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In this manuscript we study geometric regularity estimates for quasi-linear elliptic equations of $p$-Laplace type ($1 < p< \infty$) with strong absorption condition: $$ -\text{div}\,(\Phi(x, u, \nabla u)) + \lambda_0(x) u_{+}^q(x) = 0 \quad \text{in} \quad \Omega \subset \mathbb{R}^N, $$ where $\Phi: \Omega \times \mathbb{R}_{+} \times \mathbb{R}^N \to \mathbb{R}^N$ is a vector field with an appropriate $p$-structure, $\lambda_0$ is a non-negative and bounded function and $0\leq q0\} \cap \Omega$, where the regularity exponent is given explicitly by $\gamma = \frac{p}{p-1-q} \gg 1$. Some weak geometric and measure theoretical properties as non-degeneracy, uniform positive density and porosity of free boundary are proved. As an application, a Liouville-type result for entire solutions is established provided that their growth at infinity can be controlled in an appropriate manner. Finally, we obtain finiteness of $(N-1)$-Hausdorff measure of free boundary for a particular class of dead core problems. The approach employed in this article is novel even to dead core problems governed by the $p$-Laplace operator $-\Delta_p u + \lambda_0 u^q\chi_{\{u>0\}} = 0$ for any $\lambda_0>0$. \newline \newline \noindent \textbf{Keywords:} Quasi-linear elliptic operators of $p$-Laplace type, improved regularity estimates, Free boundary problems of dead core type, Liouville type results, Hausdorff measure estimates., Comment: article published in Calculus of Variations and Partial Differential Equations , 2018

We study regularity issues and the limiting behavior as $p\to\infty$ of nonnegative solutions for elliptic equations of $p-$Laplacian type ($2 \leq p< \infty$) with a strong absorption: $$ -\Delta_p u(x) + \lambda_0(x) u_{+}^q(x) = 0 \quad \text{ in } \quad \Omega \subset \mathbb{R}^N, $$ where $\lambda_0>0$ is a bounded function, $\Omega$ is a bounded domain and $0\leq q0\} \cap \Omega$ where the sharp regularity exponent is given explicitly by $\gamma = \frac{1}{1-\ell}$. Finally, some weak geometric and measure theoretical properties as non-degeneracy, uniform positive density, porosity and convergence of the free boundaries are proved., Comment: article accepted in Journal of the London Mathematical Society , 2019. arXiv admin note: substantial text overlap with arXiv:1712.06683

Recent work demonstrated the existence of critical flaws in the current use of Shapley values in explainable AI (XAI), i.e. the so-called SHAP scores. These flaws are significant in that the scores provided to a human decision-maker can be misleading. Although these negative results might appear to indicate that Shapley values ought not be used in XAI, this paper argues otherwise. Concretely, this paper proposes a novel definition of SHAP scores that overcomes existing flaws. Furthermore, the paper outlines a practically efficient solution for the rigorous estimation of the novel SHAP scores. Preliminary experimental results confirm our claims, and further underscore the flaws of the current SHAP scores.

When building dark matter (DM) models, one often imposes conserved discrete symmetries to stabilize DM candidates. The simplest choice is ${\mathbb Z}_2$ but models with larger stabilizing groups have also been explored. Can a conserved non-abelian group lead to a viable DM model? Here, we address this question within the three-Higgs-doublet model based on the group $\Sigma(36)$, in which DM stabilization by a non-abelian group is not only possible but inevitable. We show that the tight connections between the Higgs, fermion, and DM sectors repeatedly drive the model into conflict with the LHC results and DM observations, with the most recent LZ results playing a decisive role. We believe that the lessons learned from this study help chart the limits of what can be achieved within multi-Higgs-doublet DM models with large symmetry groups., Comment: 20 pages, 5 figures

Recent work revealed a tight connection between adversarial robustness and restricted forms of symbolic explanations, namely distance-based (formal) explanations. This connection is significant because it represents a first step towards making the computation of symbolic explanations as efficient as deciding the existence of adversarial examples, especially for highly complex machine learning (ML) models. However, a major performance bottleneck remains, because of the very large number of features that ML models may possess, in particular for deep neural networks. This paper proposes novel algorithms to compute the so-called contrastive explanations for ML models with a large number of features, by leveraging on adversarial robustness. Furthermore, the paper also proposes novel algorithms for listing explanations and finding smallest contrastive explanations. The experimental results demonstrate the performance gains achieved by the novel algorithms proposed in this paper., Comment: arXiv admin note: substantial text overlap with arXiv:2405.08297

The ubiquitous use of Shapley values in eXplainable AI (XAI) has been triggered by the tool SHAP, and as a result are commonly referred to as SHAP scores. Recent work devised examples of machine learning (ML) classifiers for which the computed SHAP scores are thoroughly unsatisfactory, by allowing human decision-makers to be misled. Nevertheless, such examples could be perceived as somewhat artificial, since the selected classes must be interpreted as numeric. Furthermore, it was unclear how general were the issues identified with SHAP scores. This paper answers these criticisms. First, the paper shows that for Boolean classifiers there are arbitrarily many examples for which the SHAP scores must be deemed unsatisfactory. Second, the paper shows that the issues with SHAP scores are also observed in the case of regression models. In addition, the paper studies the class of regression models that respect Lipschitz continuity, a measure of a function's rate of change that finds important recent uses in ML, including model robustness. Concretely, the paper shows that the issues with SHAP scores occur even for regression models that respect Lipschitz continuity. Finally, the paper shows that the same issues are guaranteed to exist for arbitrarily differentiable regression models., Comment: arXiv admin note: text overlap with arXiv:2405.00076

