We study multi-qubit variational quantum states that can be considered as vertex- and edge-weighted graph. These states are constructed as single-layer variational circuits with $RX$ rotations and $RZZ$ entangling gates, corresponding to graphs of arbitrary structure. In general case of quantum graph states of arbitrary structure we derive the geometric measure of entanglement and evaluate quantum correlators. It is shown that these quantities are related to the edge-weight structure around the corresponding vertices in the graph (i.e., edge weights incident to the vertices and vertex weights associated with their closed neighborhoods). In the special case of quantum states representing unweighted graphs, these quantities are related to the degrees of the corresponding vertices in the graph. As an example, we analyze the state associated with the star graph $K_{1,4}$ using noisy quantum computing on the AerSimulator. The results are in good agreement with theoretical predictions. These findings demonstrate a connection between graph structure and quantum properties, enabling the study of properties of classical graphs via quantum computing.

By work of Howlett and Muraleedaran--Taylor, a parabolic subgroup of a real or complex reflection group always admits a complement in its normalizer. In this note, we investigate this phenomenon for quaternionic reflection groups. Here, in contrast to the real and complex setting, we find that complements of parabolic subgroups do not exist in general. Indeed, there are infinitely many examples of quaternionic reflection groups in arbitrary rank greater than 2 with a parabolic subgroup that does not admit a complement in its normalizer. We give a full classification of parabolic subgroups of irreducible quaternionic reflection groups and describe their complements, if the latter exist.

The subject of the present paper is a detailed theoretical investigation of the energy spectrum and bandgaps, as well as topological and collective properties and linear response, in $d$-wave altermagnets in the presence of an off-resonance optical dressing field. We consider the altermagnets with both $d_{x^2-y^2}$ and $d_{xy}$ pairing symmetries and focus on anisotropic dressing fields applied to an anisotropic and non-linear electron Hamiltonian. We have uncovered several crucial properties of the resulting electron-dressed states; specifically, we found that a finite bandgap is opened by linearly polarized irradiation, a phenomenon not observed in Dirac materials. Some of the crucial properties of the electron dressed states in the presence of the linearly polarized light can be uncovered only in the second-order perturbation expansion, which is often omitted. We found that introducing an anisotropic driving field leads to several subtle yet important changes in the Edelstein susceptibilities of altermagents, enabling the fine-tuning of their spin polarizations. We calculate the Berry curvature for various types of altermagnets and obtain closed-form analytical expressions for circularly polarized irradiation. We demonstrate that the optical driving field can generate finite Berry curvature in the absence of altermagnetic order. All these results are expected to become a crucial contribution to the rapidly developing fields of spintronics and device physics.

HD 98800 is a nearby hierarchical quadruple system comprising two binaries orbiting each other. Surprisingly, despite its $\sim$ 10 Myr age and dynamic environment, the Ba-Bb component is surrounded by a compact gas-rich disc in a polar configuration. Previous millimetre continuum observations of this disc found a low millimetre spectral index ($α\sim$ 2.1 up to 9 mm), potentially arising from large dust grains, optically thick emission, or both. Furthermore, the interpretation was complicated by emission mechanisms other than dust thermal continuum at longer wavelengths. We present new observations of this system with the Very Large Array (VLA) at 6.8 mm and 3 cm, providing crucial additional sampling of the emission at millimetre/centimetre wavelengths. By combining these with ancillary data, we derive a dust spectral index $α_{\rm dust} <$ 3 for wavelengths $\le$ 1 cm. Our modeling suggests that the emission is optically thick at short millimetre wavelengths ($λ\le$ 3 mm) and it becomes at least partially optically thin for the VLA observations. The shallow spectral index thus indicates the existence of large grains in the disc. We also identify gyro-synchrotron emission from the A and B components at $λ\gtrsim $ 3 cm. The VLA images also reveal an azimuthal asymmetry at 6.8 mm and 8.8 mm, which is not present in high-resolution ALMA 1.3 mm data. After ruling out geometric and illumination effects, we interpret this asymmetry as a local dust overdensity, possibly induced by a vortex or a relic of the previous passage of the A component.

