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This paper reports on the spatial and temporal resolutions of an RSD 450 microns pitch pixels array measured at the DESY test beam facility. RSDs, Resistive Silicon Detectors, also known as AC-LGAD, achieve excellent position and temporal resolution by exploiting charge sharing among neighboring electrodes. The RSD matrix used in this study is part of the second FBK RSD production, RSD2, and it is composed of 450 microns pitch pixel with cross-shaped electrodes. A 7-pixel matrix was read out by the FAST2 ASIC, a 16-channel amplifier fully custom ASIC developed by INFN Torino using the 110 nm CMOS technology. The total area covered by the matrix is about 1.5 mm$^2$. The position resolution reached in this test is 15 microns, about 4\% of the pitch. The temporal resolution achieved in this work is 60 ps, dominated by the FAST2 resolution. The work also demonstrates that RSD sensors with cross-shaped electrodes achieve 100% fill factor and homogenous resolutions over the whole matrix surface, making them a suitable choice for 4D tracking applications., Comment: 33 pages, 21 figures

The reverse engineering of a complex mixture, regardless of its nature, has become significant today. Being able to quickly assess the potential toxicity of new commercial products in relation to the environment presents a genuine analytical challenge. The development of digital tools (databases, chemometrics, machine learning, etc.) and analytical techniques (Raman spectroscopy, NIR spectroscopy, mass spectrometry, etc.) will allow for the identification of potential toxic molecules. In this article, we use the example of detergent products, whose composition can prove dangerous to humans or the environment, necessitating precise identification and quantification for quality control and regulation purposes. The combination of various digital tools (spectral database, mixture database, experimental design, Chemometrics / Machine Learning algorithm{\ldots}) together with different sample preparation methods (raw sample, or several concentrated / diluted samples) Raman spectroscopy, has enabled the identification of the mixture's constituents and an estimation of its composition. Implementing such strategies across different analytical tools can result in time savings for pollutant identification and contamination assessment in various matrices. This strategy is also applicable in the industrial sector for product or raw material control, as well as for quality control purposes.

Let $Y$ be a smooth projective variety of dimension $n \geq 2$ endowed with a finite morphism $\phi:Y \to \mathbb P^n$ of degree $3$, and suppose that $Y$, polarized by some ample line bundle, is a scroll over a smooth variety $X$ of dimension $m$. Then $n \leq 3$ and either $m=1$ or $2$. When $m=1$, a complete description of the few varieties $Y$ satisfying these conditions is provided. When $m=2$, various restrictions are discussed showing that in several instances the possibilities for such a $Y$ reduce to the single case of the Segre product $\mathbb P^2 \times \mathbb P^1$. This happens, in particular, if $Y$ is a Fano threefold as well as if the base surface $X$ is $\mathbb P^2$.

Resonant metasurfaces are of paramount importance in addressing the growing demand for reduced thickness and complexity, while ensuring high optical efficiency. This becomes particularly crucial in overcoming fabrication challenges associated with high aspect ratio structures, thereby enabling seamless integration of metasurfaces with electronic components at an advanced level. However, traditional design approaches relying on lookup tables and local field approximations often fail to achieve optimal performance, especially for nonlocal resonant metasurfaces. In this study, we investigate the use of statistical learning optimization techniques for nonlocal resonant metasurfaces, with a specific emphasis on the role of near-field coupling in wavefront shaping beyond single unit cell simulations. Our study achieves significant advancements in the design of resonant metasurfaces. For transmission-based metasurfaces, a beam steering design outperforms the classical design by achieving an impressive efficiency of 80\% compared to the previous 23%. Additionally, our optimized extended depth-of-focus (EDOF) metalens yields a remarkable five-fold increase in focal depth, a four-fold enhancement in focusing power compared to conventional designs and an optical resolution superior to 600 cycle/mm across the focus region. Moreover, our study demonstrates remarkable performance with a wavelength-selected beam steering metagrating in reflection, achieving exceptional efficiency surpassing 85\%. This far outperforms classical gradient phase distribution approaches, emphasizing the immense potential for groundbreaking applications in the field of resonant metasurfaces.

We introduce a novel technique for designing color filter metasurfaces using a data-driven approach based on deep learning. Our innovative approach employs inverse design principles to identify highly efficient designs that outperform all the configurations in the dataset, which consists of 585 distinct geometries solely. By combining Multi-Valued Artificial Neural Networks and back-propagation optimization, we overcome the limitations of previous approaches, such as poor performance due to extrapolation and undesired local minima. Consequently, we successfully create reliable and highly efficient configurations for metasurface color filters capable of producing exceptionally vivid colors that go beyond the sRGB gamut. Furthermore, our deep learning technique can be extended to design various pixellated metasurface configurations with different functionalities., Comment: To be published. 25 Pages, 17 Figures

The purpose of this note is to extend the divergences analyzed in a previous work by application of the Deformed Logarithm in its most general form. In a study on entropic divergences, we have analyzed the different forms of the deformed logarithm and their applications to this type of divergence. A very general form of the deformed logarithm has been highlighted; it allows us to group the different expressions of the deformed logarithm under a unique form which includes all the others. Beyond the applications linked to the divergences based on entropy, we propose here to extend the classical divergences by application of the generalized deformed Logarithm., Comment: arXiv admin note: text overlap with arXiv:2109.12895

