We study the convergence rate for the last iterate of stochastic gradient descent (SGD) and stochastic heavy ball (SHB) in the parametric setting when the objective function $F$ is globally convex or non-convex whose gradient is $γ$-Hölder. Using only discrete Gronwall's inequality without Robbins-Siegmund theorem, we recover results for both SGD and SHB: $\min_{s\leq t} \|\nabla F(w_s)\|^2 = o(t^{p-1})$ for non-convex objectives and $F(w_{τ\wedge t}) - F_* = o(t^{2γ/(1+γ) \cdot \max(p-1,-2p+1)-ε})$ for $β\in (0, 1)$, $τ:= \inf \{ t > 0 : F(w_t) = F_*\}$, and $\min_{s \leq t} F(w_s) - F_* = o(t^{p-1})$ for convex objectives $F$ whose minimum is $F_*$. In addition, we proved that SHB with constant momentum parameter $β\in (0, 1)$ attains a convergence rate of $F(w_t) - F_* = O(t^{\max(p-1,-2p+1)} \log^2 \frac{t}δ)$ with probability at least $1-δ$ when $F$ is convex and $γ= 1$ and step size $α_t = Θ(t^{-p})$ with $p \in (\frac{1}{2}, 1)$.

Effective query expansion for web search benefits from promoting both exploration and result diversity to capture multiple interpretations and facets of a query. While recent LLM-based methods have improved retrieval performance and demonstrate strong domain generalization without additional training, they often generate narrowly focused expansions that overlook these desiderata. We propose ThinkQE, a test-time query expansion framework addressing this limitation through two key components: a thinking-based expansion process that encourages deeper and comprehensive semantic exploration, and a corpus-interaction strategy that iteratively refines expansions using retrieval feedback from the corpus. Experiments on diverse web search benchmarks (DL19, DL20, and BRIGHT) show ThinkQE consistently outperforms prior approaches, including training-intensive dense retrievers and rerankers.

Motivated by real-world settings where data collection and policy deployment -- whether for a single agent or across multiple agents -- are costly, we study the problem of on-policy single-agent reinforcement learning (RL) and federated RL (FRL) with a focus on minimizing burn-in costs (the sample sizes needed to reach near-optimal regret) and policy switching or communication costs. In parallel finite-horizon episodic Markov Decision Processes (MDPs) with $S$ states and $A$ actions, existing methods either require superlinear burn-in costs in $S$ and $A$ or fail to achieve logarithmic switching or communication costs. We propose two novel model-free RL algorithms -- Q-EarlySettled-LowCost and FedQ-EarlySettled-LowCost -- that are the first in the literature to simultaneously achieve: (i) the best near-optimal regret among all known model-free RL or FRL algorithms, (ii) low burn-in cost that scales linearly with $S$ and $A$, and (iii) logarithmic policy switching cost for single-agent RL or communication cost for FRL. Additionally, we establish gap-dependent theoretical guarantees for both regret and switching/communication costs, improving or matching the best-known gap-dependent bounds.

The non-stationary nature of electroencephalography (EEG) introduces distribution shifts across domains (e.g., days and subjects), posing a significant challenge to EEG-based neurotechnology generalization. Without labeled calibration data for target domains, the problem is a source-free unsupervised domain adaptation (SFUDA) problem. For scenarios with constant label distribution, Riemannian geometry-aware statistical alignment frameworks on the symmetric positive definite (SPD) manifold are considered state-of-the-art. However, many practical scenarios, including EEG-based sleep staging, exhibit label shifts. Here, we propose a geometric deep learning framework for SFUDA problems under specific distribution shifts, including label shifts. We introduce a novel, realistic generative model and show that prior Riemannian statistical alignment methods on the SPD manifold can compensate for specific marginal and conditional distribution shifts but hurt generalization under label shifts. As a remedy, we propose a parameter-efficient manifold optimization strategy termed SPDIM. SPDIM uses the information maximization principle to learn a single SPD-manifold-constrained parameter per target domain. In simulations, we demonstrate that SPDIM can compensate for the shifts under our generative model. Moreover, using public EEG-based brain-computer interface and sleep staging datasets, we show that SPDIM outperforms prior approaches.

We study robust high-dimensional sparse regression under finite-variance heavy-tailed noise, epsilon-contamination, and alpha-mixing dependence via two subsampling estimators: Adaptive Importance Sampling (AIS) and Stratified Sub-sampling (SS). Under sub-Gaussian design whose scopeis precisely delimited and finite-variance noise, a subsample of size m achieves the minimax-optimal rate. We close the theory-algorithm gap: Theorem 4.6 applies to AIS at termination conditional on stabilized weights (Proposition 4.1), and SS fits the median-of-means M-estimation framework of Lecue and Lerasle (Proposition 4.3). The de-biasing step is fully specified via the nodewise-Lasso precision estimator under a new sparse-precision assumption, yielding valid coordinate-wise CIs (Theorem 4.14). The alpha-mixing extension uses a calendar-time block protocol that guarantees temporal separation (Theorem 4.12). Empirically, AIS achieves 3.10 times lower error than uniform subsampling at 20% contamination, and 29.5% lower test MSE on Riboflavin (p=4,088 and n=71).

