Dust is an important tracer of the structure of interstellar clouds, as well as a central factor in the thermal balance and chemistry of the clouds. Our knowledge of the dust properties is nevertheless incomplete, especially regarding the dense star-forming clouds. The aim is to study dust evolution in the Orion Molecular Cloud 3 (OMC-3) and how uncertainty regarding dust properties affects estimates of the radiation field and the cloud mass. We constructed three-dimensional radiative transfer (RT) models to fit the far-infrared (FIR) observations of dust emission in the OMC-3 field and used near-infrared (NIR) extinction measurements as additional constraints. We examined fits to the dense star-forming filaments and to the surrounding cloud, including some tests with spatial dust property variations.The 160-250 $μ$m observations of dust emission could be fitted moderately well with any of the dust models tested, but few models are consistent with the measured NIR extinction. The best match to observations is found with dust models such as the THEMIS model of large porous grains, with or without ice mantles, and with mean grain sizes up to ~ 0.3$μ$m. The flattening of the NIR extinction curve excludes larger grain sizes, except possibly in the central ridge. Compared to models of lower column density clouds, the results were relatively insensitive to the line-of-sight (LOS) cloud size and the spectral shape of the heating radiation field. In addition, the effect of embedded stars remained very localised in OMC-3. The results suggest that the dust in the OMC-3 region is evolved with a grain of average size $a$=0.1-0.3 $μ$m, potentially with ice mantles.

In recent years, ground- and space-based photometric surveys have characterized the rotational evolution of solar-like stars to an unprecedented level of detail. In this work we focus on the slow-rotator sequence, an emergent feature recognizable in the color-period diagram of Galactic open clusters. Understanding the evolution of this sequence is a promising avenue to formulate a robust rotation period-mass-age relation, which can be used to estimate stellar ages. Our model of the rotational evolution of stars on the slow-rotator sequence takes into account magnetized wind braking and the rotational decoupling between the radiative interior and the convective envelope. This decoupling naturally develops as the internal redistribution of angular momentum lags behind the loss of angular momentum at the stellar surface, and is parameterized in the model by a rotational coupling timescale. Using literature data on rotation and membership of stars in a selection of open clusters of age between 100 Myr and 4 Gyr, we constrain the mass dependence of the two competing processes of wind braking at the surface and angular momentum transport in the interior. Consistently with our previous findings, our best-fitting model requires a mass-dependent coupling timescale; this result is insensitive to the details of the wind braking model used. We show that the mass dependence of the coupling timescale follows a broken power-law in the entire solar-like mass range (0.4-1.25 Msun), with the exponent change occurring at ~ 0.6 Msun. At the same time, our approach can be used to infer semi-empirically the mass dependence of the wind braking model that best fits the observational constraints. Based on our findings, we propose a novel wind braking law with a particularly simple mass term, directly proportional to the moment of inertia of the convective envelope of the star.

The EROS project (Expérience de Recherche d'Objets Sombres) carried out photometric surveys of dense stellar fields towards the Magellanic Clouds (LMC and SMC), the Galactic Bulge and Galactic spiral arms, over the period 1990-2003. The main goal of the experiment was to search for the Galactic Dark Matter in the form of massive compact objects (machos), through the gravitational microlensing effect. The historical record of the flux variations of the monitored stars by EROS-2 will be a unique asset for time domain astronomy and to complement current and future searches of transient sources. We describe the set of light curves obtained by EROS-2 program over the years 1996 to 2003, monitoring more than 86 million stars, which is publicly released through the Centre de Données de Strasbourg (CDS). The numbers of light curves in this data set are 28.7 and 4.0 million in LMC, respectively SMC, 42.9 million in the Galactic Bulge and 10.4 million towards the Galactic spiral arms, with several hundred measurements for each object. Data from EROS-1 is also being released. The object catalog and light curves and images are accessible through the CDS portal. This will be useful for checking the past behavior of newly discovered variable objects.

We study the spatially resolved star formation, gas ionisation, and outflow properties of 1813 active galactic nuclei (AGNs) from the MaNGA survey, which we classify into infrared (IR), broad-line (BL), narrow-line (NL), and radio (RD) AGNs based on their mid-infrared colours, optical spectra, and/or radio photometry. We also provide estimations of AGN power at different wavelengths. AGN incidence is found to increase with stellar mass following a power-law, with the high-mass end dominated by RDAGNs and the low-mass end dominated by NLAGNs. Compared to their mass-matched non-AGN counterparts, we find that IRAGNs, BLAGNs, and NLAGNs on average show enhanced specific star formation rates, younger stellar populations, and harder ionisation towards the centre. RDAGNs, in contrast, show radial profiles similar to quiescent galaxies. [OIII] outflows are more common and stronger in BL/IRAGNs, while RDAGNs on average show no outflow features. The outflow incidence increases with [OIII] luminosity, and the features in BL/IRAGNs on average extend to ~2 kpc from the nuclei. We further discuss a possible evolutionary sequence of AGNs and their host galaxies, where AGNs with strong emission lines or dust tori are present in star-forming galaxies. Later, young compact radio jets emerge, the host galaxies gradually quench, and the AGN hosts eventually evolve into globally quiescent systems with larger radio jets that prevent further gas cooling.

