Miracle-dz/UniFAR-FTUs huggingface dataset:
Rate of convergence of the Nesterov accelerated gradient method in the subcritical case α ≤ 3

In a Hilbert space setting ℋ, given Φ : ℋ → ℝ a convex continuously differentiable function, and α a positive parameter, we consider the inertial dynamic system with Asymptotic Vanishing Damping (AVD)α ẍ(t) + α/tẋ(t) + ∇Φ(x(t)) = 0. Depending on the value of α with respect to 3, we give a complete picture of the convergence properties as t → +∞ of the trajectories generated by (AVD)α, as well as iterations of the corresponding algorithms. Indeed, as shown by Su-Boyd-Candès, the case α = 3 corresponds to a continuous version of the accelerated gradient method of Nesterov, with the rate of convergence Φ(x(t)) − min Φ = O(t−2) for α ≥ 3. Our main result concerns the subcritical case α ≤ 3, where we show that Φ(x(t)) − min Φ = O(t−⅔α). This overall picture shows a continuous variation of the rate of convergence of the values Φ(x(t)) − minℋ Φ = O(t−p(α)) with respect to α > 0: the coefficient p(α) increases linearly up to 2 when α goes from 0 to 3, then displays a plateau. Then we examine the convergence of trajectories to optimal solutions. As a new result, in the one-dimensional framework, for the critical value α = 3, we prove the convergence of the trajectories. In the second part of this paper, we study the convergence properties of the associated forward-backward inertial algorithms. They aim to solve structured convex minimization problems of the form min {Θ := Φ + Ψ}, with Φ smooth and Ψ nonsmooth. The continuous dynamics serves as a guideline for this study. We obtain a similar rate of convergence for the sequence of iterates (xk): for α ≤ 3 we have Θ(xk) − min Θ = O(k−p) for all p < 2α/3, and for α > 3 Θ(xk) − min Θ = o(k−2). Finally, we show that the results are robust with respect to external perturbations.
Metacalibration: Direct Self-Calibration of Biases in Shear Measurement

One of the primary limiting sources of systematic uncertainty in forthcoming weak lensing measurements is systematic uncertainty in the quantitative relationship between the distortions due to gravitational lensing and the measurable properties of galaxy images. We present a statistically principled, general solution to this problem. Our technique infers multiplicative shear calibration parameters by modifying the actual survey data to simulate the effects of a known shear. It can be applied to any shear estimation method based on weighted averages of galaxy shape measurements, which includes all methods used to date for shear estimation with real data. Use of the real images mitigates uncertainty due to unknown galaxy morphology, which is a serious concern for calibration of shear estimates based on image simulations. We test our results on simulated images from the GREAT3 challenge, and show that the method eliminates calibration biases for several different shape measurement techniques at the level of precision measurable with the GREAT3 simulations (a few tenths of a percent).
Data-Enabled Predictive Control: In the Shallows of the DeePC

We consider the problem of optimal trajectory tracking for unknown systems. A novel data-enabled predictive control (DeePC) algorithm is presented that computes optimal and safe control policies using real-time feedback driving the unknown system along a desired trajectory while satisfying system constraints. Using a finite number of data samples from the unknown system, our proposed algorithm uses a behavioural systems theory approach to learn a non-parametric system model used to predict future trajectories. The DeePC algorithm is shown to be equivalent to the classical and widely adopted Model Predictive Control (MPC) algorithm in the case of deterministic linear time-invariant systems. In the case of nonlinear stochastic systems, we propose regularizations to the DeePC algorithm. Simulations are provided to illustrate performance and compare the algorithm with other methods.
Purification and upgrading biogas from anaerobic digestion using chemical asborption of CO2 with amines in order to produce biomethane as biofuel for vehicles: a pilot-scale study