Integrating grid-forming converters (GFMCs) into grid-following converter (GFLC)-dominated power systems enhances the grid strength, but GFMCs' current-limiting characteristic triggers dynamic switching between constant voltage control (CVC) and current limit control (CLC). This switching feature poses critical transient stability risks to GFLCs, requiring urgent investigation. This paper first develops a mathematical model for this switched system. Then, it derives switching conditions for droop-controlled GFMCs, which are separately GFMC angle-dependent and GFLC angle-dependent. On this basis, the stability boundaries of GFLC within each subsystem are analyzed, and the impact of GFMC switching arising from GFLC angle oscillation is investigated. The findings reveal that the switched system's stability boundary coincides with that of the CLC subsystem. To enhance GFLC's transient stability and ensure GFMC converges to the CVC mode, this paper introduces a virtual fixed d-axis control (VFDC) strategy. Compared with existing methods, this method achieves decoupling and self-stabilization using only local state variables from individual converters. The conclusions are validated through simulations and Controller Hardware-in-the-Loop tests.

We investigate finiteness conditions on modules of bounded projective dimension and their connection with generalized notions of coherence. For a ring $R$, we consider the class $\mathsf{FP}_n^{\le d}(R)$ of finitely $n$-presented modules of projective dimension at most $d$ and develop the corresponding relative homological theory. We establish several characterizations of left $(n,d)$-coherent rings in the sense of Mao and Ding [43], in terms of $\mathsf{FP}_n^{\le d}(R)$ and the associated classes of $\mathsf{FP}_n^{\le d}$-injective, $\mathsf{FP}_n^{\le d}$-projective, $\mathsf{FP}_n^{\le d}$-flat, and $\mathsf{FP}_n^{\le d}$-cotorsion modules. As a consequence, when $d \ge \gD(R)$ or $d=\infty$, we recover Costa's $n$-coherence [17] and obtain new characterizations of regularly coherent rings.

A bar-like central feature is commonly observed in both nearby and distant spiral-type galaxies, including the Milky Way. While many methods exist to categorise this morphology, no one method has emerged as the field-wide standard. To develop a rigorous and consistent method for identifying these bars, we investigate a classification scheme based on dynamical actions. In the Gaia era, actions can be estimated for individual stars in both observations and simulations, making this a natural and unifying diagnostic, assuming the intrinsic errors and selection functions are understood. Our approach is straightforward: stars that participate in the bar are subject to a strongly non-axisymmetric potential and, therefore, do not completely conserve their actions. We use this property to define a star-by-star criterion, formulated as an inequality and evaluated within measurement uncertainties, to identify bar members based on the degree to which their total action fails to be conserved. From tests on simulated galaxies, we find that the bar region is indeed characterised by a lower fraction of stars with conserved actions and that stars on bar orbits are represented by larger percentage changes in their actions. We are able to classify the spatial extent of barred region via the standard parameters of bar length and orientation, while also individually separating bar-located from bar-member stars on bar orbits. As proof of concept, our automated method based on dynamical actions robustly identifies bar parameters that closely match the eye's performance (average bar length variation ~9%) in barred snapshots of the test galaxy.

3I/ATLAS is the third interstellar comet identified as passing through the Solar System. Its high outgassing activity and favourable perihelion passage on October 29, 2025 UT provided an excellent opportunity to investigate the composition of its coma gases through millimeter spectroscopy. We present observations undertaken with the IRAM 30-m telescope on November 1--3, 2025 at an heliocentric distance of 1.36--1.37 au. Lines of HCN, CH$_3$OH, CO, and H$_2$CO are well detected, and $\sim$4$σ$ detections are obtained for CS and CH$_3$CN. The search for H$_2$S was unsuccessful. Abundances of CO, H$_2$CO, CH$_3$OH, and CH$_3$CN relative to HCN are in the upper ranges of values measured in Solar System comets. The sulfur-to-carbon abundance ratio in 3I/ATLAS's coma is at most the minimum value observed in comets. The unusually low expansion velocity of coma gases suggests a near-nucleus gas flow driven by heavy molecules such as CO$_2$, and/or a large fraction of the gaseous production coming from subliming icy grains.

