Search

This paper deals with the control of a kind of turbulent flows. We consider a simplified k-e model with distributed controls, locally supported in space. We proof that the system is partially locally null-controllable, in the sense that the velocity field can be driven exactly to zero if the initial state is small enough. The proof relies on an argument where we have concatenated several techniques: fixed-point formulation, linearization, energy and Carleman estimates, local inversion, etc. Ths result can be viewed as a nontrivial step towards the control of turbulent fluids., Comment: Partial null controllability for Nonlinear parabolic PDEs using Carleman estimates in Turbulence models

Fog computing can provide computational resources and low-latency communication at the network edge. But with it comes uncertainties that must be managed in order to guarantee Service Level Agreements. Service observability can help the environment better deal with uncertainties, delivering relevant and up-to-date information in a timely manner to support decision making. Observability is considered a superset of monitoring since it uses not only performance metrics, but also other instrumentation domains such as logs and traces. However, as Fog Computing is typically characterised by resource-constrained nodes and network uncertainties, increasing observability in fog can be risky due to the additional load injected into a restricted environment. There is no work in the literature that evaluated fog observability. In this paper, we first outline the challenges of achieving observability in a Fog environment, based on which we present a formal definition of fog observability. Subsequently, a real-world Fog Computing testbed running a smart city use case is deployed, and an empirical evaluation of fog observability using open-source tools is presented. The results show that under certain conditions, it is viable to provide observability in a Fog Computing environment using open-source tools, although it is necessary to control the overhead modifying their default configuration according to the application characteristics., Comment: Paper presented at Mobiquitous 2023

Extragalactic globular clusters (EGCs) are an abundant and powerful tracer of galaxy dynamics and formation, and their own formation and evolution is also a matter of extensive debate. The compact nature of globular clusters means that they are hard to spatially resolve and thus study outside the Local Group. In this work we have examined how well EGCs will be detectable in images from the Euclid telescope, using both simulated pre-launch images and the first early-release observations of the Fornax galaxy cluster. The Euclid Wide Survey will provide high-spatial resolution VIS imaging in the broad IE band as well as near-infrared photometry (YE, JE, and HE). We estimate that the galaxies within 100 Mpc in the footprint of the Euclid survey host around 830 000 EGCs of which about 350 000 are within the survey's detection limits. For about half of these EGCs, three infrared colours will be available as well. For any galaxy within 50Mpc the brighter half of its GC luminosity function will be detectable by the Euclid Wide Survey. The detectability of EGCs is mainly driven by the residual surface brightness of their host galaxy. We find that an automated machine-learning EGC-classification method based on real Euclid data of the Fornax galaxy cluster provides an efficient method to generate high purity and high completeness GC candidate catalogues. We confirm that EGCs are spatially resolved compared to pure point sources in VIS images of Fornax. Our analysis of both simulated and first on-sky data show that Euclid will increase the number of GCs accessible with high-resolution imaging substantially compared to previous surveys, and will permit the study of GCs in the outskirts of their hosts. Euclid is unique in enabling systematic studies of EGCs in a spatially unbiased and homogeneous manner and is primed to improve our understanding of many understudied aspects of GC astrophysics., Comment: Submitted to A&A

We present the Flagship galaxy mock, a simulated catalogue of billions of galaxies designed to support the scientific exploitation of the Euclid mission. Euclid is a medium-class mission of the European Space Agency optimised to determine the properties of dark matter and dark energy on the largest scales of the Universe. It probes structure formation over more than 10 billion years primarily from the combination of weak gravitational lensing and galaxy clustering data. The breath of Euclid's data will also foster a wide variety of scientific analyses. The Flagship simulation was developed to provide a realistic approximation to the galaxies that will be observed by Euclid and used in its scientific analyses. We ran a state-of-the-art N-body simulation with four trillion particles, producing a lightcone on the fly. From the dark matter particles, we produced a catalogue of 16 billion haloes in one octant of the sky in the lightcone up to redshift z=3. We then populated these haloes with mock galaxies using a halo occupation distribution and abundance matching approach, calibrating the free parameters of the galaxy mock against observed correlations and other basic galaxy properties. Modelled galaxy properties include luminosity and flux in several bands, redshifts, positions and velocities, spectral energy distributions, shapes and sizes, stellar masses, star formation rates, metallicities, emission line fluxes, and lensing properties. We selected a final sample of 3.4 billion galaxies with a magnitude cut of H_E<26, where we are complete. We have performed a comprehensive set of validation tests to check the similarity to observational data and theoretical models. In particular, our catalogue is able to closely reproduce the main characteristics of the weak lensing and galaxy clustering samples to be used in the mission's main cosmological analysis. (abridged), Comment: Paper submitted as part of the A&A special issue `Euclid on Sky', which contains Euclid key reference papers and first results from the Euclid Early Release Observations

The near-infrared calibration unit (NI-CU) on board Euclid's Near-Infrared Spectrometer and Photometer (NISP) is the first astronomical calibration lamp based on light-emitting diodes (LEDs) to be operated in space. Euclid is a mission in ESA's Cosmic Vision 2015-2025 framework, to explore the dark universe and provide a next-level characterisation of the nature of gravitation, dark matter, and dark energy. Calibrating photometric and spectrometric measurements of galaxies to better than 1.5% accuracy in a survey homogeneously mapping ~14000 deg^2 of extragalactic sky requires a very detailed characterisation of near-infrared (NIR) detector properties, as well their constant monitoring in flight. To cover two of the main contributions - relative pixel-to-pixel sensitivity and non-linearity characteristics - as well as support other calibration activities, NI-CU was designed to provide spatially approximately homogeneous (<12% variations) and temporally stable illumination (0.1%-0.2% over 1200s) over the NISP detector plane, with minimal power consumption and energy dissipation. NI-CU is covers the spectral range ~[900,1900] nm - at cryo-operating temperature - at 5 fixed independent wavelengths to capture wavelength-dependent behaviour of the detectors, with fluence over a dynamic range of >=100 from ~15 ph s^-1 pixel^-1 to >1500 ph s^-1 pixel^-1. For this functionality, NI-CU is based on LEDs. We describe the rationale behind the decision and design process, describe the challenges in sourcing the right LEDs, as well as the qualification process and lessons learned. We also provide a description of the completed NI-CU, its capabilities and performance as well as its limits. NI-CU has been integrated into NISP and the Euclid satellite, and since Euclid's launch in July 2023 has started supporting survey operations., Comment: Paper accepted for publication in A&A as part of the special issue 'Euclid on Sky', which contains Euclid key reference papers and first results from the Euclid Early Release Observations