Breast cancer is one of the most prevalent cancers worldwide and pathologists are closely involved in establishing a diagnosis. Tools to assist in making a diagnosis are required to manage the increasing workload. In this context, artificial intelligence (AI) and deep-learning based tools may be used in daily pathology practice. However, it is challenging to develop fast and reliable algorithms that can be trusted by practitioners, whatever the medical center. We describe a patch-based algorithm that incorporates a convolutional neural network to detect and locate invasive carcinoma on breast whole-slide images. The network was trained on a dataset extracted from a reference acquisition center. We then performed a calibration step based on transfer learning to maintain the performance when translating on a new target acquisition center by using a limited amount of additional training data. Performance was evaluated using classical binary measures (accuracy, recall, precision) for both centers (referred to as test reference dataset and test target dataset) and at two levels: patch and slide level. At patch level, accuracy, recall, and precision of the model on the reference and target test sets were 92.1\% and 96.3\%, 95\% and 87.8\%, and 73.9\% and 70.6\%, respectively. At slide level, accuracy, recall, and precision were 97.6\% and 92.0\%, 90.9\% and 100\%, and 100\% and 70.8\% for test sets 1 and 2, respectively. The high performance of the algorithm at both centers shows that the calibration process is efficient. This is performed using limited training data from the new target acquisition center and requires that the model is trained beforehand on a large database from a reference center. This methodology allows the implementation of AI diagnostic tools to help in routine pathology practice.

Two design innovations, low-gain avalanche (Low-Gain Avalance Diode, LGAD) and resistive read-out (Resistive Silicon Detector, RSD), have brought strong performance improvements to silicon sensors. Large signals, due to the added gain mechanism, lead to improved temporal precision, while charge sharing, introduced by resistive read-out, allows for achieving excellent spatial resolution even with large pixels. LGAD- and RSD- based silicon sensors are now adopted, or considered, in several future experiments and are the basis for almost every next 4D-trackers. New results obtained with sensors belonging to the second FBK production of RSD (RSD2) demonstrate how a combined resolution of 30 ps and 30 \microns can be obtained with pixels as large as $1 \times 1 $ mm$^2$., Comment: 8 pages, 7 figures

The basic principle of operation of silicon sensors with resistive read-out is built-in charge sharing. Resistive Silicon Detectors (RSD, also known as AC-LGAD), exploiting the signals seen on the electrodes surrounding the impact point, achieve excellent space and time resolutions even with very large pixels. In this paper, a TCT system using a 1064 nm picosecond laser is used to characterize sensors from the second RSD production at the Fondazione Bruno Kessler. The paper first introduces the parametrization of the errors in the determination of the position and time coordinates in RSD, then outlines the reconstruction method, and finally presents the results. Three different pixel sizes are used in the analysis: 200 x 340, 450 x 450, and 1300 x 1300 microns^2. At gain = 30, the 450 x 450 microns^2 pixel achieves a time jitter of 20 ps and a spatial resolution of 15 microns concurrently, while the 1300 x 1300 microns^2 pixel achieves 30 ps and 30 micron, respectively. The implementation of cross-shaped electrodes improves considerably the response uniformity over the pixel surface., Comment: 28 pages, 23 figures submitted to NIMA

A non-intrusive model order reduction (MOR) method for solving parameterized electromagnetic scattering problems is proposed in this paper. A database collecting snapshots of high-fidelity solutions is built by solving the parameterized time-domain Maxwell equations for some values of the material parameters using a fullwave solver based on a high order discontinuous Galerkin time-domain (DGTD) method. To perform a prior dimensionality reduction, a set of reduced basis (RB) functions are extracted from the database via a two-step proper orthogonal decomposition (POD) method. Projection coefficients of the reduced basis functions are further compressed through a convolutional autoencoder (CAE) network. Singular value decomposition (SVD) is then used to extract the principal components of the reduced-order matrices generated by CAE, and a cubic spline interpolation-based (CSI) approach is employed for approximating the dominating time- and parameter-modes of the reduced-order matrices. The generation of the reduced basis and the training of the CAE and CSI are accomplished in the offline stage, thus the RB solution for given time/parameter values can be quickly recovered via outputs of the interpolation model and decoder network. In particular, the offline and online stages of the proposed RB method are completely decoupled, which ensures the validity of the method. The performance of the proposed CAE-CSI ROM is illustrated with numerical experiments for scattering of a plane wave by a 2-D dielectric disk and a multi-layer heterogeneous medium., Comment: 25 pages, 16 figures

We consider the problem of designing experiments to detect the presence of a specified heteroscedastity in a non-linear Gaussian regression model. In this framework, we focus on the ${\rm D}_s$- and KL-criteria and study their relationship with the noncentrality parameter of the asymptotic chi-squared distribution of a likelihood-based test, for local alternatives. Specifically, we found that when the variance function depends just on one parameter, the two criteria coincide asymptotically and in particular, the ${\rm D}_1$-criterion is proportional to the noncentrality parameter. Differently, if the variance function depends on a vector of parameters, then the KL-optimum design converges to the design that maximizes the noncentrality parameter. Furthermore, we confirm our theoretical findings through a simulation study concerning the computation of asymptotic and exact powers of the log-likelihood ratio statistic.

