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Graph Neural Networks (GNNs) are powerful at solving graph classification tasks, yet applied problems often contain noisy labels. In this work, we study GNN robustness to label noise, demonstrate GNN failure modes when models struggle to generalise on low-order graphs, low label coverage, or when a model is over-parameterized. We establish both empirical and theoretical links between GNN robustness and the reduction of the total Dirichlet Energy of learned node representations, which encapsulates the hypothesized GNN smoothness inductive bias. Finally, we introduce two training strategies to enhance GNN robustness: (1) by incorporating a novel inductive bias in the weight matrices through the removal of negative eigenvalues, connected to Dirichlet Energy minimization; (2) by extending to GNNs a loss penalty that promotes learned smoothness. Importantly, neither approach negatively impacts performance in noise-free settings, supporting our hypothesis that the source of GNNs robustness is their smoothness inductive bias.

It is widely assumed that dust opacities in molecular clouds follow a power-law profile with an index, $\beta$. Recent studies of the Orion Molecular Cloud (OMC) 2/3 complex, however, show a flattening in the spectral energy distribution (SED) at $ \lambda > 2$ mm implying non-constant indices on scales $\gtrsim$ 0.08 pc. The origin of this flattening is not yet known but it may be due to the intrinsic properties of the dust grains or contamination from other sources of emission. We investigate the SED slopes in OMC 2/3 further using observations of six protostellar cores with NOEMA from 2.9 mm to 3.6 mm and ALMA-ACA in Band 4 (1.9 -- 2.1 mm) and Band 5 (1.6 -- 1.8 mm) on core and envelope scales of $\sim 0.02 - 0.08$ pc. We confirm flattened opacity indices between 2.9 mm and 3.6 mm for the six cores with $\beta \approx -0.16 - 1.45$, which are notably lower than the $\beta$ values of $> 1.3$ measured for these sources on $0.08$ pc scales from single-dish data. Four sources have consistent SED slopes between the ALMA data and the NOEMA data. We propose that these sources may have a significant fraction of emission coming from large dust grains in embedded disks, which biases the emission more at longer wavelengths. Two sources, however, had inconsistent slopes between the ALMA and NOEMA data, indicating different origins of emission. These results highlight how care is needed when combining multi-scale observations or extrapolating single-band observations to other wavelengths., Comment: Accepted to ApJ, 18 pages, 4 figures, 6 Tables

We present 850 $\mu$m polarization observations of the IC 348 star-forming region in the Perseus molecular cloud as part of the B-fields In STar-forming Region Observation (BISTRO) survey. We study the magnetic properties of two cores (HH 211 MMS and IC 348 MMS) and a filamentary structure of IC 348. We find that the overall field tends to be more perpendicular than parallel to the filamentary structure of the region. The polarization fraction decreases with intensity, and we estimate the trend by power-law and the mean of the Rice distribution fittings. The power indices for the cores are much smaller than 1, indicative of possible grain growth to micron size in the cores. We also measure the magnetic field strengths of the two cores and the filamentary area separately by applying the Davis-Chandrasekhar-Fermi method and its alternative version for compressed medium. The estimated mass-to-flux ratios are 0.45-2.20 and 0.63-2.76 for HH 211 MMS and IC 348 MMS, respectively, while the ratios for the filament is 0.33-1.50. This result may suggest that the transition from subcritical to supercritical conditions occurs at the core scale ($\sim$ 0.05 pc) in the region. In addition, we study the energy balance of the cores and find that the relative strength of turbulence to the magnetic field tends to be stronger for IC 348 MMS than HH 211 MMS. The result could potentially explain the different configurations inside the two cores: a single protostellar system in HH 211 MMS and multiple protostars in IC 348 MMS., Comment: Accepted for publication in ApJ. 21 pages, 12 figures

Observations suggest that filaments in molecular clouds can grow by mass accretion while forming cores via fragmentation. Here we present one of the first large sample studies of filament accretion using velocity gradient measurements of star-forming filaments on the $\sim 0.05$ pc scale with NH$_3$ observations of the Perseus Molecular Cloud, primarily obtained as a part of the GBT Ammonia Survey (GAS). In this study, we find significant correlations between velocity gradient, velocity dispersion, mass per unit length, and the number of cores per unit length of the Perseus filaments. Our results suggest a scenario in which filaments not only grow through mass accretion but also form new cores continuously in the process well into the thermally supercritical regime. Such behavior is contrary to that expected from isolated filament models but consistent with how filaments form within a more realistic cloud environment, suggesting that the cloud environment plays a crucial role in shaping core formation and evolution in filaments. Furthermore, even though velocity gradients within filaments are not oriented randomly, we find no correlation between velocity gradient orientation and the filament properties we analyzed. This result suggests that gravity is unlikely the dominant mechanism imposing order on the $\sim 0.05$ pc scale for dense star-forming gas., Comment: Accepted to ApJ (Oct 17, 2024)

