We present a joint cosmological analysis combining data from the Planck satellite, the Atacama Cosmology Telescope, and the South Pole Telescope. We construct a unified likelihood that reproduces the measured temperature and polarisation power spectra by jointly modelling the cosmic microwave background (CMB) signal, Galactic and extragalactic foregrounds, and instrumental systematics across all datasets. We reduce reliance by combining datasets and improve the robustness of parameter estimation by marginalising over the choice of foreground templates. Within this joint analysis, $Λ$CDM parameters exhibit remarkable stability with respect to variations in foreground modelling. Parameters for cosmological extensions are more sensitive to these assumptions, with uncertainties increasing by up to 35% in the neutrino sector after marginalising over foreground models. In contrast, the determination of foreground parameters depends more strongly on the assumptions made about the underlying foreground models. Overall, this work demonstrates the feasibility and reliability of a fully joint analysis of current CMB experiments and emphasizes the importance of consistent and accurate foreground modelling for the scientific goals of next-generation, high-sensitivity CMB surveys.

We examine the bulk reconstruction in the AdS/CFT correspondence. We demonstrate that the subregion duality fails to hold, highlighting discrepancies between operators in causal wedge reconstruction and those in global reconstruction at the leading order in the large $N$ limit. We argue the invalidity of the entanglement wedge reconstruction based on the holographic quantum error correction code, attributing it to non-perturbative finite $N$ effects or quantum gravity effects due to the trans-Planckian modes near the horizon. Nevertheless, we propose the subregion complementarity, illustrating that different CFT operators can describe a bulk subregion. While we expect that this complementarity is valid outside the horizon in general eternal black holes, it is inapplicable for single-sided black holes where a semi-classical description at the stretched horizon is absent.

In this work we provide a massless perturbative framework for the two dimensional non-linear sigma model (NLSM), that allows the computation of the perturbative series attached to the operator condensates in the operator product expansion (OPE). It is based on a limit of the quartic linear sigma model (LSM) and is manifestly $O(N)$ symmetric. We show, at next-to-leading order in the $1/N$ expansion, how this framework reproduces the perturbative contribution to the two-point function, as well as its first exponentially small correction due to the condensate of the Lagrangian operator, in full agreement with the exact non-perturbative large $N$ solution. We also show that, in the full LSM, the physics at the natural UV cutoff indeed decouples from the NLSM in the IR, in the weak-coupling limit. In particular, we show that the perturbative framework for the LSM at the cutoff scale is connected to the one in the NLSM. The structure of power divergences in the LSM regularization also reveals that the first renormalon on the positive Borel axis of the NLSM perturbative self-energy is an UV renormalon, which cancels against the ambiguity in the condensate.

The outer Galaxy presents an optimal setting for investigating molecular clouds and star formation in environments with low metallicity. A total of 72 Galactic edge clouds were surveyed using the CO\,(2--1) line with the IRAM\,30\,m telescope, leading to the identification of 112 CO clumps within molecular clouds with linear resolutions of 0.5--0.9\,pc. Parameters such as size, mass, surface density, and velocity dispersion of these CO clumps, derived from CO\,(2--1) observations, exhibit ranges of 0.6--3.4\,pc, 34--8250\,M$_\odot$, 12--1025\,M$_{\odot}$\,pc$^{-2}$, and 0.3--1.7\,km\,s$^{-1}$, respectively. Over the Galactocentric distance range of 14--23\,kpc, no systematic variations are found in these parameters. The velocity dispersion-size relationship of the Galactic edge clumps is modeled as $σ_{\rm v}$\,=\,0.69($\pm$0.03)$R_{\rm eff}^{0.36(\pm0.10)}$, indicating that turbulence is present within the Galactic edge clumps, akin to observations in the inner Galactic disk clouds. Furthermore, the luminous mass-size relation of the Galactic edge clumps is described by $M_{\rm lum}$\,=\,196($\pm$17)$R_{\rm eff}^{\,2.18\,(\pm0.26)}$, suggesting the average column density remains almost constant for clouds of different sizes. The virial parameters range from 0.6 to 15.3, with a median value of 2.8\,$\pm$\,0.6, suggesting that most clumps are gravitationally unbound. Furthermore, the virial parameters of our Galactic edge clumps show a decreasing trend with increasing Galactocentric distances, described by an exponential relation $α_{\rm vir}$\,=\,33.0($\pm$\,10.4)\,e$^{-R_{\rm g}/6.7(\pm0.9)}$, consistent with previous results.

