour objet l'Ă©tude d'une construction associant Ă toute droite de pente p/q (p et q premiers entre eux et qâ©œn) un mot de longueur n sur l'alphabet {0,1}. Nous montrons que nous obtenons par cette construction le langage constituĂ© de tous les facteurs des suites de Sturm. Nous formulons, aprĂ©s avoir obtenu une Ăšquation fonctionelle dont la solution est la sĂ©rie gĂ©nĂ©ratrice de ce langage, une conjecture reliant cette sĂ©rie gĂ©nĂ©ratrice Ă la fonction d'Euler.AbstractIn this paper, we study a construction which connects to each line with slope p/q (such that gcd(p, q) = 1 and qâ©œn) a word of length n over the alphabet {0, 1}. We show that this construction yields the language of all the factors of the sturmian sequences. We first obtain a functional equation whose solution is the generating function of this language, and then we give a conjecture relating this generating function to the Euler function
Cosmological inference including massive neutrinos from the matter power spectrum: biases induced by uncertainties in the covariance matrix
Data analysis from upcoming large galaxy redshift surveys, such as Euclid and
DESI will significantly improve constraints on cosmological parameters. To
optimally extract the information from these galaxy surveys, it is important to
control with a high level of confidence the uncertainty and bias arising from
the estimation of the covariance that affects the inference of cosmological
parameters. In this work, we are addressing two different but closely related
issues: (i) the sampling noise present in a covariance matrix estimated from a
finite set of simulations and (ii) the impact on cosmological constraints of
the non-Gaussian contribution to the covariance matrix of the power spectrum.
We focus on the parameter estimation obtained from fitting the matter power
spectrum in real space, using the DEMNUni N-body simulations. Regarding the
first issue, we adopt two different approaches to reduce the sampling noise in
the precision matrix that propagates in the parameter space: on the one hand
using an alternative estimator of the covariance matrix based on a non-linear
shrinkage, NERCOME; and on the other hand employing a method of fast generation
of approximate mock catalogs, COVMOS. We find that NERCOME can significantly
reduce the noise induced on the posterior distribution of parameters, but at
the cost of a systematic overestimation of the error bars on the cosmological
parameters. We show that using a COVMOS covariance matrix estimated from a
large number of realisations (10~000) results in unbiased cosmological
constraints. Regarding the second issue, we quantify the impact on cosmological
constraints of the non-Gaussian part of the power spectrum covariance purely
coming from non-linear clustering. We find that when this term is neglected,
both the errors and central values of the estimated parameters are affected for
a scale cut \kmax > 0.2\ \invMpc.Comment: 21 pages, 2 appendices, 20 figures. Submitted to A&
Impact of survey geometry and super-sample covariance on future photometric galaxy surveys
Photometric galaxy surveys probe the late-time Universe where the density field is highly non-Gaussian. A consequence is the emergence of the super-sample covariance (SSC), a non-Gaussian covariance term that is sensitive to fluctuations on scales larger than the survey window. In this work, we study the impact of the survey geometry on the SSC and, subsequently, on cosmological parameter inference. We devise a fast SSC approximation that accounts for the survey geometry and compare its performance to the common approximation of rescaling the results by the fraction of the sky covered by the survey, fSKY, dubbed âfull-sky approximationâ. To gauge the impact of our new SSC recipe, that we call âpartial-skyâ, we perform Fisher forecasts on the parameters of the (w0,âwa)-CDM model in a 3â
Ăâ
2 point analysis, varying the survey area, the geometry of the mask, and the galaxy distribution inside our redshift bins. The differences in the marginalised forecast errors âwith the full-sky approximation performing poorly for small survey areas but excellently for stage-IV-like areasâ are found to be absorbed by the marginalisation on galaxy bias nuisance parameters. For large survey areas, the unmarginalised errors are underestimated by about 10% for all probes considered. This is a hint that, even for stage-IV-like surveys, the partial-sky method introduced in this work will be necessary if tight priors are applied on these nuisance parameters. We make the partial-sky method public with a new release of the public code PySSC
Transfer Matrices and Partition-Function Zeros for Antiferromagnetic Potts Models. V. Further Results for the Square-Lattice Chromatic Polynomial
We derive some new structural results for the transfer matrix of
square-lattice Potts models with free and cylindrical boundary conditions. In
particular, we obtain explicit closed-form expressions for the dominant (at
large |q|) diagonal entry in the transfer matrix, for arbitrary widths m, as
the solution of a special one-dimensional polymer model. We also obtain the
large-q expansion of the bulk and surface (resp. corner) free energies for the
zero-temperature antiferromagnet (= chromatic polynomial) through order q^{-47}
(resp. q^{-46}). Finally, we compute chromatic roots for strips of widths 9 <=
m <= 12 with free boundary conditions and locate roughly the limiting curves.Comment: 111 pages (LaTeX2e). Includes tex file, three sty files, and 19
Postscript figures. Also included are Mathematica files data_CYL.m and
data_FREE.m. Many changes from version 1: new material on series expansions
and their analysis, and several proofs of previously conjectured results.
