The problems that we consider in this paper are as follows. Let $A_1, \ldots, A_k$ be square matrices (over reals). Let $W=w(A_1, \ldots, A_k)$ be a random product of $n$ matrices. What is the expected absolute value of the largest (in the absolute value) entry in such a random product? What is the (maximal) Lyapunov exponent for a random matrix product like that? We give an answer to the first question under some mild restrictions on the entries of $A_i$. For the second question, we offer a very simple and efficient method to produce an upper bound on the Lyapunov exponent.

Theoretical models predict that the Galaxy hosts $10^8$-$10^9$ black holes formed from the complete gravitational collapse of heavy stars and that most of these black holes are isolated, without any companion. Within 15 pc of the Solar System ($\sim 50$ ly), there may be a few black holes. If located inside one of the Local Interstellar Clouds - which occupy 5-20% of this local volume - an isolated black hole could produce detectable electromagnetic emission via accretion from the interstellar medium, given the capabilities of current or near-future observatories. However, precise predictions remain challenging due to large uncertainties in the expected accretion spectra. Outside these clouds, the accretion rate would be too low; according to our models, the resulting electromagnetic flux is well below the detection thresholds of current and near-future observational facilities. While astrometric detection via gravitational perturbation of nearby stars is conceivable, the local stellar density is too low for this method to be realistically successful. We have searched the Gaia DR3 catalog for candidate isolated black holes accreting from the interstellar medium and identified five sources. All candidates lie close to the Galactic plane, making them likely spurious astrometric solutions, for instance caused by unmodelled background sources (crowding) and/or unmodelled binarity. Our search for infrared and radio emission from these sources further suggests that they are unlikely to be black holes accreting from the interstellar medium.

The integration of artificial intelligence (AI) into healthcare has advanced significantly, yet affect recognition remains a major challenge, particularly in AI-assisted interventions such as Computerized Cognitive Training (CCT). The THERADIA-WoZ corpus was developed to enable multimodal affect recognition in the context of AI-driven CCT, focusing on an older adult population. This study extends the corpus by introducing a dataset collected from young adults, allowing direct comparison of affect recognition models across age groups. Our objective was to assess whether multimodal models based on dimensions borrowed from appraisal theories outperform those based on categorical labels and to evaluate their generalisation power across age corpora. After comparing both corpora, models were trained and tested using within-corpus, cross-corpus, and mixed-corpus evaluation. Results revealed that appraisal dimensions consistently outperformed categorical labels across all conditions, demonstrating greater predictive accuracy and stability. Notably, categorical labels failed to generalise across age corpora, as performance dropped to chance levels in cross-corpus evaluation. In contrast, appraisal dimensions maintained predictive performance above chance, reinforcing their robustness for cross-age affect recognition. Furthermore, training on both corpora did not improve generalisation beyond within-corpus training. The findings support the theoretical and practical advantages of appraisal dimensions over categorical labels in affective computing. They also highlight the importance of multimodal fusion and deep learning representations for emotion modeling. To facilitate future research, we provide an API for researchers interested in time-continuous emotion prediction, offering valuable tools for behavioral sciences to enhance the measurement of emotional states in various experimental settings.

In numeric-intensive computations, it is well known that the execution of floating-point programs is imprecise as floating-point arithmetic incurs round-off errors. Although round-off errors are small for a single floating-point operation, the aggregation of such errors may be dramatic and cause catastrophic program failures. Therefore, to ensure the correctness of floating-point programs, round-off error needs to be carefully taken into account. In this work, we consider polynomial invariant generation for floating-point programs, aiming at generating tight invariants under the perturbation of round-off errors. Our contribution is a novel framework for applying polynomial constraint solving to address the invariant generation problem, which is also the first polynomial constraint solving based approach that handles floating-point errors to our best knowledge. In our framework, we propose a novel combination of round-off error analysis and polynomial constraint solving, aiming to circumvent the cost of handling a large number of error variables in the floating-point model. Experimental results over a variety of challenging benchmarks show that our framework outperforms SOTA approaches in both time efficiency and the precision of generated invariants.