Let $(X,L)$ be any Fano manifold polarized by a positive multiple of its fundamental divisor $H$. The polynomial defining the Hilbert curve of $(X,L)$ boils down to being the Hilbert polynomial of $(X,H)$, hence it is totally reducible over $\mathbb C$; moreover, some of the linear factors appearing in the factorization have rational coefficients, e.g. if $X$ has index $\geq 2$. It is natural to ask when the same happens for all linear factors. Here the total reducibility over $\mathbb Q$ of the Hilbert polynomial is investigated for three special kinds of Fano manifolds: Fano manifolds of large index, toric Fano manifolds of low dimension, and Fano bundles of low coindex., Comment: 19 pages

This work belongs to the framework of inverse problems with linear model. The resolution of this type of problem consists in minimizing (possibly under constraints) a function of discrepancy between the measurements and a physical model of the considered phenomenon. We will here extend this study to divergence functions based on forms of entropy developed in the field of Statistical Physics. These various forms of entropy are based on "the deformed algebra" [9] and in particularly on the notion of "Deformed Logarithm" [15][9]., Comment: 46 pages

We propose a controllability method for the numerical solution of time-harmonic Maxwell's equations in their first-order formulation. By minimizing a quadratic cost functional, which measures the deviation from periodicity, the controllability method determines iteratively a periodic solution in the time domain. At each conjugate gradient iteration, the gradient of the cost functional is simply computed by running any time-dependent simulation code forward and backward for one period, thus leading to a non-intrusive implementation easily integrated into existing software. Moreover, the proposed algorithm automatically inherits the parallelism, scalability, and low memory footprint of the underlying time-domain solver. Since the time-periodic solution obtained by minimization is not necessarily unique, we apply a cheap post-processing filtering procedure which recovers the time-harmonic solution from any minimizer. Finally, we present a series of numerical examples which show that our algorithm greatly speeds up the convergence towards the desired time-harmonic solution when compared to simply running the time-marching code until the time-harmonic regime is eventually reached.

We consider finite element discretizations of Maxwell's equations coupled with a non-local hydrodynamic Drude model that accurately accounts for electron motions in metallic nanostructures. Specifically, we focus on a posteriori error estimation and mesh adaptivity, which is of particular interest since the electromagnetic field usually exhibits strongly localized features near the interface between metals and their surrounding media. We propose a novel residual-based error estimator that is shown to be reliable and efficient. We also present a set of numerical examples where the estimator drives a mesh adaptive process. These examples highlight the quality of the proposed estimator, and the potential computational savings offered by mesh adaptivity.

Strangeness enhancement and collective flow are considered signatures of the quark gluon plasma formation. These phenomena have been detected not only in relativistic heavy ion collisions but also in high energy, high multiplicity events of proton-proton and proton-nucleus (small systems) scatterings. A universal behavior emerges by considering the parton density in the transverse plane as the dynamical quantity to specify the initial condition of the collisions, which in electron-positron annihilation at the available energies is too low to expect collective effects., Comment: 40th International Conference on High Energy physics - ICHEP2020 July 28 - August 6, 2020 Prague, Czech Republic (virtual meeting)

Strangeness enhancement and collective flow are considered signatures of the quark gluon plasma formation. These phenomena have been detected not only in relativistic heavy ion collisions but also in high energy, high multiplicity events of proton-proton and proton-nucleus ("small systems") scatterings. Indeed, a universal behavior emerges by considering the parton density in the transverse plane as the dynamical quantity to specify the initial condition of the collisions. On the other hand, $e^+ e^-$ annihilation data at LEP and lower energies indicate that there is no strangeness enhancement and no flow-like effect. We show that the parton density in the transverse plane generated in $e^+ e^-$ annihilation at the available energy is too low to expect such effects. The event-by-event multiplicity where strangeness suppression and flow-like phenomenon could show up in $e^+ e^-$ is evaluated.

We study the thermodynamic curvature, $R$, around the chiral phase transition at finite temperature and chemical potential, within the quark-meson model augmented with meson fluctuations. We study the effect of the fluctuations, pions and $\sigma$-meson, on the top of the mean field thermodynamics and how these affect $R$ around the crossover. We find that for small chemical potential the fluctuations enhance the magnitude of $R$, while they do not affect substantially the thermodynamic geometry in the proximity of the critical endpoint. Moreover, in agreement with previous studies we find that $R$ changes sign in the pseudocritical region, suggesting a change of the nature of interactions at the mesoscopic level from statistically repulsive to attractive. Finally, we find that in the critical region around the critical endpoint $|R|$ scales with the correlation volume, $|R| =K\;\xi^3$, with $K = O(1)$, as expected from hyperscaling; far from the critical endpoint the correspondence between $|R|$ and the correlation volume is not as good as the one we have found at large $\mu$, which is not surprising because at small $\mu$ the chiral crossover is quite smooth; nevertheless, we have found that $R$ develops a characteristic peak structure, suggesting that it is still capable to capture the pseudocritical behavior of the condensate.