Context. Comets, asteroids, planetesimals, free-floating planets and brown dwarfs, are continuously injected into the intra-cluster environment after expulsion from their host planetary systems or binary system. The dynamics of large populations of such free-floating comets (ffcs) in a star cluster environment is not yet fully understood. Aims. We investigate the dynamical evolution of comet populations in star clusters, and characterize the kinematics and ejection rates of ffc in a star cluster. Moreover, we determine whether a different initial energy distribution affects the mass segregation of the less massive population. Methods. We carry out simulations using the N-body code NBODY6++GPU-MASSLESS (Flammini Dotti et al. 2025), which allows fast integration of star clusters that contain large numbers of massless particles, to characterize the dynamics of populations of low-mass particles with sub-virial and super-virial distributions. Results. Comets do not participate in the mass segregation process, similarly to planet-size objects, regardless of their initial energy distribution. The latter is slightly changing the whole dynamical evolution at the start of the simulation. We only observe an initial relaxation or collapse of the objects for super-virial and sub-virial ratios, respectively. The external regions of the ffcs population tend to be pulled back in the cluster core at the end of the simulation, suggesting the gravitational pull of the stars is pulling them back in the core. This phenomenon occurs at later times if the system in virial equilibrium. Compared to less massive bodies, brown dwarfs experiences more mass segregation the inner regions tend to be more mixed with the stellar population

We initiate a systematic study of Einstein-Gauss-Bonnet gravity in the presence of boundaries subject to conformal boundary conditions, in which the conformal class of the boundary metric is kept fixed. In Einstein gravity, the trace of the extrinsic curvature is also fixed at the boundary. Here we generalize this boundary condition with the appropriate higher curvature correction. We study the problem both in Euclidean and Lorentzian signature. In Euclidean signature, we show that, similarly to the Einstein gravity case, the entropy at large temperatures exhibits the behavior of a conformal field theory in one lower dimension. We also show that in the flat space limit, the higher curvature corrections do not contribute to the leading behavior at high temperatures. We conjecture that this result is a universal feature of the flat space limit in the presence of conformal boundaries. We test our conjecture by analyzing charged black holes. In Lorentzian signature, we analyze the dynamics of the boundary Weyl factor in black hole backgrounds at the linearized level.

Chemical abundance radial gradients provide key information on how the processes that affect chemical enrichment of the gas-phase interstellar medium (ISM) act at different galaxy scales. Whereas in the last decades there has been an increase in the number of galaxies studied with integral field spectroscopy, there is still not a clear picture on a subsequent characterization of the chemical abundance radial gradients in galaxies hosting Active Galactic Nuclei (AGNs). This lack of analysis is even more accentuated in the case of low-ionization nuclear emission-line regions (LINERs). For the first time, we analyze the chemical abundance radial gradients in a sample of LINER-like galaxies, whose nuclear emission has been previously (Paper I) discussed. We use a sample of 97 galaxies from the Mapping Nearby Galaxies at Apache Point Observatory (MaNGA), whose nuclear regions show LINER-like emission. We use the open-source code HII-CHI-Mistry to estimate the chemical abundance ratios 12+log(O/H) and log(N/O) in the HII regions across the disks in our sample, as well as in the nuclear parts where the LINER-like activity dominates. To fit the radial profiles we use a piecewise methodology which uses a non-fixed number of breaks to find the best fit for the data. We obtain that majority of our sample of galaxies exhibits departures from the single linear gradient both in 12+log(O/H) and log(N/O) (as expected from the inside-out scenario). We investigate whether these departures are driven by galaxy properties (stellar mass, neutral gas mass, stellar velocity dispersion), finding not correlation at all. We also report that in most cases there is no correlation between the shape of the 12+log(O/H) and log(N/O) radial profiles. We propose a model in which AGN (feed)back, acting at different scales depending on the galaxy and its evolutionary stage, might be responsible for these departures.

We prove the holding of chaos in the sense of Li-Yorke for a family of four-dimensional discrete dynamical systems that are naturally associated to ODE systems describing coupled oscillators subject to an external non-conservative force, also giving an example of a discrete map that is Li-Yorke chaotic but not topologically transitive. Analytical results are generalized to a modular definition of the problem and to a system of nonlinear oscillators described by polynomial potentials in one coordinate. We perform numerical simulations looking for a strange attractor of the system; furthermore, we perform a bifurcation analysis of the system presenting 1D and 2D bifurcation diagrams, together with spectra of Lyapunov exponents and basins of attraction.