We formulate a renormalizable complex extension of the bumblebee theory in which the bumblebee field is promoted to a complex one and coupled to an Abelian gauge sector. Besides the minimal gauge covariant interaction, the model includes a longitudinal kinetic term controlled by a dimensionless parameter $g_l$ and a non-minimal magnetic-type coupling $g_m$ between the complex bumblebee and the photon. Using dimensional regularization and minimal subtraction, we determine the one-loop UV divergences of the two-, three-, and four-point functions relevant to the renormalization of the gauge, longitudinal, and quartic sectors. We obtain the corresponding counterterms and derive the one-loop renormalization-group functions for $e$, $g_l$, $g_m$, and the bumblebee self-couplings $λ$ and $\tildeλ$. Motivated by the known gauge- and field-reparametrization subtleties of the conventional Coleman--Weinberg analysis, we formulate an RG-covariant leading-logarithmic improvement scheme for the Vilkovisky--DeWitt effective potential in normal field coordinates, in which the RG operator is governed solely by the beta functions. We apply this framework to a real constant bumblebee background and obtain the leading-logarithmic one-loop effective potential, discussing the conditions under which a nontrivial vacuum is generated by dimensional transmutation and thereby provides a dynamical realization of Lorentz symmetry breaking in this class of models.

Antarctic sea ice has undergone unprecedented changes in recent years, raising questions about how this key geophysical system is responding to climate change. Decades of slow expansion were replaced by a precipitous decline in 2014-2017, a subsequent apparent recovery, and a renewed collapse from 2022 to the present. We diagnosed sea ice concentration (SIC) from satellite observations with a hierarchical decomposition method based on Dynamic Mode Decomposition (DMD) that finds coherent spatiotemporal modes. We find that the 2014-2017 decline and apparent recovery are the result of interacting interannual modes and that a climate change signal emerges in 2012, which becomes unambiguous by 2022 when it dominates over interannual variability. These rapid changes underscore the need for seasonal-to-annual forecasts of SIC. However, existing forecasts are subject to limited prediction horizons combined with high computational costs. Our predictive DMD model (IceDMD) is regularised to prioritize the stationary spatiotemporal modes found by the decomposition. The predictive model can forecast SIC anomalies in 2023-2024 up to two years in advance, outperforming all existing approaches with the additional benefits of physical interpretability and extremely cheap computational cost. Finally, this framework for regularising predictive DMD models can be generalized to a range of multi-scale systems.

The addition of a small amount of long-chain polymers confers viscoelastic properties to Newtonian flows. The resulting non-Newtonian solution now exhibits different dynamics, such as enhanced mixing at low Reynolds, where elastic instabilities can trigger elastic turbulence even though inertial turbulence is absent. Here, we study this phenomenon in viscoelastic planar jets and, in particular, we do it from the perspective of coherent structures to understand how elastic turbulence is triggered and sustained, which remain barely explored in this setup. We introduce the spatio-temporal Koopman decomposition for extracting the dominant flow patterns, and we compare them with those from Newtonian planar jets at high Reynolds number. Global flow structures are similar between jets, with low-frequency streaks and high-frequency wave packets dominating the turbulent dynamics. However, structures are strikingly different in the near field, where elasticity-driven streaks affect the dynamics in the potential core of the viscoelastic planar jet, modifying the bulk flow and interacting with the flow instability. The analysis of the polymer field reveals stretched polymer filaments and centre-mode structures, which support the implication of the near-field streaks on sustaining elastic turbulence in three-dimensional viscoelastic planar jets.

We present a novel and unifying framework for constructing spectral approximations to fractional integral operators. These spectral approximations are based on transplanted Chebyshev polynomials, which are obtained by composing Chebyshev polynomials with a variable transform. When an algebraic transform is used, the framework produces spectral approximations based on Jacobi fractional polynomials. When an exponential transform is used, it yields a versatile spectral approximation that is applicable to a much broader class of fractional calculus problems. The construction of such spectral approximations is both numerically stable and optimal in terms of complexity. These spectral approximations lead to stable and fast spectral methods for fractional calculus. The spectral approximation based on the double-exponential transform is demonstrated through extensive numerical examples that are intractable for existing spectral methods.

