arXiv subjects
Publications and source records attributed to Pierre Laurent.
A single parameter cubic composite test for odd positive integers is given which relies on the discriminant always being a square integer. This test has no known counterexample despite extensive verifications. As well as a comparison with the Baillie-PSW tests, a related quadratic composite test is briefly examined which also has no known counterexample.
Monitoring the activity of the heart is important for diagnosing and preventing cardiovascular diseases. The electrocardiogram (ECG) is the gold standard for diagnosing such diseases. It monitors the heart's electrical activity, and while this is highly correlated with the cardiac mechanical activity, it does not provide all the information. Other sensors such as the echocardiograph are able to monitor the heart's movements, but such tools are expensive and hard to operate. Therefore, contactless monitoring of the heart using RF sensing has gained interest in recent years. In this paper, we describe a process to extract the movements of the heart from millimeter wave radar with high accuracy, and thus we provide a noninvasive and affordable way to monitor cardiac movements. We then demonstrate the correlation between the observed movements and the ECG. Furthermore, we propose an algorithm to synchronize the ECG signal and the processed signal from the radar sensor. The results we obtained provide insights on the mechanical activity of the heart, which could assist cardiologists in their diagnoses.
We present the clustering measurements of quasars in configuration space based on the Data Release 14 (DR14) of the Sloan Digital Sky Survey IV extended Baryon Oscillation Spectroscopic Survey. This dataset includes 148,659 quasars spread over the redshift range $0.8\leq z \leq 2.2$ and spanning 2112.9 square degrees. We use the Convolution Lagrangian Perturbation Theory (CLPT) approach with a Gaussian Streaming (GS) model for the redshift space distortions of the correlation function and demonstrate its applicability for dark matter halos hosting eBOSS quasar tracers. At the effective redshift $z_{\rm eff} = 1.52$, we measure the linear growth rate of structure $fσ_{8}(z_{\rm eff})= 0.426 \pm 0.077$, the expansion rate $H(z_{\rm eff})= 159^{+12}_{-13}(r_{s}^{\rm fid}/r_s){\rm km.s}^{-1}.{\rm Mpc}^{-1}$, and the angular diameter distance $D_{A}(z_{\rm eff})=1850^{+90}_{-115}\,(r_s/r_{s}^{\rm fid}){\rm Mpc}$, where $r_{s}$ is the sound horizon at the end of the baryon drag epoch and $r_{s}^{\rm fid}$ is its value in the fiducial cosmology. The quoted errors include both systematic and statistical contributions. The results on the evolution of distances are consistent with the predictions of flat $Λ$-Cold Dark Matter ($Λ$-CDM) cosmology with Planck parameters, and the measurement of $fσ_{8}$ extends the validity of General Relativity (GR) to higher redshifts($z>1$) This paper is released with companion papers using the same sample. The results on the cosmological parameters of the studies are found to be in very good agreement, providing clear evidence of the complementarity and of the robustness of the first full-shape clustering measurements with the eBOSS DR14 quasar sample.
We present measurements of the Baryon Acoustic Oscillation (BAO) scale in redshift-space using the clustering of quasars. We consider a sample of 147,000 quasars from the extended Baryon Oscillation Spectroscopic Survey (eBOSS) distributed over 2044 square degrees with redshifts $0.8 < z < 2.2$ and measure their spherically-averaged clustering in both configuration and Fourier space. Our observational dataset and the 1400 simulated realizations of the dataset allow us to detect a preference for BAO that is greater than 2.8$σ$. We determine the spherically averaged BAO distance to $z = 1.52$ to 3.8 per cent precision: $D_V(z=1.52)=3843\pm147 \left(r_{\rm d}/r_{\rm d, fid}\right)\ $Mpc. This is the first time the location of the BAO feature has been measured between redshifts 1 and 2. Our result is fully consistent with the prediction obtained by extrapolating the Planck flat $Λ$CDM best-fit cosmology. All of our results are consistent with basic large-scale structure (LSS) theory, confirming quasars to be a reliable tracer of LSS, and provide a starting point for numerous cosmological tests to be performed with eBOSS quasar samples. We combine our result with previous, independent, BAO distance measurements to construct an updated BAO distance-ladder. Using these BAO data alone and marginalizing over the length of the standard ruler, we find $Ω_Λ > 0$ at 6.6$σ$ significance when testing a $Λ$CDM model with free curvature.