This work presents measurements of the transverse-momentum-dependent observable $v_{0}(p_\mathrm{T})$ as a novel probe of radial expansion dynamics in Pb$-$Pb collisions at $\sqrt{s_\mathrm{NN}} = 5.02$ TeV with the ALICE detector. Results are reported for inclusive charged hadrons, pions, kaons, and protons across centrality intervals, using a pseudorapidity gap to suppress short-range nonflow correlations. At low $p_\mathrm{T}$, a clear mass ordering is observed, consistent with hydrodynamic expectations. For $p_\mathrm{T} > 3$ GeV/$c$, protons exhibit larger $v_{0}(p_\mathrm{T})$ than pions and kaons, in line with quark recombination models. These results demonstrate the sensitivity of $v_{0}(p_\mathrm{T})$ to collective expansion and hadronization dynamics in the quark--gluon plasma.

We revisit Gabow's $O(\sqrt{n} m)$ maximum cardinality matching algorithm (The Weighted Matching Approach to Maximum Cardinality Matching, Fundamenta Informaticae, 2017). It adapts the weighted matching algorithm of Gabow and Tarjan~\cite{GT91} to maximum cardinality matching. Gabow's algorithm works iteratively. In each iteration, it constructs a maximal number of edge-disjoint shortest augmenting paths with respect to the current matching and augments them. It is well-known that $O(\sqrt{n})$ iterations suffice. Each iteration consists of three parts. In the first part, the length of the shortest augmenting path is computed. In the second part, an auxiliary graph $H$ is constructed with the property that shortest augmenting paths in $G$ correspond to augmenting paths in $H$. In the third part, a maximal set of edge-disjoint augmenting paths in $H$ is determined, and the paths are lifted to and augmented to $G$. We give a new algorithm for the first part. Gabow's algorithm for the first part is derived from Edmonds' primal-dual algorithm for weighted matching. We believe that our approach is more direct and will be easier to teach. We have implemented the algorithm; the implementation is available at the companion webpage (https://people.mpi-inf.mpg.de/~mehlhorn/CompanionPageGenMatchingImplementation.html).

In many classification problems, misclassification costs are highly asymmetric, while training labels are often corrupted due to measurement error, annotator variability, or adversarial noise. The Neyman-Pearson multiclass classification (NPMC) framework addresses such asymmetry by controlling class-specific errors, but existing methods assume that training labels are correctly observed. To our knowledge, no existing approach handles NPMC under label noise in the multiclass setting, and the only binary method requires prior knowledge of the noise mechanism. A fundamental difficulty is that, without structural assumptions, noisy-label models are non-identifiable: distinct combinations of class-conditional distributions and noise mechanisms can induce the same observed distribution, preventing recovery of the quantities required for error control. We show that the exponential tilting density ratio model restores identifiability, and leverage this structure to develop an empirical likelihood approach for NPMC with noisy labels. The proposed method jointly estimates clean-label class proportions, posterior probabilities, and the noise mechanism from noisy data, without requiring prior knowledge of the confusion matrix. An expectation-maximization algorithm enables efficient computation. The resulting estimators are root n consistent and asymptotically normal, and the induced classifiers satisfy Neyman-Pearson oracle inequalities in both binary and multiclass settings. Simulation and real-data experiments demonstrate near-oracle performance.