The Near-Infrared Spectrometer and Photometer (NISP) on board the Euclid satellite provides multiband photometry and R>=450 slitless grism spectroscopy in the 950-2020nm wavelength range. In this reference article we illuminate the background of NISP's functional and calibration requirements, describe the instrument's integral components, and provide all its key properties. We also sketch the processes needed to understand how NISP operates and is calibrated, and its technical potentials and limitations. Links to articles providing more details and technical background are included. NISP's 16 HAWAII-2RG (H2RG) detectors with a plate scale of 0.3" pix^-1 deliver a field-of-view of 0.57deg^2. In photo mode, NISP reaches a limiting magnitude of ~24.5AB mag in three photometric exposures of about 100s exposure time, for point sources and with a signal-to-noise ratio (SNR) of 5. For spectroscopy, NISP's point-source sensitivity is a SNR = 3.5 detection of an emission line with flux ~2x10^-16erg/s/cm^2 integrated over two resolution elements of 13.4A, in 3x560s grism exposures at 1.6 mu (redshifted Ha). Our calibration includes on-ground and in-flight characterisation and monitoring of detector baseline, dark current, non-linearity, and sensitivity, to guarantee a relative photometric accuracy of better than 1.5%, and relative spectrophotometry to better than 0.7%. The wavelength calibration must be better than 5A. NISP is the state-of-the-art instrument in the NIR for all science beyond small areas available from HST and JWST - and an enormous advance due to its combination of field size and high throughput of telescope and instrument. During Euclid's 6-year survey covering 14000 deg^2 of extragalactic sky, NISP will be the backbone for determining distances of more than a billion galaxies. Its NIR data will become a rich reference imaging and spectroscopy data set for the coming decades., Comment: Paper submitted as part of the A&A special issue 'Euclid on Sky', which contains Euclid key reference papers and first results from the Euclid Early Release Observations

This paper presents the specification, design, and development of the Visible Camera (VIS) on the ESA Euclid mission. VIS is a large optical-band imager with a field of view of 0.54 deg^2 sampled at 0.1" with an array of 609 Megapixels and spatial resolution of 0.18". It will be used to survey approximately 14,000 deg^2 of extragalactic sky to measure the distortion of galaxies in the redshift range z=0.1-1.5 resulting from weak gravitational lensing, one of the two principal cosmology probes of Euclid. With photometric redshifts, the distribution of dark matter can be mapped in three dimensions, and, from how this has changed with look-back time, the nature of dark energy and theories of gravity can be constrained. The entire VIS focal plane will be transmitted to provide the largest images of the Universe from space to date, reaching m_AB>24.5 with S/N >10 in a single broad I_E~(r+i+z) band over a six year survey. The particularly challenging aspects of the instrument are the control and calibration of observational biases, which lead to stringent performance requirements and calibration regimes. With its combination of spatial resolution, calibration knowledge, depth, and area covering most of the extra-Galactic sky, VIS will also provide a legacy data set for many other fields. This paper discusses the rationale behind the VIS concept and describes the instrument design and development before reporting the pre-launch performance derived from ground calibrations and brief results from the in-orbit commissioning. VIS should reach fainter than m_AB=25 with S/N>10 for galaxies of full-width half-maximum of 0.3" in a 1.3" diameter aperture over the Wide Survey, and m_AB>26.4 for a Deep Survey that will cover more than 50 deg^2. The paper also describes how VIS works with the other Euclid components of survey, telescope, and science data processing to extract the cosmological information., Comment: Paper submitted as part of the A&A special issue `Euclid on Sky', which contains Euclid key reference papers and first results from the Euclid Early Release Observations

Blue Compact Galaxies (BCGs), also known as \HII\ galaxies, are dwarf, star-forming objects with relatively simple dynamics, which allows for the investigation of star formation mechanisms in a cleaner manner compared to late-type objects. In this study, we have examined various characteristics of the interstellar medium, in connection with the kinematics and dynamics of ionized gas, in Tol 1004-296 and Tol 0957-278. These two objects were observed using the SOAR Integral Field Spectrometer (SIFS) attached to the Southern Observatory for Astrophysical Research (SOAR). Both galaxies were observed with two gratings: one with medium resolution for monochromatic and abundance maps, and another with high resolution for kinematics and profile analysis. Additionally, we conducted an analysis on the velocity and velocity dispersion maps using intensity-velocity dispersion (I - $\sigma$) and velocity-velocity dispersion (Vr - $\sigma$) diagrams. Neither object exhibits a rotation pattern, and only Tol 1004-296 shows a velocity gradient between the two principal knots. However, the study reveals the significant role played by velocity dispersion in the star formation process. Specifically, we identified a relationship between monochromatic intensity, metallicity, and velocity dispersion, where high emission corresponds to low metallicity and low velocity dispersion. Tol 1004-296, in particular, exhibits a distinctive linear high velocity dispersion pattern between the two main knots, suggesting that both star formation sites are pushing the gas in opposite directions., Comment: 22 pages, 23 figures. Accepted for publication in MNRAS