Enriched categories are categories whose sets of morphisms are enriched with extra structure. Such categories play a prominent role in the study of higher categories, homotopy theory, and the semantics of programming languages. In this paper, we study univalent enriched categories. We prove that all essentially surjective and fully faithful functors between univalent enriched categories are equivalences, and we show that every enriched category admits a Rezk completion. Finally, we use the Rezk completion for enriched categories to construct univalent enriched Kleisli categories.

Here we present models of hot neutron star (NS) atmospheres consisting of thermonuclear ashes of various chemical compositions. These models are essential for studying thermonuclear flashes in X-ray bursting NSs in which nuclear-burning ashes are transported to the stellar surface. We consider four different mixtures, each dominated by helium, chromium, iron, or nickel. In addition to the opacity sources previously used in NS atmosphere modeling, we include photoionization from excited ionic states as well as approximately 5000 spectral lines. We also develop a method that enables the simultaneous treatment of Compton scattering and a large number of spectral lines. A key feature of the modeled NS atmospheres is the presence of a layer in the transition region between the optically thin and optically thick parts of the atmosphere where the radiation-pressure force increases significantly. This enhanced force sets an upper limit on the maximum attainable bolometric flux for a given surface gravity and chemical composition. The emergent spectra from the computed atmospheres display pronounced absorption edges, whose energies are determined by the dominant chemical species. We fit the model spectra using a diluted blackbody modified by a single absorption edge, and we investigate how the fit parameters depend on both the relative bolometric flux and the chemical composition of the atmosphere. Finally, we discuss constraints on these models imposed by the properties of X-ray bursts that exhibit absorption edges in their spectra, as observed in the systems HETE~J1900.1$-$2455 and GRS~1747$-$312.

We present a parametric component separation forecast for the QUIJOTE-MFI2 instrument (10-20 GHz), assessing its impact on constraining polarised synchrotron emission at $1^\circ$ FWHM and $N_{\rm side}=64$. Using simulated sky maps based on power-law and curved synchrotron spectra, we show that adding QUIJOTE-MFI2 to existing WMAP+$Planck$+MFI data yields statistically unbiased parameter estimates with substantial uncertainty reductions: improvement factors reach $\sim$10 for the synchrotron spectral index ($β_s$), $\sim$5 for the curvature parameter ($C_s$), and $\sim$43 for polarisation amplitudes in bright regions. Deep QUIJOTE cosmological fields enable $β_s$ constraints even in intrinsically low SNR regions where WMAP+$Planck$ alone remain prior-dominated. Current combined sensitivities are insufficient to detect a synchrotron curvature of $C_s=-0.052$ on a pixel-by-pixel basis, but a $2σ$ detection is achievable for $|C_s|\gtrsim 0.14$ in the brightest regions of the Galactic plane. In those deep cosmological fields, combining QUIJOTE-MFI2 with WMAP and $Planck$ reduces the median synchrotron residual at 100 GHz by a factor of 6, to 0.033 $μ$K$_{\rm CMB}$. These results demonstrate that QUIJOTE-MFI2 will provide critical low-frequency information for modelling Galactic synchrotron emission, offering valuable complementary constraints for future CMB surveys such as LiteBIRD and the Simons Observatory.

We analyze historic S&P500 multi-day returns: from daily returns to those accumulated over up to ten days. Despite symmetry breaking between gains and losses in the distribution of returns, resulting in its positive mean and negative skew, realized variance (volatility squared) exhibits remarkably good linear dependence on the number of days of accumulation. Mean of the distribution also shows near perfect linear dependence as well. We analyze this phenomenon both analytically and numerically using a modified Jones-Faddy skew t-distribution.