Methods based on Contrastive Language-Image Pre-training (CLIP) are nowadays extensively used in support of vision-and-language tasks involving remote sensing data, such as cross-modal retrieval. The adaptation of CLIP to this specific domain has relied on model fine-tuning with the standard contrastive objective, using existing human-labeled image-caption datasets, or using synthetic data corresponding to image-caption pairs derived from other annotations over remote sensing images (e.g., object classes). The use of different pre-training mechanisms has received less attention, and only a few exceptions have considered multilingual inputs. This work proposes a novel vision-and-language model for the remote sensing domain, exploring the fine-tuning of a multilingual CLIP model and testing the use of a self-supervised method based on aligning local and global representations from individual input images, together with the standard CLIP objective. Model training relied on assembling pre-existing datasets of remote sensing images paired with English captions, followed by the use of automated machine translation into nine additional languages. We show that translated data is indeed helpful, e.g. improving performance also on English. Our resulting model, which we named Remote Sensing Multilingual CLIP (RS-M-CLIP), obtains state-of-the-art results in a variety of vision-and-language tasks, including cross-modal and multilingual image-text retrieval, or zero-shot image classification., Comment: Accepted at ACM SIGSPATIAL 2024 - Research Papers

This article focuses on the study of the group of units of incidence rings, which is a class of infinite matrix groups indexed by ordered sets, on a topological perspective. We first show when these groups can inherit the topological structure from the incidence rings. It is later shown that infinite matrix groups of topological fields can be used to build simple topological matrix groups, generalizing a result proven in ``Topologically simple, totally disconnected, locally compact infinite matrix groups''. We finish by relating the structure of these groups with elementary totally disconnected, locally compact groups, an important class for the study of totally disconnected, locally compact groups., Comment: arXiv admin note: substantial text overlap with arXiv:2310.13238

In this work, we establish sharp and improved regularity estimates for viscosity solutions of Hardy-H\'{e}non-type equations with possibly singular weights and strong absorption governed by the $\infty$-Laplacian $$ \Delta_{\infty} u(x) = |x|^{\alpha}u_+^m(x) \quad \text{in} \quad B_1, $$ under suitable assumptions on the data. In this setting, we derive an explicit regularity exponent that depends only on universal parameters. Additionally, we prove non-degeneracy properties, providing further geometric insights into the nature of these solutions. Our regularity estimates not only improve but also extend, to some extent, the previously obtained results for zero-obstacle and dead-core problems driven by the $\infty$-Laplacian. As an application of our findings, we also address some Liouville-type results for this class of equations.

In this manuscript, we obtain sharp and improved regularity estimates for weak solutions of weighted quasilinear elliptic models of Hardy-H\'{e}non-type, featuring an explicit regularity exponent depending only on universal parameters. Our approach is based on geometric tangential methods and uses a refined oscillation mechanism, compactness, and scaling techniques. In some specific scenarios, we establish higher regularity estimates and non-degeneracy properties, providing further geometric insights into such solutions. Our regularity estimates both enhance and, to some extent, extend the results arising from the $C^{p^{\prime}}$ conjecture for the $p$-Laplacian with a bounded source term. As applications of our results, we address some Liouville-type results for our class of equations. Finally, our results are noteworthy, even in the simplest model case governed by the $p$-Laplacian with regular coefficients: $$ \mathrm{div}\left( |\nabla u|^{p-2}\mathfrak{A}(|x|) \nabla u\right) = |x|^{\alpha}u_+^m(x) \quad \text{in} \quad B_1 $$ under suitable assumptions on the data, with possibly singular weight $\mathfrak{h}(|x|) = |x|^{\alpha}$, which includes the Matukuma and Batt-Faltenbacher-Horst's equations as toy models.

Measures of voting power have been the subject of extensive research since the mid 1940s. More recently, similar measures of relative importance have been studied in other domains that include inconsistent knowledge bases, intensity of attacks in argumentation, different problems in the analysis of database management, and explainability. This paper demonstrates that all these examples are instantiations of computing measures of importance for a rather more general problem domain. The paper then shows that the best-known measures of importance can be computed for any reference set whenever one is given a monotonically increasing predicate that partitions the subsets of that reference set. As a consequence, the paper also proves that measures of importance can be devised in several domains, for some of which such measures have not yet been studied nor proposed. Furthermore, the paper highlights several research directions related with computing measures of importance.

