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Using the dual cone of sums of nonnegative circuits (SONC), we provide a relaxation of the global optimization problem to minimize an exponential sum and, as a special case, a multivariate real polynomial. Our approach builds on two key observations. First, that the dual SONC cone is contained in the primal one. Hence, containment in this cone is a certificate of nonnegativity. Second, we show that membership in the dual cone can be verified by a linear program. We implement the algorithm and present initial experimental results comparing our method to existing approaches., Comment: final version; 17 pages, 5 tables more...

Context. Direct imaging of debris discs gives important information about their nature, their global morphology, and allows us to identify specific structures possibly in connection with the presence of gravitational perturbers. It is the most straightforward technique to observe planetary systems as a whole. Aims. We present the first resolved images of the debris disc around the young F-type star HD 160305, detected in scattered light using the VLT/SPHERE instrument in the near infrared. Methods. We used a post-processing method based on angular differential imaging and synthetic images of debris discs produced with a disc modelling code (GRaTer) to constrain the main characteristics of the disc around HD 160305. All of the point sources in the field of the IRDIS camera were analysed with an astrometric tool to determine whether they are bound objects or background stars. Results. We detect a very inclined (~ 82{\deg}) ring-like debris disc located at a stellocentric distance of about 86au (deprojected width ~27 au). The disc displays a brightness asymmetry between the two sides of the major axis, as can be expected from scattering properties of dust grains. We derive an anisotropic scattering factor g>0.5. A second right-left asymmetry is also observed with respect to the minor axis. We measure a surface brightness ratio of 0.73 $\pm$ 0.18 between the bright and the faint sides. Because of the low signal-to-noise ratio (S/N) of the images we cannot easily discriminate between several possible explanations for this left-right asymmetry, such as perturbations by an unseen planet, the aftermath of the breakup of a massive planetesimal, or the pericenter glow effect due to an eccentric ring. Two epochs of observations allow us to reject the companionship hypothesis for the 15 point sources present in the field., Comment: 13 pages more...

This article considers the recovery of low-rank matrices via a convex nuclear-norm minimization problem and presents two null space properties (NSP) which characterize uniform recovery for the case of block-diagonal matrices and block-diagonal positive semidefinite matrices. These null-space conditions turn out to be special cases of a new general setup, which allows to derive the mentioned NSPs and well-known NSPs from the literature. We discuss the relative strength of these conditions and also present a deterministic class of matrices that satisfies the block-diagonal semidefinite NSP., Comment: 23 pages; revised version; accepted for publication in Linear Algebra and Its Applications more...

In this note we give a recursive formula for the derivatives of isotropic positive definite functions on the Hilbert sphere. We then use it to prove a conjecture stated by Tr\"ubner and Ziegel, which says that for a positive definite function on the Hilbert sphere to be in $C^{2\ell}([0,\pi])$, it is necessary and sufficient for its $\infty$-Schoenberg sequence to satisfy $\sum\limits_{m=0}^{\infty}a_m m^{\ell}<\infty$. more...

Planetary systems hold the imprint of the formation and of the evolution of planets especially at young ages, and in particular at the stage when the gas has dissipated leaving mostly secondary dust grains. The dynamical perturbation of planets in the dust distribution can be revealed with high-contrast imaging in a variety of structures. SPHERE, the high-contrast imaging device installed at the VLT, was designed to search for young giant planets in long period, but is also able to resolve fine details of planetary systems at the scale of astronomical units in the scattered-light regime. As a young and nearby star, NZ Lup was observed in the course of the SPHERE survey. A debris disk had been formerly identified with HST/NICMOS. We observed this system in the near-infrared with the camera in narrow and broad band filters and with the integral field spectrograph. High contrasts are achieved by the mean of pupil tracking combined with angular differential imaging algorithms. The high angular resolution provided by SPHERE allows us to reveal a new feature in the disk which is interpreted as a superimposition of two belts of planetesimals located at stellocentric distances of $\sim$85 and $\sim$115\,au, and with a mutual inclination of about 5$\degb$. Despite the very high inclination of the disk with respect to the line of sight, we conclude that the presence of a gap, that is, a void in the dust distribution between the belts, is likely. We discuss the implication of the existence of two belts and their relative inclination with respect to the presence of planets., Comment: accepted in Astronomy and Astrophysics more...