Energetic particles are ubiquitous in space and astrophysical plasmas, and interplanetary shocks are widely regarded as one of the main particle accelerators in the heliosphere. Indeed, in-situ measurements typically show that energetic particle fluxes peak at the shock, indicating a local acceleration process. Furthermore, the time profile of energetic particle fluxes is highly influenced by particle transport properties upstream and downstream of the shock. By advancing previous numerical test-particle models that simulate the transport of monoenergetic particles around an infinite planar shock, in this work we add the acceleration of such particles via energy gains at each shock crossing, in a first-order Fermi-type mechanism. Moreover, the acceleration of a 70 keV particle population, namely the seed population, is reproduced by integrating a Langevin-type equation upstream and downstream of an infinite planar shock. Particles can diffuse in the simulation box via random "kicks", which belong either to a Gaussian distribution (normal diffusion) or to a Levy distribution (superdiffusion). We perform several simulations by varying the parameters of the model. The particle energy spectra in both diffusive and superdiffusive simulations are in remarkable agreement with the theoretical predictions.The output energetic particle densities have been compared with those observed by the ACE spacecraft during an interplanetary shock crossing on December 14, 2006. We show not only that particle fluxes in different energy bins reproduce very well the observed ones upstream and downstream when superdiffusion is at work, but also that anomalous, superdiffusive transport speeds up the acceleration process and leads to values of particle energies consistent with observations.

Pyrochlore magnets of the form $R_2B_2$O$_7$, in which rare-earth ions on the $R$-site form a three-dimensional network of corner-sharing tetrahedra, provide a canonical setting for geometrical frustration. Ho-based pyrochlores host a dipolar spin-ice ground state, characterized by Ising moments constrained by the ice rules and elementary excitations analogous to magnetic monopoles. Here we examine how controlled chemical disorder influences this state by introducing site mixing on the non-magnetic $B$-site in two compounds. Ho$_2$GaSbO$_7$ contains only Ga$^{3+}$/Sb$^{5+}$ charge disorder, whereas Ho$_2$ScSbO$_7$ exhibits both charge and substantial size disorder arising from the large ionic-radius mismatch between Sc$^{3+}$ and Sb$^{5+}$. Although both materials retain the pyrochlore structure, neutron scattering measurements reveal a reduced correlation length for the $R/B$-site cation ordering and enhanced local structural distortions in Ho$_2$ScSbO$_7$. Despite these structural differences, bulk thermodynamic measurements and magnetic diffuse scattering demonstrate that both systems exhibit the defining signatures of a dipolar spin-ice state. Low-energy inelastic neutron spectroscopy further uncovers broad magnetic excitations that develop within the dipolar spin-ice regime, a feature absent in pristine Ho pyrochlores and indicative of disorder-induced splitting of the non-Kramers ground-state doublet. Together, these results show that controlled disorder generates tunable transverse-field-driven quantum fluctuations in Ho-based pyrochlores, although the dipolar spin-ice state is remarkably robust to this disorder.

We propose a quantum geometric map for the magnetononlinear Hall effect (MNHE), the planar Hall effect (PHE), and the ordinary Hall effect (OHE). These magnetotransport phenomena originate from the bilinear charge current of Bloch electrons in electromagnetic fields, incorporating both spin Zeeman coupling and orbital minimal coupling to the applied magnetic field. Benchmarked against Onsager reciprocity, we demonstrate that the spin- and orbital-induced MNHEs are governed by the time-reversal-even Zeeman quantum metric dipole and conventional quantum metric quadrupole, respectively; the spin- and orbital-induced PHEs are dominated by the time-reversal-odd Zeeman Berry curvature dipole and conventional Berry curvature quadrupole, respectively. We further show that the OHE contains an interband contribution that is related to the quantum metric quadrupole, contrary to conventional wisdom. Navigated by this map, we study the previously unexplored spin-induced PHE in the surface Dirac cone of topological insulators, where we uncover a step-like PHE. Our work offers a unified quantum geometric framework for understanding magnetotransport experiments.

The theory of quantum thermodynamics investigates how the concepts of heat, work, and temperature can be carried over to the quantum realm, where fluctuations and randomness are fundamentally unavoidable. These lecture notes provide an introduction to the thermodynamics of small quantum systems. It is illustrated how the laws of thermodynamics emerge from quantum theory and how open quantum systems can be modeled by Markovian master equations. Quantum systems that are designed to perform a certain task, such as cooling or generating entanglement are considered. Finally, the effect of fluctuations on the thermodynamic description is discussed.

