In differential privacy (DP), the generalized private testing problem was introduced by Liu and Talwar (STOC 2019). Given a dataset $X \in \mathcal{X}$ and a sequence of black-box $\varepsilon_t$-DP mechanisms $M_t:\mathcal{X}\to\{+1,-1\}$, the analyst must accept the first mechanism whose success probability $p_t=\Pr[M_t(X)=+1]$ exceeds a given threshold $p^*\in(0,1)$, while achieving DP. Accuracy is measured by the gap between $p^*$ and a rejection threshold $\bar{p}$, such that with probability $1-β$ for all $t\geq1$, if $p_t\leq\bar{p}$, then $M_t$ is rejected, and if $p_t\geq p^*$, then it is accepted. This generalizes the standard private testing problem, whose solution, the Sparse Vector Technique, is ubiquitous in DP. We introduce the Generalized Thresholding Mechanism (GTM) for generalized private testing. For $\varepsilon>0$ and any sequence of $(\varepsilon_t,δ_t)$-DP mechanisms $M_t$, the GTM is pure $\varepsilon$-DP. For $θ>0$, $γ\in(1,2]$, and $β\in(0,1)$, $\bar{p}_t=\max(p^*/γΛ_t, 1 - γΛ_t(1-p^*))-δ_t/\varepsilon_t$ for $Λ_t=(5t\ln^3(t+2))^{(2+θ)\varepsilon_t/\varepsilon}(4/β)^{(3+θ+2/θ)\varepsilon_t/\varepsilon}$. With probability $1-β$, the number of evaluations of $M_t$ is at most $O((\ln(t/β)/(γ-1)^2)\max(Λ_t/p^*,(1-p^*)^{-1}))$ for all $t\geq 1$. Our lower bounds prove near-optimality of our accuracy and sample complexity guarantees. Via the GTM, we give a black-box reduction for DP optimization from the continual observation (CO) setting to the batch setting. This gives us the first DP-CO algorithms for many maximization problems. Further, the GTM permits an adaptive choice of acceptance thresholds $(p^*_t)_{t\geq1}$, addressing a challenge mentioned in prior work on using generalized private testing for hyperparameter optimization (Papernot and Steinke (ICLR 2022)).

We present the galaxy stellar population catalogue from the JWST Advanced Deep Extragalactic Survey (JADES) Data Release 5 (DR5), providing homogeneous Bayesian inference of physical galaxy properties in GOODS-N and GOODS-S. Using deep JWST/NIRCam and MIRI imaging combined with ancillary multi-wavelength data, we model the spectral energy distributions of ~500,000 sources with the Prospector framework. Our modelling incorporates flexible non-parametric star-formation histories (SFHs), nebular emission, dust attenuation, metallicities, and mid-infrared AGN and dust emission. We adopt an evolving star-forming main sequence (SFMS) prior for modelling the SFHs, which provides a physically-motivated long-term shape of SFHs while retaining non-parametric flexibility. The prior links stellar mass growth and SFR through the observed redshift-dependent SFMS, shaping the global behaviour of the inferred SFHs but allowing substantial deviations and scatters wherever supported by the data. We derive posterior distributions for stellar masses, SFRs, SFHs, dust attenuation, metallicities, and AGN contributions. The depth and wavelength coverage of JADES enable robust stellar mass measurements down to low-mass limits, as well as improved constraints on recent star-formation activity for ~350,000 galaxies at z = 1 - 9. The adoption of a physically motivated prior mitigates unphysical solutions and reduces degeneracies between redshift, age, dust, and metallicity, particularly for faint sources. We validate the catalogue through consistency checks and comparison to spectroscopic redshifts where available. The resulting value-added catalogue provides a uniform set of stellar population parameters suitable for statistical studies of galaxy growth, quenching, and the build-up of stellar mass across cosmic time. The full catalogue and posterior summaries are publicly released as part of JADES DR5.

