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This study introduces a novel frequency-based data-driven controller for adaptive optics, using power spectral density for optimization while ensuring stability criteria. It addresses disturbance rejection, command amplitude constraints and system transfer functions through convex optimization to obtain an optimal control in an infinite input response filter form. Evaluated within the SAXO+ project, it demonstrates efficacy under diverse atmospheric conditions and operational scenarios. The proposed controller is tested in both standard and disentangled adaptive optics schemes, showcasing its adaptability and performance. Experimental validation is conducted using the COMPASS simulation tool, affirming the controller's promise for enhancing adaptive optics systems in real-world applications.

SAXO+ is a planned enhancement of the existing SAXO, the VLT/ SPHERE adaptive optics system, deployed on ESO's Very Large Telescope. This upgrade is designed to significantly enhance the instrument's capacity to detect and analyze young Jupiter-like planets. The pivotal addition in SAXO+ is a second-stage adaptive optics system featuring a dedicated near-infrared pyramid wavefront sensor and a second deformable mirror. This secondary stage is strategically integrated to address any residual wavefront errors persisting after the initial correction performed by the current primary AO loop, SAXO. However, several recent studies clearly showed that in good conditions, even in the current system SAXO, non-common path aberrations (NCPAs) are the limiting factor of the final normalized intensity in focal plane, which is the final metric for ground-based high-contrast instruments. This is likely to be even more so the case with the new AO system, with which the AO residuals will be minimized. Several techniques have already been extensively tested on SPHERE in internal source and/or on-sky and will be presented in this paper. However, the use of a new type of sensor for the second stage, a pyramid wavefront sensor, will likely complicate the correction of these aberrations. Using an end-to-end AO simulation tool, we conducted simulations to gauge the effect of measured SPHERE NCPAs in the coronagraphic image on the second loop system and their correction using focal plane wavefront sensing systems. We finally analyzed how the chosen position of SAXO+ in the beam will impact the evolution of the NCPAs in the new instrument., Comment: 16 pages, 10 figures, submitted to the proceedings of SPIE Astronomical Telescopes + Instrumentation 2024, 13096-357

SPHERE, operating at the VLT since 2014, is currently one of the high-contrast instruments with a higher performance. Its adaptive optics system, known as SAXO, will be upgraded to SAXO+, which features the addition of a second stage of adaptive optics. This stage will use a near-infrared pyramid wavefront sensor to record images of fainter exoplanets around redder stars. In this work, we compare the performance of SAXO and SAXO+. We look for the optimal values of the key system parameters of SAXO+ for various science cases and turbulence conditions. We performed numerical simulations using COMPASS, an end-to-end adaptive optics simulation tool. We simulated perfect coronagraph images of an on-axis point source, and we minimized the residual starlight intensity between 3 and 5 ${\lambda}/D$ as a performance criterion. The explored parameter space includes science cases, turbulence conditions, and key system parameters. In every science case and turbulence condition, SAXO+ reduces the residual starlight intensity inside the correction zone of the second stage by a factor of ten compared to SAXO. The optimal first stage gain is lower for SAXO+ than for SAXO alone. We quantified the gain in performance of SAXO+ when changing the second stage frequency from 2 kHz to 3 kHz, and we conclude that 2 kHz may be sufficient for most realistic conditions. We give the optimal first stage gain as well as the first and second stage frequencies for every seeing, coherence time, and science case. Finally, we find that a 2 ${\lambda_{\mathrm{WFS}}}/D$ pyramid modulation radius is a good trade-off between performance and robustness against varying turbulence conditions. This study shows that the future SAXO+ system will outperform the current SAXO system in all studied cases., Comment: 14 pages, 11 figures

The newly released enrollment data from the National Center on Education Statistics for the 2022-23 school year point to moderate enrollment gains for traditional public schools. The recent enrollment gains though are smaller than the cumulative enrollment losses since 2019-20 and are not uniform. This paper takes stock of enrollment losses today by comparing the distribution of changes in public school enrollment since the COVID-19 pandemic to the distribution of prepandemic changes across the nation. Roughly 59, 69, and 69 percent of small, medium-sized, and large schools, respectively, saw their enrollment decline between 2019-20 and 2022-23. One third of small, medium-sized, and large schools with enrollment declines lost 26, 54, and 96 students or more, respectively (i.e., top third). The share of schools experiencing such declines after COVID-19 is larger than what would be expected based on historical variation for mediumsized and large schools. Urban schools and middle schools are disproportionately represented among schools with enrollment losses in the top third.