Wavefront sensors encode phase information of an incoming wavefront into an intensity pattern that can be measured on a camera. Several kinds of wavefront sensors (WFS) are used in astronomical adaptive optics. Amongst them, Fourier-based wavefront sensors perform a filtering operation on the wavefront in the focal plane. The most well known example of a WFS of this kind is the Zernike wavefront sensor, and the pyramid wavefront sensor (PWFS) also belongs to this class. Based on this same principle, new WFSs can be proposed such as the n-faced pyramid (which ultimately becomes an axicone) or the flattened pyramid, depending on whether the image formation is incoherent or coherent. In order to test such novel concepts, the LOOPS adaptive optics testbed hosted at the Laboratoire d'Astrophysique de Marseille has been upgraded by adding a Spatial Light Modulator (SLM). This device, placed in a focal plane produces high-definition phase masks that mimic otherwise bulk optic devices. In this paper, we first present the optical design and upgrades made to the experimental setup of the LOOPS bench. Then, we focus on the generation of the phase masks with the SLM and the implications of having such a device in a focal plane. Finally, we present the first closed-loop results in either static or dynamic mode with different WFS applied on the SLM., Comment: 14 pages, 9 figures, submitted to JATIS more...

In this paper, we describe Fourier-based Wave Front Sensors (WFS) as linear integral operators, characterized by their Kernel. In a first part, we derive the dependency of this quantity with respect to the WFS's optical parameters: pupil geometry, filtering mask, tip/tilt modulation. In a second part we focus the study on the special case of convolutional Kernels. The assumptions required to be in such a regime are described. We then show that these convolutional kernels allow to drastically simplify the WFS's model by summarizing its behavior in a concise and comprehensive quantity called the WFS's Impulse Response. We explain in particular how it allows to compute the sensor's sensitivity with respect to the spatial frequencies. Such an approach therefore provides a fast diagnostic tool to compare and optimize Fourier-based WFSs. In a third part, we develop the impact of the residual phases on the sensor's impulse response, and show that the convolutional model remains valid. Finally, a section dedicated to the Pyramid WFS concludes this work, and illustrates how the slopes maps are easily handled by the convolutional model., Comment: 21 pages, 7 figures more...

Solid-solid phase boundary anisotropy is a key factor controlling the selection and evolution of non-faceted eutectic patterns during directional solidification. This is most remarkably observed during the so-called maze-to-lamellar transition. By using serial sectioning, we followed the spatio-temporal evolution of a maze pattern over long times in a large Al-Al2Cu eutectic grain with known crystal orientation of the Al and Al2Cu phases, hence known crystal orientation relationship (OR). The corresponding phase boundary energy anisotropy ($\gamma$-plot) was also known, as being previously estimated from molecular-dynamics computations. The experimental observations reveal the time-scale of the maze-to-lamellar transition and shed light on the processes involved in the gradual alignment of the phase boundaries to one distinct energy minimum which nearly corresponds to one distinct plane from the family $\{120\}^{\rm{Al}} //\{110\}^{\rm{Al2Cu}}$. This particular plane is selected due to a crystallographic bias induced by a small disorientation of the crystals relative to the perfect OR. The symmetry of the OR is thus slightly broken, which promotes lamellar alignment. Finally, the maze-to-lamellar transition leaves behind a network of fault lines inherited from the phase boundary alignment process. In the maze pattern, the fault lines align along the corners of the Wulff shape, thus allowing us to propose a link between the pattern defects and missing orientations in the Wulff shape, Comment: 26 pages, 6 figures more...

Zernike polynomials are widely used to describe the wavefront phase as they are well suited to the circular geometry of various optical apertures. Non-conventional optical systems, such as future large optical telescopes with highly segmented primary mirrors or advanced wavefront control devices using segmented mirror membrane facesheets, use approximate numerical methods to reproduce a set of Zernike or hexagonal modes with the limited degree of freedom offered by hexagonal segments. In this paper, we present a novel approach for a rigorous Zernike and hexagonal modes decomposition adapted to hexagonal segmented pupils by means of analytical calculations. By contrast to numerical approaches that are dependent on the sampling of the segment, the decomposition expressed analytically only relies on the number and positions of segments comprising the pupil. Our analytical method allows extremely quick results minimizing computational and memory costs. Further, the proposed formulae can be applied independently from the geometrical architecture of segmented optical apertures. Consequently, the method is universal and versatile per se. This work has many potential applications in particular for modern astronomy with extremely large telescopes., Comment: 12 pages, 4 figures, 3 tables, to appear in OSA Continuum more...

