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In his study of generalised permutahedra, Postnikov considered the mixed volumes of hypersimplices, giving rise to the family of mixed Eulerian numbers. It comprises usual Eulerian numbers, binomial coefficients, Catalan numbers, and the large family of hit numbers. Nadeau and Tewari further gave a polynomial refinement of these, the remixed Eulerian numbers, which recover the natural $q$-analogs of these special families. Using a probabilistic model, we give several formulas for remixed Eulerian numbers for certain subfamilies, extending the known formulas for $q$-hit numbers due to Garsia and Remmel., Comment: 19 pages, 10 figures

The innermost portions of the Milky Way's stellar halo have avoided scrutiny until recently. The lack of wide-area survey data, made it difficult to reconstruct an uninterrupted view of the density distribution of the metal-poor stars inside the Solar radius. In this study, we utilize red giant branch (RGB) stars from Gaia, with metallicities estimated using spectro-photometry from Gaia Data Release 3. Accounting for Gaia's selection function, we examine the spatial distribution of metal-poor ([M/H]<-1.3) RGB stars, from the Galactic centre (r~1 kpc) out to beyond the Solar radius (r~18 kpc). Our best-fitting single-component cored power-law model shows a vertical flattening of ~0.5 and a slope -3.4, consistent with previous studies. Motivated by the mounting evidence for two distinct stellar populations in the inner halo, we additionally test a range of two-component models. One of the components models the tidal debris from the Gaia Sausage/Enceladus merger, while the other captures the Aurora population -- stars that predate the Galactic disk formation. Our best-fit two-component model suggests that both populations contribute equally around the Solar radius, but Aurora dominates the inner halo with a steeper power-law index of -4.5, in agreement with the nitrogen-rich star distribution measured by Horta et al. (2021)., Comment: Submitted to MNRAS

We present an exploration of the Milky Way's structural parameters using an all-sky sample of RC giants to map the stellar density from the inner to the outer parts of the Galactic disc. These evolved giants are considered to be standard candles due to their low intrinsic variance in their absolute luminosities, allowing us to estimate their distances with reasonable confidence. We exploit all-sky photometry from the AllWISE mid-infrared survey and the Gaia survey, along with astrometry from Gaia Data Release 3 and recent 3D extinction maps, to develop a probabilistic scheme in order to select with high confidence \rc{}-like stars. Our curated catalogue contains about 10 million sources, for which we estimate photometric distances based on the WISE $W1$ photometry. We then derive the selection function for our sample, which is the combined selection function of sources with both \gaia{} and \allwise{} photometry. Using the distances and accounting for the full selection function of our observables, we are able to fit a two-disc, multi-parameter model to constrain the scale height (\hz{}), scale-length (\rd{}), flaring, and the relative mass ratios of the two disc components. We illustrate and verify our methodology using mock catalogues of \rc{} stars. We find that the \rc{} population is best described by a flared thin disc with scale length \rd{}=$3.56\pm0.32$ kpc and scale height at the Sun of \hzsun{}=$0.17\pm0.01$ kpc, and a shorter and thicker disc with \rd{}=$2.59\pm0.11$ kpc, \hzsun{}=$0.45\pm0.11$ kpc, with no flare. The thicker disc constitutes 64\% of the \rc{} stellar mass beyond 3 kpc, while the thin disk shows evidence of being warped beyond 9 kpc from the Galactic center. The residuals between the predicted number density of RC stars from our axisymmetric model and the measured counts show possible evidence of a two-armed spiral perturbation in the disc of the Milky Way., Comment: 27 pages, submitted to A&A

The altermagnet candidate Mn5Si3 has attracted wide attention in the context of non-relativistic spin physics, due to its composition of light elements. However, the presumed structure of the altermagnetic phase had yet to be demonstrated. In this study, we demonstrate a hallmark of altermagnetism in Mn5Si3 thin films, namely the three options, or variants, for the checkerboard distribution of the magnetic Mn atoms. The magnetic symmetries were altered by field-rotation of the N\'eel vector along relevant crystal directions, resulting in anomalous Hall effect anisotropy. The experimental results in nanoscale devices were corroborated by a theoretical model involving atomic site dependent anisotropy and bulk Dzyaloshinskii-Moriya interaction for a single variant.