The main modification to high $p_t$ jets evolving in the quark gluon plasma is the depletion of their energy to the thermal background. Despite the prominent role played by energy loss effects in jet quenching, their theoretical description is still limited, being, to a large extent, driven by phenomenological considerations. As the field moves towards the measurement of multi-scale jet substructure observables, it is necessary to develop new field theoretic techniques to describe energy loss. In this letter, we highlight a formal similarity between energy loss, and the renormalization group based track function formalism for computing jet substructure observables on charged particles. We introduce an energy loss function, $L_i(x)$, tracking the energy fraction $x$ flowing from an initial hard parton $i$ down to the measured hadrons, and show that its renormalization group evolution can be studied in perturbative QCD, and is related to that of the track functions. The features of this new approach are illustrated in the computation of projected energy correlators, opening the window to a better theoretical treatment of these observables in heavy ion collisions., Comment: 5 pages, 1 figure

This paper presents chemical abundances of twelve elements (C, Na, Mg, Al, Si, K, Ca, Ti, V, Cr, Mn, and Fe) for 80 FGK dwarfs in the Pleiades open cluster, which span a temperature range of $\sim$2000 K in T$_{\rm eff}$, using the high-resolution (R$\sim$22,500) near-infrared SDSS-IV/APOGEE spectra ($\lambda$1.51--1.69 \micron). Using a 1D LTE abundance analysis, we determine an overall metallicity of [Fe/H]=+0.03$\pm$0.04 dex, with the elemental ratios [$\alpha$/Fe]=+0.01$\pm$0.05, [odd-z/Fe]=-0.04$\pm$0.08, and [iron peak/Fe]=-0.02$\pm$0.08. These abundances for the Pleiades are in line with the abundances of other open clusters at similar galactocentric distances as presented in the literature. Examination of the abundances derived from each individual spectral line revealed that several of the stronger lines displayed trends of decreasing abundance with decreasing $T_{\rm eff}$. The list of spectral lines that yield abundances that are independent of $T_{\rm eff}$ are presented and used for deriving the final abundances. An investigation into possible causes of the temperature-dependent abundances derived from the stronger lines suggests that the radiative codes and the APOGEE line list we employ may inadequately model van der Waals broadening, in particular in the cooler K dwarfs., Comment: 16 pages, 7 figures, and 4 tables. Accepted for publication in MNRAS

The modifications imprinted on jets due to their interaction with Quark Gluon Plasma (QGP) are assessed by comparing samples of jets produced in nucleus-nucleus collisions and proton-proton collisions. The standard procedure ignores the effect of bin migration by comparing specific observables for jet populations at the same reconstructed jet transverse momentum ($p_T$). Since jet $p_T$ is itself modified by interaction with QGP, all such comparisons confound QGP induced modifications with changes that are simply a consequence of comparing jets that started out differently. The quantile matching procedure introduced by Brewer et al. directly estimates average fractional jet energy loss ($Q_{AA}$) and can thus mitigate this $p_T$ migration effect. In this work, we validate the procedure in more realistic scenarios that include medium response. We study the evolution of $Q_{AA}$ with jet radius, its sensitivity to minimum particle $p_T$ and medium response as implemented in two different models for jet evolution in heavy-ion collisions. Further, we use this procedure to establish that the difference between inclusive jet and $\gamma+$jet nuclear modification factors ($R_{AA}$) is dominated by differences in the spectral shape, leaving the colour charge of the jet initiating parton with a lesser role to play. Additionally, we compare $Q_{AA}$ to an experimentally proposed proxy for fractional jet energy loss, $S_{loss}$, showing that both quantities are similar, although the former provides a more clear physical interpretation. Finally, we show the size of the $p_T$ migration correction for four different substructure observables and how to reliably use the quantile procedure experimentally to improve existing measurements., Comment: 29 pages, 10 figures, reference added

Developing novel predictive models with complex biomedical information is challenging due to various idiosyncrasies related to heterogeneity, standardization or sparseness of the data. We previously introduced a person-centric ontology to organize information about individual patients, and a representation learning framework to extract person-centric knowledge graphs (PKGs) and to train Graph Neural Networks (GNNs). In this paper, we propose a systematic approach to examine the results of GNN models trained with both structured and unstructured information from the MIMIC-III dataset. Through ablation studies on different clinical, demographic, and social data, we show the robustness of this approach in identifying predictive features in PKGs for the task of readmission prediction., Comment: Published in the 34th Medical Informatics Europe Conference

We prove a quantitative version of a Gidas-Ni-Nirenberg-type symmetry result involving the $p$-Laplacian. Quantitative stability is achieved here via integral identities based on the proof of rigidity established by J. Serra in 2013, which extended to general dimension and the $p$-Laplacian operator an argument proposed by P. L. Lions in dimension $2$ for the classical Laplacian. Stability results for the classical Gidas-Ni-Nirenberg symmetry theorem (involving the classical Laplacian) via the method of moving planes were established by Rosset in 1994 and by Ciraolo, Cozzi, Perugini, Pollastro in 2024. To the authors' knowledge, the present paper provides the first quantitative Gidas-Ni-Nirenberg-type result involving the $p$-Laplacian for $p \neq 2$. Even for the classical Laplacian (i.e., for $p=2$), this is the first time that integral identities are used to achieve stability for a Gidas-Ni-Nirenberg-type result. In passing, we obtain a quantitative estimate for the measure of the singular set and an explicit uniform gradient bound.