We present a novel postprocessing technique for a discontinuous Galerkin (DG) discretization of time-dependent Maxwell's equations that we couple with an explicit Runge-Kutta time-marching scheme. The postprocessed electromagnetic field converges one order faster than the unprocessed solution in the H(curl)-norm. The proposed approach is local, in the sense that the enhanced solution is computed independently in each cell of the computational mesh, and at each time step of interest. As a result, it is inexpensive to compute, especially if the region of interest is localized, either in time or space. The key ideas behind this postprocessing technique stem from hybridizable discontinuous Galerkin (HDG) methods, which are equivalent to the analyzed DG scheme for specific choices of penalization parameters. We present several numerical experiments that highlight the superconvergence properties of the postprocessed electromagnetic field approximation.

We study the thermodynamics of spherically symmetric, neutral and non-rotating black holes in conformal (Weyl) gravity. To this end, we apply different methods: (i) the evaluation of the specific heat; (ii) the study of the entropy concavity; (iii) the geometrical approach to thermodynamics known as \textit{thermodynamic geometry}; (iv) the Poincar\'{e} method that relates equilibrium and out-of-equilibrium thermodynamics. We show that the thermodynamic geometry approach can be applied to conformal gravity too, because all the key thermodynamic variables are insensitive to Weyl scaling. The first two methods, (i) and (ii), indicate that the entropy of a de Sitter black hole is always in the interval $2/3\leq S\leq 1$, whereas thermodynamic geometry suggests that, at $S=1$, there is a second order phase transition to an Anti de Sitter black hole. On the other hand, we obtain from the Poincar\'{e} method (iv) that black holes whose entropy is $S < 4/3$ are stable or in a saddle-point, whereas when $S>4/3$ they are always unstable, hence there is no definite answer on whether such transition occurs., Comment: 13 pages, 6 figures

Polarized rational surfaces $(X, \mathcal L)$ of sectional genus two ruled in conics are studied. When they are not minimal, they are described as the blow-up of $\mathbb F_1$ at some points lying on distinct fibers. Ampleness and very ampleness of $\mathcal L$ are studied in terms of their location. When $\mathcal L$ is very ample and there is a line contained in $X$ and transverse to the fibers, the conic fibrations $(X, \mathcal L)$ are classified and a related property concerned with the inflectional locus is discussed., Comment: To appear in Advances in Geometry

In all Countries the political decisions aim to achieve an almost stable configuration with a small number of new infected individuals per day due to Covid-19. When such a condition is reached, the containment effort is usually reduced in favor of a gradual reopening of the social life and of the various economical sectors. However, in this new phase, the infection spread restarts and a quantitative analysis of the regrowth is very useful. We discuss a macroscopic approach which, on the basis of the collected data in the first lockdown, after few days from the beginning of the new phase, outlines different scenarios of the Covid-19 diffusion for longer time. The purpose of this paper is a demonstration-of-concept: one takes simple growth models, considers the available data and shows how the future trend of the spread can be obtained. The method applies a time dependent carrying capacity, analogously to many macroscopic growth laws in biology, economics and population dynamics. The illustrative cases of Singapore, France, Spain and Italy are analyzed.

We aim to investigate variations in the arrival time of coherent stellar pulsations due to the light-travel time effect to test for the presence of sub-stellar companions. Those companions are the key to one possible formation scenario of apparently single sub-dwarf B stars. We made use of an extensive set of ground-based observations of the four large amplitude p-mode pulsators DW Lyn, V1636 Ori, QQ Vir, and V541 Hya. Observations of the TESS space telescope are available on two of the targets. The timing method compares the phase of sinusoidal fits to the full multi-epoch light curves with phases from the fit of a number of subsets of the original time series. Observations of the TESS mission do not sample the pulsations well enough to be useful due to the (currently) fixed two-minute cadence. From the ground-based observations, we infer evolutionary parameters from the arrival times. The residual signals show many statistically significant periodic signals, but no clear evidence for changes in arrival time induced by sub-stellar companions. The signals can be explained partly by mode beating effects. We derive upper limits on companion masses set by the observational campaign., Comment: 22 pages, 23 figures, accepted for publication in A&A

Macroscopic growth laws, solutions of mean field equations, describe in an effective way an underlying complex dynamics. They are applied to study the spreading of infections, as in the case of CoviD-19, where the counting of the cumulated number $N(t)$ of detected infected individuals is a generally accepted, coarse-grain, variable to understand the epidemic phase. However $N(t)$ does not take into account the unknown number of asymptomatic, not detected, cases $A(t)$. Therefore, the question arises if the observed time series of data of $N(t)$ is a reliable tool for monitoring the evolution of the infectious disease. We study a system of coupled differential equations which includes the dynamics of the spreading among symptomatic and asymptomatic individuals and the strong containment effects due to the social isolation. The solution is therefore compared with a macroscopic law for the population $N(t)$ coming from a single, non-linear, differential equation with no explicit reference to $A(t)$, showing the equivalence of the two methods. Indeed, $N(t)$ takes into account a more complex and detailed population dynamics which permits the evaluation of the number of asymptomatic individuals also. The model is then applied to Covid-19 spreading in Italy where a transition from an exponential behavior to a Gompertz growth for $N(t)$ has been observed in more recent data. Then the information contained in the data analysis of $N(t)$ is reliable to understand the epidemic phase, although it does not describe the total infected population. The asymptomatic population is larger than the symptomatic one in the fast growth phase of the spreading.