CXOU J005245.0-722844 is an X-ray source in the Small Magellanic Cloud (SMC) that has long been known as a Be/X-ray binary (BeXRB) star, containing an OBe main sequence star and a compact object. In this paper, we report on a new very fast X-ray outburst from CXOU J005245.0-722844. X-ray observations taken by Swift constrain the duration of the outburst to less than 16 days and find that the source reached super-Eddington X-ray luminosities during the initial phases of the eruption. The XRT spectrum of CXOU J005245.0-722844 during this outburst reveals a super-soft X-ray source, best fit by an absorbed thermal blackbody model. Optical and Ultraviolet follow-up observations from the Optical Gravitational Lensing Experiment (OGLE), Asteroid Terrestrial-impact Last Alert System (ATLAS), and Swift identify a brief ~0.5 magnitude optical burst coincident with the X-ray outburst that lasted for less than 7 days. Optical photometry additionally identifies the orbital period of the system to be 17.55 days and identifies a shortening of the period to 17.14 days in the years leading up to the outburst. Optical spectroscopy from the Southern African Large Telescope (SALT) confirms that the optical companion is an early-type OBe star. We conclude from our observations that the compact object in this system is a white dwarf (WD), making this the seventh candidate Be/WD X-ray binary. The X-ray outburst is found to be the result of a very-fast, ultra-luminous nova similar to the outburst of MAXI J0158-744.

Star clusters are among the first celestial objects catalogued by early astronomers. As simple and coeval populations, their study has been instrumental in charting the properties of the Milky Way and providing insight into stellar evolution through the 20th century. Clusters were traditionally spotted as local stellar overdensities in the plane of the sky. In recent decades, for a limited number of nearby clusters, it became possible to identify cluster members through their clustering in proper motion space. With its astrometric data of unprecedented precision, the Gaia mission has completely revolutionised our ability to discover and characterise Milky Way star clusters, to map their large-scale distribution, and to investigate their internal structure. In this review we focus on the population of open clusters, residing in the Galactic disc. We summarise the current state of the Gaia-updated cluster census and studies of young clusters and associations. We discuss recent developments in techniques for cluster detection and age estimation. We also review results enabled by Gaia data concerning the dynamical evolution of gravitationally bound clusters and their stellar inventory., Comment: Accepted review article for New Astronomy Reviews (as part of a Special Issue: "Gaia, the first crop of discoveries")

Brain folding patterns have been reported to carry clinically relevant information. The brain folds mainly during the last trimester of pregnancy, and the process might be durably disturbed by preterm birth. Yet little is known about preterm-specific patterns. In this work, we train a self-supervised model (SimCLR) on the UKBioBank cohort (21070 adults) to represent the right superior temporal sulcus (STS) region and apply it to sulci images of 374 babies from the dHCP database, containing preterms and full-terms, and acquired at 40 weeks post-menstrual age. We find a lower variability in the preterm embeddings, supported by the identification of a knob pattern, missing in the extremely preterm population.

Context. Open clusters provide valuable information on stellar nucleosynthesis and the chemical evolution of the Galactic disc, as their age and distances can be measured more precisely with photometry than for field stars. Aims. Our aim is to study the chemical distribution of the Galactic disc using open clusters by analysing the existence of gradients with Galactocentric distance, azimuth or height from the plane and dependency with age. Methods. High-resolution spectra (R>60 000) of 194 stars belonging to 36 open clusters are used to determine atmospheric parameters and chemical abundances with two independent methods: equivalent widths and spectral synthesis. The sample has been complemented with 63 clusters with high-resolution spectroscopy from literature. Results. We measure local thermodynamic equilibrium abundances for 21 elements: {\alpha} (Mg, Si, Ca, and Ti), odd-Z (Na and Al), Fe-peak (Fe, Sc, V, Cr, Mn, Co, Ni, Cu, and Zn), and neutron-capture (Sr, Y, Zr, Ba, Ce, and Nd). We also provide non-local thermodynamic equilibrium abundances for elements when corrections are available. We find inner disc young clusters enhanced in [Mg/Fe] and [Si/Fe] compared to other clusters of their age. For [Ba/Fe] we report an age trend flattening for older clusters (age<2.5 Ga). The studied elements follow the expected radial gradients as a function of their nucleosynthesis groups, which are significantly steeper for the oldest systems. For the first time, we investigate the existence of an azimuthal gradient, finding some hints of its existence among the old clusters (age>2 Ga).