As LHC's Run3 unfolds, we peer deeper into the couplings of the 125GeV Higgs ($h_{125}$) and also test for extra scalars. Even before such extra scalars are found, one can probe them by using the fact that theories with multiple Higgs doublets allow for substantial deviations of the couplings of $h_{125}$ from their SM values. Indeed, the observed couplings already place stringent limits on such theories. We investigate the curious possibility that $h_{125}$ couples to the top quark mostly as a scalar, while it couples to the bottom quark mostly as a pseudoscalar. This possibility was allowed by 2017 data for the so-called C2HDM; a two Higgs doublet model with a single source of explicit CP violation. It was shown recently that this possibility disappears when using the full experimental data of 2024. Here we discuss a three Higgs doublet with explicit CP violation (C3HDM), and show that the curious CP-even/CP-odd $t$/$b$ possibility is partly resuscitated, prompting further experimental exploration of this prospect., Comment: 33 pages, 14 figures

Sentence encoder encode the semantics of their input, enabling key downstream applications such as classification, clustering, or retrieval. In this paper, we present Serafim PT*, a family of open-source sentence encoders for Portuguese with various sizes, suited to different hardware/compute budgets. Each model exhibits state-of-the-art performance and is made openly available under a permissive license, allowing its use for both commercial and research purposes. Besides the sentence encoders, this paper contributes a systematic study and lessons learned concerning the selection criteria of learning objectives and parameters that support top-performing encoders.

We discuss the constraints and phenomenology of the $Z_2 \times Z_2$ three Higgs doublet model (3HDM) with two inert scalars, originating two dark matter (DM) particles. We elucidate the competing vacua and we submit the model to all theoretical and current experimental constraints. We find unexplored regions of parameter space and investigate their experimental signatures. In particular, we find regions where the two DM particles contribute equally to the relic DM density., Comment: 24 pages, 17 figures, revtex

We study the scalar and Yukawa sectors of three Higgs doublets models with a generalized CP symmetry. We show that there are only four classes of scalar potentials, merely one more than in two Higgs doublet models (2HDM). In 2HDM with generalized CP symmetries extended to the Yukawa sector, there are only two possible cases: the usual CP, with 18 real Yukawa couplings; and a minimal generalized CP model, with 12 real Yukawa parameters. In contrast, with three Higgs there is a rich variety of allowed models. We classify all possible Yukawa textures, showing that there are 40 possibilities, several of which have only 10 real Yukawa couplings., Comment: 42 pages, Latex

We study the production of a quark-antiquark antenna in the presence of a dense and anisotropic QCD medium. We assume the antenna to originate from an unpolarized gluon state, and consider both massless and massive final states. The medium anisotropy is captured by allowing the jet quenching coefficient to take different magnitudes in orthogonal directions with respect to the jet axis. We find that the final particle distribution is sensitive to the medium anisotropy, and more importantly, that this effect couples directly to the helicity/spin of the final states. We propose to look into these effects by performing a Fourier decomposition of the particle distribution inside the jet. In our medium model, we find that the spin independent terms contribute to the even harmonics of the cosine series. The helicity/spin dependence enters only through the sine Fourier series. We further explore the spin dependence by examining the degree of polarization of the final states in different directions. Our results indicate that the anisotropies present in the QCD matter produced in heavy ion collisions can be probed by studying azimuthal and spin observables inside jets., Comment: 33 pages, 7 figures

The recent discoveries of Neptune-sized ultra-short period planets (USPs) challenge existing planet formation theories. It is unclear whether these residents of the Hot Neptune Desert have similar origins to smaller, rocky USPs, or if this discrete population is evidence of a different formation pathway altogether. We report the discovery of TOI-3261b, an ultra-hot Neptune with an orbital period $P$ = 0.88 days. The host star is a $V = 13.2$ magnitude, slightly super-solar metallicity ([Fe/H] $\simeq$ 0.15), inactive K1.5 main sequence star at $d = 300$ pc. Using data from the Transiting Exoplanet Survey Satellite and the Las Cumbres Observatory Global Telescope, we find that TOI-3261b has a radius of $3.82_{-0.35}^{+0.42}$ $R_{\oplus}$. Moreover, radial velocities from ESPRESSO and HARPS reveal a mass of $30.3_{-2.4}^{+2.2}$ $M_{\oplus}$, more than twice the median mass of Neptune-sized planets on longer orbits. We investigate multiple mechanisms of mass loss that can reproduce the current-day properties of TOI-3261b, simulating the evolution of the planet via tidal stripping and photoevaporation. Thermal evolution models suggest that TOI-3261b should retain an envelope potentially enriched with volatiles constituting $\sim$5% of its total mass. This is the second highest envelope mass fraction among ultra-hot Neptunes discovered to date, making TOI-3261b an ideal candidate for atmospheric follow-up observations., Comment: 20 pages, 11 figures, accepted to AJ

Despite the large number of studies focused on the characterisation of Li-rich stars and understanding the mechanisms leading to such enrichment, their origin remains a mystery. Magnetic activity, particularly the phenomena usually associated with it, and the Li abundance (A(Li)) of stars, are in general thought to be connected. As of today, however, just how they are connected is unclear. In this work, we study a sample of young but evolved intermediate-mass red giants that are inhabitants of open clusters where planets have been searched for. Our aim is to use radial velocity (RV) and stellar activity indicator signals to look for relations between Li abundances and stellar activity or variability. We explored how the standard deviation (STD), peak-to-peak amplitude (PTP), mean, and median of typical stellar activity indicators (BIS, FWHM, $T_\textrm{eff}$, and H$\alpha$ index) change as a function of the Li content of 82 red giants. Furthermore, we computed weighted Pearson correlation coefficients ($\rho_w$) between time series of RV measurements and the stellar activity indicators for the stars in our sample. To aid our results, we also studied generalized Lomb-Scargle periodograms (GLSP) to capture possible significant periodic temporal variations in our data. Our analysis indicates that the STD and PTP of BIS and FWHM, the mean and median of the H$\alpha$ index, and $v\sin(i)$ increase exponentially with A(Li) in our sample of red giants. Significant temporal variations and correlations between RVs and activity indicators also tend to be found preferentially for stars where high A(Li) is observed. Most of the Li-rich stars in our sample either show strong correlations of RV with at least one of the stellar activity indicators or reveal significant periodic temporal variations in their GLSPs of stellar activity indicators that are consistent with those found for RV., Comment: Published in A&A

