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Accurately diagnosing sleep disorders is essential for clinical assessments and treatments. Polysomnography (PSG) has long been used for detection of various sleep disorders. In this research, electrocardiography (ECG) and electromayography (EMG) have been used for recognition of breathing and movement-related sleep disorders. Bio-signal processing has been performed by extracting EMG features exploiting entropy and statistical moments, in addition to developing an iterative pulse peak detection algorithm using synchrosqueezed wavelet transform (SSWT) for reliable extraction of heart rate and breathing-related features from ECG. A deep learning framework has been designed to incorporate EMG and ECG features. The framework has been used to classify four groups: healthy subjects, patients with obstructive sleep apnea (OSA), patients with restless leg syndrome (RLS) and patients with both OSA and RLS. The proposed deep learning framework produced a mean accuracy of 72% and weighted F1 score of 0.57 across subjects for our formulated four-class problem., Comment: Paper is offered by the publisher as Open Acess: https://www.mdpi.com/1424-8220/20/9/2594

Just recently, the class of all Einstein-Maxwell fields solving simultaneously also any higher-order modification of the Eintein-Maxwell theory has been completely identified. In the present work, we argue that, in view of our recent results on nonabelian gauge fields, analogous identification can be in fact achieved for Einstein-Yang-Mills fields associated with any compact and semisimple gauge group. In particular, any such solution consists of a $VSI$ (vanishing scalar invariant) spacetime metric and a $VSI$ gauge field, both subject to a simple tensorial condition. Based on that, we are able to provide explicit form of all such solutions and interpret them as gravitational and Yang-Mills plane-fronted waves propagating in flat spacetime along the common recurrent wave vector. The results have consequences also for theories with a richer field content, which is further illustrated on 10D heterotic supergravity., Comment: 6 pages, 0 figures

We consider extension of some established techniques of study of tensor fields on Lorentzian manifolds of arbitrary dimension to non-Abelian gauge covariant fields. These are then applied to study of gauge fields with vanishing scalar curvature invariants and universal Yang-Mills fields, for which all possible higher-order corrections to the Yang-Mills equation identically vanish.

We obtain a full characterization of Einstein-Maxwell $p$-form solutions $(\boldsymbol{g},\boldsymbol{F})$ in $D$-dimensions for which all higher-order corrections vanish identically. These thus simultaneously solve a large class of Lagrangian theories including both modified gravities and (possibly non-minimally coupled) modified electrodynamics. Specifically, both $\boldsymbol{g}$ and $\boldsymbol{F}$ are fields with vanishing scalar invariants and further satisfy two simple tensorial conditions. They describe a family of gravitational and electromagnetic plane-fronted waves of the Kundt class and of Weyl type III (or more special). The local form of $(\boldsymbol{g},\boldsymbol{F})$ and a few examples are also provided., Comment: v2: a few minor changes in the text and proof of lemma B.6 slightly improved, results unchanged

We study almost universal spacetimes - spacetimes for which the field equations of any generalized gravity with the Lagrangian constructed from the metric, the Riemann tensor and its covariant derivatives of arbitrary order reduce to one single differential equation and one algebraic condition for the Ricci scalar. We prove that all d-dimensional Kundt spacetimes of Weyl type III and traceless Ricci type N are almost universal. Explicit examples of Weyl type II almost universal Kundt metrics are also given. The considerable simplification of the field equations of higher-order gravity theories for almost universal spacetimes is then employed to study new Weyl type II, III, and N vacuum solutions to quadratic gravity in arbitrary dimension and six-dimensional conformal gravity. Necessary conditions for almost universal metrics are also studied., Comment: 17 pages, final version, to appear in Phys. Rev. D

We consider $d$-dimensional solutions to the electrovacuum Einstein-Maxwell equations with the Weyl tensor of type N and a null Maxwell $(p+1)$-form field. We prove that such spacetimes are necessarily aligned, i.e. the Weyl tensor of the corresponding spacetime and the electromagnetic field share the same \textit{aligned null direction} (AND). Moreover, this AND is geodetic, shear-free, non-expanding and non-twisting and hence Einstein-Maxwell equations imply that Weyl type N spacetimes with a null Maxwell $(p+1)$-form field belong to the Kundt class. Moreover, these Kundt spacetimes are necessarily $CSI$ and the $(p+1)$ form is $VSI$. Finally, a general coordinate form of solutions and a reduction of the field equations are discussed., Comment: 11 pages, minor changes