Gaia can not individually resolve very close binary systems, however, the collected data can still be used to identify them. A powerful indicator of stellar multiplicity is the sources reported Renormalized Unit Weight Error (ruwe), which effectively captures the astrometric deviations from single-source solutions. We aim to characterise the imprints left on ruwe caused by binarity. By flagging potential binary systems based on ruwe, we aim to characterise which of their properties will contribute the most to their detectability. We develop a model to estimate ruwe values for observations of Gaia sources, based on the biases to the single-source astrometric track arising from the presence of an unseen companion. Then, using the recipes from previous GaiaUnlimited selection functions, we estimate the selection probability of sources with high ruwe, and discuss what binary properties contribute to increasing the sources ruwe. We compute the maximum ruwe value which is compatible with single-source solutions as a function of their location on-sky. We see that binary systems selected as sources with a ruwe higher than this sky-varying threshold have a strong detectability window in their orbital period distribution, which peaks at periods equal to the Gaia observation time baseline. We demonstrate how our sky-varying ruwe threshold provides a more complete sample of binary systems when compared to single sky-averaged values by studying the unresolved binary population in the Gaia Catalogue of Nearby Stars. We provide the code and tools used in this study, as well as the sky-varying ruwe threshold through the GaiaUnlimited Python package, Comment: 11 pages, 10 figures. Accepted for publication in A&A

Magnetic skyrmions are topological magnetic textures that hold great promise as nanoscale bits of information in memory and logic devices. Although room-temperature ferromagnetic skyrmions and their current-induced manipulation have been demonstrated, their velocity has been limited to about 100 meters per second. In addition, their dynamics are perturbed by the skyrmion Hall effect, a motion transverse to the current direction caused by the skyrmion topological charge. Here, we show that skyrmions in compensated synthetic antiferromagnets can be moved by current along the current direction at velocities of up to 900 meters per second. This can be explained by the cancellation of the net topological charge leading to a vanishing skyrmion Hall effect. Our results open an important path toward the realization of logic and memory devices based on the fast manipulation of skyrmions in tracks., Comment: The document includes the main text and the supplementary materials. This is the accepted version of the work published in Science, 384, 6693 (2024)

Gravitational waves from black-hole merging events have revealed a population of extra-galactic BHs residing in short-period binaries with masses that are higher than expected based on most stellar evolution models - and also higher than known stellar-origin black holes in our Galaxy. It has been proposed that those high-mass BHs are the remnants of massive metal-poor stars. Gaia astrometry is expected to uncover many Galactic wide-binary systems containing dormant BHs, which may not have been detected before. The study of this population will provide new information on the BH-mass distribution in binaries and shed light on their formation mechanisms and progenitors. As part of the validation efforts in preparation for the fourth Gaia data release (DR4), we analysed the preliminary astrometric binary solutions, obtained by the Gaia Non-Single Star pipeline, to verify their significance and to minimise false-detection rates in high-mass-function orbital solutions. The astrometric binary solution of one source, Gaia BH3, implies the presence of a 32.70 \pm 0.82 M\odot BH in a binary system with a period of 11.6 yr. Gaia radial velocities independently validate the astrometric orbit. Broad-band photometric and spectroscopic data show that the visible component is an old, very metal-poor giant of the Galactic halo, at a distance of 590 pc. The BH in the Gaia BH3 system is more massive than any other Galactic stellar-origin BH known thus far. The low metallicity of the star companion supports the scenario that metal-poor massive stars are progenitors of the high-mass BHs detected by gravitational-wave telescopes. The Galactic orbit of the system and its metallicity indicate that it might belong to the Sequoia halo substructure. Alternatively, and more plausibly, it could belong to the ED-2 stream, which likely originated from a globular cluster that had been disrupted by the Milky Way., Comment: 23 pages, accepted fro publication in A&A Letters. New version with small fixes