The Near-InfraRed Planet Searcher or NIRPS is a precision radial velocity spectrograph developed through collaborative efforts among laboratories in Switzerland, Canada, Brazil, France, Portugal and Spain. NIRPS extends to the 0.98-1.8 $\mu$m domain of the pioneering HARPS instrument at the La Silla 3.6-m telescope in Chile and it has achieved unparalleled precision, measuring stellar radial velocities in the infrared with accuracy better than 1 m/s. NIRPS can be used either stand-alone or simultaneously with HARPS. Commissioned in late 2022 and early 2023, NIRPS embarked on a 5-year Guaranteed Time Observation (GTO) program in April 2023, spanning 720 observing nights. This program focuses on planetary systems around M dwarfs, encompassing both the immediate solar vicinity and transit follow-ups, alongside transit and emission spectroscopy observations. We highlight NIRPS's current performances and the insights gained during its deployment at the telescope. The lessons learned and successes achieved contribute to the ongoing advancement of precision radial velocity measurements and high spectral fidelity, further solidifying NIRPS' role in the forefront of the field of exoplanets., Comment: Proceeding at the SPIE Astronomical Telescopes + Instrumentation conference [Yokohama,Japan; June 2024]

PLATO (PLAnetary Transits and Oscillations of stars) is ESA's M3 mission designed to detect and characterise extrasolar planets and perform asteroseismic monitoring of a large number of stars. PLATO will detect small planets (down to <2 R_(Earth)) around bright stars (<11 mag), including terrestrial planets in the habitable zone of solar-like stars. With the complement of radial velocity observations from the ground, planets will be characterised for their radius, mass, and age with high accuracy (5 %, 10 %, 10 % for an Earth-Sun combination respectively). PLATO will provide us with a large-scale catalogue of well-characterised small planets up to intermediate orbital periods, relevant for a meaningful comparison to planet formation theories and to better understand planet evolution. It will make possible comparative exoplanetology to place our Solar System planets in a broader context. In parallel, PLATO will study (host) stars using asteroseismology, allowing us to determine the stellar properties with high accuracy, substantially enhancing our knowledge of stellar structure and evolution. The payload instrument consists of 26 cameras with 12cm aperture each. For at least four years, the mission will perform high-precision photometric measurements. Here we review the science objectives, present PLATO's target samples and fields, provide an overview of expected core science performance as well as a description of the instrument and the mission profile at the beginning of the serial production of the flight cameras. PLATO is scheduled for a launch date end 2026. This overview therefore provides a summary of the mission to the community in preparation of the upcoming operational phases.

In recent years, the impact of machine learning (ML) and artificial intelligence (AI) in society has been absolutely remarkable. This impact is expected to continue in the foreseeable future. However,the adoption of AI/ML is also a cause of grave concern. The operation of the most advances AI/ML models is often beyond the grasp of human decision makers. As a result, decisions that impact humans may not be understood and may lack rigorous validation. Explainable AI (XAI) is concerned with providing human decision-makers with understandable explanations for the predictions made by ML models. As a result, XAI is a cornerstone of trustworthy AI. Despite its strategic importance, most work on XAI lacks rigor, and so its use in high-risk or safety-critical domains serves to foster distrust instead of contributing to build much-needed trust. Logic-based XAI has recently emerged as a rigorous alternative to those other non-rigorous methods of XAI. This paper provides a technical survey of logic-based XAI, its origins, the current topics of research, and emerging future topics of research. The paper also highlights the many myths that pervade non-rigorous approaches for XAI.

A central goal of eXplainable Artificial Intelligence (XAI) is to assign relative importance to the features of a Machine Learning (ML) model given some prediction. The importance of this task of explainability by feature attribution is illustrated by the ubiquitous recent use of tools such as SHAP and LIME. Unfortunately, the exact computation of feature attributions, using the game-theoretical foundation underlying SHAP and LIME, can yield manifestly unsatisfactory results, that tantamount to reporting misleading relative feature importance. Recent work targeted rigorous feature attribution, by studying axiomatic aggregations of features based on logic-based definitions of explanations by feature selection. This paper shows that there is an essential relationship between feature attribution and a priori voting power, and that those recently proposed axiomatic aggregations represent a few instantiations of the range of power indices studied in the past. Furthermore, it remains unclear how some of the most widely used power indices might be exploited as feature importance scores (FISs), i.e. the use of power indices in XAI, and which of these indices would be the best suited for the purposes of XAI by feature attribution, namely in terms of not producing results that could be deemed as unsatisfactory. This paper proposes novel desirable properties that FISs should exhibit. In addition, the paper also proposes novel FISs exhibiting the proposed properties. Finally, the paper conducts a rigorous analysis of the best-known power indices in terms of the proposed properties.