In the chapter "Magic with a Matrix" in \emph{Hexaflexagons and Other Mathematical Diversions} (1988), Martin Gardner describes a delightful "party trick" to fill the squares of a $d$-by-$d$ chessboard with nonnegative integers such that the sum of the numbers covered by any placement of $d$ nonthreatening rooks is a given number $N$. We consider such chessboards from a geometric perspective which gives rise to a family of lattice polytopes. The polyhedral structure of these Gardner polytopes explains the underlying trick and enables us to count such chessboards for given $N$ in three different ways. We also observe a curious duality that relates Gardner polytopes to Birkhoff polytopes., Comment: 8 pages, v4: substantially improved results and exposition, accepted for publication in American Mathematical Monthly more...

The nearby and young M star AU Mic is surrounded by a debris disk in which we previously identified a series of large-scale arch-like structures that have never been seen before in any other debris disk and that move outward at high velocities. We initiated a monitoring program with the following objectives: 1) track the location of the structures and better constrain their projected speeds, 2) search for new features emerging closer in, and ultimately 3) understand the mechanism responsible for the motion and production of the disk features. AU Mic was observed at 11 different epochs between August 2014 and October 2017 with the IR camera and spectrograph of SPHERE. These high-contrast imaging data were processed with a variety of angular, spectral, and polarimetric differential imaging techniques to reveal the faintest structures in the disk. We measured the projected separations of the features in a systematic way for all epochs. We also applied the very same measurements to older observations from the Hubble Space Telescope (HST) with the visible cameras STIS and ACS. The main outcomes of this work are 1) the recovery of the five southeastern broad arch-like structures we identified in our first study, and confirmation of their fast motion (projected speed in the range 4-12 km/s); 2) the confirmation that the very first structures observed in 2004 with ACS are indeed connected to those observed later with STIS and now SPHERE; 3) the discovery of two new very compact structures at the northwest side of the disk (at 0.40" and 0.55" in May 2015) that move to the southeast at low speed; and 4) the identification of a new arch-like structure that might be emerging at the southeast side at about 0.4" from the star (as of May 2016). Abridged., Comment: 23 pages, 20 figures, accepted for publication in Astronomy and Astrophysics more...

HD95086 (A8V, 17Myr) hosts a rare planetary system for which a multi-belt debris disk and a giant planet of 4-5MJup have been directly imaged. Our study aims to characterize the physical and orbital properties of HD95086b, search for additional planets at short and wide orbits and image the cold outer debris belt in scattered light. We used HARPS at the ESO 3.6m telescope to monitor the radial velocity of HD95086 over 2 years and investigate the existence of giant planets at less than 3au orbital distance. With the IRDIS dual-band imager and the IFS integral field spectrograph of SPHERE at VLT, we imaged the faint circumstellar environment beyond 10au at six epochs between 2015 and 2017. We do not detect additional giant planets around HD95086. We identified the nature (bound companion or background contaminant) of all point-like sources detected in the IRDIS field of view. None of them correspond to the ones recently discovered near the edge of the cold outer belt by ALMA. HD95086b is resolved for the first time in J-band with IFS. Its near-infrared spectral energy distribution is well fitted by a few dusty and/or young L7-L9 dwarf spectral templates. The extremely red 1-4um spectral distribution is typical of low-gravity objects at the L/T spectral type transition. The planet's orbital motion is resolved between January 2015 and May 2017. Together with past NaCo measurements properly re-calibrated, our orbital fitting solutions favor a retrograde low to moderate-eccentricity orbit e=0.2 (0.0 to 0.5), with a semi-major axis 52au corresponding to orbital periods of 288$ yrs and an inclination that peaks at i = 141deg, which is compatible with a planet-disk coplanar configuration. Finally, we report the detection in polarimetric differential imaging of the cold outer debris belt between 100 and 300au, consistent in radial extent with recent ALMA 1.3mm resolved observations., Comment: 23 pages, 19 figures, accepted in A&A (Dec 28th, 2017) more...

