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The proposed Habitable Worlds Observatory is intended to observe the atmospheres of nearby terrestrial exoplanets with a resolution greater than that of any previous instrument. While these observations present a substantial opportunity for astrobiology, they also incur the risk of false positives and false negatives. Here, we explore the use of systems science (in the form of network theory and thermochemical kinetics) to mitigate these risks, and briefly describe the technical specifications HWO would require in order to use these methodologies.

We present numerous aspects of the evolution of the LP 890-9 (SPECULOOS-2/TOI-4306) planetary system, focusing on the likelihood that planet c can support life. We find that the host star reaches the main sequence in 1 Gyr and that planet c lies close to the inner boundary of the habitable zone. We find the magma ocean stage can last up to 50 Myr, remove 8 Earth-oceans of water, and leave up to 2000 bars of oxygen in the atmosphere. However, if the planet forms with a hydrogen envelope as small as 0.1 Earth-masses, no water will be lost during the star's pre-main sequence phase from thermal escape processes. We find that the planets are unlikely to be in a 3:1 mean motion resonance and that both planets tidally circularize within 0.5 Gyr when tidal dissipation is held constant. However, if tidal dissipation is a function of mantle temperature and rheology, then we find that planet c's orbit may require more than 7 Gyr to circularize, during which time tidal heating may reach hundreds of terawatts. We thus conclude that the habitability of planet c depends most strongly on the initial volatile content and internal properties, but no data yet preclude the viability of an active biosphere on the planet., Comment: 16 pages, 9 figures, accepted to PSJ

The penetration of renewable energies requires additional storages to deal with intermittency. Accordingly, there is growing interest in evaluating the opportunity cost (usage value) associated with stored energy in large storages, a cost obtained by solving a multistage stochastic optimization problem. Today, to compute usage values under uncertainties, an adequacy resource problem is solved using stochastic dynamic programming assuming a hazard-decision information structure. This modelling assumes complete knowledge of the coming week uncertainties, which is not adapted to the system operation as the intermittency occurs at smaller timescale. We equip the twotimescale problem with a new information structure considering planning and recourse decisions: decision-hazard-decision. This structure is used to decompose the multistage decision-making process into a nonanticipative planning step in which the on/off decisions for the thermal units are made, and a recourse step in which the power modulation decisions are made once the uncertainties have been disclosed. In a numerical case, we illustrate how usage values are sensitive as how the disclosure of information is modelled.

Radiative transfer (RT) models are critical in the interpretation of exoplanetary spectra, in simulating exoplanet climates and when designing the specifications of future flagship observatories. However, most models differ in methodologies and input data, which can lead to significantly different spectra. In this paper, we present the experimental protocol of the MALBEC (Modeling Atmospheric Lines By the Exoplanet Community) project. MALBEC is an exoplanet model intercomparison project (exoMIP) that belongs to the CUISINES (Climates Using Interactive Suites of Intercomparisons Nested for Exoplanet Studies) framework which aims to provide the exoplanet community with a large and diverse set of comparison and validation of models. The proposed protocol tests include a large set of initial participating RT models, a broad range of atmospheres (from Hot Jupiters to temperate terrestrials) and several observation geometries, which would allow us to quantify and compare the differences between different RT models used by the exoplanetary community. Two types of tests are proposed: transit spectroscopy and direct imaging modeling, with results from the proposed tests to be published in dedicated follow-up papers. To encourage the community to join this comparison effort and as an example, we present simulation results for one specific transit case (GJ-1214 b), in which we find notable differences in how the various codes handle the discretization of the atmospheres (e.g., sub-layering), the treatment of molecular opacities (e.g., correlated-k, line-by-line) and the default spectroscopic repositories generally used by each model (e.g., HITRAN, HITEMP, ExoMol).

