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M. Levi

Publications and source records attributed to M. Levi.

13 recordsLinked to original sources
arXiv2026

Functions of Bounded Variation and Point Processes

We investigate the relationship between the analytical properties of functions of bounded variation and the statistical behavior of hyperuniform point processes. We establish several characterization formulas for the jump part of the gradient of a bounded variation function, extending and unifying previous results by Beretti--Gennaioli and D\'avila. In particular, we provide new expressions for the $L^2$-jump of the gradient using both difference quotients and Fourier transform methods. Furthermore, we connect these analytic structures to the theory of hyperuniform point processes. By analyzing the variance of linear statistics associated with bounded variation functions, we provide asymptotic estimates that depend on the specific classification of the hyperuniformity of the point process. The results show how the regularity and jump discontinuities of a function dictate the growth rate of fluctuations in point processes. Finally, we introduce an averaged quadratic BMO-type oscillation functional over translated and rotated cube partitions, similar to the one recently studied by Ambrosio et al., and prove, using results from point process, that it converges to an explicit dimensional constant times the $L^2-$jump, giving in particular a further new characterization of the perimeter of a set.

math.CA↗
arXiv2025

A measurement of $H_0$ from DESI DR1 using energy densities

We present a new measurement of the Hubble constant, independent of standard rulers and robust to pre-recombination modifications such as Early Dark Energy (EDE), obtained by calibrating the total energy density of the Universe. We start using the present-day photon density as an anchor, and use the baryon-to-photon ratio from Big Bang Nucleosynthesis based measurements and the baryon-to-matter ratio from the baryons' imprint on galaxy clustering to translate to a physical matter density at present day. We then compare this to measurements of the ratio of the matter density to the critical density ($\Omega_{\mathrm{m}}$), calculated using the relative positions of the baryon acoustic oscillations, to measure the critical density of the universe and hence $H_0$. The important measurements of the evolution of the energy density all happen at low redshift, so we consider this a low-redshift measurement. We validate our method both on a suite of $N$-body mocks and on noiseless theory vectors generated across a wide range of Hubble parameters in both $\Lambda$CDM and EDE cosmologies. Using DESI DR1 data combined with the angular CMB acoustic scale and the latest BBN constraints, we find $H_0 = 69.0 \pm 2.5$ km s$^{-1}$ Mpc$^{-1}$, consistent with existing early and late-time determinations of the Hubble constant. We consider the impact of non-standard dark energy evolution on our measurement. Future data, including that from further iterations of DESI and from Euclid, will add to these results providing a powerful test of the Hubble tension.

astro-ph.CO↗
arXiv2023

DESI Complete Calibration of the Color-Redshift Relation (DC3R2): Results from early DESI data

We present initial results from the Dark Energy Spectroscopic Instrument (DESI) Complete Calibration of the Color-Redshift Relation (DC3R2) secondary target survey. Our analysis uses 230k galaxies that overlap with KiDS-VIKING $ugriZYJHK_s$ photometry to calibrate the color-redshift relation and to inform photometric redshift (photo-z) inference methods of future weak lensing surveys. Together with Emission Line Galaxies (ELGs), Luminous Red Galaxies (LRGs), and the Bright Galaxy Survey (BGS) that provide samples of complementary color, the DC3R2 targets help DESI to span 56% of the color space visible to Euclid and LSST with high confidence spectroscopic redshifts. The effects of spectroscopic completeness and quality are explored, as well as systematic uncertainties introduced with the use of common Self Organizing Maps trained on different photometry than the analysis sample. We further examine the dependence of redshift on magnitude at fixed color, important for the use of bright galaxy spectra to calibrate redshifts in a fainter photometric galaxy sample. We find that noise in the KiDS-VIKING photometry introduces a dominant, apparent magnitude dependence of redshift at fixed color, which indicates a need for carefully chosen deep drilling fields, and survey simulation to model this effect for future weak lensing surveys.