This paper develops a model for option market making in which the hedging activity of the market maker generates price impact on the underlying asset. The option order flow is modeled by Cox processes, with intensities depending on the state of the underlying and on the market maker's quoted prices. The resulting dynamics combine stochastic option demand with both permanent and transient impact on the underlying, leading to a coupled evolution of inventory and price. We first study market manipulation and arbitrage phenomena that may arise from the feedback between option trading and underlying impact. We then establish the well-posedness of the mixed control problem, which involves continuous quoting decisions and impulsive hedging actions. Finally, we implement a numerical method based on policy optimization to approximate optimal strategies and illustrate the interplay between option market liquidity, inventory risk, and underlying impact.

We present an interesting study of Feynman integral reduction that does not employ integration-by-parts identities. Our approach proceeds by studying the equivalence relations of integral contours in the Feynman parameterization. We find that the integration contour can take a more general form than that given by the Cheng-Wu theorem. We apply this idea to one-loop integrals, and derive universal reduction formulas that can be used to efficiently reduce any one-loop integral. We expect that this approach can be useful in the reduction of multi-loop integrals as well.

The Jiangmen Underground Neutrino Observatory (JUNO) is a 20-kton liquid scintillator-based, low-radioactivity, multi-purpose neutrino detector located 693 meters (1800 m.w.e.) underground in the Guangdong province, China. To detect scintillation light produced in the target, the detector is equipped with 17,612 20-inch photomultipliers (PMTs), forming the Large PMT system (LPMT). In addition, 25,600 3-inch photomultipliers (the Small Photomultiplier System or SPMT) are deployed in the gaps between the LPMTs. This paper presents the design and performance of the underwater front-end electronics developed for the SPMT system. It details the individual electronics boards and their key components, the inter-board interfaces, the system-level design, and the firmware architecture that supports data acquisition and control. It also outlines mechanical and thermal integration, board validation procedures, and system performance metrics. The readout chain includes digitization of 128 PMT channels per unit, synchronized time-stamping, charge measurement, event packaging, and bandwidth management. Comprehensive validation confirms the system's readiness to meet JUNO's stringent physics goals. The underwater electronics achieve noise levels as low as 0.04 photoelectrons with minimal crosstalk (below 0.4%) and a bandwidth of 57 MB/s, ensuring reliable single photo-electron detection and operation under high-rate conditions. The SPMT system has now been fully integrated and installed in JUNO. Its commissioning and physics performance will be reported in a future publication.

Investigating the chemical complexity of the interstellar medium (ISM) is key for understanding its physical nature and evolution. In this work, we study parsec-scale interstellar dust clouds in the neutral ISM of the Milky Way using two different probes: dust depletion and dust extinction. We examine their relationship to investigate the distribution of metals and dust in the Solar neighbourhood, and how they are related to the Local Bubble. We use measurements of dust depletion for individual gas clouds along sight lines of sight towards bright O/B stars within 1.1 kpc of the Sun, derived from UV absorption-line spectra. We combine these with parsec-scale 3D dust extinction density maps out to 1.25 kpc. We assume a correlation between dust depletion and dust extinction density, which we use to imply that the absorption components are spatially associated with the peaks in dust extinction density, and to pinpoint the likely locations of the gas clouds in physical space. We identify peaks in the dust extinction curves, and then associate the stronger peaks with the strongest dust depletion components. Independent distance measurements along the line of sight towards one of our targets, theta1 Ori C, validates our results. In our sample, the minimum distance between clouds that have significantly different chemical properties is ~ 100pc, giving an indication on the physical scale on which chemical mixing remains incomplete in the ISM of the Milky Way. For five of the eight targets, we report dust depletion values for gas clouds associated with the Local Bubble. Additionally, we find a velocity gradient that is consistent with the expansion of the Local Bubble, further supporting our methodology. Overall, we show that it is possible to use complementary information from dust depletion and dust extinction to build more detailed maps of ISM metal and dust distributions.