Using XRISM/Resolve $439 \, \rm ks$ time-averaged spectra of the well-known Seyfert-1.5 active galactic nucleus (AGN) in NGC 3783, we investigate the nature of the Fe K$α$ emission line at 6.4 keV, the strongest and most common X-ray line observed in AGN. Even the narrow component of the line is resolved with evident Fe K$α_{1}$ (6.404 keV) and K$α_{2}$ (6.391 keV) contributions in a 2:1 flux ratio, fully consistent with a neutral gas with negligible bulk velocity. The narrow and intermediate-width components have a full-width at half maximum (FWHM) of 350 $\pm$ 50 km/s and $3510 \pm 470 \, \rm km/s$, respectively, suggesting that they arise in the outer disk/torus and/or BLR. We detect a $10\%$ excess flux around 4 $-$ 7 keV that is not well described by a symmetric Gaussian line, but is consistent with a relativistically broadened emission line. In this paper, we take the simplest approach to model the asymmetric line as a single emission line (assuming either neutral, He-like or H-like iron) convolved with a relativistic disk line model. As expected, the inferred inclination angle is highly sensitive to the assumed ionization state, and ranges between $i=17-44^{ \circ}$. This model also constrains the black hole spin via the extent of the red wing: the required gravitational redshift in the fitted disk-line profile disfavors a non-spinning (Schwarzschild) black hole. The derived inner radius is close to the radius of the innermost stable circular orbit $r_{\rm ISCO}$ and strongly correlated with the black hole spin. To better constrain the spin, we fix the inner radius at $r_{\rm ISCO}$ and derive a lower limit on the spin of $a \ge 0.29$ at the 3 $σ$ confidence level. A Compton shoulder is detected in our data as well as a $2-3 \, σ$ detection of the Cr K$α$ and Ni K$α$ lines.

The Infrared Surface Brightness (IRSB) technique is a specific application of the Baade-Wesselink method. Given a proper calibration, well covered optical and near-infrared photometry, as well as radial velocity curves, it allows for estimation of distances to individual pulsating stars and determination of their mean radii. The technique is fully empirical and does not depend on stellar atmosphere models. The goal of the work is to test the precision of distance determinations to individual RR Lyrae stars and to their host system as a whole using the IRSB technique for a relatively distant globular cluster M 3 (NGC 5272). We also aim to determine mean radii and period-radius relations for these stars in order to compare them with the existing theoretical prediction and empirical estimations for the field stars from the solar neighborhood. We use data available in the literature and the calibration of the IRSB technique based on the RR Lyrae stars from the solar neighborhood we published previously in order to determine distances to 14 RR Lyrae stars in the globular cluster M 3. We study the impact of the selection of the fitting procedure (bisector v.s. the LS fit) on the results. We apply five different empirical surface brightness-color relations from the literature in the analysis. We obtained a mean distance to M 3 of $r_{M3} = (10.07 \pm 0.19 \pm 0.29) \,kpc$ that corresponds to a distance modulus $μ_{M3} = (15.015 \pm 0.041 \pm 0.063) \,mag$ and a $7\%$ scatter of individual stellar distances for 14 RR Lyrae stars in M 3. We received a very good agreement between the two fitting techniques. We also determined mean stellar radii for pulsators from the sample with a precision of $0.5\%$ and obtained excellent agreement with a theoretical prediction of the period-radius relation for RRab stars available in the literature.

The Dark Ages (DA) provides a crucial window into the physics of the infant Universe, with the 21-cm signal offering the only direct probe for mapping out the three-dimensional distribution of matter at this epoch. To measure this cosmological signal, the Dark-ages EXplorer (DEX) has been proposed as a compact, grid-based radio array on the lunar farside. The minimal design consists of a 32 $\times$ 32 array of 3-m dipole antennas, operating in the $7 - 50$ MHz band. A practical challenge on the lunar surface is that the antennas may get displaced from their intended positions due to deployment imprecisions and non-coplanarity arising from local surface undulations. We present, for the first time, an end-to-end simulation pipeline, called SPADE-21cm, that integrates a sky model with a DA 21-cm signal model simulated in the lunar frame and incorporating lunar topography data. We study the effects of both lateral (xy) and vertical (z) offsets on the two-dimensional power spectra across the $7 - 12$ MHz and $30 - 35$ MHz spectral windows, with tolerance thresholds derived only for the latter. Our results show that positional offsets bias the power spectrum by $10 - 30$ per cent relative to the expected 21-cm power spectrum during DA. Lateral offsets within $σ_{xy}/λ\lesssim 0.027$ (at 32.5 MHz) keep the fraction of Fourier modes with strong contamination (> 50 per cent of the signal) to less than 1 per cent, whereas vertical height offsets affect a larger fraction. This conclusion holds for the 21-cm window with $k_\parallel > 0.5$ $h$ cMpc$^{-1}$ over the range of $k_\perp = 0.003 - 0.009$ $h$ cMpc$^{-1}$.

