{"id":"xBKeVishRTsArPJn5YWo0HpuD","value":"Correcting inner filter effects, a non multilinear tensor decomposition method.Among measurement used in analytical chemistry, fluorescence spectroscopy is widely spread and its applications are numerous. To recover various information on unknown components in chemical mixtures, multilinear tensor decomposition of multiway fluorescence spectra has proven extremely powerful. However, inner filter effects induce a systematic error on measurements, disturbing the decomposition. In this paper, we fully describe a non multilinear approach to include inner filter effects in the model instead of neglecting them or correcting them by linearization methods. A theoretical framework on non multilinear tensor decomposition is developed, an algorithm to recover the factors in the decomposition is detailed, and real data computer results are reported."}
{"id":"ytCa8ZJiKvT7JNfsgtbF3_HVG","value":"The VIMOS Public Extragalactic Redshift Survey (VIPERS). Measuring nonlinear galaxy bias at z~0.8.We use the first release of the VImos Public Extragalactic Redshift Survey of galaxies (VIPERS) of ~50,000 objects to measure the biasing relation between galaxies and mass in the redshift range z=[0.5,1.1]. We estimate the 1-point distribution function [PDF] of VIPERS galaxies from counts in cells and, assuming a model for the mass PDF, we infer their mean bias relation. The reconstruction of the bias relation from PDFs is performed through a novel method that accounts for Poisson noise, redshift distortions, inhomogeneous sky coverage and other selection effects. With this procedure we constrain galaxy bias and its deviations from linearity down to scales as small as 4 Mpc/h and out to z=1.1. We detect small (~3%) but significant deviations from linear bias. The mean biasing function is close to linear in regions above the mean density. The mean slope of the biasing relation is a proxy to the linear bias parameter. It increases both with luminosity, in agreement with results of previous analyses, and with redshift. However, we detect a strong bias evolution only for z>0.9 in agreement with some, but not all, previous studies. We also detected a significant increase of the bias with the scale, from 4 to 8 Mpc/h, now seen for the first time out to z=1. The amplitude of nonlinearity depends on redshift, luminosity and on scales but no clear trend is detected. Thanks to the large cosmic volume probed by VIPERS we find that the mismatch between the previous estimates of bias at z~1 from zCOSMOS and VVDS-Deep galaxy samples is fully accounted for by cosmic variance. The results of our work confirm the importance of going beyond the over-simplistic linear bias hypothesis showing that non-linearities can be accurately measured through the applications of the appropriate statistical tools to existing datasets like VIPERS."}
{"id":"4ltmTe9intX7Hq0Q1Zh4rEdEl","value":"An inverse stability result for non-compactly supported potentials by one arbitrary lateral Neumann observation.In this paper we investigate the inverse problem of determining the time independent scalar potential of the dynamic Schrödinger equation in an infinite cylindrical domain, from partial measurement of the solution on the boundary. Namely, if the potential is known in a neighborhood of the boundary of the spatial domain, we prove that it can be logarithmic stably determined in the whole waveguide from a single observation of the solution on any arbitrary strip-shaped subset of the boundary."}
{"id":"PhnlUo_d6LoJPLN3YUjh5qBLc","value":"Non-local effects by homogenization or 3D–1D dimension reduction in elastic materials reinforced by stiff fibers.We first consider an elastic thin heterogeneous cylinder of radius of order ε: the interior of the cylinder is occupied by a stiff material (fiber) that is surrounded by a soft material (matrix). By assuming that the elasticity tensor of the fiber does not scale with ε and that of the matrix scales with ε2, we prove that the one dimensional model is a nonlocal system.We then consider a reference configuration domain filled out by periodically distributed rods similar to those described above. We prove that the homogenized model is a second order nonlocal problem.In particular, we show that the homogenization problem is directly connected to the 3D–1D dimensional reduction problem."}
{"id":"ncQh8I8SU45Y7klOGFQ35_3oA","value":"On a quantum phase transition in a steady state out of equilibrium.Within the rigorous axiomatic framework for the description of quantum mechanical systems with a large number of degrees of freedom, we show that the nonequilibrium steady state, constructed in the quasifree fermionic system corresponding to the isotropic XY chain in which a finite sample, coupled to two thermal reservoirs at different temperatures, is exposed to a local external magnetic field, is breaking translation invariance and exhibits a strictly positive entropy production rate. Moreover, we prove that there exists a second-order nonequilibrium quantum phase transition with respect to the strength of the magnetic field as soon as the system is truly out of equilibrium."}