Motivated by recent progress in the problem of numerical Kähler metrics, we survey machine learning techniques in this area, discussing both advantages and drawbacks. We then revisit the algebraic ansatz pioneered by Donaldson. Inspired by his work, we present a novel approach to obtaining Ricci-flat approximations to Kähler metrics, applying machine learning within a `principled' framework. In particular, we use gradient descent on the Grassmannian manifold to identify an efficient subspace of sections for calculation of the metric. We combine this approach with both Donaldson's algorithm and learning on the $h$-matrix itself (the latter method being equivalent to gradient descent on the fibre bundle of Hermitian metrics on the tautological bundle over the Grassmannian). We implement our methods on the Dwork family of threefolds, commenting on the behaviour at different points in moduli space. In particular, we observe the emergence of nontrivial local minima as the moduli parameter is increased.

Complex systems often show macroscopic coherent behavior due to the interactions of microscopic agents like molecules, cells, or individuals in a population with their environment. However, simulating such systems poses several computational challenges during simulation as the underlying dynamics vary and span wide spatiotemporal scales of interest. To capture the fast-evolving features, finer time steps are required while ensuring that the simulation time is long enough to capture the slow-scale behavior, making the analyses computationally unmanageable. This paper showcases how deep learning techniques can be used to develop a precise time-stepping approach for multiscale systems using the joint discovery of coordinates and flow maps. While the former allows us to represent the multiscale dynamics on a representative basis, the latter enables the iterative time-stepping estimation of the reduced variables. The resulting framework achieves state-of-the-art predictive accuracy while incurring lesser computational costs. We demonstrate this ability of the proposed scheme on the large-scale Fitzhugh Nagumo neuron model and the 1D Kuramoto-Sivashinsky equation in the chaotic regime.

We consider the energy loss of a high-energy parton in the early anisotropic plasma in heavy-ion collisions. Working in the harmonic approximation, we compute the change in the mean energy of an emitted gluon in the presence of an anisotropic background, characterized by anisotropic jet quenching parameters $\hat q_{x}\neq \hat q_{y}$. Evaluating the resulting integrals numerically, we compare with isotropic media, and obtain a simple pocket formula to estimate the impact of anisotropy on the mean emitted gluon energy, which is generally small. We then combine our results with the values of the jet quenching parameter extracted from QCD kinetic theory simulations and show that the medium length dependence of this mean energy loss exhibits the characteristics of limiting attractors, which can be obtained by extrapolating to zero and infinite coupling. Our study thus relates energy loss of jet partons to universal dynamics of anisotropic plasmas.

We investigate structural and combinatorial properties of Bi-Cayley graphs defined over cyclic groups of order $p^2q^2$, where $p$ and $q$ are distinct primes. We begin by describing their fundamental group-theoretic underpinnings. The main focus is on analyzing their connectivity, girth, clique number, chromatic number, diameter, and independence number. It is shown that these Bi-Cayley graphs are connected, biregular with explicitly determined degrees, and possess girth three. Furthermore, we prove that their diameter is equal to five. We further extend several results to Bi-Cayley graphs over arbitrary finite groups under suitable restrictions on the connecting set, with particular emphasis on the case where the connecting set consists of all its involutions. These results clarify structural similarities and differences between Cayley graphs and their Bi-Cayley generalizations.

The Kolmogorov stochasticity parameter (KSP) as a sensitive descriptor of the degree of randomness of signals was used to analyze the properties of the NANOGrav pulsar timing data associated with a stochastic gravitational wave background. The time of arrival (TOA) data of white noise for 68 pulsars were analyzed regarding their KSP properties. The analysis enabled us to obtain the degree of randomness of the white noise for various pulsars and to reveal its inhomogeneity, i.e., pulsars with low and high randomness of the white noise. The time dependence of the randomness in the white noise was also studied, indicating the existence of nonstationary physical processes influencing the pulsar timing. The KSP is thus acting as an indicator for the degree of the agreement between the observations and the timing models and as a test in revealing the contribution of various physical processes in the stochastic background signal.