Assessing whether a molecule can be synthesised is a primary task in drug discovery. It enables computational chemists to filter for viable compounds or bias molecular generative models. The notion of synthesisability is dynamic as it evolves depending on the availability of key compounds. A common approach in drug discovery involves exploring the chemical space surrounding synthetically-accessible intermediates. This strategy improves the synthesisability of the derived molecules due to the availability of key intermediates. Existing synthesisability scoring methods such as SAScore, SCScore and RAScore, cannot condition on intermediates dynamically. Our approach, Leap, is a GPT-2 model trained on the depth, or longest linear path, of predicted synthesis routes that allows information on the availability of key intermediates to be included at inference time. We show that Leap surpasses all other scoring methods by at least 5% on AUC score when identifying synthesisable molecules, and can successfully adapt predicted scores when presented with a relevant intermediate compound., Comment: New Frontiers of AI for Drug Discovery and Development workshop paper

We report on the discovery of Swift J010902.6-723710, a rare eclipsing Be/X-ray Binary system by the Swift SMC Survey (S-CUBED). Swift J010902.6-723710 was discovered via weekly S-CUBED monitoring observations when it was observed to enter a state of X-ray outburst on 10 October 2023. X-ray emission was found to be modulated by a 182s period. Optical spectroscopy is used to confirm the presence of a highly-inclined circumstellar disk surrounding a B0-0.5Ve optical companion. Historical UV and IR photometry are then used to identify strong eclipse-like features re-occurring in both light curves with a 60.623 day period, which is adopted as the orbital period of the system. Eclipsing behavior is found to be the result of a large accretion disk surrounding the neutron star. Eclipses are produced when the disk passes in front of the OBe companion, blocking light from both the stellar surface and circumstellar disk. This is only the third Be/X-ray Binary to have confirmed eclipses. We note that this rare behavior provides an important opportunity to constrain the physical parameters of a Be/X-ray Binary with greater accuracy than is possible in non-eclipsing systems., Comment: 10 pages, 12 figures. To be published in the Astrophysical Journal Letters

The human cerebral cortex has many bumps and grooves called gyri and sulci. Even though there is a high inter-individual consistency for the main cortical folds, this is not the case when we examine the exact shapes and details of the folding patterns. Because of this complexity, characterizing the cortical folding variability and relating them to subjects' behavioral characteristics or pathologies is still an open scientific problem. Classical approaches include labeling a few specific patterns, either manually or semi-automatically, based on geometric distances, but the recent availability of MRI image datasets of tens of thousands of subjects makes modern deep-learning techniques particularly attractive. Here, we build a self-supervised deep-learning model to detect folding patterns in the cingulate region. We train a contrastive self-supervised model (SimCLR) on both Human Connectome Project (1101 subjects) and UKBioBank (21070 subjects) datasets with topological-based augmentations on the cortical skeletons, which are topological objects that capture the shape of the folds. We explore several backbone architectures (convolutional network, DenseNet, and PointNet) for the SimCLR. For evaluation and testing, we perform a linear classification task on a database manually labeled for the presence of the "double-parallel" folding pattern in the cingulate region, which is related to schizophrenia characteristics. The best model, giving a test AUC of 0.76, is a convolutional network with 6 layers, a 10-dimensional latent space, a linear projection head, and using the branch-clipping augmentation. This is the first time that a self-supervised deep learning model has been applied to cortical skeletons on such a large dataset and quantitatively evaluated. We can now envisage the next step: applying it to other brain regions to detect other biomarkers., Comment: 9 pages, 6 figures, 1 table, SPIE Imaging 2024

