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We consider the following Lane-Emden system with Neumann boundary conditions \[ -\Delta u= |v|^{q-1}v \text{ in } \Omega,\qquad -\Delta v= |u|^{p-1}u \text{ in } \Omega,\qquad \partial_\nu u=\partial_\nu v=0 \text{ on } \partial \Omega, \] where $\Omega$ is a bounded smooth domain of $\mathbb{R}^N$ with $N \ge 1$. We study the multiplicity of solutions and the convergence of least energy (nodal) solutions (l.e.s.) as the exponents $p, q > 0$ vary in the subcritical regime $1/(p+1) + 1/(q+1) > (N-2)/N$, or in the critical case $1/(p+1) + 1/(q+1) =(N-2)/N$ with some additional assumptions. We consider, for the first time in this setting, the cases where one or two exponents tend to zero, proving that l.e.s. converge to a problem with a sign nonlinearity. Our approach is based on an alternative characterization of least energy levels in terms of the nonlinear eigenvalue problem \[ \Delta (|\Delta u|^{\frac 1 q -1} \Delta u) = \lambda |u|^{p-1} u, \quad \partial_\nu u=\partial_\nu(|\Delta u|^{\frac 1 q -1} \Delta u)=0 \text{ on } \partial \Omega. \] As an application, we show a symmetry breaking phenomenon for l.e.s. of a bilaplacian equation with sign nonlinearity and for other equations with nonlinear higher-order operators.

The O-type long-period binary HD 168112 and triple HD 167971 star systems have been known for several decades for their non-thermal synchrotron radio emission. This emission arises from relativistic electrons accelerated in the hydrodynamic shocks of the wind collisions in these systems. Such wind collisions are expected to produce a strong X-ray emission that varies as a function of orbital phase. In wide eccentric binaries, such as our targets, the X-ray emission arises from an adiabatic plasma and its intensity should scale as the inverse of the orbital separation. We present a set of XMM-Newton observations of these systems which help us gain insight into the properties of their wind interactions., Comment: in French language. Accepted for publication in the Bulletin de la Soci\'et\'e Royale des Sciences de Li\`ege, Proceedings of the 41st Li\`ege Astrophysical Colloquium, held in Li\`ege 15-19 July 2024, edited by Y. Naz\'e, & E. Bozzo

Integrating deep learning into medical imaging is poised to greatly advance diagnostic methods but it faces challenges with generalizability. Foundation models, based on self-supervised learning, address these issues and improve data efficiency. Natural domain foundation models show promise for medical imaging, but systematic research evaluating domain adaptation, especially using self-supervised learning and parameter-efficient fine-tuning, remains underexplored. Additionally, little research addresses the issue of catastrophic forgetting during fine-tuning of foundation models. We adapted the DINOv2 vision transformer for retinal imaging classification tasks using self-supervised learning and generated two novel foundation models termed DINORET and BE DINORET. Publicly available color fundus photographs were employed for model development and subsequent fine-tuning for diabetic retinopathy staging and glaucoma detection. We introduced block expansion as a novel domain adaptation strategy and assessed the models for catastrophic forgetting. Models were benchmarked to RETFound, a state-of-the-art foundation model in ophthalmology. DINORET and BE DINORET demonstrated competitive performance on retinal imaging tasks, with the block expanded model achieving the highest scores on most datasets. Block expansion successfully mitigated catastrophic forgetting. Our few-shot learning studies indicated that DINORET and BE DINORET outperform RETFound in terms of data-efficiency. This study highlights the potential of adapting natural domain vision models to retinal imaging using self-supervised learning and block expansion. BE DINORET offers robust performance without sacrificing previously acquired capabilities. Our findings suggest that these methods could enable healthcare institutions to develop tailored vision models for their patient populations, enhancing global healthcare inclusivity., Comment: J.Zoellin, C. Merk and M. Buob contributed equally as shared-first authors. D. Cabrera DeBuc, M. D. Becker and G. M. Somfai contributed equally as senior authors for this work