The uses of machine learning (ML) have snowballed in recent years. In many cases, ML models are highly complex, and their operation is beyond the understanding of human decision-makers. Nevertheless, some uses of ML models involve high-stakes and safety-critical applications. Explainable artificial intelligence (XAI) aims to help human decision-makers in understanding the operation of such complex ML models, thus eliciting trust in their operation. Unfortunately, the majority of past XAI work is based on informal approaches, that offer no guarantees of rigor. Unsurprisingly, there exists comprehensive experimental and theoretical evidence confirming that informal methods of XAI can provide human-decision makers with erroneous information. Logic-based XAI represents a rigorous approach to explainability; it is model-based and offers the strongest guarantees of rigor of computed explanations. However, a well-known drawback of logic-based XAI is the complexity of logic reasoning, especially for highly complex ML models. Recent work proposed distance-restricted explanations, i.e. explanations that are rigorous provided the distance to a given input is small enough. Distance-restricted explainability is tightly related with adversarial robustness, and it has been shown to scale for moderately complex ML models, but the number of inputs still represents a key limiting factor. This paper investigates novel algorithms for scaling up the performance of logic-based explainers when computing and enumerating ML model explanations with a large number of inputs.

SHAP scores represent the proposed use of the well-known Shapley values in eXplainable Artificial Intelligence (XAI). Recent work has shown that the exact computation of SHAP scores can produce unsatisfactory results. Concretely, for some ML models, SHAP scores will mislead with respect to relative feature influence. To address these limitations, recently proposed alternatives exploit different axiomatic aggregations, all of which are defined in terms of abductive explanations. However, the proposed axiomatic aggregations are not Shapley values. This paper investigates how SHAP scores can be modified so as to extend axiomatic aggregations to the case of Shapley values in XAI. More importantly, the proposed new definition of SHAP scores avoids all the known cases where unsatisfactory results have been identified. The paper also characterizes the complexity of computing the novel definition of SHAP scores, highlighting families of classifiers for which computing these scores is tractable. Furthermore, the paper proposes modifications to the existing implementations of SHAP scores. These modifications eliminate some of the known limitations of SHAP scores, and have negligible impact in terms of performance.

Clinical trials are pivotal in the drug discovery process to determine the safety and efficacy of a drug candidate. The high failure rates of these trials are attributed to deficiencies in clinical model development and protocol design. Improvements in the clinical drug design process could therefore yield significant benefits for all stakeholders involved. This paper examines the current challenges faced in clinical trial design and optimization, reviews established classical computational approaches, and introduces quantum algorithms aimed at enhancing these processes. Specifically, the focus is on three critical aspects: clinical trial simulations, site selection, and cohort identification. This study aims to provide a comprehensive framework that leverages quantum computing to innovate and refine the efficiency and effectiveness of clinical trials.

Uncertainty in medical image segmentation tasks, especially inter-rater variability, arising from differences in interpretations and annotations by various experts, presents a significant challenge in achieving consistent and reliable image segmentation. This variability not only reflects the inherent complexity and subjective nature of medical image interpretation but also directly impacts the development and evaluation of automated segmentation algorithms. Accurately modeling and quantifying this variability is essential for enhancing the robustness and clinical applicability of these algorithms. We report the set-up and summarize the benchmark results of the Quantification of Uncertainties in Biomedical Image Quantification Challenge (QUBIQ), which was organized in conjunction with International Conferences on Medical Image Computing and Computer-Assisted Intervention (MICCAI) 2020 and 2021. The challenge focuses on the uncertainty quantification of medical image segmentation which considers the omnipresence of inter-rater variability in imaging datasets. The large collection of images with multi-rater annotations features various modalities such as MRI and CT; various organs such as the brain, prostate, kidney, and pancreas; and different image dimensions 2D-vs-3D. A total of 24 teams submitted different solutions to the problem, combining various baseline models, Bayesian neural networks, and ensemble model techniques. The obtained results indicate the importance of the ensemble models, as well as the need for further research to develop efficient 3D methods for uncertainty quantification methods in 3D segmentation tasks., Comment: initial technical report

The combination of language processing and image processing keeps attracting increased interest given recent impressive advances that leverage the combined strengths of both domains of research. Among these advances, the task of editing an image on the basis solely of a natural language instruction stands out as a most challenging endeavour. While recent approaches for this task resort, in one way or other, to some form of preliminary preparation, training or fine-tuning, this paper explores a novel approach: We propose a preparation-free method that permits instruction-guided image editing on the fly. This approach is organized along three steps properly orchestrated that resort to image captioning and DDIM inversion, followed by obtaining the edit direction embedding, followed by image editing proper. While dispensing with preliminary preparation, our approach demonstrates to be effective and competitive, outperforming recent, state of the art models for this task when evaluated on the MAGICBRUSH dataset.