The SHINE program is a large high-contrast near-infrared survey of 600 young, nearby stars. It is aimed at searching for and characterizing new planetary systems using VLT/SPHERE's unprecedented high-contrast and high-angular resolution imaging capabilities. It also intends at placing statistical constraints on the occurrence and orbital properties of the giant planet population at large orbits as a function of the stellar host mass and age to test planet formation theories. We use the IRDIS dual-band imager and the IFS integral field spectrograph of SPHERE to acquire high-constrast coronagraphic differential near-infrared images and spectra of the young A2 star HIP65426. It is a member of the ~17 Myr old Lower Centaurus-Crux association. At a separation of 830 mas (92 au projected) from the star, we detect a faint red companion. Multi-epoch observations confirm that it shares common proper motion with HIP65426. Spectro-photometric measurements extracted with IFS and IRDIS between 0.95 and 2.2um indicate a warm, dusty atmosphere characteristic of young low surface-gravity L5-L7 dwarfs. Hot-start evolutionary models predict a luminosity consistent with a 6-12 MJup, Teff=1300-1600 K and R=1.5 RJup giant planet. Finally, the comparison with Exo-REM and PHOENIX BT-Settl synthetic atmosphere models gives consistent effective temperatures but with slightly higher surface gravity solutions of log(g)=4.0-5.0 with smaller radii (1.0-1.3 RJup). Given its physical and spectral properties, HIP65426b occupies a rather unique placement in terms of age, mass and spectral-type among the currently known imaged planets. It represents a particularly interesting case to study the presence of clouds as a function of particle size, composition, and location in the atmosphere, to search for signatures of non-equilibrium chemistry, and finally to test the theory of planet formation and evolution., Comment: 10 pages, 8 figures, 4 tables, accepted for publication in A&A, file updated more...

Segmented aperture telescopes require an alignment procedure with successive steps from coarse alignment to monitoring process in order to provide very high optical quality images for stringent science operations such as exoplanet imaging. The final step, referred to as fine phasing, calls for a high sensitivity wavefront sensing and control system in a diffraction-limited regime to achieve segment alignment with nanometric accuracy. In this context, Zernike wavefront sensors represent promising options for such a calibration. A concept called the Zernike unit for segment phasing (ZEUS) was previously developed for ground-based applications to operate under seeing-limited images. Such a concept is, however, not suitable for fine cophasing with diffraction-limited images. We revisit ZELDA, a Zernike sensor that was developed for the measurement of residual aberrations in exoplanet direct imagers, to measure segment piston, tip, and tilt in the diffraction-limited regime. We introduce a novel analysis scheme of the sensor signal that relies on piston, tip, and tilt estimators for each segment, and provide probabilistic insights to predict the success of a closed-loop correction as a function of the initial wavefront error. The sensor unambiguously and simultaneously retrieves segment piston and tip-tilt misalignment. Our scheme allows for correction of these errors in closed-loop operation down to nearly zero residuals in a few iterations. This sensor also shows low sensitivity to misalignment of its parts and high ability for operation with a relatively bright natural guide star. Our cophasing sensor relies on existing mask technologies that make the concept already available for segmented apertures in future space missions., Comment: 11 pages, 10 figures. Accepted for publication in A&A - sec. 13 more...

This work presents an experimental design for studying low-velocity collisions into granular surfaces in low-gravity. In the experiment apparatus, reduced-gravity is simulated by releasing a free-falling projectile into a surface container with a downward acceleration less than that of Earth's gravity. The acceleration of the surface is controlled through the use of an Atwood machine, or a system of pulleys and counterweights. The starting height of the surface container and the initial separation distance between the projectile and surface are variable and chosen to accommodate collision velocities up to 20 cm/s and effective accelerations of ~0.1 - 1.0 m/s^2. Accelerometers, placed on the surface container and inside the projectile, provide acceleration data, while high-speed cameras capture the collision and act as secondary data sources. The experiment is built into an existing 5.5 m drop-tower frame and requires the custom design of all components, including the projectile, surface sample container, release mechanism and deceleration system. Data from calibration tests verify the efficiency of the experiment's deceleration system and provide a quantitative understanding of the performance of the Atwood system., Comment: 11 pages, 11 figures more...

Segmented primary mirrors are indispensable to master the steady increase in spatial resolution. Phasing optics systems must reduce segment misalignments to guarantee the high optical quality required for astronomical science programs. Modern telescopes routinely use adaptive optics systems to compensate for the atmosphere and use laser-guide-stars to create artificial stars as bright references in the field of observation. Because multiple laser-guide-star adaptive optics are being implemented in all major observatories, we propose to use man-made stars not only for adaptive optics, but for phasing optics. We propose a method called the doublet-wavelength coherence technique (DWCT), exploiting the D lines of sodium in the mesosphere using laser guide-stars. The signal coherence properties are then used. The DWCT capture range exceeds current abilities by a factor of 100. It represents a change in paradigm by improving the phasing optics capture range from micrometric to millimetric. It thereby potentially eliminates the need of a man-made mechanical pre-phasing step. Extremely large telescopes require hundreds of segments, several of which need to be substituted on a daily basis to be recoated. The DWCT relaxes mechanical integration requirements and speeds up integration and re-integration process., Comment: Accepted in A&A (Letters to the Editor) more...