Based on experimental and simulation methods we helped develop, we are advancing mechanistic understanding of how self-assembled NC metamaterials can produce distinctive near- and far-field optical properties not readily achievable in lithographically patterned structures. First, the impacts of the inevitable defects and disorder associated with self-assembly can be rationalized and, in some cases, recognized as advantageous. Second, self-assembly enables intimate nanoscale intermixing of different NC and molecular components. By incorporating probe molecules within the gaps between NCs where the electric field enhancement is strongest, we show enhanced detection of molecular vibrations that can be optimized by tuning the size and resonance frequency of the NCs. We show how metasurfaces incorporating mixtures of NCs with different doping concentrations can achieve epsilon-near-zero dielectric response over a broad frequency range. Finally, considering the NC metasurface itself as a building block, we show how photonic structures incorporating these assemblies can harness and amplify their distinctive properties. Through modeling the NC monolayer as a slab with an effective permittivity response, we designed a frequency-tunable IR perfect absorber by layering the NCs on a simple open cavity structure. Since the perfect absorption architecture further enhances the IR electric field localization strength, we expect that this integration strategy can enhance molecular vibration coupling or non-linear optical response. The versatility of the NC assembly and integration approach suggests opportunities for various metal oxide NC superstructures, including mixing and stacking of NCs beyond a single monolayer, representing a vast parameter space for design of linear and nonlinear IR optical components., Comment: 33 pages, 5 figures

We consider the two-dimensional water-wave problem with a general non-zero vorticity field in a fluid volume with a flat bed and a free surface. The nonlinear equations of motion for the chosen surface and volume variables are expressed with the aid of the Dirichlet-Neumann operator and the Green function of the Laplace operator in the fluid domain. Moreover, we provide new explicit expressions for both objects. The field of a point vortex and its interaction with the free surface is studied as an example. In the small-amplitude long-wave Boussinesq and KdV regimes, we obtain appropriate systems of coupled equations for the dynamics of the point vortex and the time evolution of the free surface variables., Comment: 36 pages, 4 figures

A quasi-consensus has steadily formed in the scientific literature on the fact that the prevention measures implemented by most countries to curb the 2020 COVID-19 pandemic have led to significant reductions in pollution levels around the world, especially in urban environments. Fewer studies have looked at the how these reductions at ground level translate into variations in the whole atmosphere. In this study, we examine the columnar values of aerosols at 51 mainland European stations of the Aerosol Robotic Network (AERONET). We show that when considered in the context of the long-term trend over the last decade, the columnar aerosol levels for 2020, at the regional level, do not appear exceptional. Both the yearly means and the number of episodes with extreme values for this period are within the one standard deviation of the long-term trends. We conclude that the spatially and temporally very localized reductions do not add up to statistically significant reductions in the global levels of aerosols. Furthermore, considering that pandemic lockdowns can be thought of as a simulation of a climate change mitigation scenario, we conclude that such lifestyle-based changes present a very low potential as a global climate change mitigation strategy.

We show how (well-established) type systems based on non-idempotent intersection types can be extended to characterize termination properties of functional programming languages with pattern matching features. To model such programming languages, we use a (weak and closed) $\lambda$-calculus integrating a pattern matching mechanism on algebraic data types (ADTs). Remarkably, we also show that this language not only encodes Plotkin's CBV and CBN $\lambda$-calculus as well as other subsuming frameworks, such as the bang-calculus, but can also be used to interpret the semantics of effectful languages with exceptions. After a thorough study of the untyped language, we introduce a type system based on intersection types, and we show through purely logical methods that the set of terminating terms of the language corresponds exactly to that of well-typed terms. Moreover, by considering non-idempotent intersection types, this characterization turns out to be quantitative, i.e. the size of the type derivation of a term t gives an upper bound for the number of evaluation steps from t to its normal form., Comment: APLAS 2024, full version (including complete proofs)