The near-term capability to characterize terrestrial exoplanet atmospheres may bring us closer to discovering alien life through atmospheric data. However, remotely detectable candidate biosignature gases are subject to possible false positive signals as they can also be produced abiotically. To distinguish biological, abiotic and anomalous sources of these atmospheric gases, we take a complex systems approach using chemical reaction network analysis of planetary atmospheres. We simulated 30,000 terrestrial atmospheres, organized in two datasets: Archean Earth-like worlds and modern Earth-like worlds. For Archean Earth-like worlds we study cases where CH4 is produced abiotically via serpentinization, biologically via methanogenesis, or from anomalous sources. We also simulate modern Earth-like atmospheres with and without industrial CFC-12. Network properties like mean degree and average shortest path length effectively distinguish scenarios where CH4 is produced from methanogenesis and serpentinization, with biologically driven networks exhibiting higher connectivity and efficiency. Network analysis also distinguishes modern Earth atmospheres with CFC-12 from those without, with industrially polluted networks showing increased mean degree. Using Bayesian analysis, we demonstrate how atmospheric network property statistics can provide stronger confidence for ruling out biological explanations compared to gas abundance statistics alone. Our results confirm how a network theoretic approach allows distinguishing biological, abiotic and anomalous atmospheric drivers, including ruling out life-as-we-know-it as a possible explanation. Developing statistical inference methods for spectral data that incorporate network properties could significantly strengthen future biosignature detection efforts., Comment: 22 pages (including references), 4 figures, 1 table

In this paper, we study functional approximations where we choose the so-called radial basis function method and more specifically, quasi-interpolation. From the various available approaches to the latter, we form new quasi-Lagrange functions when the orders of the singularities of the radial function's Fourier transforms at zero do not match the parity of the dimension of the space, and therefore new expansions and coefficients are needed to overcome this problem. We develop explicit constructions of infinite Fourier expansions that provide these coefficients and make an extensive comparison of the approximation qualities and - with a particular focus - polynomial precision and uniform approximation order of the various formulae. One of the interesting observations concerns the link between algebraic conditions of expansion coefficients and analytic properties of localness and convergence.

We present an atmospheric analysis of LTT 9779 b, a rare planet situated in the hot Neptune desert, that has been observed with HST WFC3 G102 and G141. The combined transmission spectrum, which covers 0.8 - 1.6 $\mu$m, shows a gradual increase in transit depth with wavelength. Our preferred atmospheric model shows evidence for H$_{\rm 2}$O, CO$_{\rm 2}$ and FeH with a significance of 3.1 $\sigma$, 2.4 $\sigma$ and 2.1 $\sigma$, respectively. In an attempt to constrain the rate of atmospheric escape for this planet, we search for the 1.083 $\mu$m Helium line in the G102 data but find no evidence of excess absorption that would indicate an escaping atmosphere using this tracer. We refine the orbital ephemerides of LTT 9779 b using our HST data and observations from TESS, searching for evidence of orbital decay or apsidal precession, which is not found. The phase-curve observation of LTT 9779 b with JWST NIRISS should provide deeper insights into the atmosphere of this planet and the expected atmospheric escape might be detected with further observations concentrated on other tracers such as Lyman $\alpha$., Comment: Accepted for publication in AJ

Certifying the stability of dynamical systems is a central and challenging task in control theory and systems analysis. To tackle these problems we present an algorithmic approach to finding polynomial Lyapunov functions. Our method relies on sums of nonnegative circuit functions (SONC), a certificate of nonnegativity of real polynomials. We show that both the problem of verifying as well as the more difficult task of finding Lyapunov functions can be carried out via relative entropy programming when using SONC certificates. This approach is analogue yet independent to finding Lyapunov functions via sums of squares (SOS) certificates and semidefinite programming. Furthermore, we explore whether using the related, recently introduced DSONC certificate is advantageous compared to SONC for this type of problem. We implemented our results, and present examples to show their applicability., Comment: 24 pages, 2 figures

The paper studies strictly positive definite kernels on compact Riemannian manifolds. We state new conditions to ensure strict positive definiteness for general kernels and kernels with certain convolutional structure. We also state conditions for such kernels on product manifolds. As an example conditions for products of two-point homogeneous spaces are presented., Comment: arXiv admin note: text overlap with arXiv:2005.02798

Circuit polynomials are a certificate of nonnegativity for real polynomials, which can be derived via a generalization of the classical inequality of arithmetic and geometric means. In this article, we show that similarly nonnegativity of symmetric real polynomials can be certified via a generalization of the classical Muirhead inequality. Moreover, we show that a nonnegative symmetric polynomial admits a decomposition into sums of nonnegative circuit polynomials if and only if it satisfies said generalized Muirhead condition. The latter re-proves a result by Moustrou, Naumann, Riener, Theobald, and Verdure for the case of the symmetric group in a shortened and more elementary way., Comment: 16 pages