Context. Ultra-diffuse galaxies (UDGs) lie at the extreme end of the size-luminosity distribution of low surface-brightness (LSB) galaxies. Their detection and characterization require deep imaging and reliable source detection techniques that can handle low signal-to-noise ratios and severe source blending. Aims. We aim at improving the detection and characterization of the LSB galaxies and UDG candidates in different environments. To this end, we have developed a new automated detection Python-based tool, named ATTILA. Methods. We use deep g- and r-band imaging from the VST Early-type GAlaxy Survey (VEGAS), covering the central region of Hydra I and three new additional fields. Sources are identified combining tiling processing, source detection, and iterative deblending. The structural parameters are derived through surface brightness profile analysis and Sérsic modelling. Cluster membership is determined using the early-type galaxies colour-magnitude relation. Results. We identify 24 new UDGs, doubling the known population in the Hydra-I cluster to 48, consistent with expectations from halo mass scaling relations, and 92 additional LSB galaxies. In real data, ATTILA recovers more than 80% of previously known LSB galaxies and significantly improves the automated detection rate relative to standard methods. Conclusions. By improving the recovery of faint and diffuse sources while mitigating blending and contamination effects, ATTILA enables a more complete census of the LSB galaxy population, including UDGs.

The suitability of the actuator line method (ALM) to predict flutter instability is theoretically studied by employing a two-dimensional linear model of the ALM undergoing harmonic motion. Three different analytical models of the ALM, including or not the non-circulatory and pitch-rate terms, are compared to Theodorsen's theory. First, classical methods using Theodorsen's function are employed to calculate reference values of flutter velocity and frequency. Then, the theoretical response of the ALM is predicted by replacing Theodorsen's function in the lift and aerodynamic pitching moment models with the corresponding complex function that relates the lift calculated by an unsteady ALM and the quasi-steady lift in harmonic motion. This method is applied to an airfoil typical section and to an energy harvesting device based on aeroelastic vibrations of an airfoil. From the results, it is possible to conclude that the classical ALM does not accurately predict flutter. However, we show that an ALM that considers the pitch-rate and non-circulatory terms has the capability to reproduce the results of classical methods if the ratio between ALM smearing parameter and chord is carefully chosen. These results can guide aeroelastic simulations of energy harvesting devices, large horizontal-axis wind turbines and fixed-wing aircraft.

We develop a framework for indirect discovery in the Standard Model Effective Field Theory (SMEFT) based on Bayesian model selection over operator subsets. We argue that SMEFT should be understood as a structured space of competing hypotheses rather than a single high-dimensional model, with each operator subset corresponding to a physically distinct low-energy realisation of new dynamics. Bayesian inference is applied at the level of model space itself, assigning posterior probabilities to operator subsets and marginal inclusion probabilities to individual operators. A genetic algorithm efficiently navigates the high-dimensional discrete model space, concentrating evaluations in the high-posterior region, while the Bayesian Information Criterion provides a tractable approximation to the Bayesian evidence. We apply this framework to a dataset comprising electroweak precision observables from LEP and Higgs, top-quark, and diboson measurements from LHC Run 2, at both linear and quadratic order in the Wilson coefficients, with one-loop renormalisation group evolution systematically included. The analysis finds no statistically significant evidence for any departure from the SM, and demonstrates that Bayesian Model Average posteriors on Wilson coefficients carry substantially improved characterisation potential compared to traditional global fits. The operator correlation matrix encodes the relational structure of the model posterior, identifying operator pairs that co-appear in high-posterior models and flat directions where additional measurements would be most valuable. The sensitivity of all results to the choice of matching scale $μ_0$ is assessed, and its promotion to a continuous parameter of inference is identified as a natural extension of the framework.

Whether intermediate-mass black holes reside in nearby star clusters has remained contested for decades. We address this question by training neural network and random forest regressors on synthetic catalogs generated with the {\sc Rapster} cluster evolution code, mapping observable cluster properties such as total mass and half-mass radius onto the mass of the heaviest black hole built up through repeated mergers. Applying these models to nearby globular and nuclear star clusters, we forecast the intermediate-mass black hole population that each system may host. Globular clusters are unlikely to contain black holes more massive than $\sim 100\,M_\odot$, with an occupation fraction near 0.02, although they can produce remnants within the upper mass gap with masses approaching $100\,M_\odot$. Among nuclear star clusters, a handful of cases, including NGC 5102 and NGC 5206, yield predicted central black hole masses above $100\,M_\odot$, which we contrast with kinematically inferred estimates. Where the observationally claimed masses exceed our predictions, the implication is that the assembly history involved processes beyond hierarchical mergers, most plausibly accretion of gas and stars. Finally, we employ a normalizing flow to quantify, for individual globular clusters, the likelihood that their initial conditions were favorable to a collisional runaway during the first few million years after formation.