A challenge with the Quantum Approximate Optimisation Algorithm (QAOA), and variational algorithms in general, is finding good variational parameters, a task which in itself can be NP-hard. Recent work has sought to de-variationalise QAOA by picking well-informed guesses for the variational parameters. The Linear Ramp QAOA (LR-QAOA) achieves this by using parameter schedules inspired by the quantum adiabatic algorithm. In this work, we propose Spectral Gap Informed Ramp QAOA (SGIR-QAOA), a new QAOA variant that incorporates spectral gap information from an adiabatic Hamiltonian, with the QAOA mixer Hamiltonian as the initial Hamiltonian, to construct smooth parameter schedules. SGIR-QAOA performs slow evolution where the spectral gap of the adiabatic Hamiltonian is small. We show that SGIR-QAOA has performance improvements over the LR-QAOA on Grover's problem at constant depth and that SGIR-QAOA requires shorter depths to achieve the same optimal solution probability. We then show that these performance benefits extend to a problem with potential practical applications - the Maximum Independent Set (MIS) problem. Finally, we demonstrate the scalability of the SGIR-QAOA method using extrapolated spectral gap information for scales that the spectral gap cannot be exactly evaluated, and show that the advantage appears to persist under mild depolarising noise.

Cool, dense condensations such as coronal rain and prominences suggest that coronal plasma can undergo runaway radiative cooling. Connecting this behaviour to linear thermal modes requires us to fully understand the deeper connection between eigenvalue spectra and actual time-dependent evolution. We aim to clarify this intricate link for a simplified, coronal-only model of a stratified coronal loop by combining spectral, linear initial-value, and nonlinear simulations of the same loop setup. We study waves and instabilities, as well as temporal evolutions for a 1D hydrostatic, thermally balanced loop with optically thin radiation and prescribed heating. The non-adiabatic spectrum is computed with our open-source Legolas code. We demonstrate our newly developed boundary value-initial value solver Legolas-IVP, where linear evolutions are performed for controlled perturbations, and fully equivalent nonlinear runs are carried out with MPI-AMRVAC. The spectrum contains discrete acoustic modes and a thermally unstable branch including a thermal continuum. Linear initial-value experiments with isochoric, isobaric, and isentropic pulses highlight how the polarisation of the eigenmodes demonstrates physically consistent behaviour expected from the eigenspectrum. Even in the linear stage, thermal imbalance drives siphon-like flows toward the cooling region. Growth rates from Legolas-IVP agree with spectral predictions and are reproduced in MPI-AMRVAC, which follows the condensation through runaway cooling to chromospheric temperatures, with the cool dense blob sliding under gravity toward the loop footpoint. The spectral-linear-nonlinear investigation demonstrates a direct link between thermal eigenmodes and condensation dynamics, providing a basis for extending to fully 3D MHD models.

Let \(Λ\) be a finite-dimensional quadratic monomial algebra and let \(Λ^{!}\) be its Koszul dual. We investigate the structure of graded modules over \(Λ^{!}\) and derive several consequences for Koszul duality. We prove that \(Λ^{!}\) is both graded coherent and graded co-coherent. Moreover, finitely presented and finitely copresented graded \(Λ^{!}\)-modules coincide with perfect and coperfect modules, respectively. As a consequence, the associated tails and cotails categories are hereditary abelian categories admitting explicit descriptions in terms of linear and colinear modules. We further show that every finite-dimensional quadratic monomial algebra is absolutely Koszul and has global linearity defect at most one. In particular, finitely presented graded modules have rational Poincaré and Hilbert series. Using these structural results, we refine graded and ungraded derived Koszul dualities, singular Koszul dualities, and the Bernstein--Gelfand--Gelfand correspondence. We obtain explicit descriptions of the associated triangulated categories and of the induced nonstandard \(t\)-structures. As an application, we derive new bounds on the finitistic dimension of quadratic monomial algebras in terms of finite paths in the Koszul dual algebra.

We discuss the marginal $\sqrt{T\overline{T}}$ deformation of massless scalar field theories in two dimensions from a dynamical perspective. The operator flow equations for such deformations induce a particular Legendre Transformation between flowed Lagrangians and flowed Hamiltonians. The marginal deformation does not change the conformal symmetries of the theory, until some special points in the moduli space are reached, and the relativistic conformal algebra smoothly changes to the Carrollian conformal (equivalently BMS) one. We investigate this change of symmetry from both configuration space and phase space point of view, while keeping the notion of Legendre Transformation unchanged during the flow. By expanding the actions, in the extreme limits of the flow parameter, we recover the usual ``Electric'' Carroll theory and further uncover a novel ``Magnetic'' counterpart. We discuss the intriguing geometric understanding of such dynamical maps for the deformed theories, and also provide a concrete example for the same from a deformed string theory in flat space.