This study examines the effects of question type and feedback on learning outcomes in a hybrid graduate-level course. By analyzing data from 32 students over 30,198 interactions, we assess the efficacy of unique versus repeated questions and the impact of feedback on student learning. The findings reveal students demonstrate significantly better knowledge generalization when encountering unique questions compared to repeated ones, even though they perform better with repeated opportunities. Moreover, we find that the timing of explanatory feedback is a more robust predictor of learning outcomes than the practice opportunities themselves. These insights suggest that educational practices and technological platforms should prioritize a variety of questions to enhance the learning process. The study also highlights the critical role of feedback; opportunities preceding feedback are less effective in enhancing learning., Comment: To be published in Proceedings of the Eleventh ACM Conference on Learning at Scale (L@S 24), July 18-20, 2024, Atlanta, GA, USA. ACM, New York, NY, USA, 5 pages

The Euclid mission of the European Space Agency will deliver weak gravitational lensing and galaxy clustering surveys that can be used to constrain the standard cosmological model and extensions thereof. We present forecasts from the combination of these surveys on the sensitivity to cosmological parameters including the summed neutrino mass $M_\nu$ and the effective number of relativistic species $N_{\rm eff}$ in the standard $\Lambda$CDM scenario and in a scenario with dynamical dark energy ($w_0 w_a$CDM). We compare the accuracy of different algorithms predicting the nonlinear matter power spectrum for such models. We then validate several pipelines for Fisher matrix and MCMC forecasts, using different theory codes, algorithms for numerical derivatives, and assumptions concerning the non-linear cut-off scale. The Euclid primary probes alone will reach a sensitivity of $\sigma(M_\nu)=$56meV in the $\Lambda$CDM+$M_\nu$ model, whereas the combination with CMB data from Planck is expected to achieve $\sigma(M_\nu)=$23meV and raise the evidence for a non-zero neutrino mass to at least the $2.6\sigma$ level. This can be pushed to a $4\sigma$ detection if future CMB data from LiteBIRD and CMB Stage-IV are included. In combination with Planck, Euclid will also deliver tight constraints on $\Delta N_{\rm eff}< 0.144$ (95%CL) in the $\Lambda$CDM+$M_\nu$+$N_{\rm eff}$ model, or $\Delta N_{\rm eff}< 0.063$ when future CMB data are included. When floating $(w_0, w_a)$, we find that the sensitivity to $N_{\rm eff}$ remains stable, while that to $M_\nu$ degrades at most by a factor 2. This work illustrates the complementarity between the Euclid spectroscopic and imaging/photometric surveys and between Euclid and CMB constraints. Euclid will have a great potential for measuring the neutrino mass and excluding well-motivated scenarios with additional relativistic particles., Comment: 48 pages, 33 figures

Machine learning-based techniques open up many opportunities and improvements to derive deeper and more practical insights from data that can help businesses make informed decisions. However, the majority of these techniques focus on the conventional closed-set scenario, in which the label spaces for the training and test sets are identical. Open set recognition (OSR) aims to bring classification tasks in a situation that is more like reality, which focuses on classifying the known classes as well as handling unknown classes effectively. In such an open-set problem the gathered samples in the training set cannot encompass all the classes and the system needs to identify unknown samples at test time. On the other hand, building an accurate and comprehensive model in a real dynamic environment presents a number of obstacles, because it is prohibitively expensive to train for every possible example of unknown items, and the model may fail when tested in testbeds. This study provides an algorithm exploring a new representation of feature space to improve classification in OSR tasks. The efficacy and efficiency of business processes and decision-making can be improved by integrating OSR, which offers more precise and insightful predictions of outcomes. We demonstrate the performance of the proposed method on three established datasets. The results indicate that the proposed model outperforms the baseline methods in accuracy and F1-score., Comment: Accepted for proceedings of the 57th Hawaii International Conference on System Sciences: 10 pages, 6 figures, 3-6 January 2024, Honolulu, United States

We investigate experimentally the influence of rotation on the penetration depth of a spherical projectile impacting a granular medium. We show that a rotational motion significantly increases the penetration depth achieved. Moreover, we model our experimental results by modifying the frictional term of the equation describing the penetration dynamics of an object in a granular medium. In particular, we find that the frictional drag decreases linearly with the velocity ratio between rotational (spin motion) and translational (falling motion) velocities. The good agreement between our model and our experimental measurements offers perspectives for estimating the depth that spinning projectiles reach after impacting onto a granular ground, such as happens with seeds dropped from aircraft or with landing probes.

We show that all non-developable ruled surfaces endowed with Ricci metrics in the three-dimensional Euclidean space may be constructed using curves of constant torsion and its binormal. This allows us to give characterizations of the helicoid as the only surface of this kind that admits a parametrization with plane line of striction, and as the only with constant mean curvature., Comment: 12 pages and 11 figures. All comments are welcome

We characterize the global hypoellipticity, almost hypoellipticity and solvability for a class of systems of real vector fields on the (n + 1)-dimensional torus as well as the same properties about the sum of squares associated to the system. The key result is a theorem about propagation of regularity for solutions of the system.