The spatial distribution of Galactic stars with different chemical abundances encodes information on the processes that drove the formation and evolution of the Milky Way. Survey selection functions are indispensable for analysing astronomical catalogues produced by large-scale surveys. The use of these selection functions in data modelling is more complex when data from different surveys are to be modelled simultaneously. We introduce a procedure for constructing the selection function of a sample of red clump stars that have parallaxes and elemental abundances from the Gaia mission. We separately constructed the selection function of the APOGEE DR17 red clump stars, which depends on very different observables and has a very different spatial coverage. We combined the two surveys and accounted for their joint selection function to provide strong constraints on the radial and vertical density distribution of mono-abundance populations, with Gaia offering a dense coverage of the solar neighbourhood, while APOGEE reaches larger distances near the Galactic plane. We confirm that the radial density profile steepens with increasing metallicity. The combined sample also indicates a metallicity-dependent flaring of the alpha-poor disc. We provide the code for constructing the Gaia selection function we used in this study through the GaiaUnlimited Python package., Comment: 21 pages, 18 figures, accepted for publication in Astronomy & Astrophysics

Randomizing the mapping of addresses to cache entries has proven to be an effective technique for hardening caches against contention-based attacks like Prime+Prome. While attacks and defenses are still evolving, it is clear that randomized caches significantly increase the security against such attacks. However, one aspect that is missing from most analyses of randomized cache architectures is the choice of the replacement policy. Often, only the random- and LRU replacement policies are investigated. However, LRU is not applicable to randomized caches due to its immense hardware overhead, while the random replacement policy is not ideal from a performance and security perspective. In this paper, we explore replacement policies for randomized caches. We develop two new replacement policies and evaluate a total of five replacement policies regarding their security against Prime+Prune+Probe attackers. Moreover, we analyze the effect of the replacement policy on the system's performance and quantify the introduced hardware overhead. We implement randomized caches with configurable replacement policies in software and hardware using a custom cache simulator, gem5, and the CV32E40P RISC-V core. Among others, we show that the construction of eviction sets with our new policy, VARP-64, requires over 25-times more cache accesses than with the random replacement policy while also enhancing overall performance.

With the unprecedented increase of known star clusters, quick and modern tools are needed for their analysis. In this work, we develop an artificial neural network trained on synthetic clusters to estimate the age, metallicity, extinction, and distance of $Gaia$ open clusters. We implement a novel technique to extract features from the colour-magnitude diagram of clusters by means of the QuadTree tool and we adopt a multi-band approach. We obtain reliable parameters for $\sim 5400$ clusters. We demonstrate the effectiveness of our methodology in accurately determining crucial parameters of $Gaia$ open clusters by performing a comprehensive scientific validation. In particular, with our analysis we have been able to reproduce the Galactic metallicity gradient as it is observed by high-resolution spectroscopic surveys. This demonstrates that our method reliably extracts information on metallicity from colour-magnitude diagrams (CMDs) of stellar clusters. For the sample of clusters studied, we find an intriguing systematic older age compared to previous analyses present in the literature. This work introduces a novel approach to feature extraction using a QuadTree algorithm, effectively tracing sequences in CMDs despite photometric errors and outliers. The adoption of ANNs, rather than Convolutional Neural Networks, maintains the full positional information and improves performance, while also demonstrating the potential for deriving clusters' parameters from simultaneous analysis of multiple photometric bands, beneficial for upcoming telescopes like the Vera Rubin Observatory. The implementation of ANN tools with robust isochrone fit techniques could provide further improvements in the quest for open clusters' parameters., Comment: 24 pages, 15 figures, Accepted in The Astronomical Journal. Temporally, data produced in this work are available at https://phisicslollo0.github.io/cavallo23.html