We present the astrometric identification of 80 known radio pulsars as unresolved continuum sources detected at 144 MHz in the second data release of the LOFAR Two-metre Sky Survey (LoTSS DR2), which covers 27% of the Northern hemisphere. These identifications represent the majority ($\geq$ 86%) of radio pulsars present in the LoTSS DR2 footprint and provide independent celestial positions and flux densities at 144 MHz. We compare LoTSS flux densities with literature values from various image and time-domain observations and find good agreement for all but two pulsars. We attribute these flux density deviations to intrinsic pulsar properties (nulling and off-pulse emission). We investigate criteria to select promising pulsar candidates using data from the upcoming LoTSS release of the entire Northern sky ($δ>0^\circ$), as well as the LOFAR LBA Sky Survey (LoLSS) at 54 MHz (covering $δ>24^\circ$). Of the 80 detections, 35 (44%) were blindly redetected based on their linear or circular polarization. Therefore we conclude that candidate selection based on polarization properties is a promising approach. Candidate selection can be supplemented with spectral indices via cross-matching to LoLSS sources at 54 MHz, as the high sensitivity of LoTSS is not matched by image-domain surveys at higher frequencies.

Extreme emission line galaxies (EELGs) are key tracers of intense star formation and potential analogues of the sources that reionized the early Universe. Their low-redshift counterparts offer a unique opportunity to study the physical conditions that enable high ionizing-photon escape fractions. We present a robust method to photometrically identify EELGs in the J-PAS survey, which provides 56 optical bands over 8500 deg^2. Using data from a fully observed 30 deg^2 region, we combine narrow-band equivalent widths with machine-learning techniques to select galaxies with emission lines above 300 Å. The method achieves 95% purity and 96% completeness for $i_\mathrm{SDSS}<22.5$ mag. We identify 917 EELGs up to $z=0.8$; spectroscopic cross-matching with DESI/DR1 confirms the reliability of our redshifts and emission-line measurements. The selected galaxies show strong correlations between $ξ_\mathrm{ion}$ and EW([OIII]), consistent with previous low- and high-z studies. Most sources exceed the ionizing efficiency threshold required for reionization, reinforcing their role as local analogues of early-Universe galaxies.

Accurate prediction of the 11-year solar cycle remains a major challenge in solar physics and is important for space weather forecasting. A persistent property of the cycle is its asymmetry: the rise phase is usually much shorter than the decay phase. This asymmetry is often linked to variations in the Sun's meridional circulation, but it is unclear whether these variations are mainly deterministic, produced by Lorentz-force feedback, or stochastic in nature. We investigate this question using kinematic flux-transport dynamo simulations that include three types of time-dependent meridional flow: deterministic variations, stochastic fluctuations, and hybrid combinations of both. We evaluate cycle asymmetry using the ratio of rise to decay times and correlations of cycle amplitude with rise time, rise rate, and decay rate. Our results show that the temporal evolution of the meridional flow strongly controls cycle asymmetry. When both the meridional circulation and the Babcock-Leighton mechanism vary stochastically, the model does not produce cycles in which the decay phase is consistently longer than the rise phase. In contrast, deterministic variations motivated by Lorentz-force feedback and linked to the latitude of maximum toroidal field reproduce the observed asymmetry. In these cases, the meridional flow weakens near cycle maximum, stays reduced for some time, and then recovers, producing a longer decay phase. Hybrid models that mix deterministic and stochastic variability also match the observed rise-decay asymmetry. Across all simulations, cycle amplitude correlates strongly with rise rate, while correlations with rise time and decay rate are weaker but remain significant. These results highlight the key role of meridional flow variability in shaping solar cycle asymmetry and show that incorporating such variability can improve forecasting tools such as Solar Predict.