In this paper we study continuum-marginal optimal transport. Given a time-continuous family of probability marginals, the problem is to recover the minimum-energy velocity field whose flow reproduces every marginal. This problem is the continuum limit of the classical two-marginal Benamou--Brenier formulation, and also the deterministic limit of the Nelson problem of stochastic optimal transport. We propose a practical mesh-free solver for this problem. The weak continuity equation is embedded in a reproducing kernel Hilbert space, yielding a sample-only objective that requires no spatial discretization. The velocity is parametrized by any linear-in-parameters dictionary or neural network, and is optimized by mini-batch stochastic methods. Synthetic experiments confirm that the method achieves accurate drift recovery and marginal consistency. The same computational framework also applies to the stochastic Nelson problem.

The SVOM mission is specifically designed to for the detection and localization of Gamma-Ray Bursts (GRBs) and subsequent follow-up observations. Among the four telescopes installed on the SVOM satellite, the Gamma-Ray Monitor (GRM) plays a crucial role in capturing the prompt emission of GRBs due to its wide field of view (FOV) and broad energy range. Accurate determination of the detector's energy response is vital for analyzing GRM data, particularly considering the significant impact of the atmospheric albedo effect on this response. This research focuses on deriving the detector's energy response and establishing a calibration database for the GRM, with particular emphasis on investigating the atmospheric albedo effect. The study shows that the contribution of albedo photons to the detector's effective area depends strongly on the orientation of the GRD line of sight (LoS) relative to Earth and on the incident direction of the GRB. When the GRD LoS is anti-Earth oriented, the albedo effect is minimal, with the highest proportion of albedo effective area accounting for approximately 10% of the total effective area. This occurs when the incident angle of the GRB is nearly perpendicular to the LoS. Conversely, if the GRD LoS is not pointing away from Earth and the GRB arrives from angles greater than about 90$^{\circ}$, the albedo component can become predominant, contributing up to around 100% of the total effective area. This is especially pronounced in the 8-20 keV range, where the direct effective area drops to zero due to the large GRB injection angle. Our results show that, it is necessary for GRM to consider the atmospheric albedo effects in detector response, otherwise the spectral and localization analyses will result in biased measurements.

Fully Homomorphic Encryption (FHE) is a cryptographic scheme that enables computations to be performed directly on encrypted data, as if the data were in plaintext. After all computations are performed on the encrypted data, it can be decrypted to reveal the result. The decrypted value matches the result that would have been obtained if the same computations were applied to the plaintext data. FHE supports basic operations such as addition and multiplication on encrypted numbers. Using these fundamental operations, more complex computations can be constructed, including subtraction, division, logic gates (e.g., AND, OR, XOR, NAND, MUX), and even advanced mathematical functions such as ReLU, sigmoid, and trigonometric functions (e.g., sin, cos). These functions can be implemented either as exact formulas or as approximations, depending on the trade-off between computational efficiency and accuracy. FHE enables privacy-preserving machine learning by allowing a server to process the client's data in its encrypted form through an ML model. With FHE, the server learns neither the plaintext version of the input features nor the inference results. Only the client, using their secret key, can decrypt and access the results at the end of the service protocol. FHE can also be applied to confidential blockchain services, ensuring that sensitive data in smart contracts remains encrypted and confidential while maintaining the transparency and integrity of the execution process. Other applications of FHE include secure outsourcing of data analytics, encrypted database queries, privacy-preserving searches, efficient multi-party computation for digital signatures, and more. A dynamic website version is available at (https://fhetextbook.github.io). Please report any bugs or errors to the Github issues board.

We extend the CDPR's quantum attack from ideal lattices to module lattices over $2^k$-th cyclotomic rings. Using trace orthogonality of the power basis, we decompose a rank-$d$ module into mutually orthogonal rank-$1$ submodules, and apply CDPR's analysis to each independently and return the shortest candidate. The Hermite factor $\exp(\tilde{O}(\sqrt{n}))$ matches the ideal case, with a module reduction factor $α_d=O(1)$ independent of the rank, under a balance hypothesis (proved for Gaussian distribution) automatic for MLWE-distributed bases. To enable a bounded-precision implementation, we replace coordinate-wise rounding with Chinese Remainder Theorem-scaled rounding at totally split primes, reducing the Gram-Schmidt rounding radius from $n/2$ to $\le 1$ at cost $O(d^2 r n \log n)$. Finally, we reformulate the CDPR's sign-selection step as a mixed-integer linear program and prove its optimum is no more than 1/2 for all $k$ ($\approx 0.4407$ for all tested $k\le 12$, conjecturally universal). This replaces the previous heuristic discrepancy $Θ(\sqrt{nk})$. All results build on the class number condition $h_k^+=1$ established in Part I of this series.