The multi-index model is a simple yet powerful high-dimensional regression model which circumvents the curse of dimensionality assuming $ \mathbb{E} [ Y | X ] = g(A^\top X) $ for some unknown index space $A$ and link function $g$. In this paper we introduce a method for the estimation of the index space, and study the propagation error of an index space estimate in the regression of the link function. The proposed method approximates the index space by the span of linear regression slope coefficients computed over level sets of the data. Being based on ordinary least squares, our approach is easy to implement and computationally efficient. We prove a tight concentration bound that shows $N^{-1/2}$-convergence, but also faithfully describes the dependence on the chosen partition of level sets, hence giving indications on the hyperparameter tuning. The estimator's competitiveness is confirmed by extensive comparisons with state-of-the-art methods, both on synthetic and real data sets. As a second contribution, we establish minimax optimal generalization bounds for k-nearest neighbors and piecewise polynomial regression when trained on samples projected onto any $N^{-1/2}$-consistent estimate of the index space, thus providing complete and provable estimation of the multi-index model., Comment: 30 pages, 13 figures, 1 table

This book deals with functions allowing to express the dissimilarity (discrepancy) between two data fields or ''divergence functions'' with the aim of applications to linear inverse problems. Most of the divergences found in the litterature are used in the field of information theory to quantify the difference between two probability density functions, that is between positive data whose sum is equal to one. In such context, they take a simplified form that is not adapted to the problems considered here, in which the data fields are non-negative but with a sum not necessarily equal to one. In a systematic way, we reconsider the classical divergences and we give their forms adapted to inverse problems. To this end, we will recall the methods allowing to build such divergences, and propose some generalizations. The resolution of inverse problems implies systematically the minimisation of a divergence between physical measurements and a model depending of the unknown parameters. In the context image reconstruction, the model is generally linear and the constraints that must be taken into account are the non-negativity as well as (if necessary) the sum constraint of the unknown parameters. To take into account in a simple way the sum constraint, we introduce the class of scale invariant or affine invariant divergences. Such divergences remains unchanged when the model parameters are multiplied by a constant positive factor. We show the general properties of the invariance factors, and we give some interesting characteristics of such divergences.An extension of such divergences allows to obtain the property of invariance with respect to both the arguments of the divergences; this characteristic can be used to introduce the smoothness regularization of inverse problems, that is a regularisation in the sense of Tikhonov.We then develop in a last step, minimisation methods of the divergences subject to non-negativity and sum constraints on the solution components. These methods are founded on the Karush-Kuhn-Tucker conditions that must be fulfilled at the optimum. The Tikhonov regularization is considered in these methods.Chapter 11 associated with Appendix 9 deal with the application to the NMF, while Chapter 12 is dedicated to the Blind Deconvolution problem.In these two chapters, the interest of the scale invariant divergences is highlighted.

To evaluate the effectiveness of the containment on the epidemic spreading of the new Coronavirus disease 2019, we carry on an analysis of the time evolution of the infection in a selected number of different Countries, by considering well-known macroscopic growth laws, the Gompertz law, and the logistic law. We also propose here a generalization of Gompertz law. Our data analysis permits an evaluation of the maximum number of infected individuals. The daily data must be compared with the obtained fits, to verify if the spreading is under control. From our analysis it appears that the spreading reached saturation in China, due to the strong containment policy of the national government. In Singapore a large growth rate, recently observed, suggests the start of a new strong spreading. For South Korea and Italy, instead, the next data on new infections will be crucial to understand if the saturation will be reached for lower or higher numbers of infected individuals., Comment: 8 figures

Relying on previous results that link entanglement entropy and parton distribution functions in deep inelastic scattering and focusing on the small Bjorken scaling region we present here indications that gluon shadowing might indeed be explained as due to a depletion of the entanglement entropy between observed and unobserved degrees of freedom per nucleon within a nucleus with respect to the free nucleon case. We apply to gluon shadowing the general Page approach to the calculation of the entanglement entropy in bipartite systems, giving physical motivations of the results., Comment: 7 pages, 5 figures

The single-index model is a statistical model for intrinsic regression where responses are assumed to depend on a single yet unknown linear combination of the predictors, allowing to express the regression function as $ \mathbb{E} [ Y | X ] = f ( \langle v , X \rangle ) $ for some unknown \emph{index} vector $v$ and \emph{link} function $f$. Conditional methods provide a simple and effective approach to estimate $v$ by averaging moments of $X$ conditioned on $Y$, but depend on parameters whose optimal choice is unknown and do not provide generalization bounds on $f$. In this paper we propose a new conditional method converging at $\sqrt{n}$ rate under an explicit parameter characterization. Moreover, we prove that polynomial partitioning estimates achieve the $1$-dimensional min-max rate for regression of H\"older functions when combined to any $\sqrt{n}$-convergent index estimator. Overall this yields an estimator for dimension reduction and regression of single-index models that attains statistical optimality in quasilinear time.