Giant radio galaxies (GRGs) represent the largest individual astrophysical structures, rivalling galaxy clusters in physical extent. Understanding how they attain such scales demands examining their large scale cosmic surroundings, particularly the under explored filament environment. We quantify the three dimensional (3D) distance of GRGs from the nearest filament spine; test how this distance correlates with their growth and formation of different morphological classes; assess whether their radio jets exhibit preferred orientations relative to filament axes; and examine how filament anisotropy from spine to periphery modulates radio morphology. We employed a filament catalogue from the SDSS together with the largest GRG catalogue currently available. For each source, we measured the comoving distance to the nearest filament spine, the projected jet spine orientation angle, and quantified lobe asymmetry via the arm length ratio (ALR). These metrics trace proximity, directionality, and the impact of filamentary environment on morphology. We then compared GRGs with a control sample of small radio galaxies (SRGs) to constrain the environmental factors that regulate the attainment of giant sizes. We validated the robustness of our results via bootstrap resampling and non parametric statistical tests. Our results show that GRGs and SRGs have similar filament occupancy. By contrast, GRGs preferentially display larger alignment angles relative to filament spines, while SRG orientations are consistent with a random distribution. GRGs further show enhanced morphological asymmetry, reflected in lower ALR values than SRGs. Attainment of giant sizes is not governed by proximity to filaments; rather, it correlates with jet filament alignment. Abridged.

In future 6G networks, dependable networks will enable telecommunication services such as remote control of robots or vehicles with strict requirements on end-to-end network performance in terms of delay, delay variation, tail distributions, and throughput. With respect to such networks, it is paramount to be able to determine what performance level the network segment can guarantee at a given point in time. One promising approach is to use predictive models trained using machine learning (ML). Predicting performance metrics such as one-way delay (OWD), in a timely manner, provides valuable insights for the network, user equipments (UEs), and applications to address performance trends, deviations, and violations. Over the course of time, a dynamic network environment results in distributional shifts, which causes catastrophic forgetting and drop of ML model performance. In continual learning (CL), the model aims to achieve a balance between stability and plasticity, enabling new information to be learned while preserving previously learned knowledge. In this paper, we target on the challenges of catastrophic forgetting of OWD prediction model. We propose a novel approach which introducing the concept of multi-generator for the state-of-the-art CL generative replay framework, along with tabular variational autoencoders (TVAE) as generators. The domain knowledge of UE capabilities is incorporated into the learning process for determining generator setup and relevance. The proposed approach is evaluated across a diverse set of scenarios with data that is collected in a realistic 5G testbed, demonstrating its outstanding performance in comparison to baselines.

The sparse activation mechanism of mixture of experts (MoE) model empowers edge intelligence with enhanced training efficiency and reduced computational resource consumption. However, traditional token routing in distributed MoE training faces significant challenges in resource-constrained edge networks characterized by heterogeneous computing capabilities and stochastic token arrivals, which inevitably suffer from workload backlog, resource inefficiency, and performance degradation. To address this issue, we propose a novel Lyapunov-based token routing framework for distributed MoE training over resource-heterogeneous edge networks, termed Stable-MoE. Specifically, we formulate a stochastic optimization problem to maximize both system throughput and gating consistency via optimizing the token routing strategy and computational resource allocation, while ensuring long-term stability of both token and energy queues at the edge devices. Using the Lyapunov optimization, we transform the intractable long-term optimization problem into tractable per-slot subproblems by enabling online decision-making of token routing and computation frequency utilization without the knowledge of future system states. Experimental results on the SVHN and CIFAR-100 datasets demonstrate that Stable-MoE outperforms the baselines with at least 40% and 5% gains in system throughput and test accuracy, respectively.

We investigate the stellar velocity dispersion functions (VDFs) of pressure-supported galaxies in the EAGLE cosmological simulations. The central stellar velocity dispersion is one of the fundamental dynamical tracers of the total mass of galaxy subhalos, alongside luminosity and stellar mass. Because it reflects the gravitational potential, the stellar velocity dispersion is expected to be relatively insensitive to feedback from Active Galactic Nuclei (AGN), a critical process that regulates the connection between other galaxy observables and subhalo mass. To examine the impact of AGN feedback, we analyze the VDFs from five EAGLE simulation runs, each adopting a different AGN feedback model: one "standard", two "enhanced", one "reduced", and one with no AGN feedback. We compute the stellar velocity dispersions of pressure-supported galaxies using member stellar particles, mimicking fiber spectroscopy. The VDFs from the standard and enhanced AGN feedback models show little difference. However, contrary to our initial expectation that the VDF shape would be largely insensitive to AGN feedback, the simulations with reduced and no AGN feedback show a significant excess of high velocity dispersion galaxies ($σ_{*}$ > 200 km s$^{-1}$) and a deficit of low dispersion galaxies (100 < $σ_{*}$ (km s$^{-1}$) < 200), compared to those with standard or enhanced AGN feedback. The presence of high velocity dispersion galaxies in the no-AGN model arises from enhanced central star formation, due to the absence of AGN-driven gas heating or expulsion. Our results demonstrate that the shape of the theoretical VDF is sensitive to the strength of AGN feedback. These predictions offer a theoretical benchmark for future observational studies of the galaxy velocity dispersion function using large-scale spectroscopic surveys.