The next generation of giant ground and space telescopes will have the light-collecting power to detect and characterize potentially habitable terrestrial exoplanets using high-contrast imaging for the first time. This will only be achievable if the performance of Giant Segmented Mirror Telescopes (GSMTs) extreme adaptive optics (ExAO) systems are optimized to their full potential. A key component of an ExAO system is the wavefront sensor (WFS), which measures aberrations from atmospheric turbulence. A common choice in current and next-generation instruments is the pyramid wavefront sensor (PWFS). ExAO systems require high spatial and temporal sampling of wavefronts to optimize performance, and as a result, require large detectors for the WFS. We present a closed-loop testbed demonstration of a three-sided pyramid wavefront sensor (3PWFS) as an alternative to the conventional four-sided pyramid wavefront (4PWFS) sensor for GSMT-ExAO applications on the new Comprehensive Adaptive Optics and Coronagraph Test Instrument (CACTI). The 3PWFS is less sensitive to read noise than the 4PWFS because it uses fewer detector pixels. The 3PWFS has further benefits: a high-quality three-sided pyramid optic is easier to manufacture than a four-sided pyramid. We detail the design of the two components of the CACTI system, the adaptive optics simulator and the PWFS testbed that includes both a 3PWFS and 4PWFS. A preliminary experiment was performed on CACTI to study the performance of the 3PWFS to the 4PWFS in varying strengths of turbulence using both the Raw Intensity and Slopes Map signal processing methods. This experiment was repeated for a modulation radius of 1.6 lambda/D and 3.25 lambda/D. We found that the performance of the two wavefront sensors is comparable if modal loop gains are tuned., Comment: 28 Pages, 15 Figures, and 4 Tables

We demonstrate the integration of micro-electro-mechanical-systems (MEMS) scanning mirrors as active elements for the local optical pumping of ultra-cold atoms in a magneto-optical trap. A pair of MEMS mirrors steer a focused resonant beam through a cloud of trapped atoms shelved in the \textit{F}=1 ground-state of \textsuperscript{87}Rb for spatially-selective fluorescence of the atom cloud. Two-dimensional control is demonstrated by forming geometrical patterns along the imaging axis of the cold atom ensemble. Such control of the atomic ensemble with a microfabricated mirror pair could find applications in single atom selection, local optical pumping and arbitrary cloud shaping. This approach has significant potential for miniaturisation and in creating portable control systems for quantum optic experiments., Comment: 4 pages, 3 figures

We study the $\ell^1$-summability of functions in the $d$-dimensional torus $\mathbb{T}^d$ and so-called $\ell^1$-invariant functions. Those are functions on the torus whose Fourier coefficients depend only on the $\ell^1$-norm of their indices. Such functions are characterized as divided differences that have $\cos \theta_1,\ldots,\cos\theta_d$ as knots for $(\theta_1\,\ldots, \theta_d) \in \mathbb{T}^d$. It leads us to consider the $d$-dimensional Fourier series of univariate B-splines with respect to its knots, which turns out to enjoy a simple bi-orthogonality that can be used to obtain an orthogonal series of the B-spline function.

The development and characterisation of a piezoelectric actuated high-frequency MEMS scanning mirror with on-chip frequency tuning capability is reported. The resonant scanner operates at frequencies in excess of 140 kHz, generating scan angles of 10{\deg} and 6{\deg} for two orthogonal movement modes with 40 V actuation. On-chip frequency tuning is achieved through electrothermal actuators fabricated adjacent to the mirror main suspension. The electrothermal actuators produce a global and local temperature increase which changes the suspension stiffness and therefore the resonant frequency. A resonance frequency tuning range of up to 5.5 kHz is achieved, with tuning dominant on only one of the two orthogonal scan movement modes. This opens the possibility for precise tuning of a 2D Lissajous scan pattern using a single resonant MEMS scanner with dual orthogonal resonant modes producing full frame update rates up to 20 kHz while retaining the full angular range of both resonant movement modes

The "Switchboard benchmark" is a very well-known test set in automatic speech recognition (ASR) research, establishing record-setting performance for systems that claim human-level transcription accuracy. This work highlights lesser-known practical considerations of this evaluation, demonstrating major improvements in word error rate (WER) by correcting the reference transcriptions and deviating from the official scoring methodology. In this more detailed and reproducible scheme, even commercial ASR systems can score below 5% WER and the established record for a research system is lowered to 2.3%. An alternative metric of transcript precision is proposed, which does not penalize deletions and appears to be more discriminating for human vs. machine performance. While commercial ASR systems are still below this threshold, a research system is shown to clearly surpass the accuracy of commercial human speech recognition. This work also explores using standardized scoring tools to compute oracle WER by selecting the best among a list of alternatives. A phrase alternatives representation is compared to utterance-level N-best lists and word-level data structures; using dense lattices and adding out-of-vocabulary words, this achieves an oracle WER of 0.18%., Comment: Submitted to Interspeech 2022

We present sufficient condition for a family of positive definite kernels on a compact two-point homogeneous space to be strictly positive definite based on their representation as a series of spherical harmonics. The family analyzed is a generalization of the isotropic kernels and the case of a real sphere is analyzed in details.