The identification of high-redshift quasars ($z > 4.5$) is critical for studying the early Universe, supermassive black hole growth, and cosmic reionization. Most known high-redshift quasars are located in the northern hemisphere, leaving the southern sky largely unexplored. As part of the 4-meter Multi-Object Spectroscopic Telescope (4MOST) and Chilean AGN/Galaxy Extragalactic Survey (ChANGES) S1604 survey, we aim to create a large catalog of high-redshift quasar candidates in the southern hemisphere using multiwavelength photometry and Spectral Energy Distribution (SED) fitting, with the goal of spectroscopic follow-up with 4MOST. We construct a multi-band photometric catalog by combining optical data from DELVE DR2 and DECaLS DR10, near-infrared data from VHS DR5 with an additional field of VIKING, mid-infrared data from AllWISE, and optical astrometry from Gaia DR3. After applying morphological and color-based cuts, we perform SED fitting using quasar and brown dwarf templates. Statistical outputs, including $χ^2$, BIC, and F-test are used to rank and select candidates. Our final catalog contains 6104 high-redshift quasar candidates within $4.5 < z < 7$, with detections in 7 or more photometric bands satisfying our SED-based selection criteria (BIC > 0 and F-test > 10). Spectroscopic validation using NTT/EFOSC2 and Palomar/NGPS confirmed 3 high-redshift quasars at $z > 5$ out of 6 observed candidates.

The formation and evolution of galaxies is regulated by the exchange of gas with the surrounding large-scale structures on circum- and intergalactic scales. Yet, little is known about the complex processes shaping the cycle of baryons in and out of galaxies. In this work, we present a multiline study of the gas surrounding a $z\approx3.66$ quasar known to host one of the brightest Ly$α$ nebulae at high redshift, MUSE Quasar Nebula 04 (MQN04). By combining a high-resolution MUSE detection of non-resonant HeII emission with a precise measurement of the redshift of the quasar host via the ALMA CO(4-3) line, we study the kinematics of the cool ionized gas down to $\approx1\rm\,kpc$ from the quasar. The MUSE observations reveal complex clumpy structures as well as diffuse emission extended over $\approx100\,{\rm kpc}$ and blueshifted by $\approx 0-800\,{\rm km\,s^{-1}}$ relative to the quasar systemic redshift, suggesting that the circumgalactic medium is highly asymmetric. The analysis of the HeII/Ly$α$ line ratio, and the presence of a low-column density ($\approx10^{14.6}~\rm cm^{-2}$) HI absorber along the quasar sightline suggests that MQN04 resides in a highly ionized medium. This is also supported by the gas kinematics, which, except in the most central region, shows consistent velocity shifts across the different tracers, indicative of relatively weak radiative transfer effects. Based on its morphology and kinematics, we conclude that the extended HeII emission may arise from merger-driven tidal stripping or inflows of gas illuminated by the quasar radiation. On comoving megaparsec scales, we discover a large concentration ($δ\approx41$) of star-forming galaxies lying within $|Δv_{\rm QSO}| \leq1000\rm\,km\,s^{-1}$ from the quasar. MQN04 is therefore one of the most overdense environments discovered at this epoch.

Context. Studying the kinematic and dynamic evolution of fast eruptive events from the middle to high solar corona is a primary objective of the Metis coronagraph on Solar Orbiter. During perihelion, Metis acquires visible light images at a 20s cadence, reaching a spatial resolution of around 2000 km at 0.28 au. This enables capturing coronal mass ejections (CMEs) and transient structures with unprecedented spatial and temporal resolution. Aims. On October 8-9, 2022, an extensive CME was observed by Metis at 0.3 au (resolution: 4.4 $10^{3}$ km/pixel). We aim to exploit this high resolution to resolve multiple substructures within the CME front, revealing plasma elements with distinct trajectories and speeds to provide a detailed kinematic characterization of the eruption. Methods. A normalization-based running difference algorithm was applied to enhance the complex morphology. Height-time diagrams were used to estimate propagation speeds and frequency variations. A 3D flux rope reconstruction, combined with multi-spacecraft coronagraphs and disk imagers, enabled tracking the CME from its initiation in the lower corona to approximately 5 solar radii. Joint observations with Solar Orbiter EUI-FSI provided insights into the eruption's onset, while Metis captured its development into the middle corona. Results. Metis observations resolve the CME's fine structure and internal plasma motions. The detection of circular, fast-propagating wavefronts (500 km/s, 3 minute period) at the western flank suggests wave excitation and magnetic reconfiguration processes. Multiple interpretations are proposed for these coronal wave trains, including quasi periodic propagating fast modes, offering new insights into wave generation and energy transport in the solar corona.