SAXO+ is a proposed upgrade to SAXO, the AO system of the SPHERE instrument on the ESO Very Large Telescope. It will improve the capabilities of the instrument for the detection and characterization of young giant planets. It includes a second stage adaptive optics system composed of a dedicated near-infrared wavefront sensor and a deformable mirror. This second stage will remove the residual wavefront errors left by the current primary AO loop (SAXO). This paper focuses on the numerical simulations of the second stage (SAXO+) and concludes on the impact of the main AO parameters used to build the design strategy. Using an end-to-end AO simulation tool (COMPASS), we investigate the impact of several parameters on the performance of the AO system. We measure the performance in minimizing the star residuals in the coronagraphic image. The parameters that we study are : the second stage frequency, the photon flux on each WFS, the first stage gain and the DM number of actuators of the second stage. We show that the performance is improved by a factor 10 with respect to the current AO system (SAXO). The optimal second stage frequency is between 1 and 2 kHz under good observing conditions. In a red star case, the best SAXO+ performance is achieved with a low first stage gain of 0.05, which reduces the first stage rejection., Comment: 10 pages, 8 figures. Submitted to AO4ELT7 conference proceedings

We investigate a class of mass deformations that connect pairs of 2d (0,2) gauge theories associated to different toric Calabi-Yau 4-folds. These deformations are generalizations to 2d of the well-known Klebanov-Witten deformation relating the 4d gauge theories for the C^2/Z_2 x C orbifold and the conifold. We investigate various aspects of these deformations, including their connection to brane brick models and the relation between the change in the geometry and the pattern of symmetry breaking triggered by the deformation. We also explore how the volume of the Sasaki-Einstein 7-manifold at the base of the Calabi-Yau 4-fold varies under deformation, which leads us to conjecture that it quantifies the number of degrees of freedom of the gauge theory and its dependence on the RG scale., Comment: 45 pages, 19 figures, 3 tables

In this paper, we investigate how student enrollment in public schools is different after the COVID-19 pandemic. Over the pandemic--between the 2018-19 and 2021-22 school years--about 12 percent of public elementary schools and 9 percent of middle schools experienced more than a 20 percent decline. This is a significant change from before the pandemic, when about 5 percent of elementary and middle schools saw a 20 percent enrollment decline between 2015-16 and 2018-19. Enrollment declines are widespread but differ substantially across types of schools, locales, and socioeconomic status. The analysis finds that urban districts and high-poverty districts saw larger declines in school enrollment.

SPHERE+ is a proposed upgrade of the SPHERE instrument at the VLT, which is intended to boost the current performances of detection and characterization for exoplanets and disks. SPHERE+ will also serve as a demonstrator for the future planet finder (PCS) of the European ELT. The main science drivers for SPHERE+ are 1/ to access the bulk of the young giant planet population down to the snow line ($3-10$ au), to bridge the gap with complementary techniques (radial velocity, astrometry); 2/ to observe fainter and redder targets in the youngest ($1-10$\,Myr) associations compared to those observed with SPHERE to directly study the formation of giant planets in their birth environment; 3/ to improve the level of characterization of exoplanetary atmospheres by increasing the spectral resolution in order to break degeneracies in giant planet atmosphere models. Achieving these objectives requires to increase the bandwidth of the xAO system (from $\sim$1 to 3\,kHz) as well as the sensitivity in the infrared (2 to 3\,mag). These features will be brought by a second stage AO system optimized in the infrared with a pyramid wavefront sensor. As a new science instrument, a medium resolution integral field spectrograph will provide a spectral resolution from 1000 to 5000 in the J and H bands. This paper gives an overview of the science drivers, requirements and key instrumental trade-off that were done for SPHERE+ to reach the final selected baseline concept., Comment: To appear in the Proceedings of the SPIE Astronomical Telescopes + Instrumentation (2022), 13 pages, 6 figure