This paper presents a novel two-phase method for audio representation, Discriminative and Compact Audio Representation (DCAR), and evaluates its performance at detecting events in consumer-produced videos. In the first phase of DCAR, each audio track is modeled using a Gaussian mixture model (GMM) that includes several components to capture the variability within that track. The second phase takes into account both global structure and local structure. In this phase, the components are rendered more discriminative and compact by formulating an optimization problem on Grassmannian manifolds, which we found represents the structure of audio effectively. Our experiments used the YLI-MED dataset (an open TRECVID-style video corpus based on YFCC100M), which includes ten events. The results show that the proposed DCAR representation consistently outperforms state-of-the-art audio representations. DCAR's advantage over i-vector, mv-vector, and GMM representations is significant for both easier and harder discrimination tasks. We discuss how these performance differences across easy and hard cases follow from how each type of model leverages (or doesn't leverage) the intrinsic structure of the data. Furthermore, DCAR shows a particularly notable accuracy advantage on events where humans have more difficulty classifying the videos, i.e., events with lower mean annotator confidence., Comment: An abbreviated version of this paper will be published in ACM Multimedia 2016 more...

Direct imaging of Earth-like exoplanets requires high contrast imaging capability and high angular resolution. Primary mirror segmentation is a key technological solution for large-aperture telescopes because it opens the path toward significantly increasing the angular resolution. The segments are kept aligned by an active optics system that must reduce segment misalignments below tens of nm RMS to achieve the high optical quality required for astronomical science programs. The development of cophasing techniques is mandatory for the next generation of space- and ground-based segmented telescopes, which both share the need for increasing spatial resolution. We propose a new focal plane cophasing sensor that exploits the scientific image of a coronagraphic instrument to retrieve simultaneously piston and tip-tilt misalignments. The self-coherent camera phasing sensor (SCC-PS) adequately combines the SCC properties to segmented telescope architectures with adapted segment misalignment estimators and image processing. An overview of the system architecture, and a thorough performance and sensitivity analysis, including a closed-loop efficiency, are presented by means of numerical simulations. The SCC-PS estimates simultaneously piston and tip-tilt misalignments and corrects them in closed-loop operation. The SCC-PS does not require any a priori on the signal at the segment boundaries or any dedicated optical path. It has a moderate sensitivity to misalignments, virtually none to pupil shear, and is insensitive to segment gaps and edge effects. Primary mirror phasing can be achieved with bright natural guide star. The SCC-PS is a noninvasive concept and an efficient phasing sensor from the image domain. It is an attractive candidate for segment cophasing at the instrument level or alternatively at the telescope level, as usually envisioned in current space- and ground-based observatories., Comment: 10 pages. 9 figures. Accepted for publication in Astronomy & Astrophysics more...

The YLI Multimedia Event Detection corpus is a public-domain index of videos with annotations and computed features, specialized for research in multimedia event detection (MED), i.e., automatically identifying what's happening in a video by analyzing the audio and visual content. The videos indexed in the YLI-MED corpus are a subset of the larger YLI feature corpus, which is being developed by the International Computer Science Institute and Lawrence Livermore National Laboratory based on the Yahoo Flickr Creative Commons 100 Million (YFCC100M) dataset. The videos in YLI-MED are categorized as depicting one of ten target events, or no target event, and are annotated for additional attributes like language spoken and whether the video has a musical score. The annotations also include degree of annotator agreement and average annotator confidence scores for the event categorization of each video. Version 1.0 of YLI-MED includes 1823 "positive" videos that depict the target events and 48,138 "negative" videos, as well as 177 supplementary videos that are similar to event videos but are not positive examples. Our goal in producing YLI-MED is to be as open about our data and procedures as possible. This report describes the procedures used to collect the corpus; gives detailed descriptive statistics about the corpus makeup (and how video attributes affected annotators' judgments); discusses possible biases in the corpus introduced by our procedural choices and compares it with the most similar existing dataset, TRECVID MED's HAVIC corpus; and gives an overview of our future plans for expanding the annotation effort., Comment: 47 pages; 3 figures; 25 tables. Also published as ICSI Technical Report TR-15-001 more...