Changing-Look AGN (CL-AGN) are AGN which transition between Seyfert types, challenging AGN unification models. Most CL-AGN have been identified via repeat spectroscopy, making it difficult to determine the duration and magnitude of the CL-AGN transition. As such, the physical mechanisms behind this transition are still unknown. We use synthetic photometry in combination with ZTF light curve data to develop a new criterion to identify photometric CL-AGN transitions based on changes in g-band magnitude and g-r color. We find that a CL-AGN criterion of $| Δg| > 0.4$ mag and $| Δ(g-r)| > 0.2$ mag recovers a photometric transition in $9.6^{+4.9}_{-3.4}\%$ of CL-AGN hosts over the six-year ZTF survey, including a candidate repeating changing-look event in SDSS J084957.78+274728.9. Using simulated AGN light curves, we estimate the false positive rate among the simulated Seyferts to be $1.6^{+0.19}_{-0.17}\%$. We find that the rate of similar flares among Type 1 Seyferts is $1.2^{+0.87}_{-0.50}\%$ , and among Type 2 Seyferts is $\leq 0.39\%$ over six years. Photometric CL-AGN transitions last between 21 and 560 days, with a median duration of 360 days, consistent with the thermal or orbital timescales for AGN disks. We do not detect a correlation between black hole mass and transition duration, likely due to the small sample of detected photometric transitions. This method can be applied to the upcoming Legacy Survey of Space and Time to identify CL-AGN candidates and test theories of their origins

In this work we present the results of our analysis of medium-resolution LAMOST spectra of candidate members of the cluster NGC 1647 with the aim of determining the stellar parameters, activity level, lithium abundance, and to study the cluster properties. We used the code ROTFIT to determine the atmospheric parameters (Teff, logg, and [Fe/H]), radial velocity (Vr), and projected rotation velocity (vsini) for 158 cluster members. Moreover, for solar-type and cooler stars (Teff< 6500 K), we calculated the H-alpha and LiI-6708 net equivalent width by means of the subtraction of inactive photospheric templates. We determined the rotation periods for 160 stars by analyzing the available TESS photometry. We found four double-lined spectroscopic systems for which we provide the radial velocities of the two components. The Vr distribution of the cluster members peaks at -5.3 km/s with a dispersion of 1.6 km/s, while the average metallicity is [Fe/H]=-0.08$\pm$0.08 dex, in line with previous determinations. From the fitting of the spectral energy distribution of 160 likely members we infer the existence of a differential reddening across the cluster field with an average value of $A_V$=1.1 mag. The $A_V$ values show a distinct correlation with the color offset from the lower boundary of the main sequence; conversely, this offset appears to be uncorrelated with vsini. These two findings confirm that differential reddening is the primary driver behind the observed extended Main-Sequence Turn-Off (eMSTO) in this cluster. The age of NGC 1647, obtained from the lithium abundance, is 203$\pm$27 Myr, which is compatible with the values inferred from a gyrochronological approach and the isochrone fitting.

We present 43\,GHz VLBI observations of the radio galaxy 3C~120 during its brightest $γ$-ray outburst (March 2018), recently associated with the IceCube neutrino alert IC-180213A. Despite reaching $L_γ= 3.7 \times 10^{44}$\,erg\,s$^{-1}$, contemporaneous X-ray monitoring from INTEGRAL/ISGRI, MAXI/GSC, and \textit{Swift}/XRT revealed no variability across 0.3-200\,keV, nor in B, V, R, and I band optical observations or 37 \& 235\,GHz observations, establishing an orphan flare. High-cadence VLBI imaging identified a new jet disturbance (N) propagating at $β_{\rm app} = (2.8 \pm 1.3)$ through quasi-stationary features C1-C3. The $γ$-ray peak coincided spatially and temporally with N crossing C3 ($r \sim 0.38$\,mas), where we measured a factor-of-5 increase in fractional polarization ($m = 16\%$) and $Δχ\sim 24^\circ$ EVPA rotation, indicating localized magnetic field compression. The extreme Compton dominance ($L_γ/ L_{\rm syn,blob} \approx 160$) is naturally explained by the Ring of Fire scenario, in which N ($Γ_{\rm blob} = 6$, $B_{\rm blob} = 0.023$\,G) inverse-Compton scatters synchrotron photons from C3, reproducing the observed $γ$-ray luminosity for physically reasonable parameters. Unlike the 2014-2015 orphan flares attributed to rapid spine reorientation near the BLR, the 2018 event represents a distinct physical mechanism, a propagating disturbance interacting with stationary jet structure at $\sim10\times$ the BLR radius.This work provides the first direct observational link between VLBI-resolved jet dynamics and orphan $γ$-ray emission in a radio galaxy.