The study of apsidal motion rates in eccentric eclipsing binaries provides an important observational test of theoretical models of stellar structure and evolution. Precise physical parameters of the stellar components together with systematic measurements of the periastron advance are needed. We present new results of our long-term observational project to analyze the apsidal motion in early-type eccentric eclipsing binaries. New ground and space-based photometric data were obtained, and archival spectroscopic measurements were used in this study of two detached southern-hemisphere eclipsing binaries: V1647 Sgr (P=3.28 d, e=0.41), and V2283 Sgr (3.47, 0.49). Their TESS observations in four sectors have also been included and the corresponding light curves were solved using the Phoebe code. The newly completed O-C diagrams were analyzed using all reliable timings found in the literature and calculated using the TESS light curves. New or improved values were obtained for the elements of apsidal motion. Using archival spectroscopy for V1647 Sgr, the precise absolute parameters were improved: M1 = 2.184(0.035) M$_\odot$, M2 = 1.957(0.035) M$_\odot$, and R1 = 1.839(0.015) R$_\odot$, R2 = 1.716(0.015) R$_\odot$. For V2283 Sgr the absolute dimensions were newly estimated: M1 = 2.178(0.10) M$_\odot$, M2 = 1.547(0.10) M$_\odot$, and R1 = 1.796(0.01) R$_\odot$, R2 = 1.544(0.01) R$_\odot$. We improved relatively long periods of apsidal motion of about 580 and 530 years, together with the corresponding internal structure constants, log k2, -2.394, and -2.418, for V1647 Sgr and V2283 Sgr, respectively. The relativistic contribution to apsidal motion is not negligible, making about 12 resp. 14% of the total rate of apsidal motion. No signs of the presence of an additional body were revealed in the light curves or in the O-C diagrams of both eccentric systems.

(Abridged) Complex organic molecules (COMs) are considered essential precursors to prebiotic species. While COMs were once expected to be efficiently destroyed under UV-irradiated conditions, detections in photodissociation regions (PDRs) have challenged this view. However, the mechanisms by which UV radiation contributes to their formation are still uncertain. Here, we present moderately resolved maps of simple and complex organic molecules at the UV-illuminated edge of the Horsehead nebula, obtained by combining ALMA and IRAM 30m single-dish observations at $\sim 15^{\prime\prime}$ resolution. We analyze the spatial distribution of species such as C$^{17}$O, CH$_2$CO, CH$_3$CHO, HNCO, CH$_3$CN, and HC$_3$N. By incorporating previous C$^{17}$O and C$^{18}$O single-dish data as well as PdBI maps of H$_2$CO and CH$_3$OH, we derive profiles of gas density, temperature, thermal pressure, and column densities of the organic species as a function of distance from the UV source. Our results show that most organic species$-$particularly H$_2$CO, CH$_2$CO, CH$_3$CHO, HNCO, and CH$_3$CN$-$exhibit enhanced column densities at the UV-illuminated edge compared to cloud interiors, possibly indicating efficient dust-grain surface chemistry driven by the diffusion of atomic C and radicals produced via photodissociation of CO and CH$_3$OH, as supported by recent laboratory experiments. The exceptions, HC$_3$N and CH$_3$OH, can be attributed to inefficient formation on dust grains and ineffective non-thermal desorption into the gas phase, respectively. Additionally, contributions from gas-phase hydrocarbon photochemistry, possibly seeded by grain-surface products, cannot be ruled out. Further chemical modeling is needed to confirm the efficiency of these pathways for the studied species, which could have important implications for other cold, UV-irradiated environments such as protoplanetary disks.

The rotational properties of asteroids provide critical information about not only their internal structure but also their collisional and thermal histories. Previous work has revealed a bimodal distribution of asteroid spin rates, dividing populations into fast and slow rotators, but to date this separation remains poorly understood (e.g. its dependency on composition). We investigate whether the valley separating fast and slow rotators in rotational period-diameter space depends on the composition of the asteroid, approximated by asteroids' spectral class. First, we extended the Minor Planet Physical Properties Catalogue (MP3C) to include the available spectral classes of asteroids. Then, for each asteroid we selected the best diameter, rotational period, and spectral class. Building upon a semi-supervised machine-learning method, we quantify the valley between fast and slow rotators for S- and C-complex asteroids, which are linked to ordinary and carbonaceous chondrites respectively. The method iteratively fits a linear boundary between the two populations in rotational period-diameter space to maximise their separation. We find a clear compositional dependence of the valley: for C-complex asteroids the transition occurs at longer periods than for S-complex, with P* = 14.4 D_km^0.739 (C-complex) and P* = 11.6 D_km^0.718 (S-complex), where period and diameter are given in hours and kilometres respectively. This corresponds to mu Q approximately 2 and 13 GPa, respectively, where mu is the rigidity and Q the quality factor. The dependence of the valley on spectral classes likely reflects compositional and structural differences: C-complex asteroids, being more porous and weaker, dissipate angular momentum more efficiently than stronger, more coherent S-complex asteroids. This represents quantitative evidence of class-dependent rotational valleys within asteroid populations.