The cone of sums of nonnegative circuits (SONCs) is a subset of the cone of nonnegative polynomials / exponential sums, which has been studied extensively in recent years. In this article, we construct a subset of the SONC cone which we call the DSONC cone. The DSONC cone can be seen as an extension of the dual SONC cone; membership can be tested via linear programming. We show that the DSONC cone is a proper, full-dimensional cone, we provide a description of its extreme rays, and collect several properties that parallel those of the SONC cone. Moreover, we show that functions in the DSONC cone cannot have real zeros, which yields that DSONC cone does not intersect the boundary of the SONC cone. Furthermore, we discuss the intersection of the DSONC cone with the SOS and SDSOS cones. Finally, we show that circuit functions in the boundary of the DSONC cone are determined by points of equilibria, which hence are the analogues to singular points in the primal SONC cone, and relate the DSONC cone to tropical geometry., Comment: 30 pages, 2 figures

We consider the problem of approximating $[0,1]^{d}$-periodic functions by convolution with a scaled Gaussian kernel. We start by establishing convergence rates to functions from periodic Sobolev spaces and we show that the saturation rate is $O(h^{2}),$ where $h$ is the scale of the Gaussian kernel. Taken from a discrete point of view, this result can be interpreted as the accuracy that can be achieved on the uniform grid with spacing $h.$ In the discrete setting, the curse of dimensionality would place severe restrictions on the computation of the approximation. For instance, a spacing of $2^{-n}$ would provide an approximation converging at a rate of $O(2^{-2n})$ but would require $(2^{n}+1)^{d}$ grid points. To overcome this we introduce a sparse grid version of Gaussian convolution approximation, where substantially fewer grid points are required, and show that the sparse grid version delivers a saturation rate of $O(n^{d-1}2^{-2n}).$ This rate is in line with what one would expect in the sparse grid setting (where the full grid error only deteriorates by a factor of order $n^{d-1}$) however the analysis that leads to the result is novel in that it draws on results from the theory of special functions and key observations regarding the form of certain weighted geometric sums.

In this paper we compute the spherical Fourier expansions coefficients for the restriction of the generalised Wendland functions from $d-$dimensional Euclidean space to the (d-1)-dimensional unit sphere. The development required to derive these coefficients relies heavily upon known asymptotic results for hypergeometric functions and the final result shows that they can be expressed in closed form as a multiple of a certain $_{3}F_{2}$ hypergeometric function. Using the closed form expressions we are able to provide the precise asymptotic rates of decay for the spherical Fourier coefficients which we observe have a close connection to the asymptotic decay rate of the corresponding Euclidean Fourier transform.

For ExAO instruments for the Giant Segmented Mirror Telescopes (GSMTs), alternative architectures of WFS are under consideration because there is a tradeoff between detector size, speed, and noise that reduces the performance of GSMT-ExAO wavefront control. One option under consideration for a GSMT-ExAO wavefront sensor is a three-sided PWFS (3PWFS). The 3PWFS creates three copies of the telescope pupil for wavefront sensing, compared to the conventional four-sided PWFS (4PWFS) which uses four pupils. The 3PWFS uses fewer detector pixels than the 4PWFS and should therefore be less sensitive to read noise. Here we develop a mathematical formalism based on the diffraction theory description of the Foucault knife edge test that predicts the intensity pattern after the PWFS. Our formalism allows us to calculate the intensity in the pupil images formed by the PWFS in the presence of phase errors corresponding to arbitrary Fourier modes. We then use the Object Oriented MATLAB Adaptive Optics toolbox (OOMAO) to simulate an end-to-end model of an adaptive optics system using a PWFS with modulation and compare the performance of the 3PWFS to the 4PWFS. In the case of a low read noise detector, the Strehl ratios of the 3PWFS and 4PWFS are within 0.01. When we included higher read noise in the simulation, we found a Strehl ratio gain of 0.036 for the 3PWFS using Raw Intensity over the 4PWFS using Slopes Maps at a stellar magnitude of 10. At the same magnitude, the 4PWFS RI also outperformed the 4PWFS SM, but the gain was only 0.012 Strehl. This is significant because 4PWFS using Slopes Maps is how the PWFS is conventionally used for AO wavefront sensing. We have found that the 3PWFS is a viable wavefront sensor that can fully reconstruct a wavefront and produce a stable closed-loop with correction comparable to that of a 4PWFS, with modestly better performance for high read-noise detectors., Comment: 39 pages, 15 figures