One of the imminent science goals of pulsar timing arrays (PTAs) is the detection of a continuous gravitational wave (CGW) emitted by an individual supermassive black hole binary (SMBHB). SMBHBs that cause CGWs with GW frequencies $f_\mathrm{GW} > 10 \text{nHz}$ have undergone significant orbital evolution, hence a change of $f_\mathrm{GW}$ over time. In PTA data sets with sufficiently long observational time span, this means that the Earth and pulsar terms' contributions to the CGW signal signature can eventually become resolvable. Since the pulsar term is accumulated incoherently and thus often treated as an additional source of noise, this separation can prove to be beneficial for the detection of the CGW signal in the PTA data set. We aim to investigate to what extent resolvable Earth and pulsar terms affect currently used techniques for CGW searches with PTA data sets, that treat the pulsar term as an additional source noise. We focus on the dependency of the pulsar term frequencies on the pulsar's distance. We aim to answer the question of whether adding more distant pulsars to a PTA data set can mitigate biases and improve the detection of CGWs. We show that under ideal conditions, more distant pulsars can facilitate the CGW search with PTA data sets. Bayesian parameter estimation is yielding better parameter constraints and the frequentist per-frequentist optimal statistic search becomes more stable. However, using the realistic data set simulations, it was found that other configuration parameters of a PTA, such as the anisotropic distribution of pulsars and the effective number of pulsars in a PTA, can play a crucial role to the importance of this effect.

A mixed precision Fast Fourier transform (FFT) implementation is presented. The procedure uses per-block microscaling (MX), a global power-of-two prescale, and prequantized low bit twiddles. We evaluate forward and round-trip FFT fidelity on two public MRI datasets and compare the effect of various low precision formats, image sizes, and MX block sizes on image quality. Results show that mantissa precision is the primary limiter under MX scaling while ablations suggest weak dependence on image size but a clear block-size trade-off with larger block sizes resulting in better numerical performance.

We develop a unified framework to compute band-geometric quantities in multiband systems whose low-energy Hamiltonians realize arbitrary $SU(2)$ representations. Exploiting the presence of a quantization axis, we use the Wigner--Eckart theorem to identify the allowed interband matrix elements and obtain compact analytic expressions for the quantum geometric tensor, the orbital magnetic moment, and the resulting orbital transport coefficients. The formalism applies to both multifold fermions and gapped $SU(2)$ models. Its versatility is demonstrated through explicit calculations in representative $SU(3)$ and $SU(4)$ settings, where orbital Edelstein and orbital Hall responses arise naturally from the antisymmetric components of the band geometry. Our results reveal a universal link between the algebraic structure of the Hamiltonian and emergent orbitronic phenomena.

Quasars at the dawn of Cosmic Time ($z>6$) are fundamental probes to investigate the early co-evolution of supermassive black holes and their host galaxy. Nevertheless, their infrared spectral energy distribution remains at the present time poorly constrained, due to the limited photometric coverage probing the far-infrared wavelength range where the dust modified black-body is expected to peak ($\sim80$ $\mathrm{μm}$). Here we present a study of the high-frequency dust emission via a dedicated ALMA Band 8 ($\sim$400 GHz) campaign targeting 11 quasar host galaxies at $6<z<7$. Combined with archival observations in other ALMA bands, this program enables a detailed characterization of their infrared emission, allowing for the derivation of dust masses ($M_{d}$), dust emissivity indexes ($β$), dust temperatures ($T_{d}$), infrared luminosities ($L_{IR}$), and associated star formation rates (SFRs). Our analysis confirms that dust temperature is on average higher in this sample (34-65 K) if compared to local main-sequence galaxies' values, and that this finding can be linked to the increased star formation efficiency we derive in our work, as also suggested by the [CII]$_{158μm}$ deficit. Most remarkably, we note that the average value of $T_d$ of this sample doesn't differ from the one that is observed in luminous, ultra-luminous and hyper-luminous infrared galaxies at different redshifts that show no signs of hosting a quasar. Finally, our findings suggest that the presence of a bright AGN does not significantly bias the derived infrared properties, although further high-frequency, high-spatial resolution observations might reveal more subtle impacts on sub-kiloparsec scales.