In the present paper we derive a further extension of the results contained in two recent articles, both published in Open Communications in Nonlinear Mathematical Physics, where it was shown that the integrable version of the N-species Volterra model, introduced by V. Volterra in 1937, is in fact maximally superintegrable. Here we point out that the superintegrability property applies as well to the case of infinitely many competing species, either countable or uncountable. Analytical and numerical results are given.

Understanding the connection between active galactic nuclei and star-formation (the AGN-SF connection) is one of the longest standing problems in modern astrophysics. In the age of large Integral Field Unit (IFU) surveys, studies of the AGN-SF connection greatly benefit from spatially resolving AGN and SF contributions to study the two processes independently. Using IFU data for 54 local active galaxies from the S7 sample, we present a new method to separate emission from AGN activity and SF using mixing sequences observed in the [NII]$λ6584$/H$α$ vs. [OIII]$λ5007$/H$β$ Baldwin-Phillips-Terlevich (BPT) diagram. We use the new decomposition method to calculate the H$α$ star-formation rate and AGN [OIII] luminosity for the galaxies. Our new method is robust to outliers in the line-ratio distribution and can be applied to large galaxy samples with little manual intervention. We infer star-formation histories (SFHs) using pPXF, conducting detailed recovery tests to determine the quantities that can be considered robust. We test the correlation between the AGN Eddington ratio, using the proxy L[OIII]/$σ_*^4$, and star-formation properties. We find a moderately strong correlation between the Eddington ratio and the star-formation rate (SFR). We also observe marginally significant correlations between the AGN Eddington ratio and the light-weighted stellar age under 100 Myr. Our results point to higher AGN accretion being associated with young nuclear star formation under 100 Myr, consistent with timelines presented in previous studies. The correlations found in this paper are relatively weak; extending our methods to larger samples, including radio-quiet galaxies, will help better constrain the physical mechanisms and timescales of the AGN-SF connection.

Deuterium fractionation becomes highly efficient in cold, dense cores where CO is frozen out. Cyclopropenylidene (c-C3H2), an early-formed carbon ring, and its deuterated isotopologues trace gas-phase deuteration in these environments. We present a statistical study of c-C3H2 deuteration in starless and prestellar cores of the Perseus Molecular Cloud using observations of c-C3H2, c-C3HD and c-C3D2 obtained with the Yebes 40 m, ARO 12 m and IRAM 30 m telescopes towards 16 cores. Gaussian fits and RADEX modeling yield column densities for the detected species. c-C3H2 is detected in 14/15 covered cores, c-C3HD in 15/16, and c-C3D2 in 9/16. Derived column densities range from 0.5-8.1 x 10^{13} cm^{-2} for c-C3H2, 0.2-2.1 x 10^{12} cm^{-2} for c-C3HD, and 0.6-1.6 x 10^{11} cm^{-2} for c-C3D2. The ortho-to-para ratio of c-C3H2 is obtained for all but one core, with a median value of 3.5\pm0.4. Statistically corrected D/H ratios span 0.5-9.2% (median 1.5\pm0.2%), and D2/D ratios 9-55% (median 25.9\pm4.3%). No trend is found between the c-C3H2 ortho-to-para ratio and core evolutionary stage traced by n(H2). The median D/H ratio in Perseus appears lower than values reported for Taurus and Chamaeleon, while the D2/D ratio agrees with Taurus within uncertainties. A positive correlation between D/H and n(H2) supports the use of D/H as an evolutionary tracer. D2/D does not correlate with n(H2), but shows a positive correlation with T_{kin}, suggesting that its formation is influenced by a mildly endothermic pathway.

The long-term dynamical evolution of asteroid families is governed by the interplay between orbital and rotational evolution driven by thermal forces and collision. We aim to observationally trace the rotational evolution of main-belt asteroid families over Gyr timescales. We analyzed rotational properties of 8739 asteroids with spin period measurements and 3794 asteroids with obliquity determinations across 28 asteroid families spanning ages from 14~Myrs to 3~Gyrs. We introduced a dimensionless timescale that normalizes each asteroid's family age by its classical YORP timescale, enabling direct comparison of rotational states across different evolutionary stages. We examined two key observables: the fraction of slow rotators (periods greater than or equal to 30 hours) and the polarization fraction (the degree to which asteroid spin poles align correctly with their position in the family's V-shape distribution according to the Yarkovsky theory). Evolution of both quantities were fitted to identify characteristic transition timescales. We discovered that the slow-rotator fraction increases steeply with $t$ and saturates at $f_{\rm slow} \simeq 0.25$ around a breakpoint $t_{\rm bp} \simeq 20$. This implies a stochastic YORP timescale $τ_{\rm YORP,stoc} \simeq 10\,τ_{\rm YORP}$ by comparison with rotational evolution models that include tumbling and weakened YORP torques. The polarization fraction reaches a maximum of $\simeq 0.8$ at $t \simeq 16$ and then decays toward the random limit $f_{\rm pol} \rightarrow 0.5$ for $t \gtrsim 20$, indicating an increasing dominance of collisional spin reorientation over time. The rotation properties within different asteroid families offer crucial clues to rotation evolution and can serve as a new dimension for age estimation of asteroid families with more data in the LSST era.