The paper introduces new sufficient conditions of strict positive definiteness for kernels on d-dimensional spheres which are not radially symmetric but possess specific coefficient structures. The results use the series expansion of the kernel in spherical harmonics. The kernels either have a convolutional form or are axially symmetric with respect to one axis. The given results on convolutional kernels generalise the result derived by Chen et al. [8] for radial kernels. Keywords: strictly positive definite kernels, covariance functions, sphere, Comment: arXiv admin note: text overlap with arXiv:2005.02798

The era of atmospheric characterization of terrestrial exoplanets is just around the corner. Modeling prior to observations is crucial in order to predict the observational challenges and to prepare for the data interpretation. This paper presents the report of the TRAPPIST Habitable Atmosphere Intercomparison (THAI) workshop (14-16 September 2020). A review of the climate models and parameterizations of the atmospheric processes on terrestrial exoplanets, model advancements and limitations, as well as direction for future model development was discussed. We hope that this report will be used as a roadmap for future numerical simulations of exoplanet atmospheres and maintaining strong connections to the astronomical community., Comment: Accepted in the AAS Planetary Science Journal (PSJ)

Over the past decades, direct imaging has confirmed the existence of substellar companions (exoplanets or brown dwarfs) on wide orbits (>10 au) from their host stars. To understand their formation and evolution mechanisms, we have initiated in 2015 the SPHERE infrared survey for exoplanets (SHINE), a systematic direct imaging survey of young, nearby stars to explore their demographics.} {We aim to detect and characterize the population of giant planets and brown dwarfs beyond the snow line around young, nearby stars. Combined with the survey completeness, our observations offer the opportunity to constrain the statistical properties (occurrence, mass and orbital distributions, dependency on the stellar mass) of these young giant planets.} {In this study, we present the observing and data analysis strategy, the ranking process of the detected candidates, and the survey performances for a subsample of 150 stars, which are representative of the full SHINE sample. The observations were conducted in an homogeneous way from February 2015 to February 2017 with the dedicated ground-based VLT/SPHERE instrument equipped with the IFS integral field spectrograph and the IRDIS dual-band imager covering a spectral range between 0.9 and 2.3 $\mu$m. We used coronographic, angular and spectral differential imaging techniques to reach the best detection performances for this study down to the planetary mass regime.}

The Ingot wavefront sensor is a novel pupil-plane wavefront sensor, specifically designed to cope with the elongation typical of the extended nature of the Laser Guide Star (LGS). In the framework of the ELT, we propose an optical solution suitable for a Laser launch telescope, located outside the telescope pupil. In this paper, we present the current optical design, based on a reflective roof-shaped prism, which, at the level of the focal plane, splits the light from an LGS producing three beams. The three images of the telescope pupils can be then used for the retrieval of the first derivative of the wavefront. The 3D nature of such a device requires new alignment techniques to be determined theoretically and verified in the real world. A possible fully automated procedure, relying solely on the illumination observed at the three pupils, to align the prism to the image of the LGS is discussed. Careful attention needs to be put both on the telecentricity of the system and on the reference systems of the Ingot adjustments in the 3D space. This is crucial in order to disentangle all the possible misalignment effects. In this context, we devised a test-bench able to reproduce, in a scaled manner, the 3D illumination that the Ingot will face at the ELT, in order to validate the design and to perform preliminary tests of phase retrieval., Comment: 6 pages, 8 figures, AO4ELT6 conference proceeding, http://ao4elt6.copl.ulaval.ca/proceedings.html