Final version to be published in J. Stat. Phy
Transfer matrices and partition-function zeros for antiferromagnetic Potts models. VI. Square lattice with special boundary conditions
We study, using transfer-matrix methods, the partition-function zeros of the
square-lattice q-state Potts antiferromagnet at zero temperature (=
square-lattice chromatic polynomial) for the special boundary conditions that
are obtained from an m x n grid with free boundary conditions by adjoining one
new vertex adjacent to all the sites in the leftmost column and a second new
vertex adjacent to all the sites in the rightmost column. We provide numerical
evidence that the partition-function zeros are becoming dense everywhere in the
complex q-plane outside the limiting curve B_\infty(sq) for this model with
ordinary (e.g. free or cylindrical) boundary conditions. Despite this, the
infinite-volume free energy is perfectly analytic in this region.Comment: 114 pages (LaTeX2e). Includes tex file, three sty files, and 23
Postscript figures. Also included are Mathematica files data_Eq.m,
data_Neq.m,and data_Diff.m. Many changes from version 1, including several
proofs of previously conjectured results. Final version to be published in J.
Stat. Phy
Euclid preparation. TBD. Forecast impact of super-sample covariance on 3x2pt analysis with Euclid
Deviations from Gaussianity in the distribution of the fields probed by
large-scale structure surveys generate additional terms in the data covariance
matrix, increasing the uncertainties in the measurement of the cosmological
parameters. Super-sample covariance (SSC) is among the largest of these
non-Gaussian contributions, with the potential to significantly degrade
constraints on some of the parameters of the cosmological model under study --
especially for weak lensing cosmic shear. We compute and validate the impact of
SSC on the forecast uncertainties on the cosmological parameters for the Euclid
photometric survey, obtained with a Fisher matrix analysis, both considering
the Gaussian covariance alone and adding the SSC term -- computed through the
public code PySSC. The photometric probes are considered in isolation and
combined in the `32pt' analysis. We find the SSC impact to be
non-negligible -- halving the Figure of Merit of the dark energy parameters
(, ) in the 32pt case and substantially increasing the
uncertainties on , and for cosmic shear;
photometric galaxy clustering, on the other hand, is less affected due to the
lower probe response. The relative impact of SSC does not show significant
changes under variations of the redshift binning scheme, while it is smaller
for weak lensing when marginalising over the multiplicative shear bias nuisance
parameters, which also leads to poorer constraints on the cosmological
parameters. Finally, we explore how the use of prior information on the shear
and galaxy bias changes the SSC impact. Improving shear bias priors does not
have a significant impact, while galaxy bias must be calibrated to sub-percent
level to increase the Figure of Merit by the large amount needed to achieve the
value when SSC is not included.Comment: 22 pages, 13 figure
The Bousquet-Conway directed animals
Bousquet-M'elou and Conway in [3] found algebraic equations for the area generating function of directed animals on an infinite family of regular, non planar, two-dimensional lattices by using equivalences with hard particle models. We give in this paper a bijective proof of their results which is a generalization of Viennot's heaps of pieces [6, 8]. Thanks to this proof we get exact enumeration formulas for the number of configurations with area n which could not be deduced directly from the algebraic equation and were not in [3]. Moreover, we give an extension of these results to another infinite family. 1 Introduction Directed animals were introduced by physicists to study directed site percolation models. A directed animal A is a finite set of vertices on an acyclic infinite periodic lattice L such that any vertex of A can be reached from a distinguished vertex, called the source, through an oriented path of L having all its vertices in A. Animals are defined up to a translation o..