We present 850 {\mu}m thermal dust polarization observations with a resolution of 14.4"(~ 0.13 pc) towards an infrared dark cloud G16.96+0.27 using JCMT/POL-2. The average magnetic field orientation, which roughly agrees with the larger-scale magnetic field orientation traced by the Planck 353 GHz data, is approximately perpendicular to the filament structure. The estimated plane-of-sky magnetic field strength is ~ 96 {\mu}G and ~ 60 {\mu}G using two variants of the Davis-Chandrasekhar-Fermi methods. We calculate the virial and magnetic critical parameters to evaluate the relative importance of gravity, the magnetic field, and turbulence. The magnetic field and turbulence are both weaker than gravity, but magnetic fields and turbulence together are equal to gravity, suggesting that G16.96+0.27 is in a quasi-equilibrium state. The cloud-magnetic-field alignment is found to have a trend moving away from perpendicularity in the dense regions, which may serve as a tracer of potential fragmentation in such quiescent filaments., Comment: Accepted by ApJ. 13 pages, 5 figures

Uncovering the heterogeneous effects of particular policies or "treatments" is a key concern for researchers and policymakers. A common approach is to report average treatment effects across subgroups based on observable covariates. However, the choice of subgroups is crucial as it poses the risk of $p$-hacking and requires balancing interpretability with granularity. This paper proposes a nonparametric approach to construct heterogeneous subgroups. The approach enables a flexible exploration of the trade-off between interpretability and the discovery of more granular heterogeneity by constructing a sequence of nested groupings, each with an optimality property. By integrating our approach with "honesty" and debiased machine learning, we provide valid inference about the average treatment effect of each group. We validate the proposed methodology through an empirical Monte-Carlo study and apply it to revisit the impact of maternal smoking on birth weight, revealing systematic heterogeneity driven by parental and birth-related characteristics.

ALMA-IMF observed 15 massive protoclusters capturing multiple spectral lines and the continuum emission. We focus on the G351.77 protocluster ($\sim$ 2500 M$_{\odot}$, estimated from single-dish continuum observations) located at 2 kpc. We trace the dense gas emission and kinematics with N$_2$H$^+$ (1-0) at $\sim$ 4 kau resolution. We estimate an N$_2$H$^+$ relative abundance $\sim (1.7 \pm 0.5) \times 10^{-10}$. We decompose the N$_2$H$^+$ emission into up to two velocity components, highlighting the kinematic complexity in the dense gas. By examining the position-velocity (PV) diagrams on small scales, we observe clear inflow signatures (V-shapes) associated with dense cores. The most prominent V-shape has a mass inflow rate of $\sim 9.8 \times 10^{-4}$ M$_{\odot}$ yr$^{-1}$ and a short timescale of $\sim$ 15.6 kyr. We also observe V-shapes without associated cores. This suggests both that cores or centers of accretion exist below the 1.3 mm detection limit, and that the V-shapes may be viable tracers of very early accretion and star formation on $\sim$ 4 kau scales. The large-scale PV diagram shows that the protocluster is separated into 2 principal velocity structures. Combined with smaller scale DCN and H$_2$CO emission, we propose a scenario of larger scale slow contraction with rotation in the center based on simple toy models. This scenario leads the suggestion of outside-in evolution of the protocluster as it collapses. The gas depletion times implied by the V-shapes are short ($\sim$ 0.3 Myr), requiring either very fast cluster formation, and/or continuous mass feeding of the protocluster. The latter is possible via the Mother Filament G351.77 is forming out of. The similarities in the properties of G351.77 and the recently published work in G353.41 indicate that many of the physical conditions inferred via the ALMA-IMF N$_2$H$^+$ observations may be generic to protoclusters., Comment: Submitted in A&A, 28 pages, 31 figures, 4 interactive figures, 7 tables

We propose an approach to model spatial heterogeneity in SIR-type models for the spread of epidemics via \emph{nonlocal aggregation terms}. More precisely, we first consider an SIR model with spatial movements driven by nonlocal aggregation terms, in which the inter-compartment and intra-compartment interaction terms are distinct, and modelled through smooth interaction kernels. For the Cauchy problem of said model we provide a full well-posedness theory on $\R^2$ for $L^1\cap L^\infty \cap H^1$ initial conditions. The existence part is achieved by considering an approximated model with artificial linear diffusion, for which existence and uniqueness is proven via Duhamel's principle and Banach fixed point, and by providing suitable uniform estimates on the approximated solution in order to pass to the limit via classical compactness techniques. To prove uniqueness, we use classical $L^2$-stability which relies on the $H^1$-regularity of the solution. In the second part of the paper we provide a brief, general discussion on the steady states for these type of models, and display a specific example of non-trivial steady states for an SIS model with aggregations (driven by a single repulsive-attractive potential), the existence of which is determined by a threshold condition for a suitable "space-dependent" basic reproduction rate.