Recent efforts to characterise the molecular gas content of brightest cluster galaxies (BCGs) at intermediate redshift have revealed a sub-population of gas-rich systems, whose star formation activity is likely influenced by environmental processing. In this study, we aim to investigate the molecular gas reservoirs and star formation fuelling of central galaxies in groups, also known as brightest group galaxies (BGGs), at intermediate redshifts. We present targeted carbon monoxide (CO) line observations of three BGGs in the COSMOS field at $z \sim 0.3$, obtained with the IRAM 30m telescope. The galaxies exhibit disturbed morphologies, extended blue substructures, and interaction signatures. Furthermore, they exhibit significant star formation rates derived from multiwavelength diagnostics. We detect CO(1$\rightarrow$0) emission in one system, revealing a substantial molecular gas mass of $M_{H_2} \sim 3 \times 10^{10}$ M$_\odot$, while for the other two BGGs, CO emission lines remain undetected, yielding stringent upper limits of $M_{H_2} \lesssim 10^{10}$ M$_\odot$. By combining molecular gas constraints with fiducial star formation rates derived from total infrared emission, we infer gas depletion timescales in the range of $\lesssim 0.5-1.5$ Gyr. These results may indicate that, despite their active star formation and interaction signatures, some BGGs could already experience efficient gas exhaustion or suppressed gas replenishment, suggesting that gas depletion precedes star formation quenching. Our findings hint that environmental processes in galaxy groups could strongly regulate the availability of cold gas and drive rapid evolutionary phases in central galaxies, possibly bridging the gap between gas-rich BCGs and passively evolving systems.

We study algebraic locality principles on a 2+1D closed lattice in the presence of a Gauss law for a non-invertible symmetry. Prior work in arXiv:2509.03589 showed that when enforcing the Gauss law of an invertible symmetry, the principle of "Haag duality" is preserved exactly, and "disjoint additivity" is preserved after appropriate treatment of discreteness artifacts. Here we show that for a large class of non-invertible on-site symmetries, Haag duality is preserved exactly only for sufficiently nice, "cuspless" regions. For cusped regions, we instead have a weak form of Haag duality that requires adding a collar. Our results apply to double models with a purely magnetic constraint, and to the more general framework of constraints induced by the on-site action of a Hopf algebra. In particular, we treat a class of extended string-net models explicitly. We also demonstrate disjoint additivity for double models based on a group, and a weakened form of disjoint additivity in the setting of a general Hopf algebra.

We examine the potential for a 10~TeV lepton collider to carry out precision measurements of the W boson mass and W boson couplings strength, i.e. the CKM matrix elements. We consider the several W boson production mechanisms and focus on the most copious at 10~TeV, that is effective $γW \to W$, a process viable at both opposite sign and same-sign leptonic colliders. We find that the leptonic W decay channel can hardly be competitive with present determinations, due to lack of rate. The hadronic channel has potential to improve over the current $\simeq$10~MeV from measurements at hadron colliders, motivating detector developments towards high-precision hadronic energy measurements. We find that the precision understanding of the detector response to hadrons can also lead to a determination of the CKM matrix elements. We expect determination of CKM matrix elements surpassing by far the present precision for couplings involving heavy quarks, notably $V_{cb}$, avoiding the present bottle-necks due to poor knowledge of hadronic matrix elements needed in low energy extractions of CKM matrix elements. Our findings motivate detector developments towards high-precision hadronic energy measurements and flavor tagging.