ABSTRACT Methane from biogas is a promising option for the transition to a circular economic system based on renewable and sustainable energy. Currently, there is a wide variety of technologies capable of efficiently extracting the impurities contained in biogas in order to produce biomethane. In the present study, work was carried out in a pilot plant for cleaning and upgrading real biogas from anaerobic digestion by means of the chemical absorption method. In contrast to other technologies, chemical absorption stands out for having the lowest CH4 losses, which was crucial for this study. The objective was to purify and upgrade the biogas from anaerobic digestion of a WWTP to achieve a high concentration of methane and use it as biofuel in vehicles. The two aqueous solutions used as absorbents were mono-ethanolamine (MEA) and N-methyldiethanolamine (MDEA), both at 20% and 40% concentrations. It was found that the most effective solution was the MEA at 20% concentration, since it has the highest CO2 removal efficiency (94%) and, therefore, CH4 richness (96%). Finally, for every 100 m3 of biomethane generated after the chemical absorption process, 62 Nm3 of biofuel were obtained.
Energy transfer in compressible magnetohydrodynamic turbulence

Magnetic fields, compressibility and turbulence are important factors in many terrestrial and astrophysical processes. While energy dynamics, i.e. how energy is transferred within and between kinetic and magnetic reservoirs, has been previously studied in the context of incompressible magnetohydrodynamic (MHD) turbulence, we extend shell-to-shell energy transfer analysis to the compressible regime. We derive four new transfer functions specifically capturing compressibility effects in the kinetic and magnetic cascade, and capturing energy exchange via magnetic pressure. To illustrate their viability, we perform and analyze four simulations of driven isothermal MHD turbulence in the sub- and supersonic regime with two different codes. On the one hand, our analysis reveals robust characteristics across regime and numerical method. For example, energy transfer between individual scales is local and forward for both cascades with the magnetic cascade being stronger than the kinetic one. Magnetic tension and magnetic pressure related transfers are less local and weaker than the cascades. We find no evidence for significant nonlocal transfer. On the other hand, we show that certain functions, e.g., the compressive component of the magnetic energy cascade, exhibit a more complex behavior that varies both with regime and numerical method. Having established a basis for the analysis in the compressible regime, the method can now be applied to study a broader parameter space.
Detection of Hermitian connections in wave equations with cubic non-linearity

We consider the geometric non-linear inverse problem of recovering a Hermitian connection $A$ from the source-to-solution map of the cubic wave equation $\Box_{A}\phi+\kappa |\phi|^{2}\phi=f$, where $\kappa\neq 0$ and $\Box_{A}$ is the connection wave operator in the Minkowski space $\mathbb{R}^{1+3}$. The equation arises naturally when considering the Yang-Mills-Higgs equations with Mexican hat type potentials. Our proof exploits the microlocal analysis of nonlinear wave interactions, but instead of employing information contained in the geometry of the wave front sets as in previous literature, we study the principal symbols of waves generated by suitable interactions. Moreover, our approach relies on inversion of a novel non-abelian broken light ray transform.
Blue Supergiant X-Ray Binaries in the Nearby Dwarf Galaxy IC 10

In young starburst galaxies, the X-ray population is expected to be dominated by the relics of the most massive and short-lived stars, black hole and neutron-star high-mass X-ray binaries (XRBs). In the closest such galaxy, IC 10, we have made a multi-wavelength census of these objects. Employing a novel statistical correlation technique, we have matched our list of 110 X-ray point sources, derived from a decade of Chandra observations, against published photometric data. We report an 8σ correlation between the celestial coordinates of the two catalogs, with 42 X-ray sources having an optical counterpart. Applying an optical color–magnitude selection to isolate blue supergiant (SG) stars in IC 10, we find 16 matches. Both cases show a statistically significant overabundance versus the expectation value for chance alignments. The blue objects also exhibit systematically higher ratios than other stars in the same magnitude range. Blue SG-XRBs include a major class of progenitors of double-degenerate binaries, hence their numbers are an important factor in modeling the rate of gravitational-wave sources. We suggest that the anomalous features of the IC 10 stellar population are explained if the age of the IC 10 starburst is close to the time of the peak of interaction for massive binaries.
Finite element convergence for the time-dependent Joule heating problem with mixed boundary conditions