astro-ph.CO↗
arXiv2021

Testing the 10 spectrograph units for DESI: approach and results

The recently commissioned Dark Energy Spectroscopic Instrument (DESI) will measure the expansion history of the Universe using the Baryon Acoustic Oscillation technique. The spectra of 35 million galaxies and quasars over 14000 sqdeg will be measured during the life of the experiment. A new prime focus corrector for the KPNO Mayall telescope delivers light to 5000 fiber optic positioners. The fibers in turn feed ten broad-band spectrographs. A consortium of Aix-Marseille University (AMU) and CNRS laboratories (LAM, OHP and CPPM) together with LPNHE (CNRS, IN2P3, Sorbonne Universit\'e and Universit\'e de Paris) and the WINLIGHT Systems company based in Pertuis (France), were in charge of integrating and validating the performance requirements of the ten full spectrographs, equipped with their cryostats, shutters and other mechanisms. We present a summary of our activity which allowed an efficient validation of the systems in a short-time schedule. We detail the main results. We emphasize the benefits of our approach and also its limitations.

astro-ph.IM↗
arXiv2016

Single-photon emitters based on NIR colour centres in diamond coupled with solid immersion lenses

Single-photon sources represent a key enabling technology in quantum optics, and single colour centres in diamond are a promising platform to serve this purpose, due to their high quantum efficiency and photostability at room temperature. The widely studied nitrogen vacancy centres are characterized by several limitations, thus other defects have recently been considered, with a specific focus of centres emitting in the Near Infra-Red. In the present work, we report on the coupling of native near-infrared-emitting centres in high-quality single crystal diamond with Solid Immersion Lens structures fabricated by Focused Ion Beam lithography. The reported improvements in terms of light collection efficiency make the proposed system an ideal platform for the development of single-photon emitters with appealing photophysical and spectral properties.

cond-mat.mtrl-sci↗
arXiv2014

Attractive forces in microporous carbon electrodes for capacitive deionization

The recently developed modified Donnan (mD) model provides a simple and useful description of the electrical double layer in microporous carbon electrodes, suitable for incorporation in porous electrode theory. By postulating an attractive excess chemical potential for each ion in the micropores that is inversely proportional to the total ion concentration, we show that experimental data for capacitive deionization (CDI) can be accurately predicted over a wide range of applied voltages and salt concentrations. Since the ion spacing and Bjerrum length are each comparable to the micropore size (few nm), we postulate that the attraction results from fluctuating bare Coulomb interactions between individual ions and the metallic pore surfaces (image forces) that are not captured by meanfield theories, such as the Poisson-Boltzmann-Stern model or its mathematical limit for overlapping double layers, the Donnan model. Using reasonable estimates of the micropore permittivity and mean size (and no other fitting parameters), we propose a simple theory that predicts the attractive chemical potential inferred from experiments. As additional evidence for attractive forces, we present data for salt adsorption in uncharged microporous carbons, also predicted by the theory.

physics.chem-ph↗
arXiv2011

Euclid Definition Study Report

Euclid is a space-based survey mission from the European Space Agency designed to understand the origin of the Universe's accelerating expansion. It will use cosmological probes to investigate the nature of dark energy, dark matter and gravity by tracking their observational signatures on the geometry of the universe and on the cosmic history of structure formation. The mission is optimised for two independent primary cosmological probes: Weak gravitational Lensing (WL) and Baryonic Acoustic Oscillations (BAO). The Euclid payload consists of a 1.2 m Korsch telescope designed to provide a large field of view. It carries two instruments with a common field-of-view of ~0.54 deg2: the visual imager (VIS) and the near infrared instrument (NISP) which contains a slitless spectrometer and a three bands photometer. The Euclid wide survey will cover 15,000 deg2 of the extragalactic sky and is complemented by two 20 deg2 deep fields. For WL, Euclid measures the shapes of 30-40 resolved galaxies per arcmin2 in one broad visible R+I+Z band (550-920 nm). The photometric redshifts for these galaxies reach a precision of dz/(1+z) < 0.05. They are derived from three additional Euclid NIR bands (Y, J, H in the range 0.92-2.0 micron), complemented by ground based photometry in visible bands derived from public data or through engaged collaborations. The BAO are determined from a spectroscopic survey with a redshift accuracy dz/(1+z) =0.001. The slitless spectrometer, with spectral resolution ~250, predominantly detects Ha emission line galaxies. Euclid is a Medium Class mission of the ESA Cosmic Vision 2015-2025 programme, with a foreseen launch date in 2019. This report (also known as the Euclid Red Book) describes the outcome of the Phase A study.