Dynamic facility location problems aim at placing one or more valuable resources over a planning horizon to meet customer demand. Existing literature commonly assumes that customer demand quantities are defined independently for each time period. In many planning contexts, however, unmet demand carries over to future time periods. Unmet demand at some time periods may therefore affect decisions of subsequent time periods. This work studies a novel location problem, where the decision maker relocates a single temporary facility over time to capture cumulative customer demand. We propose two mixed-integer programming models for this problem, and show that one of them has a tighter continuous relaxation and allows the representation of more general customer demand behaviour. We characterize the computational complexity for this problem, and analyze which problem characteristics result in NP-hardness. We then propose an exact branch-and-Benders-cut method, and show how optimality cuts can be computed efficiently through an analytical procedure. Computational experiments show that our method is approximately 30 times faster than solving the tighter formulation directly. Our results also quantify the benefit of accounting for cumulative customer demand within the optimization framework, since the corresponding planning solutions perform much better than those obtained by ignoring cumulative demand or employing myopic heuristics., Comment: 35 pages, 4 figures

LensMC is a weak lensing shear measurement method developed for Euclid and Stage-IV surveys. It is based on forward modelling to deal with convolution by a point spread function with comparable size to many galaxies; sampling the posterior distribution of galaxy parameters via Markov Chain Monte Carlo; and marginalisation over nuisance parameters for each of the 1.5 billion galaxies observed by Euclid. The scientific performance is quantified through high-fidelity images based on the Euclid Flagship simulations and emulation of the Euclid VIS images; realistic clustering with a mean surface number density of 250 arcmin$^{-2}$ ($I_{\rm E}<29.5$) for galaxies, and 6 arcmin$^{-2}$ ($I_{\rm E}<26$) for stars; and a diffraction-limited chromatic point spread function with a full width at half maximum of $0.^{\!\prime\prime}2$ and spatial variation across the field of view. Objects are measured with a density of 90 arcmin$^{-2}$ ($I_{\rm E}<26.5$) in 4500 deg$^2$. The total shear bias is broken down into measurement (our main focus here) and selection effects (which will be addressed elsewhere). We find: measurement multiplicative and additive biases of $m_1=(-3.6\pm0.2)\times10^{-3}$, $m_2=(-4.3\pm0.2)\times10^{-3}$, $c_1=(-1.78\pm0.03)\times10^{-4}$, $c_2=(0.09\pm0.03)\times10^{-4}$; a large detection bias with a multiplicative component of $1.2\times10^{-2}$ and an additive component of $-3\times10^{-4}$; and a measurement PSF leakage of $\alpha_1=(-9\pm3)\times10^{-4}$ and $\alpha_2=(2\pm3)\times10^{-4}$. When model bias is suppressed, the obtained measurement biases are close to Euclid requirement and largely dominated by undetected faint galaxies ($-5\times10^{-3}$). Although significant, model bias will be straightforward to calibrate given the weak sensitivity. LensMC is publicly available at https://gitlab.com/gcongedo/LensMC, Comment: 29 pages, 18 figures, 2 tables

Identifying partial differential equations (PDEs) from data is crucial for understanding the governing mechanisms of natural phenomena, yet it remains a challenging task. We present an extension to the ARGOS framework, ARGOS-RAL, which leverages sparse regression with the recurrent adaptive lasso to identify PDEs from limited prior knowledge automatically. Our method automates calculating partial derivatives, constructing a candidate library, and estimating a sparse model. We rigorously evaluate the performance of ARGOS-RAL in identifying canonical PDEs under various noise levels and sample sizes, demonstrating its robustness in handling noisy and non-uniformly distributed data. We also test the algorithm's performance on datasets consisting solely of random noise to simulate scenarios with severely compromised data quality. Our results show that ARGOS-RAL effectively and reliably identifies the underlying PDEs from data, outperforming the sequential threshold ridge regression method in most cases. We highlight the potential of combining statistical methods, machine learning, and dynamical systems theory to automatically discover governing equations from collected data, streamlining the scientific modeling process., Comment: 18 pages, 6 figures, 1 table

We propose an exact algorithm for the Graph Burning Problem ($\texttt{GBP}$), an NP-hard optimization problem that models the spread of influence on social networks. Given a graph $G$ with vertex set $V$, the objective is to find a sequence of $k$ vertices in $V$, namely, $v_1, v_2, \dots, v_k$, such that $k$ is minimum and $\bigcup_{i = 1}^{k} \{u\! \in\! V\! : d(u, v_i) \leq k - i\} = V$, where $d(u,v)$ denotes the distance between $u$ and $v$. We formulate the problem as a set covering integer programming model and design a row generation algorithm for the $\texttt{GBP}$. Our method exploits the fact that a very small number of covering constraints is often sufficient for solving the integer model, allowing the corresponding rows to be generated on demand. To date, the most efficient exact algorithm for the $\texttt{GBP}$, denoted here by $\texttt{GDCA}$, is able to obtain optimal solutions for graphs with up to 14,000 vertices within two hours of execution. In comparison, our algorithm finds provably optimal solutions approximately 236 times faster, on average, than $\texttt{GDCA}$. For larger graphs, memory space becomes a limiting factor for $\texttt{GDCA}$. Our algorithm, however, solves real-world instances with almost 200,000 vertices in less than 35 seconds, increasing the size of graphs for which optimal solutions are known by a factor of 14., Comment: 10 pages, 1 figure and 2 tables

Linguistic ambiguity continues to represent a significant challenge for natural language processing (NLP) systems, notwithstanding the advancements in architectures such as Transformers and BERT. Inspired by the recent success of instructional models like ChatGPT and Gemini (In 2023, the artificial intelligence was called Bard.), this study aims to analyze and discuss linguistic ambiguity within these models, focusing on three types prevalent in Brazilian Portuguese: semantic, syntactic, and lexical ambiguity. We create a corpus comprising 120 sentences, both ambiguous and unambiguous, for classification, explanation, and disambiguation. The models capability to generate ambiguous sentences was also explored by soliciting sets of sentences for each type of ambiguity. The results underwent qualitative analysis, drawing on recognized linguistic references, and quantitative assessment based on the accuracy of the responses obtained. It was evidenced that even the most sophisticated models, such as ChatGPT and Gemini, exhibit errors and deficiencies in their responses, with explanations often providing inconsistent. Furthermore, the accuracy peaked at 49.58 percent, indicating the need for descriptive studies for supervised learning., Comment: in Portuguese language, 16 p\'aginas, 5 p\'aginas de ap\^endice e 4 imagens