The Large Deviation Principle (LDP) and the Central Limit Theorem (CLT) are central pillars of probability theory. While their formulations are established under the i.i.d. assumption, the probabilistic foundation for power-law distributions has primarily evolved through descriptive models or variational principles, rather than a constructive derivation comparable to the classical binomial process. This paper establishes a constructive probabilistic framework for power-law distributions, proceeding from the nonlinear differential equation $dy/dx = y^q$ without assuming a specific distribution a priori. We build the algebraic and combinatorial foundations, which lead to a generalized binomial distribution based on finite counting. We prove the LDP for this generalized binomial distribution in the regime $0 < q < 1$, demonstrating that the $α$-divergence is identified as the rate function, and clarify the breakdown of this macroscopic scaling for heavier tails ($q > 1$). This result connects our constructive framework to the structures of information geometry. Furthermore, we prove a generalized de Moivre-Laplace theorem, showing that the generalized binomial distribution converges to a heavy-tailed limit distribution (the $q$-Gaussian distribution). We derive that the scaling law follows the order of $n^{q/2}$ as a consequence of the underlying nonlinearity. These analytical results are numerically verified for distinct values of $q \in (0, 2)$. This framework provides a constructive basis that unifies the shift-invariant exponential family and the rescaling-invariant power-law family.

We introduce a new method of expressing a $k$-graph $C^*$-algebra as a Cuntz-Pimsner algebra. Kumjian, Pask, and Sims have done this directly, using a linking algebra approach and a $(k-1)$-graph algebra. This can be iterated downward. Our process, on the other hand, starts at the bottom, with Pimsner's theorem for graph algebras, and iterates upward. We actually work with product systems over $\mathbb N^k$, and the result for $k$-graphs is a special case. Our iteration step involves a ``decategorization'' of a recent theorem showing that the Cuntz-Pimsner construction is functorial at the level of ``enchilada categories''.

This work presents COmPOSER, an open-source, end-to-end framework for RF/mm-wave design automation that translates target specifications into optimized circuits with layouts. It unifies schematic synthesis, layout generation for actives and passives, and placement/routing, incorporating physics-based equations and machine-learning-driven electromagnetic models. Based on post-layout validation on multiple LNAs and PAs operating at up to 60GHz in a commercial 65nm process-kit, COmPOSER meets performance targets, comparable to expert manual designs, while delivering a 100-300x productivity gain. Github repo github[dot]com[slash]UMN-EDA[slash]COmPOSER

The dense Kondo lattice Ce$_5$CoGe$_2$ exhibits superconductivity once the magnetic ordering is suppressed by pressure. Here the ambient pressure magnetic state is investigated via magnetization, heat capacity, powder neutron diffraction, and muon spin relaxation ($μ$SR) measurements. Neutron diffraction results reveal a noncollinear ferromagnetic structure, where the four inequivalent Ce sites exhibit different magnetic moments. Point-charge model calculations of the crystalline-electric field (CEF) ground states corroborate different moments between the sites, and suggest sizeable components of the moments along different directions, consistent with the non-collinear structure. Analysis of the Dzyaloshinskii-Moriya (DM) interaction for the bonds connecting Ce atoms demonstrates that most of these bonds exhibit a nonzero DM vector, suggesting that competition between intersite magnetic exchange interactions, CEF driven single-ion anisotropy, the Kondo effect and the DM interaction may drive the non-collinear ferromagnetism.

We show that any $L^2$-bounded rational function in free semicircular random variables is a bounded operator, which implies the coincidence of the usual spectrum and $L^2$-spectrum for rational functions. Based on this observation, we also compute the spectra of several polynomials in free circular random variables.

We present a study of dark matter and the strong CP problem within a globally consistent framework of Type IIA string theory, compactified on a $T^6/(\mathbb{Z}_2 \times \mathbb{Z}_2)$ orientifold with intersecting D6-branes (Model A), for which we provide a complete moduli stabilization and supersymmetry breaking scenario based on the STU model and the KL mechanism. This setup naturally gives rise to a 3-generation MSSM-like spectrum with $\mathcal{N}=1$ supersymmetry. Phenomenologically, the model predicts a multi-component dark matter scenario comprising both axions and neutralino. We also explore how to embed the four-form flux mechanism into Type IIA $T^6/(\mathbb{Z}_2 \times \mathbb{Z}_2)$ orientifold string theory model to address the strong CP problem. We compute the relic abundance of these candidates and explore their observational signatures. In conclusion, our analysis provides a concrete unified, UV-complete framework that successfully addresses two of the most important problems in particle physics and cosmology.