astro-ph.CO↗
arXiv2011

The BigBOSS Experiment

BigBOSS is a Stage IV ground-based dark energy experiment to study baryon acoustic oscillations (BAO) and the growth of structure with a wide-area galaxy and quasar redshift survey over 14,000 square degrees. It has been conditionally accepted by NOAO in response to a call for major new instrumentation and a high-impact science program for the 4-m Mayall telescope at Kitt Peak. The BigBOSS instrument is a robotically-actuated, fiber-fed spectrograph capable of taking 5000 simultaneous spectra over a wavelength range from 340 nm to 1060 nm, with a resolution R = 3000-4800. Using data from imaging surveys that are already underway, spectroscopic targets are selected that trace the underlying dark matter distribution. In particular, targets include luminous red galaxies (LRGs) up to z = 1.0, extending the BOSS LRG survey in both redshift and survey area. To probe the universe out to even higher redshift, BigBOSS will target bright [OII] emission line galaxies (ELGs) up to z = 1.7. In total, 20 million galaxy redshifts are obtained to measure the BAO feature, trace the matter power spectrum at smaller scales, and detect redshift space distortions. BigBOSS will provide additional constraints on early dark energy and on the curvature of the universe by measuring the Ly-alpha forest in the spectra of over 600,000 2.2 < z < 3.5 quasars. BigBOSS galaxy BAO measurements combined with an analysis of the broadband power, including the Ly-alpha forest in BigBOSS quasar spectra, achieves a FOM of 395 with Planck plus Stage III priors. This FOM is based on conservative assumptions for the analysis of broad band power (kmax = 0.15), and could grow to over 600 if current work allows us to push the analysis to higher wave numbers (kmax = 0.3). BigBOSS will also place constraints on theories of modified gravity and inflation, and will measure the sum of neutrino masses to 0.024 eV accuracy.

astro-ph.IM↗
arXiv2008

On bicycle tire tracks geometry, hatchet planimeter, Menzin's conjecture and oscillation of unicycle tracks

The model of a bicycle is a unit segment AB that can move in the plane so that it remains tangent to the trajectory of point A (the rear wheel is fixed on the bicycle frame); the same model describes the hatchet planimeter. The trajectory of the front wheel and the initial position of the bicycle uniquely determine its motion and its terminal position; the monodromy map sending the initial position to the terminal one arises. According to R. Foote's theorem, this mapping of a circle to a circle is a Moebius transformation. We extend this result to multi-dimensional setting. Moebius transformations belong to one of the three types: elliptic, parabolic and hyperbolic. We prove a 100 years old Menzin's conjecture: if the front wheel track is an oval with area at least pi then the respective monodromy is hyperbolic. We also study bicycle motions introduced by D. Finn in which the rear wheel follows the track of the front wheel. Such a ''unicycle" track becomes more and more oscillatory in forward direction. We prove that it cannot be infinitely extended backward and relate the problem to the geometry of the space of forward semi-infinite equilateral linkages.

math.DG↗
arXiv2004

Supernova / Acceleration Probe: A Satellite Experiment to Study the Nature of the Dark Energy

The Supernova / Acceleration Probe (SNAP) is a proposed space-based experiment designed to study the dark energy and alternative explanations of the acceleration of the Universe's expansion by performing a series of complementary systematics-controlled measurements. We describe a self-consistent reference mission design for building a Type Ia supernova Hubble diagram and for performing a wide-area weak gravitational lensing study. A 2-m wide-field telescope feeds a focal plane consisting of a 0.7 square-degree imager tiled with equal areas of optical CCDs and near infrared sensors, and a high-efficiency low-resolution integral field spectrograph. The SNAP mission will obtain high-signal-to-noise calibrated light-curves and spectra for several thousand supernovae at redshifts between z=0.1 and 1.7. A wide-field survey covering one thousand square degrees resolves ~100 galaxies per square arcminute. If we assume we live in a cosmological-constant-dominated Universe, the matter density, dark energy density, and flatness of space can all be measured with SNAP supernova and weak-lensing measurements to a systematics-limited accuracy of 1%. For a flat universe, the density-to-pressure ratio of dark energy can be similarly measured to 5% for the present value w0 and ~0.1 for the time variation w'. The large survey area, depth, spatial resolution, time-sampling, and nine-band optical to NIR photometry will support additional independent and/or complementary dark-energy measurement approaches as well as a broad range of auxiliary science programs. (Abridged)

astro-ph↗