Braids are periodic solutions to the general N-body problem in gravitational dynamics. These solutions seem special and unique, but they may result from rather usual encounters between four bodies. We aim at understanding the existence of braids in the Galaxy by reverse engineering the interactions in which they formed. We simulate self-gravitating systems of N particles, starting with the constructing of a specific braid, and bombard it with a single object. We study how frequently the bombarded braid dissolves in four singles, a triple and a single, a binary and 2 singles, or 2 binaries. The relative proportion of those events gives us insight into how easy it is to generate a braid through the reverse process. It turns out that braids are easily generated from encounters between 2 binaries, or a triple with a single object, independent on the braid's stability. We find that 3 of the explored braids are linearly stable against small perturbations, whereas one is unstable and short-lived. The shortest-lived braid appears the least stable and the most chaotic. nonplanar encounters also lead to braid formation, which, in our experiments, themselves are planar. The parameter space in azimuth and polar angle that lead to braid formation via binary-binary or triple-single encounters is anisotropic, and the distribution has a low fractal dimension. Since a substantial fraction of ~9% of our calculations lead to periodic 3-body systems, braids may be more common than expected. They could form in multi-body interactions. We do not expect many to exist for time, but they may be common as transients, as they survive for tens to hundreds of periodic orbits. We argue that braids are common in relatively shallow-potential background fields, such as the Oort cloud or the Galactic halo. If composed of compact objects, they potentially form interesting targets for gravitational wave detectors.

Trans-Neptunian objects (TNOs) are among the most primitive remnants of the early Solar System, and constraining their sizes, shapes, albedos, and surface properties is essential for understanding their origin and evolution. Stellar occultations provide highly accurate size and shape measurements for TNOs, while photometry constrains their albedo and surface colours. (28978) Ixion is one of the largest TNOs and a prominent Plutino, making it a key target for comparative studies. We aim to constrain Ixion's projected size, shape, absolute magnitude, geometric albedo, and surface colours, and to search for evidence of an atmosphere or circum-object material. We analysed stellar occultation campaigns by Ixion conducted between 2020 and 2023 within the Lucky Star collaboration, comprising 51 observations from eight events, including 30 positive detections. Five multi-chord events enabled a global limb fit and an accurate reconstruction of Ixion's projected shape. The occultations reveal a slightly elongated limb well represented by a single projected ellipse, yielding an area-equivalent diameter of $D_{\mathrm{equiv}} = 696.78^{+10.75}_{-8.87}$ km and an apparent oblateness $ε' = 0.081^{+0.004}_{-0.010}$. Typical radial residuals of order $\sim$10 km indicate a largely stable shape across epochs, with modest epoch-dependent variations. Calibrated photometric data yield an absolute magnitude of $H_V = 3.845 \pm 0.006$, a phase-curve slope of $β= 0.1301 \pm 0.0078$ mag deg$^{-1}$, and a visible geometric albedo of $p_V = 0.106^{+0.003}_{-0.003}$, with colours consistent with moderately red TNO surfaces. No atmosphere or circum-object material is detected down to our sensitivity limits. The best-sampled event also allows a precise measurement of the angular diameter of the occulted star Gaia DR3 4056440205544338944, $θ_\star = 0.670 \pm 0.010$ mas.

Long-period companions are detected and characterized thanks to long-baseline radial velocity surveys. Combining Doppler time-series with astrometry, and in particular with proper motion anomalies technique, it is possible to put strong constraints on their orbital inclination and true mass. This work aims to present a model that combines Hipparcos and Gaia astrometric data with radial velocity measurements to constrain the orbital inclinations and true masses of long-period companions. Additionally, we re-analyse a small sample of targets that have not yet been studied using this combined approach. This research leverages the simultaneous modelling of proper motion anomalies and radial velocities, in conjunction with an analysis of the sensitivity curve. This approach serves not only as a verification of the parameters but also as a means to acquire valuable insights into planetary systems. The new analyses reveal that some of the targets classified as brown dwarfs or small-mass stars have a planetary nature. HD 5388 b and HD 6718 b are likely planets. HD 141937 b is likely a planet, but the current dataset does not allow us to firmly constrain its true mass. HD 16760 b belongs to the brown dwarf regime and it has a probable second companion. 30 Ari B b falls within the stellar regime, but the presence of an additional stellar companion could compromise the reliability of the final results. For HD 148427 b, HD 96127 b and HIP 65891 b we determined a range for the orbital inclinations.