As planetary nebulae evolve, they fade and dissipate into the surrounding interstellar medium making them harder to detect. Modern, advanced amateur equipment can help to uncover this hidden population of ancient 'ghost' planetary nebulae. Via careful processing of long-integration, narrow-band imagery with modest aperture telescopes at a dark-sky site, we reveal three new candidate planetary nebulae (JAM 2, JAM 3, and JAM 4). Each measures several arcminutes across with [O iii] surface brightnesses of order 30 mag arcsec$^{-2}$. For each nebula, we identify a candidate central star, the parallaxes of which lead to nebular age estimates in the range 50-100 thousand years. The candidate central star of JAM 2 also shows indications of photometric variability, potentially due to spots on the stellar surface.

In this paper, we study a system of bosons trapped in a confining potential, interacting with a quantized field of coherent photons in the mean field description of non-relativistic Quantum Electrodynamics (QED) obtained by [N. Leopold and P. Pickl , 2017]. We derive the effective nonlinear cascade equations governing the emission and absorption of coherent photons by the boson subsystem in a combined weak-coupling and macroscopic time limit. We demonstrate that solutions to this nonlinear cascade describe a monotone decreasing energy flow in the boson subsystem. Thereby, we prove that a Bose-Einstein condensate (BEC) forms dynamically, under conservation of the total boson $L^2$ mass. We note that this process is crucially different from thermal relaxation to the ground state, and fundamentally depends on the nonlinear nature of the cascade dynamics.

On the Hertzsprung-Russell diagram, F-type solar pulsators connect the Sun to intermediate mass stars located on the instability strip. With respect to lower mass stars, they are structurally peculiar in the sense that they are constituted of three distinct dynamical layers: a small convective core, a deep radiative interior, and a shallow convective envelope. Current asteroseismic techniques only provide limited information on the interior dynamics of these stars. Indeed only gravity modes (g modes), for which unambiguous characterisation is lacking, are able to probe the deep stellar layers. A better understanding of the excitation and behaviour in F-type solar pulsators is therefore necessary in order to consider their detection. In this work, we simulate for the first time the global stellar structure of an F-type star (core, radiative interior, envelope). We show that the contribution of the core strongly affects the spectrum of excited g modes, with low-order high-degree modes unable to form due to their interaction with the turbulent convection of the core. Finally, by computing the disc-integrated signature of the modes, we are able to demonstrate that they preserve their integrity up to the top of the convective envelope, which is a strong argument in favour of their detectability with spaceborne photometry.

The supermassive black hole Sagittarius A* (Sgr A*) exhibits temporal and spectral variability across the electromagnetic spectrum. However, variability at radio frequencies below ~ 5 GHz for timescales shorter than a day remains largely unexplored. We investigate the variability of Sgr A* at 2.79 GHz on short timescales (1 min), to probe an under-explored regime of its emission process. Through point-source model fitting in the uv-domain, we analyse the flux density variation of Sgr A* over an 8 h observation. We detect flux variation on a few tens of minute timescale with a modulation index of 6.11 %, a mean flux density of ($827 \pm 0.1_{\mathrm{stat}} \pm 33_{\mathrm{sys}}) \, \mathrm{mJy}$, and a mean spectral slope of $0.08\pm0.03$. Furthermore, we measure the slope of the structure function of the observed light curve as $0.81 \pm 0.05$ with a characteristic timescale of about 120 min. Our study at low radio frequencies is a critical step toward constraining the physical mechanisms that drive Sgr A*'s variable emission and its spectral energy distribution. Our study suggests that variability at centimetre and millimetre wavelengths is likely more closely related than previously thought.