Modern artificial intelligence (AI) systems are powered by foundation models. This paper presents a new set of foundation models, called Llama 3. It is a herd of language models that natively support multilinguality, coding, reasoning, and tool usage. Our largest model is a dense Transformer with 405B parameters and a context window of up to 128K tokens. This paper presents an extensive empirical evaluation of Llama 3. We find that Llama 3 delivers comparable quality to leading language models such as GPT-4 on a plethora of tasks. We publicly release Llama 3, including pre-trained and post-trained versions of the 405B parameter language model and our Llama Guard 3 model for input and output safety. The paper also presents the results of experiments in which we integrate image, video, and speech capabilities into Llama 3 via a compositional approach. We observe this approach performs competitively with the state-of-the-art on image, video, and speech recognition tasks. The resulting models are not yet being broadly released as they are still under development.

We consider the Hamiltonian system with Neumann boundary conditions: \[ -\Delta u + \mu u=v^{q }, \quad -\Delta v+ \mu v=u^{p} \quad \text{ in $\Omega$}, \qquad u, v >0 \quad \text{ in $\Omega$,} \qquad \partial_\nu u= \partial_\nu v=0 \quad \text{ on $\partial \Omega$, } \] where $\mu >0$ is a parameter and $\Omega$ is a smooth bounded domain in $\mathbb R^N .$ When $(p, q)$ approaches from below the critical hyperbola $N/(p+1) + N/(q+1)=N-2$, we build a solution which blows-up at a boundary point where the mean curvature achieves its minimum and negative value.

The long-period O-star binary system HD 168112 and the triple O-star system HD 167971 are well-known sources of non-thermal radio emission that arises from a colliding wind interaction. The wind-wind collisions in these systems should result in phase-dependent X-ray emissions. The presence of a population of relativistic electrons in the wind interaction zone could affect the properties of the X-ray emission and make it deviate from the behaviour expected for adiabatic shocks. We investigate the X-ray emission of these systems with the goals of quantifying the fraction of the X-ray flux arising from wind interactions and determining whether these emissions follow the predictions for adiabatic wind-wind collisions. Six X-ray observations were collected with XMM-Newton. Three observations were scheduled around the most recent periastron passage of HD 168112. Spectra and light curves were analysed and compared with simple predictions of model calculations for X-ray emission from colliding wind systems. The X-ray emission of HD 168112 varies as the inverse of the orbital separation, as expected for an adiabatic wind interaction zone. The relative contribution of intrinsic X-ray emission from wind-embedded shocks varies between 38% at periastron to 81% at apastron. The wind-wind collision zone remains adiabatic even around periastron passage. The X-ray emission of HD 167971 displays variations on the orbital timescale of the inner eclipsing binary. The existing data of this system do not allow us to probe variations on the timescale of the outer orbit. Shock modification due to the action of relativistic electrons does not seem to be efficiently operating in the HD 168112 system. In the existing observations, a significant part of the emission of HD 167971 must arise in the inner eclipsing binary. The origin of this emission is as yet unclear., Comment: Accepted for publication in Astronomy & Astrophysics

Aerosols' impact on the performance of a clear-sky solar irradiance model is often evaluated from the perspective of the overall accuracy of estimates. This study assesses the aerosol role in clear-sky solar irradiance modelling from a totally different perspective, namely the ability of a model to accurately separate global solar irradiance into its fundamental direct and diffuse components. In an innovative approach, the analysis is focused on the sensitivity of parametric solar irradiance models to changes in aerosol conditions. A new measure, the aerosol influence quantifier, is introduced for assessing the correlation strength between the relative variation in clear-sky diffuse fraction and the relative variation in atmospheric aerosol load. The effectiveness of the aerosol influence quantifier is explored as a tool for assessing the sensitivity of three parametric clear-sky models to variations in input aerosol data. A rather surprising result is reported, e.g. if high quality aerosol data are not available, one could potentially maximize the estimate's accuracy by using a parametric clear-sky solar irradiance model with low sensitivity to aerosol variations. In such cases, it is shown that the aerosol influence quantifier can be used as a tool for identifying an adequate model for input data with a given uncertainty.