Recent observations of galaxies continue to reveal new ultraluminous X-ray sources (ULXs), increasing their known population and improving the statistics needed to understand their nature. We study the ULX populations of NGC 4631 and NGC 1097 using archival Chandra, XMM-Newton, and Swift/XRT observations to identify new ULXs and investigate their X-ray and optical properties. We analyzed X-ray data spanning 2000-2025. Spectral fitting was performed for sources with sufficient counts using absorbed power-law and diskbb models. Variability analyses, including hardness-intensity diagrams and light curves, were used to assess short- and long-term variability. Optical color-magnitude diagrams and near-infrared (NIR) spectral energy distributions (SEDs) were employed to identify possible donor stars. In NGC 4631, we identified two new transient ULXs, X-6 and X-7, with X-ray count rates varying by more than an order of magnitude. The LX-T^4 relation from diskbb fits provides strong evidence that NGC 4631 X-6 is powered by a stellar-mass black hole accreting via a standard disk. The optical sources within the X-ray error circles of X-6 and X-7 are candidate counterparts, suggesting these systems are candidate HMXBs. In NGC 1097, we discovered a new transient ULX, ULX-3, showing X-ray luminosity variations by a factor of about 30 and evidence for spectral state transitions, consistent with either a stellar-mass black hole or a neutron star. We identified a unique optical and NIR counterpart. While the optical emission is variable, the NIR emission is stable. The NIR SED is consistent with a blackbody temperature of about 3300 K, compatible with a red supergiant donor with a radius of about 200 solar radii.

Changing-state active galactic nuclei (CSAGNs) exhibit rapid variability, with mass accretion rates that can change by several orders of magnitude in a few years. This provides us with a unique opportunity to study the evolution of the inner accretion flow almost in real time. Here, we used over 1000 observations to study the broadband X-ray spectra of a sample of five CSAGNs, spanning three orders of magnitude in Eddington ratio ($λ_{\rm Edd}$), using phenomenological models to trace the evolution of key spectral components. We derive several fundamental parameters, such as the photon index, soft excess strength, reflection strength, and luminosities of the soft excess and primary continuum. We find that the soft excess and primary continuum emissions show a very strong positive correlation ($p \ll 10^{-10}$), suggesting a common physical origin. The soft excess strength does not show any dependency on the reflection parameter, suggesting that in these objects the soft excess is not dominated by a blurred ionized reflection process. On the other hand, the strength of the soft excess is found to be strongly positively correlated with the Eddington ratio ($p \ll 10^{-10}$), and we find that the soft excess vanishes below $\log λ_{\rm Edd} \sim -2.5$. Moreover, we find a clear `V'-shaped relation for $Γ-λ_{\rm Edd}$, with a break at $\log λ_{\rm Edd} = -2.47 \pm 0.09$. Our findings indicate a change in the geometry of the inner accretion flow at low Eddington ratios, and that the soft excess is primarily produced via warm Comptonization.

In 1+1-dimensions, an extension of the canonical solitonic Dym equation has previously been derived both in a geometric torsion evolution context and in the analysis of peakon solitonic phenomena in hydrodynamics. Here, a novel 2+1-dimensional S-integrable extended Dym-type equation is introduced. As Lax pair is constructed and an associated $\bar{\partial}$-dressing scheme detailed. Integrable modulated versions of the 2+1-dimensional extended Dym equation are generated via application of a class of involutory transformations with genesis in classical Ermakov theory.

Abell 3571 is a nearby, X-ray bright galaxy cluster located in the Shapley Supercluster. Although it appears morphologically relaxed in X-ray images, multiwavelength observations reveal subtle indications of residual dynamical activity, likely associated with past merger events. Using wide-field ($1^{\circ} \times 1^{\circ}$) data from the Einstein Probe Follow-up X-ray Telescope (EP-FXT), we extend measurements of the cluster's properties beyond its $R_{500}$ radius. We detect surface-brightness excesses on both the northern and southern sides, consistent with previous XMM-Newton results. The temperature, pressure, and entropy in the northern excess region are lower than the average values, whereas those on the southern side are slightly higher. However, we find no evidence for cold fronts or shocks. These features can be interpreted as sloshing motions triggered by an off-center minor merger. Our findings suggest that, despite its symmetric appearance, A3571 is still recovering from a minor merger and is currently in a post-merger phase. This work also demonstrates the excellent capability of EP-FXT for probing the outskirts of galaxy clusters.