We use a Kernel Density Estimator method to evaluate the stellar velocity dispersion in the open cluster NGC 2571. We derive the 3-D velocity dispersion using both proper motions as extracted from Gaia DR3 and single epoch radial velocities as obtained with the instrument FLAMES at ESO VLT. The mean-square velocity along the line-of-sight is found to be larger than the one in the tangential direction by a factor in the interval [6,8]. We argue that the most likely explanation for such an occurrence is the presence of a significant quantity of unresolved binary and multiple stars in the radial velocity sample. Special attention should be paid to single line spectroscopic binaries (SB1) since in this case we observe the spectral lines of the primary component only, and therefore the derived radial velocity is not the velocity of the binary system center of mass. To investigate this scenario, we performed numerical experiments at varying the fractional abundance of SB1 in the observed sample. These experiments show that the increase of the mean-square radial velocity depends actually on the fractional abundance of SB1 to a power in the range of [0.39,0.45]. We used the 3-D velocity dispersion obtained by the dispersions in the tangential directions and the assumption that the radial velocity dispersion is the same as a tangential one to estimate the virial cluster mass and the cluster mass taking into account the gravitational field of the Galaxy and the non-stationarity of the cluster. These estimates are $650\pm30 \; M_\odot$ and $310\pm80 \; M_\odot$, respectively, and they are in substantial agreement with the photometric cluster mass., Comment: 16 pages, 7 figures, accepted for publication in the Astronomical Journal

Weyl nodal loop semimetals are gapless topological phases that, unlike their insulator counterparts, may be unstable to small perturbations that respect their topology-protecting symmetries. Here, we analyze a clean system perturbed by chiral off-diagonal disorder using numerically exact methods. We establish that the ballistic semimetallic phase is unstable towards the formation of an unconventional topological diffusive metal hosting topological multifractal surface states. Although, as in the clean case, surface states are exponentially localized along the direction perpendicular to the nodal loop, disorder induces a multifractal structure in the remaining directions. Surprisingly, the number of these states also increases with a small amount of disorder. Eventually, as disorder is further increased, the number of surface states starts decreasing. In the strong disordered regime we predict that some types of disorder induce an Anderson transition into an electrically-polarized insulator whose signature may be detected experimentally.

We have detected solar-like oscillations in the mid K-dwarf $\varepsilon$ Indi A, making it the coolest dwarf to have measured oscillations. The star is noteworthy for harboring a pair of brown dwarf companions and a Jupiter-type planet. We observed $\varepsilon$ Indi A during two radial velocity campaigns, using the high-resolution spectrographs HARPS (2011) and UVES (2021). Weighting the time series, we computed the power spectra and established the detection of solar-like oscillations with a power excess located at $5265 \pm 110 \ \mu$Hz -- the highest frequency solar-like oscillations so far measured in any star. The measurement of the center of the power excess allows us to compute a stellar mass of $0.782 \pm 0.023 \ M_\odot$ based on scaling relations and a known radius from interferometry. We also determine the amplitude of the peak power and note that there is a slight difference between the two observing campaigns, indicating a varying activity level. Overall, this work confirms that low-amplitude solar-like oscillations can be detected in mid-K type stars in radial velocity measurements obtained with high-precision spectrographs., Comment: 10 pages, 3 figures, accepted for publication in ApJ

The complex two-Higgs doublet model (C2HDM) is one of the simplest extensions of the Standard Model with a source of CP-violation in the scalar sector. It has a $\mathbb{Z}_2$ symmetry, softly broken by a complex coefficient. There are four ways to implement this symmetry in the fermion sector, leading to models known as Type-I, Type-II, Lepton-Specific and Flipped. In the latter three models, there is a priori the surprising possibility that the 125 GeV Higgs boson couples mostly as a scalar to top quarks, while it couples mostly as a pseudoscalar to bottom quarks. This ``maximal'' scenario was still possible with the data available in 2017. Since then, there have been more data on the 125 GeV Higgs boson, direct searches for CP-violation in angular correlations of $\tau$-leptons produced in Higgs boson decays, new results on the electron electric dipole moment, new constraints from LHC searches for additional Higgs bosons and new results on $b\to s \gamma$ transitions. Highlighting the crucial importance of the physics results of LHC's Run 2, we combine all these experiments and show that the ``maximal'' scenario is now excluded in all models. Still, one can have a pseudoscalar component in $h \tau\bar{\tau}$ couplings in the Lepton-Specific case as large as $87\%$ of the scalar component for all mass orderings of the neutral scalar bosons., Comment: 24 pages, 7 figures, v2: minor changes, matches published version

To foster the neural encoding of Portuguese, this paper contributes foundation encoder models that represent an expansion of the still very scarce ecosystem of large language models specifically developed for this language that are fully open, in the sense that they are open source and openly distributed for free under an open license for any purpose, thus including research and commercial usages. Like most languages other than English, Portuguese is low-resourced in terms of these foundational language resources, there being the inaugural 900 million parameter Albertina and 335 million Bertimbau. Taking this couple of models as an inaugural set, we present the extension of the ecosystem of state-of-the-art open encoders for Portuguese with a larger, top performance-driven model with 1.5 billion parameters, and a smaller, efficiency-driven model with 100 million parameters. While achieving this primary goal, further results that are relevant for this ecosystem were obtained as well, namely new datasets for Portuguese based on the SuperGLUE benchmark, which we also distribute openly.