There is now clear evidence, from a variety of studies, that galactic bars contribute to and/or accelerate processes which quench galaxies. However, bars have a variety of strengths and pattern speeds, and previous work has suggested that slow and strong bars impact their hosts the most. In this paper, we continue to investigate the impact of bar strength and bar speed on host galaxy evolution in a sample of barred galaxies identified via classifications from Galaxy Zoo. We perform a comprehensive assessment of star-formation tracers spanning a variety of timescales, based on spatially resolved spectroscopic information from the Mapping Nearby Galaxies at Apache Point Observatory (MaNGA) survey. Specifically, we examine the radial distributions of EW[Halpha], HdeltaA, Hbeta, and Dn4000; spectral data that trace star-formation on current, intermediate, and much longer timescales. We investigate how these star-formation tracers vary with respect to each other in diagnostic evolutionary planes for eight categories of barred galaxies (combinations of star forming or quenching; strong and weak; fast and slow). We continue to find that slow-strong bars drive the quenching of their hosts the most by triggering active star-formation throughout the barred region; however, we note some additional complexity: we observe that stronger bars boost star-formation at the bar centre while slower bars have increased star-formation along the bar. This work adds to the growing evidence that galactic bars have both global and local impacts on their host galaxies.

In previous work, it was reported that the Galactic black hole candidate MAXI J1810-222 exhibited a notable absorption spectral feature at around 1 keV in low-resolution X-ray spectra of CCD-like detectors. The feature was correlated with the spectral state of the source, being stronger in the soft states, as it occurs in the typical Fe K winds of X-ray binaries (XRBs). However, the results hinted towards rather extreme wind velocities of up to ~0.1 c. We therefore requested and obtained an observation with XMM-Newton to take advantage of the 10-fold higher spectral resolution (R ~200-400) provided by the RGS detector in order to resolve the lines and break the degeneracy between different models and interpretations. We applied state-of-the-art models of plasma in photoionisation equilibrium and multiphase interstellar medium. Further comparisons are performed with a re-analysis of NICER and NuSTAR data. The XMM-Newton/RGS spectrum is consistent with the presence of a mildly relativistic wind, confirming the earlier indications obtained with NICER, but places tighter constraints on the outflow properties, with the lines being intrinsically broad. The data would then favour magnetically driven winds, although thermal effects may still contribute to mass loading. NuSTAR and XMM-Newton (EPIC) show a further hotter component indicating a stratified or multiphase outflow. Fe K spectra taken with calorimetric detectors (e.g., Resolve on XRISM) will enable a high-resolution view of the complex extreme outflow in this source and shed new light on outflow processes in XRBs.

We assess the advantage of combining univariate and multivariate portfolio risk forecasts with the aid of forecast reconciliation techniques. In our analyzes, we assume knowledge of portfolio weights, a standard for portfolio risk management applications. With an extensive simulation experiment, we show that, if the true covariance is known, forecast reconciliation improves over a standard multivariate approach, in particular when the adopted multivariate model is misspecified. However, if noisy proxies are used, correctly specified models and the misspecified ones (for instance, neglecting spillovers) turn out to be, in several cases, indistinguishable, with forecast reconciliation still providing improvements. The noise in the covariance proxy plays a crucial role in determining the improvement of both the forecast reconciliation and the correct model specification. An empirical analysis shows how forecast reconciliation can be adopted with real data to improve traditional GARCH-based portfolio variance forecasts.

It is a well known that, for odd $n$, the number of subsets of $\{1,2,\dots,n\}$ the sum of whose elements is divisible by $n$ equals the number of binary necklaces of length $n$. In this paper generalize this result in two directions. On the one hand, we introduce a parameter $r$ so that requiring the subset sums to be congruent to $r$ modulo $n$ translates into imposing some periodicity conditions on the necklaces. On the other hand, we refine these relations by the size $k$ of the subset, showing that it matches the number of ones in the necklace. We describe the precise conditions on $n$, $k$ and $r$ for which the equalities hold. We also extend some of our formulas to $q$-ary necklaces. The classical results correspond to the case $r=0$. When $r=1$, our identity is related to a conjecture of Baker et al. connecting subsets the sum of whose elements is congruent to $1$ modulo $n$ and unimodal permutations which consist of one cycle. We prove this conjecture using generating functions. Finding bijective proofs of most of our identities remains an open problem.