Recent numerical works, including ours, lend credence to the thesis that ambient environment, i.e., external pressure, affects star-forming ability of clouds & filaments. In continuation with our series of papers on the subject we explore this thesis further by developing hydrodynamic simulations of accreting filaments confined by external pressures in the range $10^{4 -7}$ $K\ cm^{-3}$. Our findings are-\textbf{(i)} irrespective of linemass, filaments fragment to yield spheroidal cores. Initially sub-critical filaments in low to intermediate external pressure environments form broad cores which suggests, weakly self-gravitating filaments must fragment via \emph{collect-and-collapse} mode to form broad cores. Transcritical filaments, by contrast, become susceptible to Jeans-type instability and form pinched cores; \textbf{(ii)} ambient environment bears upon physical properties of filaments including their {\small FWHM$_{fil}$}. Only those initially suffused with subsonic turbulence in Solar Neighbourhood-like environs, however, have {\small FWHM$_{fil}$}$\sim$ 0.1 $pc$. In high pressure environs they not only have smaller widths, but become severely eviscerated. On the contrary, filaments suffused with initially supersonic turbulence are typically broader; \textbf{(iii)} quasi-oscillatory nature of velocity gradients is ubiquitous along filament lengths and its magnitude generally increases with increasing pressure. The periodicity of the velocity gradients approximately matches the fragmentation lengthscale of filaments; \textbf{(iv)} oscillatory features of the radial component of the velocity gradient are a unreliable proxy for detecting signatures of accretion onto filaments; \textbf{(v)} filaments at either extreme of external pressure are inefficient at cycling gas into the dense phase which could reconcile the corresponding inefficiency of star-formation in such environments., Comment: 23 pgs, 15 figures & 2 tables; To appear in Publications of the Astronomical Society of Australia

The use of data collection to support decision making through the reduction of uncertainty is ubiquitous in the management, operation, and design of building energy systems. However, no existing studies in the building energy systems literature have quantified the economic benefits of data collection strategies to determine whether they are worth their cost. This work demonstrates that Value of Information analysis (VoI), a Bayesian Decision Analysis framework, provides a suitable methodology for quantifying the benefits of data collection. Three example decision problems in building energy systems are studied: air-source heat pump maintenance scheduling, ventilation scheduling for indoor air quality, and ground-source heat pump system design. Smart meters, occupancy monitoring systems, and ground thermal tests are shown to be economically beneficial for supporting these decisions respectively. It is proposed that further study of VoI in building energy systems would allow expenditure on data collection to be economised and prioritised, avoiding wastage., Comment: 28 pages, 10 figures. arXiv admin note: text overlap with arXiv:2305.16117

The stellar initial mass function (IMF) is critical to our understanding of star formation and the effects of young stars on their environment. On large scales, it enables us to use tracers such as UV or Halpha emission to estimate the star formation rate of a system and interpret unresolved star clusters across the universe. So far, there is little firm evidence of large-scale variations of the IMF, which is thus generally considered universal. Stars form from cores and it is now possible to estimate core masses and compare the core mass function (CMF) with the IMF, which it presumably produces. The goal of the ALMA-IMF large program is to measure the core mass function at high linear resolution (2700 au) in 15 typical Milky Way protoclusters spanning a mass range of 2500 to 32700 Msun. In this work, we used two different core extraction algorithms to extract about 680 gravitationally bound cores from these 15 protoclusters. We adopt per core temperature using the temperature estimate from the PPMAP Bayesian method. A power-law fit to the CMF of the sub-sample of cores above the 1.64 Msun completeness limit, 330 cores, through the maximum likelihood estimate technique yields a slope of 1.97 +/- 0.06, significantly flatter than the 2.35 Salpeter slope. Assuming a self-similar mapping between the CMF and the IMF, this result implies that these 15 high-mass protoclusters will generate atypical IMFs. This sample is the largest to date produced and analysed self-consistently, derived at matched physical resolution, with per-core temperature estimates and cores as massive as 150 Msun. We provide the raw source extraction catalogues and the source derived size, temperature, mass, and spectral indices in the 15 protoclusters., Comment: Accepted by A&A

Magnetic fields play an important role in shaping and regulating star formation in molecular clouds. Here, we present one of the first studies examining the relative orientations between magnetic ($B$) fields and the dust emission, gas column density, and velocity centroid gradients on the 0.02 pc (core) scales, using the BISTRO and VLA+GBT observations of the NGC 1333 star-forming clump. We quantified these relative orientations using the Project Rayleigh Statistic (PRS) and found preferential global parallel alignment between the $B$ field and dust emission gradients, consistent with large-scale studies with Planck. No preferential global alignments, however, are found between the $B$ field and velocity gradients. Local PRS calculated for subregions defined by either dust emission or velocity coherence further revealed that the $B$ field does not preferentially align with dust emission gradients in most emission-defined subregions, except in the warmest ones. The velocity-coherent structures, on the other hand, also showed no preferred $B$ field alignments with velocity gradients, except for one potentially bubble-compressed region. Interestingly, the velocity gradient magnitude in NGC 1333 ubiquitously features prominent ripple-like structures that are indicative of magnetohydrodynamic (MHD) waves. Finally, we found $B$ field alignments with the emission gradients to correlate with dust temperature and anticorrelate with column density, velocity dispersion, and velocity gradient magnitude. The latter two anticorrelations suggest that alignments between gas structures and $B$ fields can be perturbed by physical processes that elevate velocity dispersion and velocity gradients, such as infall, accretions, and MHD waves., Comment: Accepted to the Monthly Notices of the Royal Astronomical Society Main Journal