In this study, we probe the transition to cosmic homogeneity in the Large Scale Structure (LSS) of the Universe using the CMASS galaxy sample of BOSS spectroscopic survey which covers the largest effective volume to date, $3\ h^{-3}\ \mathrm{Gpc}^3$ at $0.43 \leq z \leq 0.7$. We study the scaled counts-in-spheres, $\mathcal{N}( 2.97$ for $r>\mathcal{R}_H$, we find $\mathcal{R}_H = (63.3\pm0.7) \ h^{-1}\ \mathrm{Mpc}$, in agreement at the percentage level with the predictions of the $Λ$CDM model $\mathcal{R}_H=62.0\ h^{-1}\ \mathrm{Mpc}$. Thanks to the large cosmic depth of the survey, we investigate the redshift evolution of the transition to homogeneity scale and find agreement with the $Λ$CDM prediction. Finally, we find that $\mathcal{D}_2$ is compatible with $3$ at scales larger than $300\ h^{-1}\ $Mpc in all redshift bins. These results consolidate the Cosmological Principle and represent a precise consistency test of the $ΛCDM$ model.
We study the first year of the eBOSS quasar sample in the redshift range $0.9<z<2.2$ which includes 68,772 homogeneously selected quasars. We show that the main source of systematics in the evaluation of the correlation function arises from inhomogeneities in the quasar target selection, particularly related to the extinction and depth of the imaging data used for targeting. We propose a weighting scheme that mitigates these systematics. We measure the quasar correlation function and provide the most accurate measurement to date of the quasar bias in this redshift range, $b_Q = 2.45 \pm 0.05$ at $\bar z=1.55$, together with its evolution with redshift. We use this information to determine the minimum mass of the halo hosting the quasars and the characteristic halo mass, which we find to be both independent of redshift within statistical error. Using a recently-measured quasar-luminosity-function we also determine the quasar duty cycle. The size of this first year sample is insufficient to detect any luminosity dependence to quasar clustering and this issue should be further studied with the final $\sim$500,000 eBOSS quasar sample.
In current and future surveys, quasars play a key role. The new data will extend our knowledge of the Universe as it will be used to better constrain the cosmological model at redshift $z>1$ via baryon acoustic oscillation and redshift space distortion measurements. Here, we present the first clustering study of quasars observed by the extended Baryon Oscillation Spectroscopic Survey. We measure the clustering of $\sim 70,000$ quasars located in the redshift range $0.9<z<2.2$ that cover 1,168 deg$^2$. We model the clustering and produce high-fidelity quasar mock catalogues based on the BigMultiDark Planck simulation. Thus, we use a modified (Sub)Halo Abundance Matching model to account for the specificities of the halo population hosting quasars. We find that quasars are hosted by halos with masses $\sim10^{12.7}M_\odot$ and their bias evolves from 1.54 ($z=1.06$) to 3.15 ($z=1.98$). Using the current eBOSS data, we cannot distinguish between models with different fractions of satellites. The high-fidelity mock light-cones, including properties of halos hosting quasars, are made publicly available.