It has been frequently observed that Neyman orthogonality, the central device underlying double/debiased machine learning (Chernozhukov et al., 2018), and pathwise differentiability, a cornerstone concept from semiparametric theory, often lead to the same debiased estimators in practice. Despite the widespread adoption of both ideas, the precise nature of this equivalence has remained elusive, with the two concepts having been developed in largely separate traditions. In this work, we revisit the semiparametric framework of van der Laan and Robins (2003) and identify an implicit regularity assumption on the relationship between target and nuisance parameters -- a local product structure -- that allows us to establish a formal equivalence between Neyman orthogonality and pathwise differentiability. We also show that the two directions of this equivalence impose fundamentally different structural requirements. Finally, we illustrate the theory through three detailed examples of estimating the average treatment effect and expected density in a nonparametric model, as well as the slope in a partially linear model. This helps clarify the relationship between these two foundational frameworks and provides a useful reference for practitioners working at their intersection.

Simplifying composite open quantum systems through model reduction is central to enable their analytical and numerical understanding. In this work, we introduce a self-consistent approach to eliminate the cavity degrees of freedom of cavity quantum electrodynamics (CQED) devices in the non-adiabatic regime, where the cavity memory time is comparable with the timescales of the atom dynamics. To do so, we consider a CQED system consisting of a two-level atom coupled to a single-mode cavity, both subsystems interacting with the environment through an arbitrary number of ports, within the input-output formalism. A self-consistency equation is derived for the reduced atom dynamics. This allows retrieving an exact expression for the effective Purcell-enhanced emission rate and, under reasonable approximations, a set of self-consistent dynamical equations and input-output relations for the effective two level atom. The resulting reduced model captures non-Markovian features, characterized through an effective Lindblad equation exhibiting two decoherence rates, a positive and a negative one. In the continuous-wave excitation regime, we benchmark our approach by computing effective steady states and output flux expressions beyond the low-power excitation regime, for which a semi-classical treatment is usually applied. We also compute two-time correlations and spectral densities, showing an excellent agreement with full cavity quantum electrodynamics simulations, except in the strong-coupling, high-excitation regime. Our results provide a practical framework for reducing the size of CQED models, which could be generalized to more complex atom and cavity configurations.

Haumea is the third-largest of the five officially recognized dwarf planets and one of the four that reside in the trans-Neptunian region. It is among the most exotic bodies in the Solar System, with an exceptionally rapid rotation, a highly elongated triaxial shape, and a ring that orbits about three times more slowly than Haumea itself. Because of its large heliocentric distance, direct exploration by dedicated space missions is not feasible in the short term, so progress must rely on ground- and near-Earth facilities. Stellar occultations are among the most powerful tools to investigate trans-Neptunian objects. We present new predictions of stellar occultations by Haumea and its ring for stars down to Gaia G = 21, and assess their scientific potential, with special emphasis on the 4 May 2026 event. We computed occultation opportunities for the coming years and evaluated the 4 May 2026 geometry in detail, including Haumea's rotation phase, known 3D shape, pole orientation, and sky-plane motion, to estimate the expected shadow-path width. Because the target star has a very large Gaia RUWE, we also carried out a dedicated reliability analysis, including speckle observations. We identify eleven valuable events through 2030. For 4 May 2026, we derive an expected sky-plane shadow width of $2224 \pm 30$ km, substantially larger than conservative nominal assumptions and therefore highly favorable for observations. Speckle imaging reveals a companion at $\sim 0.12$ arcsec and $Δm \sim 3.1$; this companion is also expected to be occulted and shifts the nominal main-star path prediction on Earth by about 8 mas. These results confirm the strong scientific return expected from coordinated observations of upcoming Haumea occultations, especially the 4 May 2026 event, and provide an updated framework to improve constraints on Haumea's shape, density, ring properties, and environment.