{"id":"jMUQvk86JWbm39dl0b7F2lzF0","value":"Some trace monotonicity properties and applications.We present some results on the monotonicity of some traces involving functions of self-adjoint operators with respect to the natural ordering of their associated quadratic forms. We also apply these results to complete a proof of the Wegner estimate for continuum models of random Schrödinger operators as given."}
{"id":"NvIAnm4oZpwBaAaovW1hK9Auq","value":"On Generalized Bohr–Sommerfeld Quantization Rules for Operators with PT Symmetry.We give Bohr-Sommerfeld quantization rules corresponding to quasi-eigenvalues for a 1-D h-Pseudodifferential operator verifying PT symmetry."}
{"id":"xprqtrTCQwRYI5IXrK2m5bw5r","value":"Is Time's Arrow Perspectival?.We observe entropy decrease towards the past. Does this imply that in the past the world was in a non-generic microstate? I point out an alternative. The subsystem to which we belong interacts with the universe via a relatively small number of quantities, which define a coarse graining. Entropy happens to depends on coarse-graining. Therefore the entropy we ascribe to the universe depends on the peculiar coupling between us and the rest of the universe. Low past entropy may be due to the fact that this coupling (rather than microstate of the universe) is non-generic. I argue that for any generic microstate of a sufficiently rich system there are always special subsystems defining a coarse graining for which the entropy of the rest is low in one time direction (the \"past\"). These are the subsystems allowing creatures that \"live in time\" ---such as those in the biosphere--- to exist. I reply to some objections raised to an earlier presentation of this idea, in particular by Bob Wald, David Albert and Jim Hartle."}
{"id":"cWryO870YbHKYyktwONiHsAGY","value":"Weyl gravity and Cartan geometry.We point out that the Cartan geometry known as the second-order conformalstructure provides a natural differential geometric framework underlying gaugetheories of conformal gravity. We are concerned by two theories: the first onewill be the associated Yang-Mills-like Lagrangian, while the second, inspiredby J.T. Wheeler in Phys. Rev. D90 (2014), will be a slightly more general one which will relax theconformal Cartan geometry. The corresponding gauge symmetry is treated withinthe BRST language. We show that the Weyl gauge potential is a spurious degreeof freedom, analogous to a Stueckelberg field, that can be eliminated throughthe dressing field method. We derive sets of field equations for both thestudied Lagrangians. For the second one, they constrain the gauge field to bethe `normal conformal Cartan connection'. Finally, we provide in a Lagrangianframework a justification of the identification, in dimension $4$, of the Bachtensor with the Yang-Mills current of the normal conformal Cartan connection,as proved in Class. Quant. Grav. 20 (2003)."}
{"id":"y3193mVJnI8UleYE0ZiuvpAkT","value":"Spectral analysis and the Aharonov-Bohm effect on certain almost-Riemannian manifolds.We study spectral properties of the Laplace-Beltrami operator on two relevant almost-Riemannian manifolds, namely the Grushin structures on the cylinder and on the sphere. As for general almost-Riemannian structures (under certain technical hypothesis), the singular set acts as a barrier for the evolution of the heat and of a quantum particle, although geodesics can cross it. This is a consequence of the self-adjointness of the Laplace-Beltrami operator on each connected component of the manifolds without the singular set. We get explicit descriptions of the spectrum, of the eigenfunctions and their properties. In particular in both cases we get a Weyl law with dominant term . We then study the effect of an Aharonov-Bohm non-apophantic magnetic potential that has a drastic effect on the spectral properties. Other generalized Riemannian structures including conic and anti-conic type manifolds are also studied. In this case, the Aharonov-Bohm magnetic potential may affect the self-adjointness of the Laplace-Beltrami operator."}
{"id":"eq2YQ89J8vWaw1LrUpj9HP4Ye","value":"Random walk of passive tracers among randomly moving obstacles.Background: This study is mainly motivated by the need of understanding how the diffusion behaviour of a biomolecule (or even of a larger object) is affected by other moving macromolecules, organelles, and so on, inside a living cell, whence the possibility of understanding whether or not a randomly walking biomolecule is also subject to a long-range force field driving it to its target. Method: By means of the Continuous Time Random Walk (CTRW) technique the topic of random walk in random environment is here considered in the case of a passively diffusing particle in a crowded environment made of randomly moving and interacting obstacles. Results: The relevant physical quantity which is worked out is the diffusion cofficient of the passive tracer which is computed as a function of the average inter-obstacles distance. Coclusions: The results reported here suggest that if a biomolecule, let us call it a test molecule, moves towards its target in the presence of other independently interacting molecules, its motion can be considerably slowed down. Hence, if such a slowing down could compromise the efficiency of the task to be performed by the test molecule, some accelerating factor would be required. Intermolecular electrodynamic forces are good candidates as accelerating factors because they can act at a long distance in a medium like the cytosol despite its ionic strength."}