For constructing neuronal network models computational neuroscientists have access to wide-ranging anatomical data that nevertheless tend to cover only a fraction of the parameters to be determined. Finding and interpreting the most relevant data, estimating missing values, and combining the data and estimates from various sources into a coherent whole is a daunting task. With this chapter we aim to provide guidance to modelers by describing the main types of anatomical data that may be useful for informing neuronal network models. We further discuss aspects of the underlying experimental techniques relevant to the interpretation of the data, list particularly comprehensive data sets, and describe methods for filling in the gaps in the experimental data. Such methods of `predictive connectomics' estimate connectivity where the data are lacking based on statistical relationships with known quantities. It is instructive, and in certain cases necessary, to use organizational principles that link the plethora of data within a unifying framework where regularities of brain structure can be exploited to inform computational models. In addition, we touch upon the most prominent features of brain organization that are likely to influence predicted neuronal network dynamics, with a focus on the mammalian cerebral cortex. Given the still existing need for modelers to navigate a complex data landscape full of holes and stumbling blocks, it is vital that the field of neuroanatomy is moving toward increasingly systematic data collection, representation, and publication.

Full detector simulation was among the largest CPU consumer in all CERN experiment software stacks for the first two runs of the Large Hadron Collider (LHC). In the early 2010's, the projections were that simulation demands would scale linearly with luminosity increase, compensated only partially by an increase of computing resources. The extension of fast simulation approaches to more use cases, covering a larger fraction of the simulation budget, is only part of the solution due to intrinsic precision limitations. The remainder corresponds to speeding-up the simulation software by several factors, which is out of reach using simple optimizations on the current code base. In this context, the GeantV R&D project was launched, aiming to redesign the legacy particle transport codes in order to make them benefit from fine-grained parallelism features such as vectorization, but also from increased code and data locality. This paper presents extensively the results and achievements of this R&D, as well as the conclusions and lessons learnt from the beta prototype., Comment: 34 pages, 26 figures, 24 tables

Finite volume methods (FVMs) constitute a popular class of methods for the numerical simulation of fluid flows. Among the various components of these methods, the discretisation of the gradient operator has received less attention despite its fundamental importance with regards to the accuracy of the FVM. The most popular gradient schemes are the divergence theorem (DT) (or Green-Gauss) scheme, and the least-squares (LS) scheme. Both are widely believed to be second-order accurate, but the present study shows that in fact the common variant of the DT gradient is second-order accurate only on structured meshes whereas it is zeroth-order accurate on general unstructured meshes, and the LS gradient is second-order and first-order accurate, respectively. This is explained through a theoretical analysis and is confirmed by numerical tests. The schemes are then used within a FVM to solve a simple diffusion equation on unstructured grids generated by several methods; the results reveal that the zeroth-order accuracy of the DT gradient is inherited by the FVM as a whole, and the discretisation error does not decrease with grid refinement. On the other hand, use of the LS gradient leads to second-order accurate results, as does the use of alternative, consistent, DT gradient schemes, including a new iterative scheme that makes the common DT gradient consistent at almost no extra cost. The numerical tests are performed using both an in-house code and the popular public domain PDE solver OpenFOAM., Comment: Minor corrections compared to the previous version

This paper describes a new multilevel procedure that can solve the discrete Navier-Stokes system arising from finite volume discretizations on composite grids, which may consist of more than one level. SIMPLE is used and tested as the smoother, but the multilevel procedure is such that it does not exclude the use of other smoothers. Local refinement is guided by a criterion based on an estimate of the truncation error. The numerical experiments presented test not only the behaviour of the multilevel algebraic solver, but also the efficiency of local refinement based on this particular criterion.

A methodology is proposed for the calculation of the truncation error of finite volume discretisations of the incompressible Navier-Stokes equations on colocated grids. The truncation error is estimated by restricting the solution obtained on a given grid to a coarser grid and calculating the image of the discrete Navier-Stokes operator of the coarse grid on the restricted velocity and pressure field. The proposed methodology is not a new concept but its application to colocated finite volume discretisations of the incompressible Navier-Stokes equations is made possible by the introduction of a variant of the momentum interpolation technique for mass fluxes where the pressure-part of the mass fluxes is not dependent on the coefficients of the linearised momentum equations. The theory presented is supported by a number of numerical experiments. The methodology is developed for two-dimensional flows, but extension to three-dimensional cases should not pose problems.