We study the geometrical properties of null congruences generated by an aligned null direction of the Weyl tensor (WAND) in spacetimes of the Weyl and Ricci type N (possibly with a non-vanishing cosmological constant) in an arbitrary dimension. We prove that a type N Ricci tensor and a type III or N Weyl tensor have to be aligned. In such spacetimes, the multiple WAND has to be geodetic. For spacetimes with type N aligned Weyl and Ricci tensors, the canonical form of the optical matrix in the twisting and non-twisting case is derived and the dependence of the Weyl and the Ricci tensors and Ricci rotation coefficients on the affine parameter of the geodetic null congruence generated by the WAND is obtained., Comment: 16 pages, section 6 added, section 7 reduced, tables 1 and 3 added, other minor changes

Compared to the previous INPOP versions, the INPOP10a planetary and lunar ephemeris has several improvements. For the planets of our solar system, no big change was brought in the dynamics but improvements were implemented in the fitting process, the data sets used in the fit and in the selection of fitted parameters. We report here the main characteristics of the planetary part of INPOP10a like the fit of the product of the Solar mass with the gravitational constant (GM$_{\odot}$) instead of the astronomical unit. Determinations of PPN parameters as well as adjustments of the Sun J2 and of asteroid masses are also presented. New advances of nodes and perihelia of planets were also estimated and are given here. As for INPOP08, INPOP10a provides to the user, positions and velocities of the planets, the moon, the rotation angles of the Earth and the Moon as well as TT-TDB chebychev polynomials at http://www.imcce.fr/inpop, Comment: accepted for publication in celestial mechanics and dynamical astronomy

Context. Ceres is the most massive body of the asteroid belt and contains about 25 wt.% (weight percent) of water. Understanding its thermal evolution and assessing its current state are major goals of the Dawn Mission. Constraints on internal structure can be inferred from various observations. Especially, detailed knowledge of the rotational motion can help constrain the mass distribution inside the body, which in turn can lead to information on its geophysical history. Aims. We investigate the signature of the interior on the rotational motion of Ceres and discuss possible future measurements performed by the spacecraft Dawn that will help to constrain Ceres' internal structure. Methods. We compute the polar motion, precession-nutation, and length-of-day variations. We estimate the amplitudes of the rigid and non-rigid response for these various motions for models of Ceres interior constrained by recent shape data and surface properties. Results. As a general result, the amplitudes of oscillations in the rotation appear to be small, and their determination from spaceborne techniques will be challenging. For example, the amplitudes of the semi-annual and annual nutations are around ~364 and ~140 milli-arcseconds, and they show little variation within the parametric space of interior models envisioned for Ceres. This, combined with the very long-period of the precession motion, requires very precise measurements. We also estimate the timescale for Ceres' orientation to relax to a generalized Cassini State, and we find that the tidal dissipation within that object was probably too small to drive any significant damping of its obliquity since formation. However, combining the shape and gravity observations by Dawn offers the prospect to identify departures of non-hydrostaticity at the global and regional scale, which will be instrumental in constraining Ceres' past and current thermal state. We also discuss the existence of a possible Chandler mode in the rotational motion of Ceres, whose potential excitation by endogenic and/or exogenic processes may help detect the presence of liquid reservoirs within the asteroid., Comment: submitted to Astronomy and Astrophysics

The Planetary and Lunar ephemerides INPOP10a version has several improvements in the fitting process, the data sets used in the fit and in the general features of the solution. No big change was brought in the dynamics. As a consequence of these changes, the extrapolation capabilities of INPOP10a are improved compared to INPOP08, especially for the Earth, Mars, Mercury and Saturn orbits. As for INPOP08, INPOP10a provides to the user, positions, velocities of the planets and the moon and TT-TDB chebychev polynomials at \url{http://www.imcce.fr/inpop}., Comment: documentation of INPOP10A available on www.imcce.fr/inpop