Digital contents are typically sold online through centralized and custodian marketplaces, which requires the trading partners to trust a central entity. We present FileBounty, a fair protocol which, assuming the cryptographic hash of the file of interest is known to the buyer, is trust-free and lets a buyer purchase data for a previously agreed monetary amount, while guaranteeing the integrity of the contents. To prevent misbehavior, FileBounty guarantees that any deviation from the expected participants' behavior results in a negative financial payoff; i.e. we show that honest behavior corresponds to a subgame perfect Nash equilibrium. Our novel deposit refunding scheme is resistant to extortion attacks under rational adversaries. If buyer and seller behave honestly, FileBounty's execution requires only three on-chain transactions, while the actual data is exchanged off-chain in an efficient and privacy-preserving manner. We moreover show how FileBounty enables a flexible peer-to-peer setting where multiple parties fairly sell a file to a buyer., Comment: Simon Janin and Kaihua Qin contributed equally to this work

Extremely Large Telescopes have overwhelmingly opted for the Pyramid wavefront sensor (PyWFS) over the more widely used Shack-Hartmann WaveFront Sensor (SHWFS) to perform their Single Conjugate Adaptive Optics (SCAO) mode. The PyWFS, a sensor based on Fourier filtering, has proven to be highly successful in many astronomy applications. However, it exhibits non-linearity behaviors that lead to a reduction of its sensitivity when working with non-zero residual wavefronts. This so-called Optical Gains (OG) effect, degrades the close loop performance of SCAO systems and prevents accurate correction of Non-Common Path Aberrations (NCPA). In this paper, we aim at computing the OG using a fast and agile strategy in order to control the PyWFS measurements in adaptive optics closed loop systems. Using a novel theoretical description of the PyFWS, which is based on a convolutional model, we are able to analytically predict the behavior of the PyWFS in closed-loop operation. This model enables us to explore the impact of residual wavefront error on particular aspects such as sensitivity and associated OG. The proposed method relies on the knowledge of the residual wavefront statistics and enables automatic estimation of the current OG. End-to-End numerical simulations are used to validate our predictions and test the relevance of our approach. We demonstrate, using on non-invasive strategy, that our method provides an accurate estimation of the OG. The model itself only requires AO telemetry data to derive statistical information on atmospheric turbulence. Furthermore, we show that by only using an estimation of the current Fried parameter r_0 and the basic system-level characteristics, OGs can be estimated with an accuracy of less than 10%. Finally, we highlight the importance of OG estimation in the case of NCPA compensation. The proposed method is applied to the PyWFS.

The paper introduces a new characterisation of strictly positive definiteness for kernels on the 2-sphere without assuming the kernel to be radially (isotropic) or axially symmetric. The results use the series expansion of the kernel in spherical harmonics. Then additional sufficient conditions are proven for kernels with a block structure of expansion coefficients. These generalise the result derived by Chen et al. 2003 for radial kernels to non-radial kernels.

Background: Rapid testing for an infection is paramount during a pandemic to prevent continued viral spread and excess morbidity and mortality. This study aimed to determine whether alternative testing strategies based on sample pooling can increase the speed and throughput of screening for SARS-CoV-2. Methods: A mathematical modelling approach was chosen to simulate six different testing strategies based on key input parameters (infection rate, test characteristics, population size, testing capacity etc.). The situations in five countries (US, DE, UK, IT and SG) currently experiencing COVID-19 outbreaks were simulated to reflect a broad variety of population sizes and testing capacities. The primary study outcome measurements that were finalised prior to any data collection were time and number of tests required; number of cases identified; and number of false positives. Findings: The performance of all tested methods depends on the input parameters, i.e. the specific circumstances of a screening campaign. To screen one tenth of each country's population at an infection rate of 1% - e.g. when prioritising frontline medical staff and public workers -, realistic optimised testing strategies enable such a campaign to be completed in ca. 29 days in the US, 71 in the UK, 25 in Singapore, 17 in Italy and 10 in Germany (ca. eight times faster compared to individual testing). When infection rates are considerably lower, or when employing an optimal, yet logistically more complex pooling method, the gains are more pronounced. Pool-based approaches also reduces the number of false positive diagnoses by 50%. Interpretation: The results of this study provide a clear rationale for adoption of pool-based testing strategies to increase speed and throughput of testing for SARS-CoV-2. The current individual testing approach unnecessarily wastes valuable time and resources., Comment: Revision; 16 pages, 3 figures, 2 tables, 2 supplementary figures

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

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

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

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 $\sum\limits_{m=0}^{\infty}a_m m^{\ell}<\infty$.

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

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