With the arrival of JWST observations of the TRAPPIST-1 planets, it is timely to reassess the contribution of tidal heating to their heat budget. JWST thermal phase curves could reveal endogenic heating through an anomalously high nightside temperature, providing an opportunity to estimate tidal heating. In this study, we revisit the tidal heating of these planets and propose a simple method to compute the tidal heating profile across a broad range of parameters. Our approach leverages a known formulation for synchronously rotating planets on low-eccentricity orbits and the fact that the profile shape depends solely on internal structure. We calculate the tidal heating contributions for all T-1 planets, with a particular focus on the impact of internal structure and eccentricity uncertainties on their total heat budget. Although the masses and radii of these planets are well constrained, degeneracies remain in their internal structure and composition. For volatile-poor planets of silicate-rock compositions, we investigate the role of core iron content by exploring a range of core sizes. For each structure, we compute the degree-two gravitational Love number, $k_2$, and the corresponding tidal heating profiles. We assume sub-solidus temperatures profiles that are decoupled from interior heat production, which means our estimates are conservative and likely represent minimum values. We find that the tidal heat flux for T-1b and c can exceed Io's heat flux, with uncertainties primarily driven by eccentricity. These high fluxes may be detectable with JWST. For T-1f to g, the tidal flux remains below Earth's geothermal flux, suggesting that tidal heating is unlikely to be the dominant energy source. For planets d and e, however, tidal heating likely dominates their heat budget, potentially driving intense volcanic and tectonic activity, which could enhance their habitability prospects.

Stellar variability may originate from various phenomena such as binarity, pulsations, or rotation. These mechanisms can induce flux variations of similar magnitudes, shapes, and periods. We aim to determine mechanisms responsible for the sinusoidal variations in main-sequence stars hotter than 6500 K. We conducted our analysis using TESS long-cadence data complemented with high-resolution spectra from three spectrographs. From the initial sample of almost 46000 objects, we selected 35 targets for spectroscopic follow-up. Comparison of light curves and radial velocity curves allowed for robust classification of these targets. Among the 35 selected objects, 18 displayed variability, suggesting the presence of a companion (including the discovery of 7 new binary systems and 1 candidate for a triple-star system), 1 was identified as a new pulsator, 9 as new candidates for spotted stars, and 7 objects had uncertain classification. Our analysis shows that at least half of randomly selected stars with sinusoidal brightness variations are binaries. The presented results illustrate the need for an individual approach to stellar classification, especially in cases where the photometric data alone is insufficient for determining the underlying phenomena behind the observed variations.

The gravitational-wave signal from the neutron star-black hole (NSBH) merger GW200105 is consistent with this binary having significant orbital eccentricity close to merger. This raises the question of how eccentric NSBHs form. Compact binaries that evolve in isolation radiate away any orbital eccentricity long before their gravitational-wave signal enters the sensitive frequency range of the LIGO-Virgo-KAGRA detector network. Meanwhile, dynamical environments -- which can be conducive to mergers on eccentric orbits -- produce very few NSBHs. Here, we focus on a formation channel that efficiently produces NSBHs with both misaligned spins and significant eccentricity close to merger: isolated field triples. We estimate the minimum measurable eccentricity of NSBHs at 10 Hz orbit-averaged gravitational-wave frequency, e_min,10, finding that for GW200105, GW200115, and GW230529-like systems, e_min,10 is O(0.01). For a GW190814-like unequal-mass binary with significant higher-order mode content, e_min,10 = 0.003; this is an order of magnitude lower than when higher modes are not present. For dominant-mode signals from binaries with $m_2=1.5$~M$_\odot$ and total masses from $3\,{\rm M_\odot} \leq M \leq50\,\rm M_\odot$, we find $0.008 \leq$ e_min,10 $\leq 0.022$. The relationship between $M$ and e_min,10 is linear when the binaries are non-spinning. When the binaries are maximally spin-precessing, e_min,10 decreases as mass ratio becomes more unequal. We estimate the sensitivity of a quasi-circular aligned-spin templated search to NSBH mergers from field triples, finding that we recover only 46% of systems that would have been detected with a search containing the full physics of the injected population. Finally, we show that if $\sim\nicefrac{1}{3}$ of present NSBH detections are measurably eccentric, then $\geq40\%$ are consistent with an isolated field triple origin.