Parsec-scale jets of blazars have so far been spatially resolved only in millimeter and submillimeter wavelengths, where very long baseline interferometry can be used to obtain milliarcsecond-scale images of the jets. We have attempted to spatially resolve the near-infrared emission in jet-dominated blazars for the first time. We used the VLTI-GRAVITY instrument to obtain milliarcsecond-scale near-infrared interferometric observations of a flaring blazar Ton 599. Additionally, we observed four non-flaring blazars using the GRAVITY-wide mode, where a nearby bright star is used as a fringe tracker. We modeled the squared visibilities of Ton 599 and found that they are incompatible with a single unresolved point source unless there is a significant amount of additional unknown coherence loss in the instrument. With the present data, we cannot distinguish between a model with an unresolved point source and extended emission or coherence loss and a model with a single Gaussian component. This suggests that we are seeing the unresolved or only partially resolved jet-base in near-infrared wavelengths. The wide-field mode of GRAVITY was challenging for the additional relatively faint targets, resulting in either non-detections or poor-quality data that could not be modeled. Our observations demonstrate that it is possible to detect the compact jet emission in blazars with near-infrared interferometry, suggesting that with the improved GRAVITY+ instrument it will be possible to spatially resolve and image the near-infrared emission of blazar jets.

We present a comprehensive reassessment of the region containing the large smooth patch on comet 9P/Tempel 1, leveraging data from the Deep Impact and Stardust-NExT missions, an updated stereophotoclinometry-based shape model, and numerical simulations. The study seeks to understand the nature, the triggering mechanism, and the chronology of this distinctive feature. Morphological and spectral analysis reveals that the smooth patch has a thickness of approximately 25 meters, a notable lobate U-shape, and a spectral composition indistinguishable from the surrounding terrain, which favors an endogenous origin. Gravitational flow simulations demonstrate that a single event could have formed the large smooth patch, the secondary smooth units observed on other faces of the comet, and the topographic terrace features adjacent to the northern smooth unit. We estimate this event occurred between 600 and 1,200 years ago, a temporal window that notably coincides with a period of abrupt orbital changes caused by multiple close encounters with Jupiter. We propose that these encounters may have played a role in triggering a mass flow. Although with the underlying mechanism still unresolved, these results shed new light on the geology of cometary nuclei and on the role of external dynamical processes in shaping their surfaces.

We investigate the connection between supermassive black holes (SMBHs), their host galaxies, and large-scale dark-matter halos using broad-line X-ray AGN from the XMM--XXL and Stripe\,82X surveys, together with galaxies from VIPERS and SDSS/Stripe\,82. Building on the homogeneous host-galaxy catalogue presented in Paper~I, we test whether AGN with a given black-hole mass, $M_{\rm BH}$, inhabit different large-scale environments from non-AGN galaxies with similar host properties. We first examine the empirical $M_{\rm BH}$--$M_{\star}$ relation of the AGN sample. We find a shallow trend with substantial scatter, likely driven by flux-limited selection effects and uncertainties in virial black-hole mass estimates. The ratio $M_{\rm BH}/M_{\star}$ decreases with increasing stellar mass, and AGN lying above and below the empirical relation show different median host properties, consistent with non-synchronous SMBH and stellar growth. We then divide the AGN into two black-hole mass bins, $8.0 \le \log(M_{\rm BH}/M_\odot) < 8.5$ and $8.5 \le \log(M_{\rm BH}/M_\odot) < 9.0$, and construct galaxy control samples matched in $M_{\star}$, SFR, and sSFR using a multivariate nearest-neighbour method. From AGN--galaxy cross-correlation functions, we infer the characteristic halo masses of AGN and matched galaxies. In the lower-$M_{\rm BH}$ bin, AGN occupy halos statistically indistinguishable from those of their controls. In the higher-$M_{\rm BH}$ bin, we find a mild indication that AGN may reside in somewhat more massive halos, with a difference of about 0.4 dex, although still consistent within the uncertainties. If confirmed with larger samples, this would suggest that halo-scale processes become important mainly at the highest $M_{\rm BH}$.