A large fraction of planet-forming disks observed with ALMA show faint CO emission, often interpreted as strong CO depletion. However, faint emission may also arise from spatially unresolved disks, whose sizes are overestimated, making them appear intrinsically faint. The limited sensitivity of previous observations has prevented testing this scenario, hindering our understanding of disk evolution and planet formation. We present new ALMA Band 7 observations of 12CO (J=3-2) and 13CO (J=3-2) in 17 of the faintest disks in Lupus, aiming to assess whether compact disk structure can explain their weak CO emission. The data reach an angular resolution of 0.25arcsec (about 20 au at 160 pc) and are an order of magnitude deeper than archival observations. We apply line stacking to enhance sensitivity and compare the derived CO luminosities with physical-chemical models of compact and extended disks, also estimating gas and dust sizes. We detect both isotopologues in 10 disks, only 12CO in 4, and neither in 3. Several disks are consistent with being intrinsically compact and optically thick in both lines, providing an alternative to the CO depletion scenario. The inferred gas radii (Rco less than 40 au) support this interpretation and suggest that a significant fraction of disks may be born compact, in line with recent Class 0/I results. Gas-to-dust size ratios show no clear evidence for dust evolution, indicating these disks are not drift-dominated.

[Abridged] We aim to study the radial and vertical extents of 12CO gas, millimeter dust thermal emission and optical/NIR scattered light by dust in disks. We analyze a sample of 14 highly inclined protoplanetary disks. We present ALMA high angular resolution band 7 (0.9 mm) continuum images and 12CO (3-2) gas moment maps as well as HST and VLT/SPHERE scattered light images. The majority of disks in our sample (11 out of 14) follow Rgas > Rdust,micron > Rdust,mm. The other 3 disks appear more extended in millimeter continuum than in scattered light. Highly inclined disks tend to appear less radially extended in CO gas line emission than in millimeter dust continuum compared to less inclined disks. This results from optical depth effects and/or radial drift. The known correlation between disk size and millimeter continuum and line fluxes are confirmed in our sample with highly inclined disks significantly fainter than disks seen at lower inclination for a given disk radius. We found that this correlation is significantly tightened once fluxes are corrected for the disk inclination, consistent with the disks being optically thick at millimeter wavelengths. Regarding the vertical extent defined as the apparent emitting height, most disks in our sample follow Hgas > Hdust, mm. This strengthens our previous findings that the millimeter dust is highly decoupled from the gas and forms a layer in the disk midplane due to vertical settling. Most disks appear more vertically extended in gas than in scattered light, suggesting that the micron-sized dust is not fully coupled to the gas. We also estimated dynamical masses using PV diagrams for the first time for most of the objects in our sample. We found an anti-correlation between the dynamical mass and the aspect ratio, emphasizing the dominant role of gravity in setting the disk vertical extent, but no correlation with the disk radius.

Spin-orbit Mott insulators with the $t_{2g}^5$ electron configuration are promising platforms for the Kitaev spin liquid, yet fine-tuning of their crystal structures is essential to suppress non-Kitaev interactions. Here, we investigate the local electronic structures of the ilmenite iridates $A\mathrm{IrO}_3$ ($A = \mathrm{Mg}, \mathrm{Zn}, \mathrm{Cd}$) and the hyperhoneycomb $β\text{-}\mathrm{ZnIrO}_3$ using Ir $L_3$-edge resonant inelastic x-ray scattering (RIXS). Multiplet analysis of the RIXS spectra reveals a systematic evolution of the crystal field and intraionic interaction parameters upon chemical substitution at the $A$-site. We observe an enhancement of the trigonal distortion with increasing $A$-site ionic radius. This provides a microscopic explanation for the deviation from the ideal $J=1/2$ state and the antiferromagnetic interactions identified in $\mathrm{CdIrO}_3$. Furthermore, the local multiplet parameters of ilmenite $\mathrm{ZnIrO}_3$ and hyperhoneycomb $β\text{-}\mathrm{ZnIrO}_3$ are found to be nearly identical, demonstrating that their different magnetic ground states are primarily governed by their distinct lattice structures rather than the single-ion properties. These findings establish a solid foundation for understanding how local crystal-field distortions control the magnetic Hamiltonian in Kitaev candidate materials.