Several evaluation notions for lambda calculus qualify as reasonable cost models according to Slot and van Emde Boas' Invariance Thesis. A notable result achieved by Accattoli and Dal Lago is that leftmost-outermost reduction is reasonable, where the term representation uses sharing and the steps are useful. These results, initially studied in call-by-name, have also been extended to call-by-value. However, the existing formulations of usefulness lack inductive structure, making it challenging in particular to define and reason about type systems on top of the untyped syntax. Additionally, no type-based quantitative interpretations exist for useful evaluation. In this work, we establish the first inductive definition of useful evaluation for open weak call-by-value. This new useful strategy connects to a previous implementation of usefulness through a low-level abstract machine, incurring only in linear time overhead, thus providing a reasonable cost model for open call-by-value implementation. We also propose a semantic interpretation of useful call-by-value using a non-idempotent intersection type system equipped with a notion of tightness. The resulting interpretation is quantitative, i.e. provides exact step-count information for program evaluation. This turns out to be the first semantical interpretation in the literature for a notion of useful evaluation.

Intersection type systems have been independently applied to different evaluation strategies, such as call-by-name (CBN) and call-by-value (CBV). These type systems have been then generalized to different subsuming paradigms being able, in particular, to encode CBN and CBV in a unique unifying framework. However, there are no intersection type systems that explicitly enable CBN and CBV to cohabit together without making use of an encoding into a common target framework. This work proposes an intersection type system for PCF with a specific notion of evaluation, called PCFH. Evaluation in PCFH actually has a hybrid nature, in the sense that CBN and CBV operational behaviors cohabit together. Indeed, PCFH combines a CBV-like operational behavior for function application with a CBN-like behavior for recursion. This hybrid nature is reflected in the type system, which turns out to be sound and complete with respect to PCFH: not only typability implies normalization, but also the converse holds. Moreover, the type system is quantitative, in the sense that the size of typing derivations provides upper bounds for the length of the reduction sequences to normal form. This type system is then refined to a tight one, offering exact information regarding the length of normalization sequences. This is the first time that a sound and complete quantitative type system has been designed for a hybrid computational model., Comment: 38 pages

This paper studies the strength of embedding Call-by-Name ({\tt dCBN}) and Call-by-Value ({\tt dCBV}) into a unifying framework called the Bang Calculus ({\tt dBANG}). These embeddings enable establishing (static and dynamic) properties of {\tt dCBN} and {\tt dCBV} through their respective counterparts in {\tt dBANG}. While some specific static properties have been already successfully studied in the literature, the dynamic ones are more challenging and have been left unexplored. We accomplish that by using a standard embedding for the (easy) {\tt dCBN} case, while a novel one must be introduced for the (difficult) {\tt dCBV} case. Moreover, a key point of our approach is the identification of {\tt dBANG} diligent reduction sequences, which eases the preservation of dynamic properties from {\tt dBANG} to {\tt dCBN}/{\tt dCBV}. We illustrate our methodology through two concrete applications: confluence/factorization for both {\tt dCBN} and {\tt dCBV} are respectively derived from confluence/factorization for {\tt dBANG}.

This paper studies the notion of meaningfulness for a unifying framework called dBang-calculus, which subsumes both call-by-name (dCbN) and call-by-value (dCbV). We first characterize meaningfulness in dBang by means of typability and inhabitation in an associated non-idempotent intersection type system previously proposed in the literature. We validate the proposed notion of meaningfulness by showing two properties (1) consistency of the theory $\mathcal{H}$ equating meaningless terms and (2) genericity, stating that meaningless subterms have no bearing on the significance of meaningful terms. The theory $\mathcal{H}$ is also shown to have a unique consistent and maximal extension. Last but not least, we show that the notions of meaningfulness and genericity in the literature for dCbN and dCbV are subsumed by the respectively ones proposed here for the dBang-calculus.