The most recently formed young stellar objects (YSOs) in active star forming regions are excellent tracers of their parent cloud motion. Their positions and dynamics provide insight into cluster formation and constrain kinematic decoupling timescales between stars and gas. However, because of their strong extinction and young age, embedded YSOs are mainly visible at infrared wavelengths and thus absent from astrometric surveys such as Gaia. We measured the proper motions of 6,769 sources toward the NGC 2024 cluster in the Flame Nebula using multi-epoch near-infrared observations from three ESO public surveys: VISIONS, VHS, and the VISTA/VIRCAM science verification program. Cross-validation of our results with Gaia using optically visible stars shows excellent agreement, with uncertainties on the same order of magnitude. For 362 YSO candidates identified from the literature, we derived proper motions on the order of <5 mas/yr with mean measurement uncertainties of ~0.22 mas/yr. This is the first homogeneous proper motion measurement of this quality for more than half of these stars. For Class I and flat-spectrum sources, our results provide a >13-fold increase in available proper motion measurements. We analyzed the positional and kinematic differences between YSO classes and confirmed a previously reported inside-out age segregation from younger to older stars, likely driven by an outward movement of older stars. No evidence of prolonged hierarchical assembly was found. Instead, the results support a rapid (<1 Myr) cluster collapse. This scenario also accounts for the observed slightly higher 1D velocity dispersion of Class I sources relative to Class flat objects. YSO radial velocities generally align with the gas velocities measured from 12CO(3-2), HNC(1-0), HCN(1-0), and show a weaker correlation with N_2H+(1-0). Some Class II and III objects appear to be already decoupling.

Aims: We aim to characterize the physical and morphological properties of the binary system AFGL 4106, composed of two evolved massive stars. Understanding its mass-loss processes and circumstellar environment offers insight into the late stages of stellar evolution in massive binary systems. Methods: We obtained high-angular--resolution, high-contrast imaging using VLT/SPHERE with ZIMPOL (optical) and IRDIS (near-infrared) across multiple filters. We used aperture photometry to extract the spectral energy distributions (SEDs) of each star, and applied radiative transfer modelling to study the system and its surrounding dusty environment. Results: The observations resolve both components of the binary and unveil a complex, dusty nebula featuring asymmetric structures and cavities. SED fitting yields stellar temperatures of T$_1 = 6723\pm196$ K and T$_2 = 3394\pm264$ K, along with bolometric luminosities of L$_1 = (7.9 \pm 0.18) \times 10^4$ L$_\odot$ and L$_2 = (3.8 \pm 0.11) \times 10^4$ L$_\odot$. These values support the classification of the primary as being in a post-red supergiant (post-RSG) phase and the secondary as an active red supergiant (RSG). The luminosity ratio, combined with the inferred radii, indicates that both stars are at close yet distinct stages of their evolution. The binary is surrounded by an extended shell whose asymmetric morphology and large-scale features suggest interaction with the stellar winds and interstellar medium (ISM), and possibly the presence of a third, undetected companion. Conclusions: These observations provide the first resolved view of AFGL 4106's system and its dusty envelope. Our analysis sets constraints on the physical properties and evolutionary status of the system. This work contributes to understanding mass-loss processes in massive binaries and the shaping of nebulae around evolved stars.

In high-contrast imaging, a novel detection algorithm for angular differential imaging (ADI) sequences has recently been introduced: the Regime Switching Model (RSM). In this study, we apply the RSM algorithm to analyze the F150 sample from the SHINE high-contrast imaging survey carried out with VLT/SPHERE, aiming to enhance detection limits and identify new exoplanet candidates. Additionally, we investigate how environmental conditions influence post-processed noise distributions and detection thresholds. We generate detection maps and contrast curves for 213 observations in the F150 SHINE sample using the RSM algorithm. A clustering approach based on environmental parameters is used to group observations with similar noise characteristics. We propose two methods for defining radial detection thresholds in the RSM maps: fitting a log-normal distribution to the post-processed noise and maximizing the F1 score. We also assess the performance of various combinations of post-processing techniques within the RSM framework to identify optimal configurations. This study demonstrates the utility of clustering based on observational parameters, effectively distinguishing features like wind-driven halos and low-wind effects. Detection thresholds vary significantly across clusters, differing by up to a factor of 10, highlighting the importance of considering observational environments. Log-normal thresholds provide conservative, noise-aware limits, while F1 score-based thresholds offer observation-specific results, both showing compatibility overall. RSM improves detection limits by an average factor of two at 1arcsec and five at inner working angles compared to standard PCA processing. This study reports more than 30 newly detected signals, including one promising candidate awaiting second-epoch confirmation.

The dissipative quantum Rabi model exhibits rich non-equilibrium physics, including a dissipative phase transition from the normal phase to the superradiant phase. In this work, we investigate the stability of the superradiant phase in the presence of a weak spin relaxation. We find that even a weak spin relaxation can render the superradiant phase a superradiant metastable phase, in which symmetry-breaking states are stable only for a finite time. This arises because each spin jump induced by relaxation applies as a strong perturbation to the system, potentially driving the system from a symmetry-breaking state to the symmetry-preserving saddle point with finite probability, before it eventually relaxes back to a symmetry-breaking state. Such dynamical processes lead to a finite lifetime of the symmetry-breaking states and restore the symmetry in the steady state. To substantiate these results, we combine mean-field and cumulant expansion analyses with exact numerical simulations. The lifetimes of the symmetry-breaking states are analyzed in finite-size systems and the conclusions are extrapolated to the thermodynamic limit via finite-size scaling. Our findings establish the metastable nature of the symmetry-breaking states in the dissipative quantum Rabi model and reveal the complexity of the dissipative phase transition beyond their equilibrium counterpart. The mechanisms uncovered here can be generalized to a broad class of open quantum systems, highlighting fundamental distinctions between equilibrium phase transitions and steady-state phase transitions.