The BOSS quasar sample is used to study cosmic homogeneity with a 3D survey in the redshift range $2.2<z<2.8$. We measure the count-in-sphere, $N(<\! r)$, i.e. the average number of objects around a given object, and its logarithmic derivative, the fractal correlation dimension, $D_2(r)$. For a homogeneous distribution $N(<\! r) \propto r^3$ and $D_2(r)=3$. Due to the uncertainty on tracer density evolution, 3D surveys can only probe homogeneity up to a redshift dependence, i.e. they probe so-called "spatial isotropy". Our data demonstrate spatial isotropy of the quasar distribution in the redshift range $2.2<z<2.8$ in a model-independent way, independent of any FLRW fiducial cosmology, resulting in $3-\langle D_2 \rangle < 1.7 \times 10^{-3}$ (2 $σ$) over the range $250<r<1200 \, h^{-1}$Mpc for the quasar distribution. If we assume that quasars do not have a bias much less than unity, this implies spatial isotropy of the matter distribution on large scales. Then, combining with the Copernican principle, we finally get homogeneity of the matter distribution on large scales. Alternatively, using a flat $Λ$CDM fiducial cosmology with CMB-derived parameters, and measuring the quasar bias relative to this $Λ$CDM model, our data provide a consistency check of the model, in terms of how homogeneous the Universe is on different scales. $D_2(r)$ is found to be compatible with our $Λ$CDM model on the whole $10<r<1200 \, h^{-1}$Mpc range. For the matter distribution we obtain $3-\langle D_2 \rangle < 5 \times 10^{-5}$ (2 $σ$) over the range $250<r<1200 \, h^{-1}$Mpc, consistent with homogeneity on large scales.
The Extended Baryon Oscillation Spectroscopic Survey (eBOSS) will conduct novel cosmological observations using the BOSS spectrograph at Apache Point Observatory. Observations will be simultaneous with the Time Domain Spectroscopic Survey (TDSS) designed for variability studies and the Spectroscopic Identification of eROSITA Sources (SPIDERS) program designed for studies of X-ray sources. eBOSS will use four different tracers to measure the distance-redshift relation with baryon acoustic oscillations (BAO). Using more than 250,000 new, spectroscopically confirmed luminous red galaxies at a median redshift z=0.72, we project that eBOSS will yield measurements of $d_A(z)$ to an accuracy of 1.2% and measurements of H(z) to 2.1% when combined with the z>0.6 sample of BOSS galaxies. With ~195,000 new emission line galaxy redshifts, we expect BAO measurements of $d_A(z)$ to an accuracy of 3.1% and H(z) to 4.7% at an effective redshift of z= 0.87. A sample of more than 500,000 spectroscopically-confirmed quasars will provide the first BAO distance measurements over the redshift range 0.9 2.1; these new data will enhance the precision of $d_A(z)$ and H(z) by a factor of 1.44 relative to BOSS. Furthermore, eBOSS will provide improved tests of General Relativity on cosmological scales through redshift-space distortion measurements, improved tests for non-Gaussianity in the primordial density field, and new constraints on the summed mass of all neutrino species. Here, we provide an overview of the cosmological goals, spectroscopic target sample, demonstration of spectral quality from early data, and projected cosmological constraints from eBOSS.
As part of the Sloan Digital Sky Survey IV the extended Baryon Oscillation Spectroscopic Survey (eBOSS) will improve measurements of the cosmological distance scale by applying the Baryon Acoustic Oscillation (BAO) method to quasar samples. eBOSS will adopt two approaches to target quasars over 7500 sq. deg. First, a "CORE" quasar sample will combine optical selection in ugriz using a likelihood-based routine called XDQSOz, with a mid-IR-optical color-cut. eBOSS CORE selection (to g < 22 OR r < 22) should return ~ 70 quasars per sq. deg. at redshifts 0.9 < z < 2.2 and ~7 z > 2.1 quasars per sq. deg. Second, a selection based on variability in multi-epoch imaging from the Palomar Transient Factory should recover an additional ~3-4 z > 2.1 quasars per sq. deg. to g < 22.5. A linear model of how imaging systematics affect target density recovers the angular distribution of eBOSS CORE quasars over 96.7% (76.7%) of the SDSS North (South) Galactic Cap area. The eBOSS CORE quasar sample should thus be sufficiently dense and homogeneous over 0.9 < z < 2.2 to yield the first few-percent-level BAO constraint near z~1.5. eBOSS quasars at z > 2.1 will be used to improve BAO measurements in the Lyman-alpha Forest. Beyond its key cosmological goals, eBOSS should be the next-generation quasar survey, comprising > 500,000 new quasars and > 500,000 uniformly selected spectroscopically confirmed 0.9 < z < 2.2 quasars. At the conclusion of eBOSS, the SDSS will have provided unique spectra of over 800,000 quasars.