Recent observations have revealed a unique class of active galactic nuclei (AGNs), termed little red dots (LRDs). These objects are hypothesized to be powered by massive black holes rapidly accreting in dense gaseous environments. Theoretical studies suggest that the circum-nuclear gas can form an optically thick black hole envelope (BHE), whose structure resembles the atmospheres of convective stars near the Hayashi limit. Given that such cool stars typically generate magnetic fields, we propose a dynamical and spectral model for an LRD enshrouded by a magnetized BHE. Assuming spherical free-fall accretion onto a rotating, magnetized BHE, our model accounts for key observational properties of LRDs. We propose that the Doppler component of broad emission lines originates from plasma clumps co-rotating within the BHE magnetosphere. Including additional broadening due to electron scattering allows the resulting line profile to be fitted by a combination of a Gaussian core and an exponential tail. This model can reproduce Doppler components up to a few thousand ${\rm km~s^{-1}}$. We suggest that conventional black hole mass estimation methods based on the virial relation may yield erroneous results. Furthermore, our model is consistent with X-ray non-detections in LRDs. We evaluate the X-ray luminosities of two potential sources: the post-shock region of accretion shocks and a magnetically heated corona. We find that these X-ray luminosities are constrained to $\lesssim 10^{41}~{\rm erg~s^{-1}}$ across a wide range of black hole masses ($10^5 M_\odot \lesssim M_{\rm BH}\lesssim 10^7M_\odot$) and accretion rates, consistent with current upper limits on X-ray emission.

The $\mathrm{U}(1)$ Dirac spin liquid provides a useful organizing framework for frustrated magnets: it offers an algebraic parent state from which competing orders, confinement patterns, and low-energy spectral features can be understood. Whether such a state can occur as a stable ground state of a two-dimensional spin Hamiltonian remains an open question, because monopole events of the compact gauge field can proliferate and confine the spinons. Here, we show that the maple-leaf lattice provides a distinct route to this problem. Its Dirac spin liquid realizes QED$_3$ with $N_f=12$ Dirac fermions, substantially more than the $N_f=4$ theories of the triangular and kagome lattices. We classify the fundamental monopoles under the full microscopic symmetry group and find five charge-one spin-singlet monopoles that are trivial under lattice symmetries, time reversal, and spin rotation. The phase is therefore not protected by symmetry in the usual sense: its stability depends on whether these allowed monopoles are dynamically irrelevant. Available large-$N_f$ and Monte Carlo estimates place the charge-one monopole dimension close to the relevance threshold in $(2+1)$ dimensions, making the maple-leaf lattice a concrete large-flavor platform for testing the stability of compact QED$_3$ in a quantum magnet. The same monopole classification gives direct numerical predictions, identifying the symmetry sectors in which singlet, triplet, and quintet monopole excitations should appear. This provides a route to testing the $N_f=12$ Dirac spin liquid through symmetry-resolved exact diagonalization and variational studies of maple-leaf spin Hamiltonians.

We re-examine the claim by Wiseman et al. (2026) that progenitor-age bias has a negligible impact on cosmological inferences from Type Ia supernovae (SNe Ia). We show that their inferred host-age-Hubble residual (HR) slope is severely underestimated because their combined SN Ia sample spans an unusually wide redshift range ($0.04 < z < 0.42$), over which the mean host age evolves by $\sim$\,3 Gyr. As a result, SNe Ia spanning substantial host-age differences are effectively assigned similar HR values prior to regression, artificially flattening the inferred age-HR relation. In addition, their application of the Pantheon+ host-mass correction further suppresses the slope, but the underlying dust model is highly incompatible with the measured dust attenuation curves of galaxies. We also demonstrate that our age bias correction is robust to uncertainties in host-progenitor age mapping arising from different choices of the SN Ia delay-time distribution. The reduced progenitor-age evolution argued by Wiseman et al. (2026) must, by the same logic, be accompanied by a steeper inferred progenitor-age-HR slope. When these two effects are consistently combined in computing the redshift-dependent magnitude correction, the final correction, and hence the resulting cosmological impact, remain largely unchanged from Son et al. (2025).