Cosmological inference including massive neutrinos from the matter power spectrum: biases induced by uncertainties in the covariance matrix
International audienceData analysis from upcoming large galaxy redshift surveys, such as Euclid and DESI will significantly improve constraints on cosmological parameters. To optimally extract the information from these galaxy surveys, it is important to control with a high level of confidence the uncertainty and bias arising from the estimation of the covariance that affects the inference of cosmological parameters. In this work, we are addressing two different but closely related issues: (i) the sampling noise present in a covariance matrix estimated from a finite set of simulations and (ii) the impact on cosmological constraints of the non-Gaussian contribution to the covariance matrix of the power spectrum. We focus on the parameter estimation obtained from fitting the matter power spectrum in real space, using the DEMNUni N-body simulations. Regarding the first issue, we adopt two different approaches to reduce the sampling noise in the precision matrix that propagates in the parameter space: on the one hand using an alternative estimator of the covariance matrix based on a non-linear shrinkage, NERCOME; and on the other hand employing a method of fast generation of approximate mock catalogs, COVMOS. We find that NERCOME can significantly reduce the noise induced on the posterior distribution of parameters, but at the cost of a systematic overestimation of the error bars on the cosmological parameters. We show that using a COVMOS covariance matrix estimated from a large number of realisations (10~000) results in unbiased cosmological constraints. Regarding the second issue, we quantify the impact on cosmological constraints of the non-Gaussian part of the power spectrum covariance purely coming from non-linear clustering. We find that when this term is neglected, both the errors and central values of the estimated parameters are affected for a scale cut \kmax > 0.2\ \invMpc
Cosmological inference including massive neutrinos from the matter power spectrum: biases induced by uncertainties in the covariance matrix
International audienceData analysis from upcoming large galaxy redshift surveys, such as Euclid and DESI will significantly improve constraints on cosmological parameters. To optimally extract the information from these galaxy surveys, it is important to control with a high level of confidence the uncertainty and bias arising from the estimation of the covariance that affects the inference of cosmological parameters. In this work, we are addressing two different but closely related issues: (i) the sampling noise present in a covariance matrix estimated from a finite set of simulations and (ii) the impact on cosmological constraints of the non-Gaussian contribution to the covariance matrix of the power spectrum. We focus on the parameter estimation obtained from fitting the matter power spectrum in real space, using the DEMNUni N-body simulations. Regarding the first issue, we adopt two different approaches to reduce the sampling noise in the precision matrix that propagates in the parameter space: on the one hand using an alternative estimator of the covariance matrix based on a non-linear shrinkage, NERCOME; and on the other hand employing a method of fast generation of approximate mock catalogs, COVMOS. We find that NERCOME can significantly reduce the noise induced on the posterior distribution of parameters, but at the cost of a systematic overestimation of the error bars on the cosmological parameters. We show that using a COVMOS covariance matrix estimated from a large number of realisations (10~000) results in unbiased cosmological constraints. Regarding the second issue, we quantify the impact on cosmological constraints of the non-Gaussian part of the power spectrum covariance purely coming from non-linear clustering. We find that when this term is neglected, both the errors and central values of the estimated parameters are affected for a scale cut \kmax > 0.2\ \invMpc