The Profiler of Moon Limb is a recent instrument dedicated to the monitoring of optical turbulence profile of the atmosphere. Fluctuations of the Moon or the Sun limb allow to evaluate the index refraction structure constant C_n^2(h) and the wavefront coherence outer scale L_0(h) as a function of the altitude $h$. The atmosphere is split into 33 layers with an altitude resolution varying from 100m (at the ground) to 2km (in the upper atmosphere). Profiles are obtained every 3mn during daytime and nighttime. We report last advances on the instrument and present some results obtained at the Plateau de Calern (France)., Comment: AO4ELT6, Qu\'ebec, June 2019

Recent experimental results in proton-proton and in proton-nucleus collisions at Large Hadron Collider energies show a strong similarity to those observed in nucleus-nucleus collisions, where the formation of a quark-gluon plasma is expected. We discuss the comparison between small colliding systems and nucleus-nucleus collisions, for: a)~the strangeness suppression factor $\gamma_s$ and yields of multi-strange hadrons; b)~the average transverse momentum, $p_t$, with particular attention to the low $p_t$ region where soft, non-perturbative effects are important; c)~the elliptic flow scaled by the participant eccentricity. The universal behavior in hadronic and nuclear high energy collisions emerges for all these observables in terms of a specific dynamical variable which corresponds to the entropy density of initial system in the collision and which takes into account the transverse size of the initial configuration and its fluctuations., Comment: 5 pages, 4 figures, submitted to journal

We present rotation period measurements for 107 M dwarfs in the mass range $0.15-0.70 M_\odot$ observed within the context of the APACHE photometric survey. We measure rotation periods in the range 0.5-190 days, with the distribution peaking at $\sim$ 30 days. We revise the stellar masses and radii for our sample of rotators by exploiting the Gaia DR2 data. For $\sim 20\%$ of the sample, we compare the photometric rotation periods with those derived from different spectroscopic indicators, finding good correspondence in most cases. We compare our rotation periods distribution to the one obtained by the Kepler survey in the same mass range, and to that derived by the MEarth survey for stars in the mass range $0.07-0.25 M_\odot$. The APACHE and Kepler periods distributions are in good agreement, confirming the reliability of our results, while the APACHE distribution is consistent with the MEarth result only for the older/slow rotators, and in the overlapping mass range of the two surveys. Combining the APACHE/Kepler distribution with the MEarth distribution, we highlight that the rotation period increases with decreasing stellar mass, in agreement with previous work. Our findings also suggest that the spin-down time scale, from fast to slow rotators, changes crossing the fully convective limit at $\approx0.3 M_\odot$ for M dwarfs. The catalogue of 107 rotating M dwarfs presented here is particularly timely, as the stars are prime targets for the potential identification of transiting small planets with TESS and amenable to high-precision mass determination and further atmospheric characterization measurements.

The formalism of Riemannian geometry is applied to study the phase transitions in Nambu -Jona Lasinio (NJL) model. Thermodynamic geometry reliably describes the phase diagram, both in the chiral limit and for finite quark masses. The comparison between the geometrical study of NJL model and of (2+1) Quantum Chromodynamics at high temperature and small baryon density shows a clear connection between chiral symmetry restoration/breaking and deconfinement/confinement regimes.

In dimension $n = 2m-2 \geq 4$ adjunction theoretic scrolls over a smooth $m$-fold may not be classical scrolls, due to the existence of divisorial fibers. A $4$-dimensional scroll $(X,L)$ over $\mathbb P^3$ of this type is considered, and the equation of its Hilbert curve $\Gamma$ is determined in two ways, one of which relies on the fact that $(X,L)$ is at the same time a classical scroll over a threefold $Y \not=\mathbb P^3$. It turns out that $\Gamma$ does not perceive divisorial fibers. The equation we obtain also shows that a question raised in a previous article by Beltrametti, Lanteri and Sommese, has negative answer in general for non-classical scrolls over a $3$-fold. More precisely, the answer for $(X,L)$ is negative or positive according to whether $(X,L)$ is regarded as an adjunction theoretic scroll or as a classical scroll; in other words, it is the answer to this question to distinguish between the existence of jumping fibers or not., Comment: 9 pages

The thermodynamic geometry formalism is applied to strongly interacting matter to estimate the deconfinement temperature. The curved thermodynamic metric for Quantum Chromodynamics (QCD) is evaluated on the basis of lattice data, whereas the hadron resonance gas model is used for the hadronic sector. Since the deconfinement transition is a crossover, the geometric criterion used to define the \mbox{(pseudo-)critical} temperature, as a function of the baryonchemical potential $\mu_B$, is $R(T,\mu_B)=0$, where $R$ is the scalar curvature. The (pseudo-)critical temperature, $T_c$, resulting from QCD thermodynamic geometry is in good agreement with lattice and phenomenological freeze-out temperature estimates. The crossing temperature, $T_h$, evaluated by the hadron resonance gas, which suffers of some model dependence, is larger than $T_c$ (about $20\%$) signaling remnants of confinement above the transition., Comment: 12 pages, 5 figs