The Extremely Large Telescopes (ELTs), thanks to their large apertures and cutting-edge Multi-Conjugate Adaptive Optics (MCAO) systems, promise to deliver sharper and deeper data even than the JWST. SHARP is a concept study for a near-IR (0.95-2.45 $\mu$m) spectrograph conceived to fully exploit the collecting area and the angular resolution of the upcoming generation of ELTs. In particular, SHARP is designed for the 2nd port of MORFEO@ELT. Composed of a Multi-Object Spectrograph, NEXUS, and a multi-Integral Field Unit, VESPER, MORFEO-SHARP will deliver high angular ($\sim$30 mas) and spectral (R$\simeq$300, 2000, 6000, 17000) resolution, outperforming NIRSpec@JWST (100 mas). SHARP will enable studies of the nearby Universe and the early Universe in unprecedented detail. NEXUS is fed by a configurable slit system deploying up to 30 slits with $\sim$2.4 arcsec length and adjustable width, over a field of about 1.2"$\times$1.2" (35 mas/pix). Each slit is fed by an inversion prism able to rotate by an arbitrary angle the field that can be seen by the slit. VESPER is composed of 12 probes of 1.7"$\times$1.5" each (spaxel 31 mas) probing a field 24"$\times$70". SHARP is conceived to exploit the ELTs apertures reaching the faintest flux and the sharpest angular resolution by joining the sensitivity of NEXUS and the high spatial sampling of VESPER to MORFEO capabilities. This article provides an overview of the scientific design drivers, their solutions, and the resulting optical design of the instrument achieving the required optical performance., Comment: Proceedings of the SPIE Astronomical Telescopes and Instrumentation 2024, Volume 13096, Paper No. 130965I, 11 pp, 11 figs

We present a catalogue of dense cores and filaments in a $3.8^{\circ}\times2.4^{\circ}$ field around the TMC1 region of the Taurus Molecular Cloud. The catalogue was created using photometric data from the Herschel SPIRE and PACS instruments in the 70 $\mu$m, 160 $\mu$m, 250 $\mu$m, 350 $\mu$m, and 500 $\mu$m continuum bands. Extended structure in the region was reconstructed from a Herschel column density map. Power spectra and PDFs of this structure are presented. The PDF splits into log-normal and power-law forms, with the high-density power-law component associated primarily with the central part of TMC1. The total mass in the mapped region is 2000 M$_\odot$, of which 34% is above an extinction of AV $\sim$ 3 mag -- a level that appears as a break in the PDF and as the minimum column density at which dense cores are found. A total of 35 dense filaments were extracted from the column density map. These have a characteristic FWHM width of 0.07 pc, but the TMC1 filament itself has a mean FWHM of $\sim$ 0.13 pc. The thermally supercritical filaments in the region are aligned orthogonal to the prevailing magnetic field direction. Derived properties for the supercritical TMC1 filament support the scenario of it being relatively young. A catalogue of 44 robust and candidate prestellar cores is created and is assessed to be complete down to 0.1 M$_\odot$. The combined prestellar CMF for the TMC1 and L1495 regions is well fit by a single log-normal distribution and is comparable to the standard IMF., Comment: 21 pages, 23 figures, accepted for publication in MNRAS. For data products see http://gouldbelt-herschel.cea.fr/archives

We study a system of two continuity equations with nonlocal velocity fields using interaction potentials of both attractive and repulsive Morse type. Such a system is of interest in many contexts in multi-population modelling. We prove existence, uniqueness and stability in the 2-Wasserstein spaces of probability measures via Jordan-Kinderlehrer-Otto scheme and gradient flow solutions in the spirit of the Ambrosio-Gigli-Savar\'e theory. We then formulate a deterministic particle scheme for this model and prove that gradient flow solutions are obtained in the many particle limit by discrete densities constructed out of moving particles satisfying a suitable system of ODEs. The ODE system is formulated in a non standard way in order to bypass the Lipschitz singularity of the kernel, with difference quotients of the kernel replacing its derivative.