Local grid refinement aims to optimise the relationship between accuracy of the results and number of grid nodes. In the context of the finite volume method no single local refinement criterion has been globally established as optimum for the selection of the control volumes to subdivide, since it is not easy to associate the discretisation error with an easily computable quantity in each control volume. Often the grid refinement criterion is based on an estimate of the truncation error in each control volume, because the truncation error is a natural measure of the discrepancy between the algebraic finite-volume equations and the original differential equations. However, it is not a straightforward task to associate the truncation error with the optimum grid density because of the complexity of the relationship between truncation and discretisation errors. In the present work several criteria based on a truncation error estimate are tested and compared on a regularised lid-driven cavity case at various Reynolds numbers. It is shown that criteria where the truncation error is weighted by the volume of the grid cells perform better than using just the truncation error as the criterion. Also it is observed that the efficiency of local refinement increases with the Reynolds number. The truncation error is estimated by restricting the solution to a coarser grid and applying the coarse grid discrete operator. The complication that high truncation error develops at grid level interfaces is also investigated and several treatments are tested.

Quantifying global photosynthesis remains a challenge due to a lack of accurate remote sensing proxies. Solar-induced chlorophyll fluorescence (SIF) has been shown to be a good indicator of photosynthetic activity across various spatial scales. However, a global and spatially challenging estimate of terrestrial gross primary production (GPP) based on satellite SIF remains unresolved due to the confounding effects of species-specific physical and physiological traits and external factors, such as canopy structure or photosynthetic pathway (C3orC4). Here we analyze an ensemble of far-red SIF data from OCO-2 satellite and ground observations at multiple sites, using the spectral invariant theory to reduce the effects of canopy structure and to retrieve a structure-corrected total canopy SIF emission (SIF total). We find that the relationships between observed canopy-leavingSIF and ecosystem GPP vary significantly among biomes. In contrast, the relationships between SIF total and GPP converge around two unique models, one for C3and one for C4plants. We show that the two single empirical models can be used to globally scale satellite SIF observations to terrestrial GPP. We obtain an independent estimate of global terrestrial GPP of 129.56 ± 6.54 PgC/year for the 2015–2017 period, which is consistent with the state-of-the-art data- and process-oriented models. The new GPP product shows improved sensitivity to previously undetected ‘hotspots’ of productivity, being able to resolve the double-peak in GPP due to rotational cropping systems. We suggest that the direct scheme to estimate GPP presented here, which is based on satelliteSIF, may open up new possibilities to resolve the dynamics of global terrestrial GPP across space and time.

Remote sensing of solar-induced chlorophyll fluorescence (SIF) is a rapidly advancing front in terrestrial vegetation science, with emerging capability in space-based methodologies and diverse application prospects. Although remote sensing of SIF – especially from space – is seen as a contemporary new specialty for terrestrial plants, it is founded upon a multi-decadal history of research, applications, and sensor developments in active and passive sensing of chlorophyll fluorescence. Current technical capabilities allow SIF to be measured across a range of biological, spatial, and temporal scales. As an optical signal, SIF may be assessed remotely using highly-resolved spectral sensors and state-of-the-art algorithms to distinguish the emission from reflected and/or scattered ambient light. Because the red to far-red SIF emission is detectable non-invasively, it may be sampled repeatedly to acquire spatio-temporally explicit information about photosynthetic light responses and steady-state behaviour in vegetation. Progress in this field is accelerating with innovative sensor developments, retrieval methods, and modelling advances. This review distills the historical and current developments spanning the last several decades. It highlights SIF heritage and complementarity within the broader field of fluorescence science, the maturation of physiological and radiative transfer modelling, SIF signal retrieval strategies, techniques for field and airborne sensing, advances in satellite-based systems, and applications of these capabilities in evaluation of photosynthesis and stress effects. Progress, challenges, and future directions are considered for this unique avenue of remote sensing.

The Fluorescence Explorer (FLEX) mission has been recently selected as the 8th Earth Explorer by the European Space Agency (ESA). It will be the first mission specifically designed to measure from space vegetation fluorescence emission, by making use of very high spectral resolution imaging spectroscopy techniques. Vegetation fluorescence is the best proxy to actual vegetation photosynthesis which can be measurable from space, allowing an improved quantification of vegetation carbon assimilation and vegetation stress conditions, thus having key relevance for global mapping of ecosystems dynamics and aspects related with agricultural production and food security. The FLEX mission carries the FLORIS spectrometer, with a spectral resolution in the range of 0.3 nm, and is designed to fly in tandem with Copernicus Sentinel-3, in order to provide all the necessary spectral / angular information to disentangle emitted fluorescence from reflected radiance, and to allow proper interpretation of the observed fluorescence spatial and temporal dynamics.