The application of Riemannian geometry to the analysis of the equilibrium thermodynamics in Quantum Chromodynamics (QCD) at finite temperature and baryon density gives a new method to evaluate the critical temperature, $T_c$, of the deconfinement transition. In the confined phase, described by the thermodynamic geometry of the Hadron Resonance Gas, the estimate of $T_c$ turns out completely consistent with lattice QCD simulations of the quark-gluon plasma phase if the hadron excluded volume and the interaction effects are taken into account.

The cosmological evolution can be described in terms of directly measurable cosmological scalar parameters (deceleration $q$, jerk $j$, snap $s$, etc...) constructed out of high order derivatives of the scale factor. Their behavior at the critical temperature of the Quantum Chromodynamics (QCD) phase transition in early universe could be a specific tool to study the transition, analogously to the fluctuations of conserved charges in QCD. We analyze the effect of the crossover transition from quarks and gluons to hadrons in early universe on the cosmological scalars and on the gravitational wave spectrum, by using the recent lattice QCD equation of state and including the electroweak degrees of freedom and different models of dark matter. Near the transition the cosmological parameters follow the behavior of QCD trace anomaly and of the speed of sound of the entire system. The effects of deconfinement turn out to be more relevant for the modification of the primordial spectrum of gravitational waves and our complete analysis, based on lattice QCD simulations and on the hadron resonance gas below the critical temperature, refines previous results., Comment: 13 pages,13 figures

Hilbert curves of special varieties like Fano manifolds of low coindex as well as fibrations having such a manifold as general fiber, endowed with appropriate polarizations, are investigated. In particular, all most relevant varieties arising in adjunction theory are characterized in terms of their Hilbert curves., Comment: 29 pages, 3 Tables and 3 Algorithms

V391 Peg (alias HS2201+2610) is a subdwarf B (sdB) pulsating star that shows both p- and g-modes. By studying the arrival times of the p-mode maxima and minima through the O-C method, in a previous article the presence of a planet was inferred with an orbital period of 3.2 yr and a minimum mass of 3.2 M_Jup. Here we present an updated O-C analysis using a larger data set of 1066 hours of photometric time series (~2.5x larger in terms of the number of data points), which covers the period between 1999 and 2012 (compared with 1999-2006 of the previous analysis). Up to the end of 2008, the new O-C diagram of the main pulsation frequency (f1) is compatible with (and improves) the previous two-component solution representing the long-term variation of the pulsation period (parabolic component) and the giant planet (sine wave component). Since 2009, the O-C trend of f1 changes, and the time derivative of the pulsation period (p_dot) passes from positive to negative; the reason of this change of regime is not clear and could be related to nonlinear interactions between different pulsation modes. With the new data, the O-C diagram of the secondary pulsation frequency (f2) continues to show two components (parabola and sine wave), like in the previous analysis. Various solutions are proposed to fit the O-C diagrams of f1 and f2, but in all of them, the sinusoidal components of f1 and f2 differ or at least agree less well than before. The nice agreement found previously was a coincidence due to various small effects that are carefully analysed. Now, with a larger dataset, the presence of a planet is more uncertain and would require confirmation with an independent method. The new data allow us to improve the measurement of p_dot for f1 and f2: using only the data up to the end of 2008, we obtain p_dot_1=(1.34+-0.04)x10**-12 and p_dot_2=(1.62+-0.22)x10**-12 ..., Comment: 13 pages, 11 figures, accepted for publication in Astronomy and Astrophysics

We propose Hybridizable Discontinuous Galerkin (HDG) methods for solving the frequency-domain Maxwell's equations coupled to the Nonlocal Hydrodynamic Drude (NHD) and Generalized Nonlocal Optical Response (GNOR) models, which are employed to describe the optical properties of nano-plasmonic scatterers and waveguides. Brief derivations for both the NHD model and the GNOR model are presented. The formulations of the HDG method are given, in which we introduce two hybrid variables living only on the skeleton of the mesh. The local field solutions are expressed in terms of the hybrid variables in each element. Two conservativity conditions are globally enforced to make the problem solvable and to guarantee the continuity of the tangential component of the electric field and the normal component of the current density. Numerical results show that the proposed HDG methods converge at optimal rate. We benchmark our implementation and demonstrate that the HDG method has the potential to solve complex nanophotonic problems., Comment: 21 pages, 8figures