Re-ranking systems aim to reorder an initial list of documents to satisfy better the information needs associated with a user-provided query. Modern re-rankers predominantly rely on neural network models, which have proven highly effective in representing samples from various modalities. However, these models typically evaluate query-document pairs in isolation, neglecting the underlying document distribution that could enhance the quality of the re-ranked list. To address this limitation, we propose Graph Neural Re-Ranking (GNRR), a pipeline based on Graph Neural Networks (GNNs), that enables each query to consider documents distribution during inference. Our approach models document relationships through corpus subgraphs and encodes their representations using GNNs. Through extensive experiments, we demonstrate that GNNs effectively capture cross-document interactions, improving performance on popular ranking metrics. In TREC-DL19, we observe a relative improvement of 5.8% in Average Precision compared to our baseline. These findings suggest that integrating the GNN segment offers significant advantages, especially in scenarios where understanding the broader context of documents is crucial., Comment: This preprint is the result of work in progress, therefore it should still be considered a draft

We consider a class of nonlocal conservation laws with an interaction kernel supported on the negative real half-line and featuring a decreasing jump at the origin. We provide, for the first time, an existence and uniqueness theory for said model with initial data in the space of probability measures. Our concept of solution allows to sort a lack of uniqueness problem which we exhibit in a specific example. Our approach uses the so-called \emph{quantile}, or \emph{pseudo-inverse} formulation of the PDE, which has been largely used for similar types of nonlocal transport equations in one-space dimension. Partly related to said approach, we then provide a deterministic particle approximation theorem for the equation under consideration, which works for general initial data in the space of probability measures with compact support. As a crucial step in both results, we use that our concept of solution (which we call \emph{dissipative measure solution}) implies an instantaneous \emph{measure-to-$L^\infty$} smoothing effect, a property which is known to be featured as well by local conservation laws with genuinely nonlinear fluxes.

Despite recent progress, the question of what regulates the star formation efficiency in galaxies remains one of the most debated problems in astrophysics. According to the dominant picture, star formation (SF) is regulated by turbulence and feedback, and the SFE is 1-2% per local free-fall time. In an alternate scenario, the SF rate in galactic disks is linearly proportional to the mass of dense gas above a critical density threshold. We aim to discriminate between these two pictures thanks to high-resolution observations tracing dense gas and young stellar objects (YSOs) for a comprehensive sample of 49 nearby massive SF complexes out to d < 3 kpc in the Galactic disk. We use data from CAFFEINE, a 350/450 $\mu$m survey with APEX/ArT\'eMiS of the densest portions of all southern molecular clouds, in combination with Herschel data to produce column density maps at 8" resolution. Our maps are free of saturation and resolve the structure of dense gas and the typical 0.1 pc width of molecular filaments at 3 kpc, which is impossible with Herschel data alone. Coupled with SFR estimates derived from Spitzer observations of the YSO content of the same clouds, this allows us to study the dependence of the SFE with density in the CAFFEINE clouds. We also combine our findings with existing SFE measurements in nearby clouds to extend our analysis down to lower column densities. Our results suggest that the SFE does not increase with density above the critical threshold and support a scenario in which the SFE in dense gas is approximately constant. However, the SFE measurements traced by Class I YSOs in nearby clouds are more inconclusive, since they are consistent with both the presence of a density threshold and a dependence on density above the threshold. Overall, we suggest that the SFE in dense gas is primarily governed by the physics of filament fragmentation into protostellar cores., Comment: In press; accepted: 18/05/2024

We have investigated the physical properties of Planck Galactic Cold Clumps (PGCCs) located in the Galactic Plane, using the JCMT Plane Survey (JPS) and the SCUBA-2 Continuum Observations of Pre-protostellar Evolution (SCOPE) survey. By utilising a suite of molecular-line surveys, velocities and distances were assigned to the compact sources within the PGCCs, placing them in a Galactic context. The properties of these compact sources show no large-scale variations with Galactic environment. Investigating the star-forming content of the sample, we find that the luminosity-to-mass ratio (L/M) is an order of magnitude lower than in other Galactic studies, indicating that these objects are hosting lower levels of star formation. Finally, by comparing ATLASGAL sources that are associated or are not associated with PGCCs, we find that those associated with PGCCs are typically colder, denser, and have a lower L/M ratio, hinting that PGCCs are a distinct population of Galactic Plane sources., Comment: 18 pages, 14 figures, 7 tables. Accepted for publication in MNRAS

The fear of social stigma leads many individuals worldwide to hesitate in disclosing their sexual orientation. Since concealing identity is costly, it is crucial to understand the extent of anti-LGB sentiments and reactions to coming out. This paper uses an innovative data source from a popular online game together with a natural experiment to overcome existing data and endogeneity issues. We exploit exogenous variation in the identity of a character to identify the effects of coming out on players' revealed preferences for that character across diverse regions globally. Our findings reveal a substantial and persistent negative impact of coming out., Comment: Updating new version of the paper with new results

We study the T-system of type $A_\infty$, also known as the octahedron recurrence/equation, viewed as a 2+1-dimensional discrete evolution equation. Generalizing the study of [P. Di Francesco and R. Soto-Garrido. Arctic curves of the octahedron equation. J. Phys. A, 47(28):285204, 34, 2014], we consider initial data along parallel ``slanted" planes perpendicular to an arbitrary admissible direction $(r,s,t)\in {\mathbb Z}_+^3$. The solution of the T-system is interpreted as the partition function of a dimer model on some suitable ``pinecone" graph introduced in [M. Bousquet-M\'elou, J. Propp, and J. West. Perfect matchings for the three-term Gale-Robinson sequences. Electron. J. Combin., 16(1):Research Paper 125, 37, 2009]. The T-system formulation and some exact solutions in uniform or periodic cases allow us to explore the thermodynamic limit of the corresponding dimer models and to derive exact arctic curves separating the various phases of the system., Comment: 69 pages, 42 figures