Density functional theory augmented with a Hubbard correction (DFT+U) is widely used to treat localized electronic states, but its predictions are often sensitive to the choice of the local projection space defining the correlated subspace. This sensitivity poses a practical challenge for computational reproducibility, particularly when projection parameters vary across codes, basis sets, or materials. In this work, we systematically investigate how the effective on-site Coulomb interaction $U_{\mathrm{eff}}$, determined \textit{ab initio} using constrained density functional theory, depends on the size of the local projection space in all-electron APW+lo calculations. Using rutile and anatase TiO$_2$ and $β$-MnO$_2$ as representative test cases, we show that applying a single fixed $U_{\mathrm{eff}}$ across different projection choices introduces artificial projection-driven errors in total energies, including spurious magnetic ordering transitions and unphysical sensitivity of phase stability. These artifacts are eliminated when $U_{\mathrm{eff}}$ is determined in an internally consistent manner for each projection space, yielding projection-consistent DFT+U predictions for lattice parameters, phase energetics, and magnetic ground states. By analyzing total-energy trends alongside the spatial characteristics of the localized $d$ orbitals, we demonstrate that the systematic reduction of $U_{\mathrm{eff}}$ with increasing projection size originates from orbital relaxation and enhanced electronic screening associated with orbital spatial extension. These results provide a physically motivated framework for controlling projection-space artifacts in DFT+U calculations and for obtaining energetically robust predictions across diverse correlated materials and computational setups.

This paper develops a mathematical framework for interpreting observations of solar inertial waves in an idealized setting. Under the assumption of purely toroidal linear waves on the sphere, the stream function of the flow satisfies a fourth-order scalar equation. We prove well-posedness of wave solutions under explicit conditions on differential rotation. Moreover, we study the inverse problem of simultaneously reconstructing viscosity and differential rotation parameters from either complete or partial surface data. We establish convergence guarantee of iterative regularization methods by verifying the tangential cone condition, and prove local unique identifiability of the unknown parameters. Numerical experiments with Nesterov-Landweber iteration confirm reconstruction robustness across different observation strategies and noise levels.

Inferring the star formation rates (SFR) in high redshift galaxies remains challenging, owing to observational limitations or uncertainties in calibration methods that link luminosities to SFRs. We utilize two state-of-the-art hydrodynamical simulations NewHorizon and NewCluster, post-processed with the radiative transfer code Skirt, to investigate the systematic uncertainties and biases in the inferred SFRs for z=5 galaxies; an epoch where galaxies build-up their stellar mass. We create synthetic observables for widely-used tracers: Halpha nebular line, [CII] 158 micron fine-structure line, total infrared (IR) continuum luminosity, and hybrid (IR + UV). We find that Halpha-inferred SFRs, time-averaged over 10 Myr, are sensitive to the choice of calibration and exhibit substantial scatter driven by dust attenuation, viewing angle, and dust-to-metal ratio. Adopting a steeper attenuation curve reduces this scatter significantly but does not fully eliminate systematic uncertainties. IR continuum-based SFRs trace intrinsic SFRs time-averaged over 100 Myr timescales when a well-sampled continuum emission between restframe 8 and 1000 micron is available and underestimate them with typical approaches when IR data are limited. Nevertheless, IR SFRs display a considerable scatter, largely due to UV photon leakage and strong variations in the star formation history. When UV data are available, hybrid (IR + UV) SFRs provide a more robust estimate, reducing scatter compared to IR-based SFRs while avoiding explicit attenuation corrections. Finally, we derive a [CII]-SFR relation finding a steeper relation than previous studies, however with significant scatter linked to gas density and metallicity. Overall, IR-, hybrid-, and [CII]-based tracers remain more robust than Halpha against variations in optical depth.

We characterize virtual double categories of enriched categories, functors, and profunctors by introducing a new notion of double-categorical colimits. Our characterization is strict in the sense that it is up to equivalence between virtual double categories and, at the level of objects, up to isomorphism of enriched categories. Throughout the paper, we treat enrichment in a unital virtual double category rather than in a bicategory or a monoidal category, and, for consistency and better visualization of pasting diagrams, we adopt augmented virtual double categories as a fundamental language for double-categorical concepts.