The classification of higher-order photon emission becomes important with more methods being developed for deterministic multiphoton generation. The widely-used second-order correlation g(2) is not sufficient to determine the quantum purity of higher photon Fock states. Traditional characterization methods require a large amount of photon detection events which leads to increased measurement and computation time. Here, we demonstrate a Machine Learning model based on a 2D Convolutional Neural Network (CNN) for rapid classification of multiphoton Fock states up to |3> with an overall accuracy of 94%. By fitting the g(3) correlation with simulated photon detection events, the model exhibits efficient performance particularly with sparse correlation data, with 800 co-detection events to achieve an accuracy of 90%. Using the proposed experimental setup, this CNN classifier opens up the possibility for quasi real-time classification of higher photon states, which holds broad applications in quantum technologies.

Gender and race inferred from an individual's name are a notable source of stereotypes and biases that subtly influence social interactions. Abundant evidence from human experiments has revealed the preferential treatment that one receives when one's name suggests a predominant gender or race. As large language models acquire more capabilities and begin to support everyday applications, it becomes crucial to examine whether they manifest similar biases when encountering names in a complex social interaction. In contrast to previous work that studies name-based biases in language models at a more fundamental level, such as word representations, we challenge three prominent models to predict the outcome of a modified Trust Game, a well-publicized paradigm for studying trust and reciprocity. To ensure the internal validity of our experiments, we have carefully curated a list of racially representative surnames to identify players in a Trust Game and rigorously verified the construct validity of our prompts. The results of our experiments show that our approach can detect name-based biases in both base and instruction-tuned models.

For a foliation by CMC hypersurfaces on a complete Riemannian manifold $M^{n+1}$ with sectional curvature bounded from below by $-nK_0\leq 0$ and such that the mean curvature $H$ of the leaves of the foliation satisfies $|H|\geq \sqrt{K_0}$, under certain additional hypotheses, for instance, if $M$ is a compact (without boundary) or if ${\rm div} (\nabla_N N)=0$ where the gradient of the function ${\rm div} (N)$ is non zero, then we prove that $|H|\equiv \sqrt{K_0}$, where $N$ is a unit vector field orthogonal to the foliation. Moreover, in the the case that $M$ is compact, we prove also that all the leaves are totally umbilical. This gives, in particular, a generalization for the result proved by Barbosa, Kenmotsu and Oshikiri (1991), where was proved the above result in the case $K_0=0$ and $M$ compact. Under the same additional hypotheses as above, we obtain that for a foliation by CMC hypersurfaces on a complete Riemannian manifold $M$ with Ricci curvature bounded from below by $-nK_0\leq 0$, the mean curvature $H$ of the leaves of the foliation satisfies $|H|\leq \sqrt{K_0}$. This gives a positive partial answer to a conjecture due to Meeks III, P\'erez and Ros. We also provide some partial answers to several other problems., Comment: We have found a mistake in our proof. Our proof only works if we add some hypothesis on the foliation, for instance, if N(H) is constant on the leaves or div(\nabla_N N)=0 where the gradient of H is not zero. Thus, the conjectures are still open. We slightly rewrote the text and changed the title. Subsection 4.1 and Section 5 are new. 31 pages

In the extreme near-field, when the spatial extension of the atomic wavefunction is no longer negligible compared to the atom-surface distance, the dipole approximation is no longer sufficient to describe Casimir-Polder interactions. Here we calculate the higher-order, quadrupole and octupole, contributions to Casimir-Polder energy shifts of Rydberg atoms close to a dielectric surface. We subsequently investigate the effects of these higher-order terms in thin-cell and selective reflection spectroscopy. Beyond its fundamental interest, this new regime of extremely small atom surface separations is relevant for quantum technology applications with Rydberg or surface-bound atoms interfacing with photonic platforms., Comment: to appear in Physical Review Research

Model evaluation is of crucial importance in modern statistics application. The construction of ROC and calculation of AUC have been widely used for binary classification evaluation. Recent research generalizing the ROC/AUC analysis to multi-class classification has problems in at least one of the four areas: 1. failure to provide sensible plots 2. being sensitive to imbalanced data 3. unable to specify mis-classification cost and 4. unable to provide evaluation uncertainty quantification. Borrowing from a binomial matrix factorization model, we provide an evaluation metric summarizing the pair-wise multi-class True Positive Rate (TPR) and False Positive Rate (FPR) with one-dimensional vector representation. Visualization on the representation vector measures the relative speed of increment between TPR and FPR across all the classes pairs, which in turns provides a ROC plot for the multi-class counterpart. An integration over those factorized vector provides a binary AUC-equivalent summary on the classifier performance. Mis-clasification weights specification and bootstrapped confidence interval are also enabled to accommodate a variety of of evaluation criteria. To support our findings, we conducted extensive simulation studies and compared our method to the pair-wise averaged AUC statistics on benchmark datasets.