Context. With CAPOS, we can mitigate the observational difficulties limiting access to bulge globular clusters in the optical and investigate them in more detail in the near-IR. Aims. To perform a rigorous abundance analysis of the metal-rich bulge globular cluster NGC 6304, in order to determine its detailed chemical composition and identify multiple populations. Methods. We analyzed APOGEE-2 near-IR spectra of 27 giant members. The abundances of 17 elements (C, N, O, Na, Mg, Al, Si, S, K, Ca, Ti, V, Cr, Mn, Fe, Ni, and Ce) were derived using the BACCHUS code, using atmospheric parameters from both ASPCAP and photometry (Gaia and 2MASS). Results. We derived $[{\rm Fe/H}] = -0.45\pm0.05$ using the ASPCAP parameters, and $[{\rm Fe/H}] = -0.45\pm0.08$ when using photometric parameters, with no evidence of an intrinsic metallicity spread. NGC 6304 shows $[α/{\rm Fe}]_{\rm spec} = 0.24\pm0.07$ and $[α/{\rm Fe}]_{\rm phot} = 0.23\pm0.08$. We find a significant spread in $[{\rm N/Fe}]$, with $σ_{\rm spec} = 0.54$ and $σ_{\rm phot} = 0.46$, along with a C-N anticorrelation. Furthermore, we detect a correlation of Ce with both N and Al, consistent with patterns observed in some metal-rich bulge globular clusters. Conclusions. We find a significant star-to-star variation in Na, but a minimal variation in O. The absence of the Mg-Al anticorrelation supports the evidence that the MgAl cycle is not active in globular clusters at high metallicity. The observed correlation between Ce and both N and Al suggests that the enrichment of these elements may be driven by asymptotic giant branch stars, positioning Ce as an element involved in multiple populations in metal-rich globular clusters. We find that abundances are consistent with those of bulge field stars of similar metallicity, suggesting a similar origin and chemical evolution.

The Binarity at LOw Metallicity (BLOeM) survey is an ESO large programme designed to obtain multi-epoch spectroscopy for 929 massive stars in the Small Magellanic Cloud (SMC). It will provide binary fractions and orbital configurations of binary systems, and search for dormant black-hole binary candidates (OB+BH). Here we present projected rotational velocities (vsini) of all sources and, using the multiplicity properties presented in previous papers, we derive the vsini distributions of apparent single stars, single lined spectroscopic (SB1) binaries, and SB2 systems. We identify a locus in the Hertzsprung-Russell diagram where rotational velocities decrease significantly; we interpret this feature as broadly corresponding to the terminal-age main sequence. The main sequence cohort is distinguished by a broad range of vsini values, but with a strong peak in the distribution in the range 30-60 km/s, close to the resolution limit of 30 km/s. Sources in this low vsini peak are distributed throughout the main sequence, and are also present in the SB1 sample, though less prominent than in the single star distribution. A preliminary analysis of the lowest vsini cohort, that includes SB1 systems, implies that roughly one third may be nitrogen rich and we speculate that this cohort is a mix of pristine single stars, long period binaries, and merger products. The SB2 systems appear to be mostly short period binaries in synchronous rotation and have vsini estimates distributed around a mean value of approximately 140 km/s . Higher vsini sources are also present in the single and SB1 systems, all of which have tail to higher vsini values, consistent with tidal and mass-transfer effects. The supergiants, with a few exceptions, have low vsini, the bulk of these systems being essentially unresolved at current spectral resolution.

The multi-band HSC-CLAUDS survey comprises several sky regions with varying observing conditions, only one of which, the COSMOS Ultra Deep Field (UDF), offers extensive redshift coverage. We aim to exploit a complete sample of labeled galaxies from the COSMOS UDF at i<25 (z<~5) to train a convolutional neural network (CNN) and infer more accurate photometric redshifts in the other regions than those currently available from SED-fitting methods. To address the severe domain mismatch problem we observed when applying the trained CNN to regions other than the COSMOS UDF, we developed an unsupervised adversarial domain adaptation network that we grafted onto the CNN. The method is validated by three tests: the predicted redshifts are compared to the spectroscopic redshifts that are available for limited samples of mostly bright galaxies; the predicted redshift distributions of the entire galaxy population of a given field in several intervals of magnitude are compared to those of the COSMOS UDF, assumed to be representative; the redshifts predicted for a sample of galaxies selected by narrow-band filter observations sensitive to [OII] emitters at z~1.47 are compared to those of confirmed [OII] emission line galaxies. The results show successful domain adaptation: the network is able to transfer its redshift classification capability learnt from the COSMOS UDF to other regions of HSC-CLAUDS. Accuracy varies depending on magnitude and redshift, following that of the labels we used, but far exceeds that of currently available photometric redshifts. The catalogs of CNN redshifts we inferred for the XMM, DEEP2 and ELAIS fields and for the remaining COSMOS region (~4 million sources in total at i<25) are made public.