Within the framework of the first phase of MYRRHA (Multi-purpose hYbrid Research Reactor for High-tech Applications) project, called MINERVA, IJCLab was in charge of a fully equipped Spoke cryomodule prototype development, tested at 2K. It integrates two superconducting single spoke cavities, the RF power couplers and the Cold Tuning Systems associated. On the control side, a MTCA.4-based Low Level Radio Frequency (LLRF) system prototype and the Software/EPICS developments has been realized by IJCLab and the SCK CEN in collaboration with the company IOxOS Technologies. The final version of the global system and the results of the tests at 2K will show with some perspectives., Comment: Poster pr\'esent\'e au LLRF Workshop 2023 (LLRF2023, arXiv : 2310.03199)

Gaia's readout window strategy is challenged by very dense fields in the sky. Therefore, in addition to standard Gaia observations, full Sky Mapper (SM) images were recorded for nine selected regions in the sky. A new software pipeline exploits these Service Interface Function (SIF) images of crowded fields (CFs), making use of the availability of the full two-dimensional (2D) information. This new pipeline produced half a million additional Gaia sources in the region of the omega Centauri ($\omega$ Cen) cluster, which are published with this Focused Product Release. We discuss the dedicated SIF CF data reduction pipeline, validate its data products, and introduce their Gaia archive table. Our aim is to improve the completeness of the {\it Gaia} source inventory in a very dense region in the sky, $\omega$ Cen. An adapted version of {\it Gaia}'s Source Detection and Image Parameter Determination software located sources in the 2D SIF CF images. We validated the results by comparing them to the public {\it Gaia} DR3 catalogue and external Hubble Space Telescope data. With this Focused Product Release, 526\,587 new sources have been added to the {\it Gaia} catalogue in $\omega$ Cen. Apart from positions and brightnesses, the additional catalogue contains parallaxes and proper motions, but no meaningful colour information. While SIF CF source parameters generally have a lower precision than nominal {\it Gaia} sources, in the cluster centre they increase the depth of the combined catalogue by three magnitudes and improve the source density by a factor of ten. This first SIF CF data publication already adds great value to the {\it Gaia} catalogue. It demonstrates what to expect for the fourth {\it Gaia} catalogue, which will contain additional sources for all nine SIF CF regions.

One of the most exciting applications of artificial intelligence (AI) is automated scientific discovery based on previously amassed data, coupled with restrictions provided by known physical principles, including symmetries and conservation laws. Such automated hypothesis creation and verification can assist scientists in studying complex phenomena, where traditional physical intuition may fail. Here we develop a platform based on a generalized Onsager principle to learn macroscopic dynamical descriptions of arbitrary stochastic dissipative systems directly from observations of their microscopic trajectories. Our method simultaneously constructs reduced thermodynamic coordinates and interprets the dynamics on these coordinates. We demonstrate its effectiveness by studying theoretically and validating experimentally the stretching of long polymer chains in an externally applied field. Specifically, we learn three interpretable thermodynamic coordinates and build a dynamical landscape of polymer stretching, including the identification of stable and transition states and the control of the stretching rate. Our general methodology can be used to address a wide range of scientific and technological applications., Comment: Fix figure visibility issue

Magnetic skyrmions are topological spin textures which are envisioned as nanometre scale information carriers in magnetic memory and logic devices. The recent demonstration of room temperature stabilization of skyrmions and their current induced manipulation in industry compatible ultrathin films were first steps towards the realisation of such devices. However, important challenges remain regarding the electrical detection and the low-power nucleation of skyrmions, which are required for the read and write operations. Here, we demonstrate, using operando magnetic microscopy experiments, the electrical detection of a single magnetic skyrmion in a magnetic tunnel junction (MTJ) and its nucleation and annihilation by gate voltage via voltage control of magnetic anisotropy. The nucleated skyrmion can be further manipulated by both gate voltage and external magnetic field, leading to tunable intermediate resistance states. Our results unambiguously demonstrate the readout and voltage controlled write operations in a single MTJ device, which is a major milestone for low power skyrmion based technologies.