We prove strong convergence for a large class of finite element methods for the time-dependent Joule heating problem in three spatial dimensions with mixed boundary conditions on Lipschitz domains. We consider conforming subspaces for the spatial discretization and the backward Euler scheme for the temporal discretization. Furthermore, we prove uniqueness and higher regularity of the solution on creased domains and additional regularity in the interior of the domain. Due to a variational formulation with a cut-off functional, the convergence analysis does not require a discrete maximum principle, permitting approximation spaces suitable for adaptive mesh refinement, responding to the difference in regularity within the domain.
The Effects of Stellar Activity on Optical High-resolution Exoplanet Transmission Spectra

Chromospherically sensitive atomic lines display different spectra in stellar active regions, spots, and the photosphere, raising the possibility that exoplanet transmission spectra are contaminated by the contrast between various portions of the stellar disk. To explore this effect, we performed transit simulations of G-type and K-type stars for the spectral lines Ca ii K at 3933 Å, Na i 5890 Å, H i 6563 Å (Hα), and He i 10830 Å. We find that strong facular emission and large coverage fractions can contribute a non-negligible amount to transmission spectra, especially for Hα, Ca ii K, and Na i D, while spots and filaments are comparatively unimportant. The amount of contamination depends strongly on the location of the active regions and the intrinsic emission strength. In particular, active regions must be concentrated along the transit chord in order to produce a consistent in-transit signal. Mean absorption signatures in Na i and Hα, for example, can reach ≈0.2% and 0.3%, respectively, for transits of active latitudes with line emission similar in strength to moderate solar flares. Transmission spectra of planets transiting active stars, such as HD 189733, are likely contaminated by the contrast effect, although the tight constraints on active region geometry and emission strength make it unlikely that consistent in-transit signatures are due entirely to the contrast effect. He i 10830 Å is not strongly affected and absorption signatures are likely diluted, rather than enhanced, by stellar activity. He i 10830 Å should thus be considered a priority for probing extended atmospheres, even in the case of active stars.
VLTI/MIDI atlas of disks around low- and intermediate-mass young stellar objects

Context. Protoplanetary disks show large diversity regarding their morphology and dust composition. With mid-infrared interferometry the thermal emission of disks can be spatially resolved, and the distribution and properties of the dust within can be studied. Aims. Our aim is to perform a statistical analysis on a large sample of 82 disks around low- and intermediate-mass young stars, based on mid-infrared interferometric observations. We intend to study the distribution of disk sizes, variability, and the silicate dust mineralogy. Methods. Archival mid-infrared interferometric data from the MIDI instrument on the Very Large Telescope Interferometer are homogeneously reduced and calibrated. Geometric disk models are used to fit the observations to get spatial information about the disks. An automatic spectral decomposition pipeline is applied to analyze the shape of the silicate feature. Results. We present the resulting data products in the form of an atlas, containing N band correlated and total spectra, visibilities, and differential phases. The majority of our data can be well fitted with a continuous disk model, except for a few objects, where a gapped model gives a better match. From the mid-infrared size–luminosity relation we find that disks around T Tauri stars are generally colder and more extended with respect to the stellar luminosity than disks around Herbig Ae stars. We find that in the innermost part of the disks (r ≲ 1 au) the silicate feature is generally weaker than in the outer parts, suggesting that in the inner parts the dust is substantially more processed. We analyze stellar multiplicity and find that in two systems (AB Aur and HD 72106) data suggest a new companion or asymmetric inner disk structure. We make predictions for the observability of our objects with the upcoming Multi-AperTure mid-Infrared SpectroScopic Experiment (MATISSE) instrument, supporting the practical preparations of future MATISSE observations of T Tauri stars.
Ineffective Higher Derivative Black Hole Hair