In the steel production domain, recycling ferrous scrap is essential for environmental and economic sustainability, as it reduces both energy consumption and greenhouse gas emissions. However, the classification of scrap materials poses a significant challenge, requiring advancements in automation technology. Additionally, building trust among human operators is a major obstacle. Traditional approaches often fail to quantify uncertainty and lack clarity in model decision-making, which complicates acceptance. In this article, we describe how conformal prediction can be employed to quantify uncertainty and add robustness in scrap classification. We have adapted the Split Conformal Prediction technique to seamlessly integrate with state-of-the-art computer vision models, such as the Vision Transformer (ViT), Swin Transformer, and ResNet-50, while also incorporating Explainable Artificial Intelligence (XAI) methods. We evaluate the approach using a comprehensive dataset of 8147 images spanning nine ferrous scrap classes. The application of the Split Conformal Prediction method allowed for the quantification of each model's uncertainties, which enhanced the understanding of predictions and increased the reliability of the results. Specifically, the Swin Transformer model demonstrated more reliable outcomes than the others, as evidenced by its smaller average size of prediction sets and achieving an average classification accuracy exceeding 95%. Furthermore, the Score-CAM method proved highly effective in clarifying visual features, significantly enhancing the explainability of the classification decisions.

The Neural Tangent Kernel (NTK) has emerged as a fundamental concept in the study of wide Neural Networks. In particular, it is known that the positivity of the NTK is directly related to the memorization capacity of sufficiently wide networks, i.e., to the possibility of reaching zero loss in training, via gradient descent. Here we will improve on previous works and obtain a sharp result concerning the positivity of the NTK of feedforward networks of any depth. More precisely, we will show that, for any non-polynomial activation function, the NTK is strictly positive definite. Our results are based on a novel characterization of polynomial functions which is of independent interest., Comment: Comments welcome

Future data provided by the Euclid mission will allow us to better understand the cosmic history of the Universe. A metric of its performance is the figure-of-merit (FoM) of dark energy, usually estimated with Fisher forecasts. The expected FoM has previously been estimated taking into account the two main probes of Euclid, namely the three-dimensional clustering of the spectroscopic galaxy sample, and the so-called 3x2pt signal from the photometric sample (i.e., the weak lensing signal, the galaxy clustering, and their cross-correlation). So far, these two probes have been treated as independent. In this paper, we introduce a new observable given by the ratio of the (angular) two-point correlation function of galaxies from the two surveys. For identical (normalised) selection functions, this observable is unaffected by sampling noise, and its variance is solely controlled by Poisson noise. We present forecasts for Euclid where this multi-tracer method is applied and is particularly relevant because the two surveys will cover the same area of the sky. This method allows for the exploitation of the combination of the spectroscopic and photometric samples. When the correlation between this new observable and the other probes is not taken into account, a significant gain is obtained in the FoM, as well as in the constraints on other cosmological parameters. The benefit is more pronounced for a commonly investigated modified gravity model, namely the $\gamma$ parametrisation of the growth factor. However, the correlation between the different probes is found to be significant and hence the actual gain is uncertain. We present various strategies for circumventing this issue and still extract useful information from the new observable., Comment: 16 pages, 7 figures, submitted to A&A

As a result of recent advancements in generative AI, the field of Data Science is prone to various changes. This review critically examines the Data Analysis (DA) capabilities of ChatGPT assessing its performance across a wide range of tasks. While DA provides researchers and practitioners with unprecedented analytical capabilities, it is far from being perfect, and it is important to recognize and address its limitations., Comment: 15 pages with figures and appendix

Precise and accurate mass calibration is required to exploit galaxy clusters as astrophysical and cosmological probes in the Euclid era. Systematic errors in lensing signals by galaxy clusters can be empirically estimated by comparing different surveys with independent and uncorrelated systematics. To assess the robustness of the lensing results to systematic errors, we carried out end-to-end tests across different data sets. We performed a unified analysis at the catalogue level by leveraging the Euclid combined cluster and weak-lensing pipeline (COMB-CL). COMB-CL will measure weak lensing cluster masses for the Euclid Survey. Heterogeneous data sets from five independent, recent, lensing surveys (CHFTLenS, DES~SV1, HSC-SSP~S16a, KiDS~DR4, and RCSLenS), which exploited different shear and photometric redshift estimation algorithms, were analysed with a consistent pipeline under the same model assumptions. We performed a comparison of the amplitude of the reduced excess surface density and of the mass estimates using lenses from the Planck PSZ2 and SDSS redMaPPer cluster samples. Mass estimates agree with literature results collected in the LC2 catalogues. Mass accuracy was further investigated considering the AMICO detected clusters in the HSC-SSP XXL North field. The consistency of the data sets was tested using our unified analysis framework. We found agreement between independent surveys, at the level of systematic noise in Stage-III surveys or precursors. This indicates successful control over systematics. If such control continues in Stage-IV, Euclid will be able to measure the weak lensing masses of around 13000 (considering shot noise only) or 3000 (noise from shape and large-scale-structure) massive clusters with a signal-to-noise ratio greater than 3., Comment: 25 pages; in press on A&A

This article deals with the $\dot{H}^{1}$--level exact controllability for the defocusing critical nonlinear Schr\"{o}dinger equation in $\mathbb{R}^3$. Firstly, we show the problem under consideration to be well-posed using Strichartz estimates. Moreover, through the Hilbert uniqueness method, we prove the linear Schr\"{o}dinger equation to be controllable. Finally, we use a perturbation argument and show local exact controllability for the critical nonlinear Schr\"{o}dinger equation., Comment: 20 pages. Comments are welcome

Raster Forge is a Python library and graphical user interface for raster data manipulation and analysis. The tool is focused on remote sensing applications, particularly in wildfire management. It allows users to import, visualize, and process raster layers for tasks such as image compositing or topographical analysis. For wildfire management, it generates fuel maps using predefined models. Its impact extends from disaster management to hydrological modeling, agriculture, and environmental monitoring. Raster Forge can be a valuable asset for geoscientists and researchers who rely on raster data analysis, enhancing geospatial data processing and visualization across various disciplines.