To advance the neural decoding of Portuguese, in this paper we present a fully open Transformer-based, instruction-tuned decoder model that sets a new state of the art in this respect. To develop this decoder, which we named Gerv\'asio PT*, a strong LLaMA~2 7B model was used as a starting point, and its further improvement through additional training was done over language resources that include new instruction data sets of Portuguese prepared for this purpose, which are also contributed in this paper. All versions of Gerv\'asio are open source and distributed for free under an open license, including for either research or commercial usage, and can be run on consumer-grade hardware, thus seeking to contribute to the advancement of research and innovation in language technology for Portuguese.

In this work, we establish universal moduli of continuity for viscosity solutions to fully nonlinear elliptic equations with oblique boundary conditions, whose general model is given by $$ \left\{ \begin{array}{rcl} F(D^2u,x) &=& f(x) \quad \mbox{in} \,\, \Omega\\ \beta(x) \cdot Du(x) + \gamma(x) \, u(x)&=& g(x) \quad \mbox{on} \,\, \partial \Omega. \end{array} \right. $$ Such regularity estimates are achieved by exploring the integrability properties of $f$ based on different scenarios, making a $\text{VMO}$ assumption on the coefficients of $F$, and by considering suitable smoothness properties on the boundary data $\beta, \gamma$ and $g$. Particularly, we derive sharp estimates for borderline cases where $f \in L^n(\Omega)$ and $f\in p-\textrm{BMO}(\Omega)$. Additionally, for source terms in $L^p(\Omega)$, for $p \in (n, \infty)$, we obtain sharp gradient estimates. Finally, we also address Schauder-type estimates for convex/concave operators and suitable H\"{o}lder data.

Image captioning and cross-modal retrieval are examples of tasks that involve the joint analysis of visual and linguistic information. In connection to remote sensing imagery, these tasks can help non-expert users in extracting relevant Earth observation information for a variety of applications. Still, despite some previous efforts, the development and application of vision and language models to the remote sensing domain have been hindered by the relatively small size of the available datasets and models used in previous studies. In this work, we propose RS-CapRet, a Vision and Language method for remote sensing tasks, in particular image captioning and text-image retrieval. We specifically propose to use a highly capable large decoder language model together with image encoders adapted to remote sensing imagery through contrastive language-image pre-training. To bridge together the image encoder and language decoder, we propose training simple linear layers with examples from combining different remote sensing image captioning datasets, keeping the other parameters frozen. RS-CapRet can then generate descriptions for remote sensing images and retrieve images from textual descriptions, achieving SOTA or competitive performance with existing methods. Qualitative results illustrate that RS-CapRet can effectively leverage the pre-trained large language model to describe remote sensing images, retrieve them based on different types of queries, and also show the ability to process interleaved sequences of images and text in a dialogue manner.

The Alqueva Multi-Purpose Project (EFMA) is a massive abduction and storage infrastructure system in the Alentejo, which has a water quality monitoring network with almost thousands of water quality stations distributed across three subsystems: Alqueva, Pedrog\~ao, and Ardila. Identification of pollution sources in complex infrastructure systems, such as the EFMA, requires recognition of water flow direction and delimitation of areas being drained to specific sampling points. The transfer channels in the EFMA infrastructure artificially connect several water bodies that do not share drainage basins, which further complicates the interpretation of water quality data because the water does not flow exclusively downstream and is not restricted to specific basins. The existing user-friendly GIS tools do not facilitate the exploration and visualisation of water quality data in spatial-temporal dimensions, such as defining temporal relationships between monitoring campaigns, nor do they allow the establishment of topological and hydrological relationships between different sampling points. This thesis work proposes a framework capable of aggregating many types of information in a GIS environment, visualising large water quality-related datasets and, a graph data model to integrate and relate water quality between monitoring stations and land use. The graph model allows to exploit the relationship between water quality in a watercourse and reservoirs associated with infrastructures. The graph data model and the developed framework demonstrated encouraging results and has proven to be preferred when compared to relational databases.

Air pollution constitutes a global problem of paramount importance that affects not only human health, but also the environment. The existence of spatial and temporal data regarding the concentrations of pollutants is crucial for performing air pollution studies and monitor emissions. However, although observation data presents great temporal coverage, the number of stations is very limited and they are usually built in more populated areas. The main objective of this work is to create models capable of inferring pollutant concentrations in locations where no observation data exists. A machine learning model, more specifically the random forest model, was developed for predicting concentrations in the Iberian Peninsula in 2019 for five selected pollutants: $NO_2$, $O_3$ $SO_2$, $PM10$, and $PM2.5$. Model features include satellite measurements, meteorological variables, land use classification, temporal variables (month, day of year), and spatial variables (latitude, longitude, altitude). The models were evaluated using various methods, including station 10-fold cross-validation, in which in each fold observations from 10\% of the stations are used as testing data and the rest as training data. The $R^2$, RMSE and mean bias were determined for each model. The $NO_2$ and $O_3$ models presented good values of $R^2$, 0.5524 and 0.7462, respectively. However, the $SO_2$, $PM10$, and $PM2.5$ models performed very poorly in this regard, with $R^2$ values of -0.0231, 0.3722, and 0.3303, respectively. All models slightly overestimated the ground concentrations, except the $O_3$ model. All models presented acceptable cross-validation RMSE, except the $O_3$ and $PM10$ models where the mean value was a little higher (12.5934 $\mu g/m^3$ and 10.4737 $\mu g/m^3$, respectively).