We investigate how isochrones computed with different input physics and initial conditions affect the age dating of the open cluster NGC 6866, and compare the results with asteroseismic ages derived from Kepler photometry. Using Gaia DR3 data, we identified 180 cluster members with a clustering algorithm. We then developed an isochrone-cloud fitting method that accounts for a range of free parameters in the input physics. Variable stars were subsequently identified among the cluster members. For 19 g-mode pulsators, we carried out modelling with a dedicated grid of rotating stellar models, constrained by spectroscopic and photometric parameters, the asymptotic gravity-mode period spacing, and the near-core rotation rate. We considered two cases: modelling each pulsator individually and modelling them under the assumption of a common cluster age. PARSEC and MIST isochrones yield discrepant ages of 690 and 467 Myr, respectively. The isochrone-cloud fit indicates an initial critical rotation distribution peaking at 0.6, about a factor of two higher than inferred from asteroseismology. The seismic modelling shows agreement between seismic and isochronal masses, but substantial differences in the derived ages due to differences in internal mixing. When the g-mode pulsators are modelled with a shared cluster age, we obtain 759 Myr, consistent with the PARSEC isochronal age. We conclude that age dating of open clusters is sensitive to the adopted input physics and initial conditions, highlighting the need for better calibrated stellar evolutionary models.

Dark Matter-neutrino interactions affect the propagation of astrophysical neutrinos, attenuating the flux of neutrinos arriving at Earth. Using the highest-energy neutrino event detected to date by the KM3NeT collaboration as an example, and assuming an extragalactic origin, we derive limits on these interactions at $E_ν= 220^{+570}_{-110}\, \mathrm{PeV}$. Considering only the propagation on the Milky Way Dark Matter halo, we constrain the interaction cross section over the mass of the Dark Matter candidate to be, $σ_{\rm DM-ν}/m_{\rm DM} \lesssim 10^{-22}\, \mathrm{cm}^2\,\mathrm{GeV}^{-1}$. If a transient source was positively identified, the high-energy neutrino would have crossed the dark-matter halo of the source host as well, resulting in more stringent constraints (e.g., up to $ \sim$ 6 orders of magnitude assuming the blazar PKS 0605-085 is the source). These bounds on the Dark Matter-neutrino interaction cross section are translated into limits on the mass of the Dark Matter candidate, the mass of the mediator, and the coupling strength for different simplified models. We find that the constraints from the KM3-230213A high-energy event for these simplified models are almost entirely ruled out for masses above the MeV by unitarity constraints. Therefore, the attenuation of such energetic neutrinos by Dark Matter calls for richer dark sectors in order to produce meaningful constraints.

String theories naturally exhibit dualities that lead to hidden symmetries in the low-energy effective description, which have been used to great effect to generate supergravity solutions. We review recent progress in using hidden symmetries arising from T-duality to generate higher-derivative-corrected solutions, as well as the problems that arise from non-perturbative effects when extending this paradigm to hidden symmetries arising from U-duality.

Analysis of data from randomized controlled trials in vulnerable populations requires special attention when assessing treatment effect by a score measuring, e.g., disease stage or activity together with onset of prevalent terminal events. In reality, it is impossible to disentangle a disease score from the terminal event, since the score is not clinically meaningful after this event. In this work, we propose to assess treatment interventions simultaneously on the terminal event and the disease score in the absence of a terminal event. Our proposal is based on a natural data-generating mechanism, respecting that a disease score does not exist beyond the terminal event. We use modern semi-parametric statistical methods to provide robust and efficient estimation of the risk of terminal event and expected disease score conditional on no terminal event at a pre-specified landmark time. We also use the simultaneous asymptotic behaviour of our estimators to develop a powerful closed testing procedure for confirmatory assessment of treatment effect on both onset of terminal event and level of disease score in the absence of a terminal event. A simulation study mimicking a large-scale outcome trial in chronic kidney patients as well as an analysis of that trial is provided to assess performance.

Accurately forecasting GPU workloads is essential for AI infrastructure, enabling efficient scheduling, resource allocation, and power management. Modern workloads are highly volatile, multiple periodicity, and heterogeneous, making them challenging for traditional predictors. We propose PRISM, a primitive-based compositional forecasting framework combining dictionary-driven temporal decomposition with adaptive spectral refinement. This dual representation extracts stable, interpretable workload signatures across diverse GPU jobs. Evaluated on large-scale production traces, PRISM achieves state-of-the-art results. It significantly reduces burst-phase errors, providing a robust, architecture-aware foundation for dynamic resource management in GPU-powered AI platforms.