We assess the ability of a solid ring to model a global perturbation induced by several thousands of main-belt asteroids. The ring is first studied in an analytical framework that provides an estimate of all the ring's parameters excepting mass. In the second part, numerically estimated perturbations on the Earth-Mars, Earth-Venus, and Earth-Mercury distances induced by various subsets of the main-belt population are compared with perturbations induced by a ring. To account for large uncertainties in the asteroid masses, we obtain results from Monte Carlo experiments based on asteroid masses randomly generated according to available data and the statistical asteroid model. The radius of the ring is analytically estimated at 2.8 AU. A systematic comparison of the ring with subsets of the main belt shows that, after removing the 300 most perturbing asteroids, the total main-belt perturbation of the Earth-Mars distance reaches on average 246 m on the 1969-2010 time interval. A ring with appropriate mass is able to reduce this effect to 38 m. We show that, by removing from the main belt ~240 asteroids that are not necessarily the most perturbing ones, the corresponding total perturbation reaches on average 472 m, but the ring is able to reduce it down to a few meters, thus accounting for more than 99% of the total effect., Comment: 18 pages, accepted in A&A

In this Letter, we give new constraints on planet migration. They were obtained under the assumption that Saturn's current obliquity is due to a capture in resonance with Neptune's ascending node. If planet migration is too fast, then Saturn crosses the resonance without being captured and it keeps a small obliquity. This scenario thus gives a lower limit on the migration time scale tau. We found that this boundary depends strongly on Neptune's initial inclination. For two different migration types, we found that tau should be at least greater than 7 Myr. This limit increases rapidly as Neptune's initial inclination decreases from 10 to 1 degree. We also give an algorithm to know if Saturn can be tilted for any migration law., Comment: 5 pages, 4 figures, published in ApJL

In this paper, we present several gravity tests made in using the last INPOP08 planetary ephemerides. We first propose two methods to estimate the PPN parameter $\beta$ and its correlated value, the Sun J2 and we discuss the correlation between the Sun J2 and the mass of the asteroid ring. We estimate possible advance in the planet perihelia. In the end we show that no constant acceleration larger than 1/4 the Pioneer anomaly can affect the planets of our solar system., Comment: 11 pages. submitted to proceedings of IAU symposium 264 "Relativity in Fundamental Astronomy: Dynamics, Reference Frames and Data analysis"

The latest version of the planetary ephemerides developed at the Paris Observatory and at the Besancon Observatory is presented here. INPOP08 is a 4-dimension ephemeris since it provides to users positions and velocities of planets and the relation between TT and TDB. Investigations leading to improve the modeling of asteroids are described as well as the new sets of observations used for the fit of INPOP08. New observations provided by the European Space Agency (ESA) deduced from the tracking of the Mars Express (MEX) and Venus Express (VEX) missions are presented as well as the normal point deduced from the Cassini mission. We show the huge impact brought by these observations in the fit of INPOP08, especially in terms of Venus, Saturn and Earth-Moon barycenter orbits., Comment: 14 pages. submitted to A&A. accepted in A&A

Mars ranging observations are available over the past 10 years with an accuracy of a few meters. Such precise measurements of the Earth-Mars distance provide valuable constraints on the masses of the asteroids perturbing both planets. Today more than 30 asteroid masses have thus been estimated from planetary ranging data (see [1] and [2]). Obtaining unbiased mass estimations is nevertheless difficult. Various systematic errors can be introduced by imperfect reduction of spacecraft tracking observations to planetary ranging data. The large number of asteroids and the limited a priori knowledge of their masses is also an obstacle for parameter selection. Fitting in a model a mass of a negligible perturber, or on the contrary omitting a significant perturber, will induce important bias in determined asteroid masses. In this communication, we investigate a simplified version of the mass determination problem. Instead of planetary ranging observations from spacecraft or radar data, we consider synthetic ranging observations generated with the INPOP [2] ephemeris for a test model containing ~25000 asteroids. We then suggest a method for optimal parameter selection and estimation in this simplified framework.