We construct an embedding of the Arthamonov-Shakirov algebra of genus 2 knot operators into the quantized coordinate ring of the cluster Poisson variety of exceptional finite mutation type $X_7$. The embedding is equivariant with respect to the action of the mapping class group of the closed surface of genus 2. The cluster realization of the mapping class group action leads to a formula for the coefficient of each monomial in the genus 2 Macdonald polynomial of type $A_1$ as sum over lattice points in a convex polyhedron in 7-dimensional space.

In the past years, Graph Neural Networks (GNNs) have become the `de facto' standard in various deep learning domains, thanks to their flexibility in modeling real-world phenomena represented as graphs. However, the message-passing mechanism of GNNs faces challenges in learnability and expressivity, hindering high performance on heterophilic graphs, where adjacent nodes frequently have different labels. Most existing solutions addressing these challenges are primarily confined to specific benchmarks focused on node classification tasks. This narrow focus restricts the potential impact that link prediction under heterophily could offer in several applications, including recommender systems. For example, in social networks, two users may be connected for some latent reason, making it challenging to predict such connections in advance. Physics-Inspired GNNs such as GRAFF provided a significant contribution to enhance node classification performance under heterophily, thanks to the adoption of physics biases in the message-passing. Drawing inspiration from these findings, we advocate that the methodology employed by GRAFF can improve link prediction performance as well. To further explore this hypothesis, we introduce GRAFF-LP, an extension of GRAFF to link prediction. We evaluate its efficacy within a recent collection of heterophilic graphs, establishing a new benchmark for link prediction under heterophily. Our approach surpasses previous methods, in most of the datasets, showcasing a strong flexibility in different contexts, and achieving relative AUROC improvements of up to 26.7%., Comment: 7 pages, 1 figure

Sites associated with high-mass star and cluster formation exhibit a so-called hot core phase, characterized by high temperatures and column densities of complex organic molecules. We built a comprehensive census of hot core candidates towards the ALMA-IMF protoclusters based on the detection of two CH3OCHO emission lines at 216.1 GHz. We used the source extraction algorithm GExt2D to identify peaks of methyl formate (CH3OCHO) emission that is a complex species commonly observed towards sites of star formation. We built up a catalog of 76 hot core candidates with masses ranging from about 0.2 to 80 Msun , of which 56 are new detections. A large majority of these objects are compact, rather circular, with deconvolved FWHM sizes of about 2300 au on average. About 30% of our sample of methyl formate sources have core masses above 8 Msun within sizes ranging from about 1000 au to 13400 au, which well correspond to archetypical hot cores. The origin of the CH3OCHO emission toward the lower-mass cores can be explained by a mixture of contribution from shocks, or may correspond to objects in a more evolved state, i.e. beyond the hot core stage. We find that the fraction of hot core candidates increases with the core mass. The large fraction of hot core candidates towards the most massive cores suggests that they rapidly enter the hot core phase and feedback effects from the forming protostar(s) impact their environment on short time-scales.

We give a description of the Halln\"as--Ruijsenaars eigenfunctions of the 2-particle hyperbolic Ruijsenaars system as matrix coefficients for the order 4 element $S\in SL(2,\mathbb{Z})$ acting on the Hilbert space of $GL(2)$ quantum Teichm\"uller theory on the punctured torus. The $GL(2)$ Macdonald polynomials are then obtained as special values of the analytic continuation of these matrix coefficients. The main tool used in the proof is the cluster structure on the moduli space of framed $GL(2)$-local systems on the punctured torus, and an $SL(2,\mathbb{Z})$-equivariant embedding of the $GL(2)$ spherical DAHA into the quantized coordinate ring of the corresponding cluster Poisson variety.

We report 850 $\mu$m continuum polarization observations toward the filamentary high-mass star-forming region NGC 2264, taken as part of the B-fields In STar forming Regions Observations (BISTRO) large program on the James Clerk Maxwell Telescope (JCMT). These data reveal a well-structured non-uniform magnetic field in the NGC 2264C and 2264D regions with a prevailing orientation around 30 deg from north to east. Field strengths estimates and a virial analysis for the major clumps indicate that NGC 2264C is globally dominated by gravity while in 2264D magnetic, gravitational, and kinetic energies are roughly balanced. We present an analysis scheme that utilizes the locally resolved magnetic field structures, together with the locally measured gravitational vector field and the extracted filamentary network. From this, we infer statistical trends showing that this network consists of two main groups of filaments oriented approximately perpendicular to one another. Additionally, gravity shows one dominating converging direction that is roughly perpendicular to one of the filament orientations, which is suggestive of mass accretion along this direction. Beyond these statistical trends, we identify two types of filaments. The type-I filament is perpendicular to the magnetic field with local gravity transitioning from parallel to perpendicular to the magnetic field from the outside to the filament ridge. The type-II filament is parallel to the magnetic field and local gravity. We interpret these two types of filaments as originating from the competition between radial collapsing, driven by filament self-gravity, and the longitudinal collapsing, driven by the region's global gravity., Comment: Accepted for publication in the Astrophysical Journal. 43 pages, 32 figures, and 4 tables (including Appendix)