The upper atmospheres of temperate sub-Neptunes are strongly influenced by atmospheric dynamics due to their cool equilibrium temperature and thereby longer chemical timescales than the atmospheric dynamical timescales. In this study, we used a three-dimensional (3D) general circulation model to investigate the transport-induced disequilibrium chemistry and vertical mixing on temperate gas-rich mini-Neptunes, using K2-18b as an example. We model K2-18b assuming 180 times solar metallicity and consider it as either a synchronous or an asynchronous rotator, exploring spin-orbit resonances of 2:1, 6:1, and 10:1. We find that the vertical transport affects the chemical structure significantly, making CO$_2$ and CO more abundant ($\sim$10$^{-3}$) in the upper atmosphere compared to the chemical equilibrium abundance (<10$^{-15}$), and horizontal winds further homogenize the chemical composition zonally in this region. Molecular abundances in the photosphere generally agree across different rotation periods. We employ a passive tracer in the model to estimate the one-dimensional (1D) equivalent eddy-diffusion coefficient ($K_{zz}$) of K2-18b, providing a parameter useful for future 1D atmospheric models. Additionally, synthetic transmission spectra generated from our model are compared with the JWST observations, and we find that our model can provide a comparable fit to the observations. This work offers a 3D perspective on transport-induced chemistry on a temperate sub-Neptune and derives vertical mixing parameters to support 1D modelling.

Young transiting exoplanets provide unique opportunities to probe planetary atmospheres during the critical early phases of evolution. HIP 67522 b, a 17 Myr old hot Jupiter with an extraordinarily low bulk density, represents an ideal target for high-resolution transmission spectroscopy. We aim to characterize the atmospheric composition, thermal structure, and dynamics of HIP 67522 b using ground-based high-resolution near-infrared spectroscopy. We obtained high-resolution spectra with VLT/CRIRES+ in the K2166 band during a transit on 30 January 2025. We applied cross-correlation techniques and Bayesian nested sampling retrievals to constrain molecular abundances, temperature structure, and atmospheric dynamics. We detect H$_2$O at 20$σ$ and CO at 5$σ$, confirming the extremely extended atmosphere of this low-mass giant. A velocity offset of $-2.9 \pm 0.2$ km s$^{-1}$ indicates day-to-night winds. The rotation velocity is constrained to <1.8 km s$^{-1}$ at 3$σ$, consistent with tidal locking. Retrieval analysis suggests a planetary mass of 29.8 $\pm$ 3 Earth masses and a vertically isothermal atmosphere. This mass is two times larger than the mass estimated from JWST atmospheric observations and inconsistent at 3$σ$ hence leaving a doubt on the actual planetary density of the planet. Using the mass derived from the CRIRES+ data, we derive a C/O ratio of $0.83 \pm 0.09$, about 1.5 times solar, and a subsolar metallicity [C+O/H] $= -0.8 \pm 0.4$ which can be increased if the atmosphere is cloudy, a degeneracy our data alone cannot resolve. We report a tentative 2$σ$ detection of HDO with an extreme enrichment factor of $\sim$1000 relative to the protosolar D/H ratio. If confirmed, this would be the first detection of deuterium in an exoplanet atmosphere and would require intense escape rate to be explained.

Context. Episodic accretion in young stellar objects (YSOs) is thought to play a critical role in addressing the "luminosity problem" associated with star formation. However, optical surveys tend to bias against sources that are heavily obscured. Infrared time-domain surveys, such as unTimely WISE, facilitate the identification of such sources within the dense star formation regions of our Galaxy. Aims. We aim to systematically identify and characterize FUor outbursts in infrared-selected YSOs using high-resolution spectroscopy and detailed disk modeling. Methods. We conducted follow-up high-resolution spectroscopy with Gemini South/IGRINS for four FUor candidates discovered in infrared time-domain surveys. Using a combination of photometric and spectroscopic observations, we constructed spectral energy distributions and fit them with a disk model that incorporates an actively accreting inner disk together with a passively irradiated outer disk. Results. All objects show CO and H$_2$O absorption bands at 2.3$μ$m, and their positions in the Na + Ca versus CO equivalent width diagram further corroborate their classification as FUors. The best-fitting model spectra closely match both the observed spectral features and the overall continuum, providing additional confirmation of the FUor classification. The best-fit models reveal high extinction values ($A_V$ = 10-20 mag), with $M_*\dot{M}$ comparable to those of classical FUors such as FU Orionis. Among 18 sources initially selected via infrared light curves, $6-$7 out of 8 with available spectra exhibit FUor characteristics, implying a high selection efficiency.