We establish a sharp upper bound on the number of properly $3$-edge-colored $K_4$'s in graphs with $R$ red, $G$ green and $B$ blue edges. We give a computer-free flag-algebra proof of this bound, and we also convert our proof into a classical counting proof and an entropy proof. Additionally, for every $k\ge 4$, for a fixed rainbow coloring $F$ of a complete graph $K_k$, we give a sharp upper bound on the number copies of $F$ in a $\binom{k}{2}$-edge-colored graph. Our proof of this result relies on a new flag-algebra version of Hölder's inequality. We also give a computer-free flag-algebra proof of the fact that a graph with $R$ red, $G$ green, and $B$ blue edges has at most $\sqrt{2 RGB}$ rainbow triangles, which was originally proven by T.-W. Chao and H.-H. H. Yu using the entropy method. We also provide an even shorter entropy proof of their result.

Resonance lines encode rich information about astrophysical sources and their environments, yet fully analytic treatments of multi-line radiative transfer remain almost entirely unexplored. We present exact, closed-form solutions for steady-state resonant-line radiative transfer in "V-shaped" atomic networks, where a single ground state couples to multiple transitions. Starting from the full angle-dependent transfer equation, we generalize absorption and emission coefficients to an arbitrary number of lines, derive a modified Fokker-Planck expansion of the frequency-redistribution COLT Monte Carlo radiative transfer code and find excellent agreement with the analytic predictions across a wide range of line separations, optical depths, and damping parameters, establishing our solutions as stringent validation benchmarks. For concrete applications related to the Lyman-alpha transition of neutral hydrogen, we examine how fine-structure splitting and deuterium injection modify the emergent spectra, internal radiation field, and radiative force multiplier. We show that these effects leave previous conclusions about Lyman-alpha feedback in the early universe essentially unchanged. Even when direct observational diagnostics are subtle, our framework provides novel analytic and numerical insights into coupled resonance-line transport and facilitates progress in general modeling of multi-line radiative transfer in diverse astrophysical settings.

Learning effective pricing strategies is crucial in digital marketplaces, especially when buyers' valuations are unknown and must be inferred through interaction. We study the online contextual pricing problem, where a seller observes a stream of context-valuation pairs and dynamically sets prices. Moreover, departing from traditional online learning frameworks, we consider a strategic setting in which buyers may misreport valuations to influence future prices, a challenge known as strategic overfitting (Amin et al. 2013). We introduce a strategy-robust notion of regret for multi-buyer online environments, capturing worst-case strategic behavior in the spirit of the Price of Anarchy. Our first contribution is a polynomial-time approximation scheme (PTAS) for learning linear pricing policies in adversarial, adaptive environments, enabled by a novel online sketching technique. Building on this result, we propose our main construction: the Sparse Update Mechanism (SUM), a simple yet effective sequential mechanism that ensures robustness to all Nash equilibria among buyers. Moreover, our construction yields a black-box reduction from online expert algorithms to strategy-robust learners.

Accurate network-traffic forecasting enables proactive capacity planning and anomaly detection in Internet Service Provider (ISP) networks. Recent advances in time-series foundation models (TSFMs) have demonstrated strong zero-shot and few-shot generalization across diverse domains, yet their effectiveness for computer networking remains unexplored. This paper presents a systematic evaluation of a TSFM, IBM's Tiny Time Mixer (TTM), on the CESNET-TimeSeries24 dataset, a 40-week real-world ISP telemetry corpus. We assess TTM under zero-shot and few-shot settings across multiple forecasting horizons (hours to days), aggregation hierarchies (institutions, subnets, IPs), and temporal resolutions (10-minute and hourly). Results show that TTM achieves consistent accuracy (RMSE 0.026-0.057) and stable $R^2$ scores across horizons and context lengths, outperforming or matching fully trained deep learning baselines such as GRU and LSTM. Inference latency remains under 0.05s per 100 points on a single MacBook Pro using CPU-only computation, confirming deployability without dedicated GPU or MPS acceleration. These findings highlight the potential of pretrained TSFMs to enable scalable, efficient, and training-free forecasting for modern network monitoring and management systems.