We propose a deterministic particle method for a one-dimensional nonlocal equation with interactions through the repulsive Morse potential. We show that the particle method converges as the number of particles goes to infinity towards weak measure solutions to the nonlocal equation. Such a results is proven under the assumption of initial data in the space of probability measures with finite second moment. In particular, our method is able to capture a measure-to-$L^\infty$ smoothing effect of the limit equation. Moreover, as the Morse potential is rescaled to approach a Dirac delta, corresponding to strongly localised repulsive interactions, the scheme becomes a particle approximation for the quadratic porous medium equation. We show that in the joint limit (localised repulsion and increasing number of particles) the reconstructed density converges to a weak solution of the porous medium equation. The strategy relies on various estimates performed at the particle level, including $L^p$ estimates and an entropy dissipation estimate, which benefit from the particular structure of our particle scheme and from the absolutely continuous reconstruction of the density from the particle locations.

We show how averages of exponential functions of path dependent quantities, such as those of Work Fluctuation Theorems, detect phase transitions in deterministic and stochastic systems. State space truncation -- the restriction of the observations to a subset of state space with prescribed probability -- is introduced to obtain that result. Two stochastic processes undergoing first-order phase transitions are analyzed both analytically and numerically: the Ehrenfest urn model and the 2D Ising model subject to a magnetic field. In presence of phase transitions, we prove that even minimal state space truncation makes averages of exponentials of path dependent variables sensibly deviate from full state space values. Specifically, in the case of discontinuous phase transitions, this approach is strikingly effective in locating the critical transition value of the control parameter. As this approach works even with variables different from those of fluctuation theorems, it provides a new recipe to identify order parameters in the study of nonequilibrium phase transitions, profiting from the often incomplete statistics that are available.

The artist similarity quest has become a crucial subject in social and scientific contexts. Modern research solutions facilitate music discovery according to user tastes. However, defining similarity among artists may involve several aspects, even related to a subjective perspective, and it often affects a recommendation. This paper presents GATSY, a recommendation system built upon graph attention networks and driven by a clusterized embedding of artists. The proposed framework takes advantage of a graph topology of the input data to achieve outstanding performance results without relying heavily on hand-crafted features. This flexibility allows us to introduce fictitious artists in a music dataset, create bridges to previously unrelated artists, and get recommendations conditioned by possibly heterogeneous sources. Experimental results prove the effectiveness of the proposed method with respect to state-of-the-art solutions., Comment: 6 pages, Submitted to MLSP 2023

We present a catalog of 315 protostellar outflow candidates detected in SiO J=5-4 in the ALMA-IMF Large Program, observed with ~2000 au spatial resolution, 0.339 km/s velocity resolution, and 2-12 mJy/beam (0.18-0.8 K) sensitivity. We find median outflow masses, momenta, and kinetic energies of ~0.3 M$_{\odot}$, 4 M$_{\odot}$ km/s, and 10$^{45}$ erg, respectively. Median outflow lifetimes are 6,000 years, yielding median mass, momentum, and energy rates of $\dot{M}$ = 10$^{-4.4}$ M$_{\odot}$ yr$^{-1}$, $\dot{P}$ = 10$^{-3.2}$ M$_{\odot}$ km/s yr$^{-1}$, and $\dot{E}$ = 1 L$_{\odot}$. We analyze these outflow properties in the aggregate in each field. We find correlations between field-aggregated SiO outflow properties and total mass in cores (~3$-$5$\sigma$), and no correlations above 3$\sigma$ with clump mass, clump luminosity, or clump luminosity-to-mass ratio. We perform a linear regression analysis and find that the correlation between field-aggregated outflow mass and total clump mass - which has been previously described in the literature - may actually be mediated by the relationship between outflow mass and total mass in cores. We also find that the most massive SiO outflow in each field is typically responsible for only 15-30% of the total outflow mass (60% upper limit). Our data agree well with the established mechanical force-bolometric luminosity relationship in the literature, and our data extend this relationship up to L $\geq$ 10$^6$ L$_{\odot}$ and $\dot{P}$ $\geq$ 1 M$_{\odot}$ km/s yr$^{-1}$. Our lack of correlation with clump L/M is inconsistent with models of protocluster formation in which all protostars start forming at the same time., Comment: 46 pages, 14 figures, 10 tables. This publication has an associated Zenodo entry, which can be found here: https://zenodo.org/records/8350595