We performed spin-, time- and angle-resolved extreme ultraviolet photoemission spectroscopy (STARPES) of excitons prepared by photoexcitation of inversion-symmetric 2H-WSe$_2$ with circularly polarized light. The very short probing depth of XUV photoemission permits selective measurement of photoelectrons originating from the top-most WSe$_2$ layer, allowing for direct measurement of hidden spin polarization of bright and momentum-forbidden dark excitons. Our results reveal efficient chiroptical control of bright excitons' hidden spin polarization. Following optical photoexcitation, intervalley scattering between nonequivalent K-K' valleys leads to a decay of bright excitons' hidden spin polarization. Conversely, the ultrafast formation of momentum-forbidden dark excitons acts as a local spin polarization reservoir, which could be used for spin injection in van der Waals heterostructures involving multilayer transition metal dichalcogenides.

We aim to contribute to the folklore of function spaces on Lipschitz domains. We prove the boundedness of the trace operator for homogeneous Sobolev and Besov spaces on a special Lipschitz domain with sharp regularity. To achieve this, we provide appropriate definitions and properties, ensuring our construction of these spaces is suitable for non-linear partial differential equations and boundary value problems. The trace theorem holds with the sharp range $s \in (\frac{1}{p}, 1 + \frac{1}{p})$. While the case of inhomogeneous function spaces is well-known, the case of homogeneous function spaces appears to be new, even for a smooth half-space. We refine several arguments from a previous paper on function spaces on the half-space and include a treatment for the endpoint cases $p=1$ and $p=+\infty$., Comment: The paper has been thoroughly revised. The main results are now valid even in the absence of completeness of the normed spaces, and there is also a study of the endpoint cases $p=1$ and $p=+\infty$. For the reader's convenience, an appendix has been added that briefly reviews a few known facts. Importantly, Part B of the Appendix contains few results on the interpolation of non-complete spaces. To conduct an in-depth study, the preliminary section contains refined and sharpened results for the homogeneous function spaces on $\mathbb{R}^n$.70 pages. 3 Figures. Comments are welcome.This work was partially supported by the ANR project RAGE ANR-18-CE40-0012

In this work, we present an automated platform for trapping and stretching individual micro- and nanoscale objects in solution using electrokinetic forces. The platform can trap objects at the stagnation point of a planar elongational electrokinetic field for long time scales, as demonstrated by the trapping of ~100 nanometer polystyrene beads and DNA molecules for minutes, with a standard deviation in displacement from the trap center < 1 micrometer. This capability enables the stretching of deformable nanoscale objects in a high-throughput fashion, as illustrated by the stretching of more than 400 DNA molecules within ~4 hours. The flexibility of the electrokinetic stretcher opens up numerous possibilities for contact-free manipulation, with size-based sorting of DNA molecules performed as an example. The platform described provides an automated, high-throughput method to track and manipulate objects for real-time studies of micro- and nanoscale systems., Comment: 9 pages, 7 figures

Gaia EDR3 has provided unprecedented data that generate a lot of interest in the astrophysical community, despite the fact that systematics affect the reported parallaxes at the level of ~ 10 muas. Independent distance measurements are available from asteroseismology of red-giant stars with measurable parallaxes, whose magnitude and colour ranges more closely reflect those of other stars of interest. In this paper, we determine distances to nearly 12,500 red-giant branch and red clump stars observed by Kepler, K2, and TESS. This is done via a grid-based modelling method, where global asteroseismic observables, constraints on the photospheric chemical composition, and on the unreddened photometry are used as observational inputs. This large catalogue of asteroseismic distances allows us to provide a first comparison with Gaia EDR3 parallaxes. Offset values estimated with asteroseismology show no clear trend with ecliptic latitude or magnitude, and the trend whereby they increase (in absolute terms) as we move towards redder colours is dominated by the brightest stars. The correction model proposed by Lindegren et al. (2021) is not suitable for all the fields considered in this study. We find a good agreement between asteroseismic results and model predictions of the red clump magnitude. We discuss possible trends with the Gaia scan law statistics, and show that two magnitude regimes exist where either asteroseismology or Gaia provides the best precision in parallax., Comment: 11 pages, 8 figures, Accepted for publication in A&A