Inspired by the possibility that the Schwarzschild black hole may not be the unique spherically symmetric vacuum solution to generalizations of general relativity, we consider black holes in pure fourth order higher derivative gravity treated as an effective theory. Such solutions may be of interest in addressing the issue of higher derivative hair or during the later stages of black hole evaporation. Non-Schwarzschild solutions have been studied but we have put earlier results on a firmer footing by finding a systematic asymptotic expansion for the black holes and matching them with known numerical solutions obtained by integrating out from the near-horizon region. These asymptotic expansions can be cast in the form of trans-series expansions which we conjecture will be a generic feature of non-Schwarzschild higher derivative black holes. Excitingly we find a new branch of solutions with lower free energy than the Schwarzschild solution, but as found in earlier work, solutions only seem to exist for black holes with large curvatures, meaning that one should not generically neglect even higher derivative corrections. This suggests that one effectively recovers the nonhair theorems in this context.
Ru doping in iron-based pnictides: The "unfolded" dominant role of structural effects for superconductivity

We present an ab initio study of Ru substitution in two different compounds, ${\mathrm{BaFe}}_{2}{\mathrm{As}}_{2}$ and LaFeAsO, pure and F doped. Despite the many similarities among them, Ru substitution has very different effects on these compounds. By means of an unfolding technique, which allows us to trace back the electronic states into the primitive cell of the pure compounds, we are able to disentangle the effects brought by the local structural deformations and by the impurity potential to the states at the Fermi level. Our results are compared with available experiments and show (i) satisfying agreement of the calculated electronic properties with experiments, confirming the presence of a magnetic order on a short-range scale, and (ii) Fermi surfaces strongly dependent on the internal structural parameters, more than on the impurity potential. These results enter a widely discussed field in the literature and provide a better understanding of the role of Ru in iron pnictides: although isovalent to Fe, the Ru-Fe substitution leads to changes in the band structure at the Fermi level mainly related to local structural modifications.
Non-Integer Arrays for Array Signal Processing

Linear arrays with sensors at integer locations are widely used in array signal processing. This paper considers arrays where sensor locations can be rational numbers. It is demonstrated that such rational arrays have some important advantages over integer arrays. For example, they offer more flexibility and reduced DOA estimation error when a limited number of sensors are to be distributed in a fixed aperture. Sparse and coprime rational arrays are introduced to achieve this. Extensive Monte-Carlo simulations demonstrate that rational arrays can perform close to CRB even at low SNR and a small number of snapshots compared to the integer arrays. Furthermore, they can resolve the closely spaced sources and provide smaller MSE for almost all two-DOA configurations. Next, if the signals are impinging from a restricted spatial scope, rational arrays can better utilize this information and place sensors over a larger aperture while still maintaining unique identifiability property. Results on steering vector invertibility of general rational arrays and unique identifiability with rational coprime arrays are provided. In order to do this, some rational extensions of integer number theoretic concepts such as greatest common divisor and coprimality are required, which are introduced as well. The theoretical results are further extended to arbitrary arrays where sensor locations may even be irrational.
A new yield simulator for transiting planets and false positives: application to the Next Generation Transit Survey

We present a yield simulator to predict the number and characteristics of planets, false positives and false alarms in transit surveys. The simulator is based on a galactic model and the planet occurrence rates measured by the Kepler mission. It takes into account the observation window function and measured noise levels of the investigated survey. Additionally, it includes vetting criteria to identify false positives. We apply this simulator to the Next Generation Transit Survey (NGTS), a wide-field survey designed to detect transiting Neptune-sized exoplanets. We find that red noise is the main limitation of NGTS up to 14th magnitude, and that its obtained level determines the expected yield. Assuming a red noise level of 1 mmag, the simulation predicts the following for a four-year survey: 4+-3 Super-Earths, 19+-5 Small Neptunes, 16+-4 Large Neptunes, 55+-8 Saturn-sized planets and 150+-10 Jupiter-sized planets, along with 4688+-45 eclipsing binaries and 843+-75 background eclipsing binaries. We characterize the properties of these objects to enhance the early identification of false positives and discuss follow-up strategies for transiting candidates.
Self-dual Einstein ACH metrics and CR GJMS operators in dimension three