A procedure for quantifying the U $5f$ electrons' covalence and degree of localization in U intermetallic compounds is presented. To this end, bulk sensitive hard and soft x-ray photoelectron spectroscopy were utilized in combination with density-functional theory (DFT) plus dynamical mean-field theory (DMFT) calculations. The energy dependence of the photoionization cross-sections allows the disentanglement of the U\,$5f$ contribution to the valence band from the various other atomic subshells so that the computational parameters in the DFT\,+\,DMFT can be reliably determined. Applying this method to UGa$_2$ and UB$_2$ as model compounds from opposite ends of the (de)localization range, we have achieved excellent simulations of the valence band and core-level spectra. The width in the distribution of atomic U\,$5f$ configurations contributing to the ground state, as obtained from the calculations, quantifies the correlated nature and degree of localization of the U\,5$f$. The findings permit answering the longstanding question why different spectroscopic techniques give seemingly different numbers for the U 5$f$ valence in intermetallic U compounds., Comment: 14 pages, 9 figures

The adoption of Deep Learning algorithms in the medical imaging field is a prominent area of research, with high potential for advancing AI-based Computer-aided diagnosis (AI-CAD) solutions. However, current solutions face challenges due to a lack of interpretability features and high data demands, prompting recent efforts to address these issues. In this study, we propose the ProtoAL method, where we integrate an interpretable DL model into the Deep Active Learning (DAL) framework. This approach aims to address both challenges by focusing on the medical imaging context and utilizing an inherently interpretable model based on prototypes. We evaluated ProtoAL on the Messidor dataset, achieving an area under the precision-recall curve of 0.79 while utilizing only 76.54\% of the available labeled data. These capabilities can enhances the practical usability of a DL model in the medical field, providing a means of trust calibration in domain experts and a suitable solution for learning in the data scarcity context often found.

To develop new devices based on synthetic ferrimagnetic (S-FiM) heterostructures, understanding the material's physical properties is pivotal. Here, the induced magnetic moment (IMM), magnetic exchange-coupling, and spin textures were investigated at room-temperature in Pt/Co/Gd multilayers using a multiscale approach. The magnitude and direction of the IMM were interpreted experimentally and theoretically in the framework of both X-ray magnetic circular dichroism (XMCD) and density functional theory (DFT). The results demonstrate that the IMM transferred by Co across the Gd paramagnetic (PM) thickness leads to a flipped spin state (FSS) within the Gd layers, in which their magnetic moments couple antiparallel/parallel with the ferromagnetic (FM) Co near/far from the Co/Gd interface, respectively. For the Pt, in both Pt/Co and Gd/Pt interfaces the IMM follows the same direction as the Co magnetic moment, with negligible IMM in the Gd/Pt interface. Additionally, zero-field spin spirals were imaged using scanning transmission X-ray microscopy (STXM), while micromagnetic simulations employed to unfold the interactions stabilizing the FiM configurations, where the existence of a sizable Dzyaloshinskii-Moriya interaction is demonstrated to be crucial for the formation of those spin textures. Our outcomes may add fundamental physical and technological aspects for using FiM films in antiferromagnetic spintronic devices.

Autonomous navigation in unstructured natural environments poses a significant challenge. In goal navigation tasks without prior information, the limited look-ahead of onboard sensors utilised by robots compromises path efficiency. We propose a novel approach that leverages an above-the-canopy aerial map for improved ground robot navigation. Our system utilises aerial lidar scans to create a 3D probabilistic occupancy map, uniquely incorporating the uncertainty in the aerial vehicle's trajectory for improved accuracy. Novel path planning cost functions are introduced, combining path length with obstruction risk estimated from the probabilistic map. The D-Star Lite algorithm then calculates an optimal (minimum-cost) path to the goal. This system also allows for dynamic replanning upon encountering unforeseen obstacles on the ground. Extensive experiments and ablation studies in simulated and real forests demonstrate the effectiveness of our system., Comment: To appear in IEEE Robotics and Automation Letters (RA-L) 2024

In the current digital security ecosystem, where threats evolve rapidly and with complexity, companies developing Endpoint Detection and Response (EDR) solutions are in constant search for innovations that not only keep up but also anticipate emerging attack vectors. In this context, this article introduces the HookChain, a look from another perspective at widely known techniques, which when combined, provide an additional layer of sophisticated evasion against traditional EDR systems. Through a precise combination of IAT Hooking techniques, dynamic SSN resolution, and indirect system calls, HookChain redirects the execution flow of Windows subsystems in a way that remains invisible to the vigilant eyes of EDRs that only act on Ntdll.dll, without requiring changes to the source code of the applications and malwares involved. This work not only challenges current conventions in cybersecurity but also sheds light on a promising path for future protection strategies, leveraging the understanding that continuous evolution is key to the effectiveness of digital security. By developing and exploring the HookChain technique, this study significantly contributes to the body of knowledge in endpoint security, stimulating the development of more robust and adaptive solutions that can effectively address the ever-changing dynamics of digital threats. This work aspires to inspire deep reflection and advancement in the research and development of security technologies that are always several steps ahead of adversaries., Comment: 50 pages, 23 figures, HookChain, Bypass EDR, Evading EDR, IAT Hook, Halo's Gate

The integration of data science into Geographic Information Systems (GIS) has facilitated the evolution of these tools into complete spatial analysis platforms. The adoption of machine learning and big data techniques has equipped these platforms with the capacity to handle larger amounts of increasingly complex data, transcending the limitations of more traditional approaches. This work traces the historical and technical evolution of data science and GIS as fields of study, highlighting the critical points of convergence between domains, and underlining the many sectors that rely on this integration. A GIS application is presented as a case study in the disaster management sector where we utilize aerial data from Tr\'oia, Portugal, to emphasize the process of insight extraction from raw data. We conclude by outlining prospects for future research in integration of these fields in general, and the developed application in particular., Comment: The peer-reviewed version of this paper is published in IEEE Xplore at https://doi.org/10.1109/YEF-ECE62614.2024.10624902. This version is typeset by the author and differs only in pagination and typographical detail