We investigate the link between optical obscuration and X-ray absorption in active galactic nuclei (AGN) by combining X-ray spectroscopy from 4XMM-DR11 with SDSS DR16Q spectroscopy. Bayesian X-ray spectral fits were obtained within the XMM2Athena project, and host-galaxy properties were derived via \textsc{CIGALE} SED fitting. Our final sample comprises 241 X-ray AGN at $z<1.9$. For 172 sources ($\sim70\%$), the optical broad-line (BL) or narrow-line (NL) classification agrees with their X-ray obscuration based on $N_{\rm H}$, but two mismatched populations emerge. Eleven BL AGN show signs of X-ray absorption (BLAbs) and elevated gas-to-dust ratios compared to BL AGN, consistent with dust-free or host-scale absorbers. Conversely, 58 NL AGN appear unobscured in X-rays (NLUnabs) and low gas-to-dust ratios. Nearly half are assigned type~1 properties by SED fitting, suggesting diluted or intrinsically weak broad-line regions, host contamination, or variability. Optical line diagnostics support this picture: NL AGN show higher Balmer decrements than NLUnabs, indicating stronger extinction and different ionization conditions. Host diagnostics further reinforce the contrasts: at $\rm z<0.8$, NLUnabs show star-formation rates and accretion efficiencies that are comparable to BL AGN, whereas NL AGN reside in more quiescent hosts with lower star formation and less efficient black-hole growth. BLAbs match BL AGN in host and accretion properties, with their peculiarity lying in excess X-ray absorption. These findings demonstrate that obscuration arises not only from orientation but also from multi-scale distributions of gas and dust. Identifying such mismatched populations will be crucial for interpreting AGN demographics in ongoing and upcoming surveys such as \emph{Euclid} and VRO/LSST.

Understanding the relative roles of large-scale environment and internal host-galaxy processes in shaping AGN activity is essential for constraining models of black-hole growth and galaxy evolution. We investigate how the environment of X-ray selected active galactic nuclei (AGN) relates to black-hole growth and accretion properties, and whether these introduce an environmental dependence beyond that expected from the host galaxy itself. Combining the XXL and Stripe 82X surveys, we construct samples of 427 broad-line AGN at $0.5<z<1.2$ and more than $20,000$ galaxies, with host-galaxy properties derived consistently using the same spectral energy distribution fitting methodology. Dark matter halo (DMH) masses are inferred from AGN--galaxy cross-correlation functions, while a multivariate nearest-neighbour matching algorithm is used to isolate trends with black-hole mass ($M_{\mathrm{BH}}$), Eddington ratio ($λ_{\mathrm{Edd}}$), and X-ray luminosity ($L_{\mathrm{X}}$) under controlled host-galaxy conditions. Within the uncertainties of the present dataset, X-ray AGN typically reside in halos of $\log(M_{\mathrm{DMH}}/h^{-1}M_\odot)\simeq13$, with no significant variation as a function of $M_{\mathrm{BH}}$, $λ_{\mathrm{Edd}}$, or $L_{\mathrm{X}}$. These results suggest that neither long-term black-hole growth nor short-term accretion variability is strongly linked to large-scale environment, and instead support a scenario in which AGN properties are regulated primarily by internal host-galaxy processes, while large-scale structure sets the broader boundary conditions for gas supply and duty cycle.

In the most general formulation of gravity, the metric and connection are independent degrees of freedom, and the connection may include torsion and non-metricity (or distortion, collectively) degrees of freedom, resulting in a huge number of possible dynamical fields. However, the most fields are either non-dynamical or extremely heavy and the general relativity is recovered at low energy. We find a unique naturally light vector- or scalar-like distortion field, which can be dynamical and have phenomenological implications. In particular, a light scalar particle that mixes with the Higgs boson naturally appears.