By refining Matsumoto's construction of Einstein ACH metrics, we construct a one parameter family of ACH metrics which solve the Einstein equation to infinite order and have a given three dimensional CR structure at infinity. When the parameter is 0, the metric is self-dual to infinite order. As an application, we give another proof of the fact that three dimensional CR manifolds admit CR invariant powers of the sublaplacian (CR GJMS operators) of all orders, which has been proved by Gover-Graham. We also prove the convergence of the formal solutions when the CR structure is real analytic.
SRF Rearrangements in Soft Tissue Tumors with Muscle Differentiation

The Serum Response Factor (SRF) is a transcription factor that regulates the expression of a wide set of genes involved in cell proliferation, migration, cytoskeletal organization and myogenesis. Accumulating evidence suggests that SRF may play a role in carcinogenesis and tumor progression in various neoplasms, where it is often involved in different fusion events. Here we investigated SRF rearrangements in soft tissue tumors, along with a gene expression profile analysis to gain insight into the oncogenic mechanism driven by SRF fusion. Whole transcriptome analysis of cell lines transiently overexpressing the SRF::E2F1 chimeric transcript uncovered the specific gene expression profile driven by the aberrant gene fusion, including overexpression of SRF-dependent target genes and of signatures related to myogenic commitment, inflammation and immune activation. This result was confirmed by the analysis of two cases of myoepitheliomas harboring SRF::E2F1 fusion with respect to EWSR1-fusion positive tumors. The recognition of the specific gene signature driven by SRF rearrangement in soft tissue tumors could aid the molecular classification of this rare tumor entity and support therapeutic decisions.
Study of the orientation of narrow-line Seyfert I

We study a sample of narrow-line Seyfert 1 galaxies (NLS1) in their optical and radio features to understand the differences between their radio silent, radio-loud, and radio-quiet subclasses. We first show that the different redshift and mass distributions of radio-loud and radio-quiet NLS1s could be ascribed to observational biases. We then present a geometrical model according to which most of the different observational features of radio-loud and radio-quiet NLS1s are ascribed to the orientation of an intrinsically structured jet. We estimate the fraction of intrinsically jetted sources among NLS1s that justifies the observed radio-detected population. Noticeably, under the assumptions of the geometrical model, we derive a fraction of jetted sources significantly larger than in standard AGN.
Friedmann-Lemaitre cosmologies via roulettes and other analytic methods

In this work a series of methods are developed for understanding the Friedmann equation when it is beyond the reach of the Chebyshev theorem. First it will be demonstrated that every solution of the Friedmann equation admits a representation as a roulette such that information on the latter may be used to obtain that for the former. Next the Friedmann equation is integrated for a quadratic equation of state and for the Randall-Sundrum II universe, leading to a harvest of a rich collection of new interesting phenomena. Finally an analytic method is used to isolate the asymptotic behavior of the solutions of the Friedmann equation, when the equation of state is of an extended form which renders the integration impossible, and to establish a universal exponential growth law.
Local Dirichlet forms, Hodge theory, and the Navier-Stokes equations on topologically one-dimensional fractals

We consider finite energy and $L^2$ differential forms associated with strongly local regular Dirichlet forms on compact connected topologically one-dimensional spaces. We introduce notions of local exactness and local harmonicity and prove the Hodge decomposition, which in our context says that the orthogonal complement to the space of all exact 1-forms coincides with the closed span of all locally harmonic 1-forms. Then we introduce a related Hodge Laplacian and define a notion harmonicity for finite energy 1-forms. As as corollary, under a certain capacity-separation assumption, we prove that the space of harmonic 1-forms is nontrivial if and only if the classical \v{C}ech cohomology is nontrivial. In the examples of classical self-similar fractals these spaces typically are either trivial or infinitely dimensional. Finally, we study Navier-Stokes type models and prove that under our assumptions they have only steady state divergence-free solutions. In particular, we solve the existence and uniqueness problem for the Navier-Stokes and Euler equations for a large class of fractals that are topologically one-dimensional but can have arbitrary Hausdorff and spectral dimensions.