{"id":"OuqMuWsK2dzGRNFT7EuBrafZv","value":"On the dynamical emergence of de Sitter spacetime.We present and discuss an asynchronous coordinate system covering de Sitter spacetime, notably in a complete way in 1+1 dimensions. The new coordinates have several interesting cosmological properties: the worldlines of comoving ($x^i=const$) observers are geodesics, cosmic time is finite in the past, and the coordinates asymptotically tend to that of a flat Robertson & Walker model at large times. This analysis also provides an argument in favor of the natural emergence of an equation of state of the type $p=-\\rho$ in the context of the standard cosmological model."}
{"id":"yN9VF7_JjWPvmPcE6oEw91i70","value":"Minimal cosmography.The minimal requirement for cosmography—a non-dynamical description of the uni-verse—is a prescription for calculating null geodesics, and time-like geodesics as a function of their proper time. In this paper, we consider the most general linear connection compatible with homogeneity and isotropy, but not necessarily with a metric. A light-cone structure is assigned by choosing a set of geodesics representing light rays. This defines a \" scale factor \" and a local notion of distance, as that travelled by light in a given proper time interval. We find that the velocities and relativistic energies of free-falling bodies decrease in time as a consequence of cosmic expansion, but at a rate that can be different than that dictated by the usual metric framework. By extrapolating this behavior to photons' redshift, we find that the latter is in principle independent of the \" scale factor \". Interestingly, redshift-distance relations and other standard geometric observables are modified in this extended framework, in a way that could be experimentally tested. An extremely tight constraint on the model, however, is represented by the blackbody-ness of the Cosmic Microwave Background. Finally, as a check, we also consider the effects of a non-metric connection in a different setup , namely, that of a static, spherically symmetric spacetime."}
{"id":"zst90ECaPqHae22UfQIJLrdZy","value":"Einstein-Cartan, Bianchi I and the Hubble Diagram.We try to solve the dark matter problem in the fit between theory and the Hubble diagram of supernovae by allowing for torsion via Einstein-Cartan's gravity and for anisotropy via the axial Bianchi I metric. Otherwise we are conservative and admit only the cosmological constant and dust. The failure of our model is quantified by the relative amount of dust in our best fit: Omega_{m0}= 27 % +/- 5 % at 1 sigma level."}
{"id":"x_KdUWWuwQznbCSEIo_CfGn2W","value":"Planck 2015 results. I. Overview of products and scientific results.The European Space Agency's Planck satellite, dedicated to studying the early Universe and its subsequent evolution, was launched 14~May 2009 and scanned the microwave and submillimetre sky continuously between 12~August 2009 and 23~October 2013. In February~2015, ESA and the Planck Collaboration released the second set of cosmology products based on data from the entire Planck mission, including both temperature and polarization, along with a set of scientific and technical papers and a web-based explanatory supplement. This paper gives an overview of the main characteristics of the data and the data products in the release, as well as the associated cosmological and astrophysical science results and papers. The science products include maps of the cosmic microwave background (CMB), the thermal Sunyaev-Zeldovich effect, and diffuse foregrounds in temperature and polarization, catalogues of compact Galactic and extragalactic sources (including separate catalogues of Sunyaev-Zeldovich clusters and Galactic cold clumps), and extensive simulations of signals and noise used in assessing the performance of the analysis methods and assessment of uncertainties. The likelihood code used to assess cosmological models against the Planck data are described, as well as a CMB lensing likelihood. Scientific results include cosmological parameters deriving from CMB power spectra, gravitational lensing, and cluster counts, as well as constraints on inflation, non-Gaussianity, primordial magnetic fields, dark energy, and modified gravity."}