MISTRAL is the new Faint Object Spectroscopic Camera mounted at the folded Cassegrain focus of the 1.93m telescope of Haute-Provence Observatory. We describe the design and components of the instrument and give some details about its operation. We emphasise in particular the various observing modes and the performances of the detector. A short description is also given about the working environment. Various types of objects, including stars, nebulae, comets, novae, galaxies have been observed during various test phases to evaluate the performances of the instrument. The instrument covers the range of 4000 to 8000A with the blue setting, or from 6000 to 10000A with the red setting, at an average spectral resolution of 700. Its peak efficiency is about 22% at 6000A. In spectroscopy, a limiting magnitude of 19.5 can be achieved for a point source in one hour with a signal to noise of 3 in the continuum (and better if emission lines are present). In imaging mode, limiting magnitudes of 20-21 can be obtained in 10-20mn (with average seing conditions of 2.5 arcsec at OHP). The instrument is very users-friendly and can be put into operations in less than 15mn (rapid change-over from the other instrument in use) if required by the science (like for Gamma-Rays Bursts). Some first scientific results are described for various types of objects, and in particular for the follow-up of GRBs. While some further improvements are still under way, in particular to ease the switch from blue to red setting and add more grisms or filters, MISTRAL is ready for the follow-up of transients and other variable objects, in the soon-to-come era of e.g. the SVOM satellite and of the Rubin telescope., Comment: Accepted in A&A

The flux of ultra-high energy cosmic rays reaching Earth above the ankle energy (5 EeV) can be described as a mixture of nuclei injected by extragalactic sources with very hard spectra and a low rigidity cutoff. Extragalactic magnetic fields existing between the Earth and the closest sources can affect the observed CR spectrum by reducing the flux of low-rigidity particles reaching Earth. We perform a combined fit of the spectrum and distributions of depth of shower maximum measured with the Pierre Auger Observatory including the effect of this magnetic horizon in the propagation of UHECRs in the intergalactic space. We find that, within a specific range of the various experimental and phenomenological systematics, the magnetic horizon effect can be relevant for turbulent magnetic field strengths in the local neighbourhood of order $B_{\rm rms}\simeq (50-100)\,{\rm nG}\,(20\rm{Mpc}/{d_{\rm s})( 100\,\rm{kpc}/L_{\rm coh}})^{1/2}$, with $d_{\rm s}$ the typical intersource separation and $L_{\rm coh}$ the magnetic field coherence length. When this is the case, the inferred slope of the source spectrum becomes softer and can be closer to the expectations of diffusive shock acceleration, i.e., $\propto E^{-2}$. An additional cosmic-ray population with higher source density and softer spectra, presumably also extragalactic and dominating the cosmic-ray flux at EeV energies, is also required to reproduce the overall spectrum and composition results for all energies down to 0.6~EeV., Comment: Matches published version

The power prior is a popular class of informative priors for incorporating information from historical data. It involves raising the likelihood for the historical data to a power, which acts as a discounting parameter. When the discounting parameter is modeled as random, the normalized power prior is recommended. Bayesian hierarchical modeling is a widely used method for synthesizing information from different sources, including historical data. In this work, we examine the analytical relationship between the normalized power prior (NPP) and Bayesian hierarchical models (BHM) for \emph{i.i.d.} normal data. We establish a direct relationship between the prior for the discounting parameter of the NPP and the prior for the variance parameter of the BHM. Such a relationship is first established for the case of a single historical dataset, and then extended to the case with multiple historical datasets with dataset-specific discounting parameters. For multiple historical datasets, we develop and establish theory for the BHM-matching NPP (BNPP) which establishes dependence between the dataset-specific discounting parameters leading to inferences that are identical to the BHM. Establishing this relationship not only justifies the NPP from the perspective of hierarchical modeling, but also provides insight on prior elicitation for the NPP. We present strategies on inducing priors on the discounting parameter based on hierarchical models, and investigate the borrowing properties of the BNPP.

This paper deals with the numerical simulation of the Gross-Pitaevskii (GP) equation, for which a well-known feature is the appearance of quantized vortices with core size of the order of a small parameter $\varepsilon$. Without a magnetic field and with suitable initial conditions, these vortices interact, in the singular limit $\varepsilon\to0$, through an explicit Hamiltonian dynamics. Using this analytical framework, we develop and analyze a numerical strategy based on the reduced-order Hamiltonian system to efficiently simulate the infinite-dimensional GP equation for small, but finite, $\varepsilon$. This method allows us to avoid numerical stability issues in solving the GP equation, where small values of $\varepsilon$ typically require very fine meshes and time steps. We also provide a mathematical justification of our method in terms of rigorous error estimates of the error in the supercurrent, together with numerical illustrations.

In this Letter we introduce some field-theoretic approach for computing the critical properties of $\gamma_{KLS}$-generalized systems undergoing continuous phase transitions, namely $\gamma_{KLS}$-statistical field theory. From this new approach emerges the new generalized O($N$)$_{\gamma_{KLS}}$ universality class, which is capable of encompassing nonconventional critical exponents for real imperfect systems known as manganites not described by standard statistical field theory. We compare the generalized results with those obtained from measurements in manganites. The agreement was satisfactory, where the relative errors are $< 5\%$ for the most of manganites used. Although the present approach describes the aforementioned nonconventional critical indices, we show that it is not complete. For example, it does not explain the results for some other manganites, being explained only for nonextensive statistical field theory recently introduced in literature. So, $\gamma_{KLS}$-statistical field theory has to be discarded for statistical mechanics generalization purposes., Comment: 8 pages, IV tables