The diversity of pulsar light-curves and radio polarisation properties originates in the structure of the magnetic field close to the stellar surface. For millisecond pulsars, this complexity is particularly puzzling. Fortunately, some means exist to uncover the magnetic field topology which indeed impacts the emission within the magnetosphere but also on the surface through its hot spot thermal radiation. We aim at deducing a plausible magnetic field geometry for the millisecond pulsar J0437$-$4715 by using combined information from the soft X-ray hot spot geometry deduced from NICER observations by pulse profile modelling and from radio and $γ$-ray pulse profile fitting. We also check the consistency between the geometry obtained and the radio polarisation data. Our $γ$-ray light-curve shapes rely on the striped wind model, whereas the radio polarisation fits rely on the rotating vector model. The magnetosphere structure is obtained from dipolar force-free magnetosphere simulations. We demonstrate that a slightly off-centred dipole augmented by a small scale dipole located on one polar cap explains simultaneously the shape of the hot spot and the radio and $γ$-ray data with a magnetic obliquity of $α\approx (42\pm5) \degr$ and a line-of-sight inclination angle of $ζ\approx (136 \pm5) \degr$. Our simple dipole model reproduces all the radio and $γ$-ray characteristics of PSR~J0437$-$4715, including its radio polarisation data. It shows that the radio emission could be produced in regions where the magnetic field is mainly of dipolar nature.

Transit timing variations (TTVs) provide a powerful means to detect and characterise additional bodies in known planetary systems, even when they do not transit their host stars. We investigate the dynamical architecture of the HD 332231 system by analysing the TTVs of its close-in gas giant, HD 332231 b. Our goal is to assess whether the observed deviations from a linear ephemeris can be explained by the presence of an additional planetary companion. We refine the transit ephemeris of HD 332231 b using high-precision TESS photometry and complementary ground-based observations. We extract individual transit mid-times, construct an O-C diagram for transit timing data, and model the observed TTV signal through an extensive suite of N-body integrations covering a broad range of possible companion masses and orbital configurations. We detect a coherent TTV pattern with a period of approximately 6.7 years and an amplitude of about 45 minutes. Although numerous orbital configurations reproduce the observed TTVs, the combination of current radial velocity and photometric constraints yields a modest improvement in likelihood for solutions with an external planet on an orbit longer than 60 days, likely near a high-order mean-motion resonance and with moderate to high eccentricity. Our results suggest that HD~332231 b is part of a dynamically interacting multi-planet system. Continued transit monitoring and radial velocity follow-up will be essential to confirm the perturber's nature and refine the system's dynamical architecture.

We investigate the origin of the observed X-ray weakness in high z LRDs and other JWST-selected broad line AGN by comparing their X-ray and optical properties with those of a diverse sample of low z AGN, including super-Eddington accreting massive black holes (SEAMBHs), NLS1s, and type I AGN from large surveys. We examine the relations between X-ray luminosity, broad Hα line luminosity, Eddington ratio, bolometric luminosity and X-ray-to-bolometric luminosity correction, and explore whether high z sources may represent analogues of local highly accreting systems. While a few LRDs and JWST-selected AGN are consistent with the SEAMBHs population in the $L_x/L_{Hα}$ versus $λ_{Edd}$ plane, most lie below it, suggesting either more extreme accretion conditions, suppressed coronal emission or heavy obscuration. We identify an anti-correlation between $L_x/L_{Hα}$ and $λ_{Edd}$ in the low z, high accreting subsample, consistent with theoretical expectations of slim-disc accretion. We further show that, for SEAMBHs, $Hα$-based bolometric luminosities underestimate SED-based values even after dust correction. We find that SEAMBHs, LRDs, and JWST-selected AGN occupy a similar high-$κ_{bol,x}$ regime, indicating that the relative deficit of X-ray emission compared to the bolometric output could potentially support the view that soft X-ray spectra arising from relatively cold coronae is a common feature of highly accreting systems across cosmic time. Our results are consistent with the idea that the observed X-ray weakness of LRDs and JWST-selected AGN may be linked to the physics of highly accreting SMBHs. Moreover, observational limitations at high z, including instrumental sensitivity and the steep X-ray spectra expected for highly accreting systems, likely further suppress the detected X-ray signal.