Understanding the formation of substructures in protoplanetary disks is vital for gaining insights into dust growth and the process of planet formation. Studying these substructures in highly embedded Class 0 objects using the Atacama Large Millimeter/submillimeter Array (ALMA), however, poses significant challenges. Nonetheless, it is imperative to do so to unravel the mechanisms and timing behind the formation of these substructures. In this study, we present high-resolution ALMA data at Bands 6 and 4 of the NGC1333 IRAS4A Class 0 protobinary system. This system consists of two components, A1 and A2, separated by 1.8" and located in the Perseus molecular cloud at $\sim$293 pc distance. To gain a comprehensive understanding of the dust properties and formation of substructures in the early stages, we conducted a multi-wavelength analysis of IRAS4A1. Additionally, we sought to address whether the lack of observed substructures in very young disks, could be attributed to factors such as high degrees of disk flaring and large scale heights. To explore this phenomenon, we employed radiative transfer models using RADMC-3D. Our multi-wavelength analysis of A1 discovered characteristics such as high dust surface density, substantial dust mass within the disk, and elevated dust temperatures. These findings suggest the presence of large dust grains compared to the ones in the interstellar medium (ISM), greater than 100 microns in size within the region. Furthermore, while there's no direct detection of any substructure, our models indicate that some, such as a small gap, must be present. In summary, this result implies that disk substructures may be masked or obscured by a large scale height in combination with a high degree of flaring in Class 0 disks. [Abridged], Comment: Accepted for publication in A&A, 13 pages, 7 figures

MORFEO (Multi-conjugate adaptive Optics Relay For ELT Observations, formerly MAORY), the MCAO system for the ELT, will provide diffraction-limited optical quality to the large field camera MICADO. MORFEO has officially passed the Preliminary Design Review and it is entering the final design phase. We present the current status of the project, with a focus on the adaptive optics system aspects and expected milestones during the next project phase.

Empirical studies in various social sciences often involve categorical outcomes with inherent ordering, such as self-evaluations of subjective well-being and self-assessments in health domains. While ordered choice models, such as the ordered logit and ordered probit, are popular tools for analyzing these outcomes, they may impose restrictive parametric and distributional assumptions. This paper introduces a novel estimator, the ordered correlation forest, that can naturally handle non-linearities in the data and does not assume a specific error term distribution. The proposed estimator modifies a standard random forest splitting criterion to build a collection of forests, each estimating the conditional probability of a single class. Under an "honesty" condition, predictions are consistent and asymptotically normal. The weights induced by each forest are used to obtain standard errors for the predicted probabilities and the covariates' marginal effects. Evidence from synthetic data shows that the proposed estimator features a superior prediction performance than alternative forest-based estimators and demonstrates its ability to construct valid confidence intervals for the covariates' marginal effects.

Structural Health Monitoring (SHM) technologies offer much promise to the risk management of the built environment, and they are therefore an active area of research. However, information regarding material properties, such as toughness and strength is instead measured in destructive lab tests. Similarly, the presence of geometrical anomalies is more commonly detected and sized by inspection. Therefore, a risk-optimal combination should be sought, acknowledging that different scenarios will be associated with different data requirements. Value of Information (VoI) analysis is an established statistical framework for quantifying the expected benefit of a prospective data collection activity. In this paper the expected value of various combinations of inspection, SHM and testing are quantified, in the context of supporting risk management of a location of stress concentration in a railway bridge. The Julia code for this analysis (probabilistic models and influence diagrams) is made available. The system-level results differ from a simple linear sum of marginal VoI estimates, i.e. the expected value of collecting data from SHM and inspection together is not equal to the expected value of SHM data plus the expected value of inspection data. In summary, system-level decision making, requires system-level models.

Studies of dense core morphologies and their orientations with respect to gas flows and the local magnetic field have been limited to only a small sample of cores with spectroscopic data. Leveraging the Green Bank Ammonia Survey alongside existing sub-millimeter continuum observations and Planck dust polarization, we produce a cross-matched catalogue of 399 dense cores with estimates of core morphology, size, mass, specific angular momentum, and magnetic field orientation. Of the 399 cores, 329 exhibit 2D $\mathrm{v}_\mathrm{LSR}$ maps that are well fit with a linear gradient, consistent with rotation projected on the sky. We find a best-fit specific angular momentum and core size relationship of $J/M \propto R^{1.82 \pm 0.10}$, suggesting that core velocity gradients originate from a combination of solid body rotation and turbulent motions. Most cores have no preferred orientation between the axis of core elongation, velocity gradient direction, and the ambient magnetic field orientation, favouring a triaxial and weakly magnetized origin. We find, however, strong evidence for a preferred anti-alignment between the core elongation axis and magnetic field for protostellar cores, revealing a change in orientation from starless and prestellar populations that may result from gravitational contraction in a magnetically-regulated (but not dominant) environment. We also find marginal evidence for anti-alignment between the core velocity gradient and magnetic field orientation in the L1228 and L1251 regions of Cepheus, suggesting a preferred orientation with respect to magnetic fields may be more prevalent in regions with locally ordered fields., Comment: 33 pages, 28 figures, accepted to MNRAS