On a smooth complex projective variety $X$ of dimension $n$, consider an ample vector bundle $\mathcal{E}$ of rank $r \leq n-2$ and an ample line bundle $H$. A numerical character $m_2=m_2(X,\mathcal{E},H)$ of the triplet $(X,\mathcal{E},H)$ is defined, extending the well-known second class of a polarized manifold $(X,H)$, when either $n=2$ or $H$ is very ample. Under some additional assumptions on $\mathcal{F}: = \mathcal{E} \oplus H^{\oplus (n-r-2)}$, triplets $(X,\mathcal{E},H)$ as above whose $m_2$ is small with respect to the invariants $d:=c_{n-2}(\mathcal{F})H^2$ and $g:=1+\frac{1}{2}\big(K_X + c_1(\mathcal{F})+H\big) \cdot c_{n-2}(\mathcal{F}) \cdot H$ are studied and classified., Comment: 23 pages; the final presentation of the main topics has been improved with some changes, especially in Table 1, and some typos have been corrected

The deconfinement transition and the hadronization mechanism at high energy are related to the quark-antiquark string breaking and the corresponding temperature depends on the string tension $\sigma$. In the Unruh scheme of hadron production it turns out $T = \sqrt{\sigma/2\pi}$, with $\sigma \simeq \E$, the vacuum energy density. In heavy ion collisions at lower energy, i.e. large baryonchemical potential, $\mu_B$, the dynamics is dominated by Fermi statistics and baryon repulsion. However one can still consider $\E$ as the relevant physical scale and its evaluation as a function of the baryon density, in a nuclear matter approach, gives dynamical information on the $\mu_B$ dependence of the hadronization temperature and on the value of the critical end point in the $T-\mu_B$ plane., Comment: 8 pages, 6 figures, typos corrections and changes in the figures. In press in PRD

Simulation of wave propagation through complex media relies on proper understanding of the properties of numerical methods when the wavenumber is real and complex. Numerical methods of the Hybrid Discontinuous Galerkin (HDG) type are considered for simulating waves that satisfy the Helmholtz and Maxwell equations. It is shown that these methods, when wrongly used, give rise to singular systems for complex wavenumbers. A sufficient condition on the HDG stabilization parameter for guaranteeing unique solvability of the numerical HDG system, both for Helmholtz and Maxwell systems, is obtained for complex wavenumbers. For real wavenumbers, results from a dispersion analysis are presented. An asymptotic expansion of the dispersion relation, as the number of mesh elements per wave increase, reveal that some choices of the stabilization parameter are better than others. To summarize the findings, there are values of the HDG stabilization parameter that will cause the HDG method to fail for complex wavenumbers. However, this failure is remedied if the real part of the stabilization parameter has the opposite sign of the imaginary part of the wavenumber. When the wavenumber is real, values of the stabilization parameter that asymptotically minimize the HDG wavenumber errors are found on the imaginary axis. Finally, a dispersion analysis of the mixed hybrid Raviart-Thomas method showed that its wavenumber errors are an order smaller than those of the HDG method.

Routinely operating since July 2012, the APACHE survey has celebrated its second birthday. While the main goal of the Project is the detection of transiting planets around a large sample of bright, nearby M dwarfs in the northern hemisphere, the APACHE large photometric database for hundreds of different fields represents a relevant resource to search for and provide a first characterization of new variable stars. We celebrate here the conclusion of the second year of observations by reporting the discovery of 14 new variables., Comment: 25 pages, accepted for publication on The Journal of the American Association of Variable Star Observers (JAVVSO)

We present more than 80 new variable stars discovered during the first observing season of the APACHE survey. APACHE is a project aimed at detecting extrasolar planets transiting nearby, bright M dwarfs by using an array of small-aperture telescopes. Despite the fact that the survey is targeted to a well-defined sample of cool stars, we also reduce and analyze data for all the detected field stars. Since July 2012 dozens of different stellar fields have been monitored, leading to the detection of several variables for which we propose a classification and estimate a period, when a periodicity is evident in the data. Thanks to the SuperWASP public archive, we have also retrieved and analyzed photometric data collected by the SWASP survey, which helped us to refine the classification and the period estimation of many variables found in the APACHE database. Some of the variables present peculiarities and thus are discussed separately., Comment: accepted for publications in Journal of the American Association of Variable Star Observers (JAAVSO), Vol. 42. Typos in Table 1, column "Amplitude": from page 6 to 9 the first digit (equal to the page number) is actually an artifact and must be not considered

This paper addresses the problem of minimizing a convex cost function under non-negativity and equality constraints, with the aim of solving the linear unmixing problem encountered in hyperspectral imagery. This problem can be formulated as a linear regression problem whose regression coefficients (abundances) satisfy sum-to-one and positivity constraints. A normalized scaled gradient iterative method (NSGM) is proposed for estimating the abundances of the linear mixing model. The positivity constraint is ensured by the Karush Kuhn Tucker conditions whereas the sum-to-one constraint is fulfilled by introducing normalized variables in the algorithm. The convergence is ensured by a one-dimensional search of the step size. Note that NSGM can be applied to any convex cost function with non negativity and flux constraints. In order to compare the NSGM with the well-known fully constraint least squares (FCLS) algorithm, this latter is reformulated in term of a penalized function, which reveals its suboptimality. Simulations on synthetic data illustrate the performances of the proposed algorithm in comparison with other unmixing algorithms and, more particulary, demonstrate its efficiency when compared to the popular FCLS. Finally, results on real data are given.