The single-band Hubbard model is one of the most extensively studied models in condensed matter physics, giving rise to intertwined spin and charge stripes that coexist with, or lie in the vicinity of, superconductivity in the phase diagram. However, whether the low energy physics of the single-band Hubbard model is fully equivalent to the multi-band (multi-orbital) Emery model remains an unsettled question. While the intertwined stripes and nematicity have been studied in the single-band Hubbard model, a comprehensive picture in the Emery model is lacking. In this paper, we focus on the less investigated intertwined charge stripes using complementary density matrix renormalization group (DMRG) and determinant quantum Monte Carlo (DQMC) techniques. Our ground state DMRG confirms the presence of the oxygen-centered charge stripes at a reduced amplitude in the Emery model parameter regime widely used in the study of intertwined stripes. Close analysis of the oxygen orbital structure of the static charge correlation function from DQMC reveals the charge stripe pattern in real-space, showcasing stronger charge density modulation on $p$-orbitals pointing along ``the rivers of charge'', consistent with DMRG. For the parameter set with the largest fermion signs, we managed to reach a temperature where the system first demonstrated tendencies to form purely unidirectional spin and charge stripes, and the $B_{1g}$ component becomes dominant in the bond-charge nematic susceptibility. This observation correlates with the doping dependence of the kinetic energy anisotropy, suggesting a close relation between the nematicity and charge stripes in the Emery model.

Nucleon decay searches provide uniquely sensitive probes of baryon number violation and physics beyond the Standard Model. We propose a new class of nucleon decay observables involving long-lived particles (LLPs), characterized by spatially separated but temporally correlated "echo" vertices not captured by conventional prompt searches. Focusing on vector LLPs, we construct effective operators and ultraviolet realizations, and show that Super-Kamiokande, Hyper-Kamiokande and JUNO can achieve geometric acceptances approaching 80% over a broad range of LLP decay lengths. Echo signatures could in principle arise from any visibly decaying LLP.

The chiral Lagrangian is a cornerstone of modern particle physics, offering a systematic and quantitative description of low-energy pions. Using tools from the modern scattering amplitudes program, we show that consistent multiparticle dynamics impose novel constraints on the coupling constants of this theory. In the planar limit, these constraints imply that certain Wilson coefficients of the chiral Lagrangian are bounded from below by the chiral anomaly. Our results reveal a subtle connection between the anomalous and nonanomalous sectors of the underlying strong interactions, while introducing a novel formulation of multipositivity bounds that holds for any planar tree-level theory.

We investigate the role of mass ratio reversal (MRR), in which the initially less massive star in a binary forms the more massive compact object, in shaping the astrophysical binary black hole (BBH) merger rate and mass distribution inferred by LIGO-Virgo-KAGRA, comparing simulation outcomes from population synthesis frameworks COMPAS and SEVN. We find that the observational imprint of MRR differs qualitatively between the two models. In COMPAS, MRR systems dominate the merger rate density at high primary masses ( $\gtrsim$ 12 M$_\odot$), high secondary masses ( $\gtrsim$ 20 M$_\odot$), and high mass ratios ($q>0.6$), whereas in SEVN, MRR systems remain subdominant across the BBH mass distribution. This implies that the initially less massive star can massquerade as the observed primary black hole, such that the primary-mass distribution is not a direct tracer of the initially more massive stars, but instead a superposition of physically distinct evolutionary populations. We identify in the simulations three distinct evolutionary pathways leading to MRR systems: core-growth, in which stable mass transfer increases the helium-core mass of the secondary; PPISN-shrinking, where pulsational pair-instability episodes reduce the primary remnant mass; and asymmetric-CCSN, where differential supernova mass loss drives the reversal. When weighted by the local BBH merger-rate density, the core-growth channel dominates almost exclusively. MRR systems predominantly originate from massive ($\gtrsim$ 50 M$_\odot$), low-metallicity progenitors, with most of the systems forming below 0.1 $Z_\odot$. Our results demonstrate that MRR is a physically distinct and potentially observable feature of isolated binary evolution. Accounting for MRR will be important for robustly connecting future gravitational-wave observations to the physics of massive binary evolution and compact-object formation.

Interstellar medium (ISM) structures gravitationally perturb stellar orbits in galactic disks, driving orbital heating and migration. However, studies of these transport processes tend to model the ISM very crudely, e.g., as a collection of compact, spherical ``clouds'' moving in the disk plane. Here, we revisit this problem with more realistic models of ISM density fluctuations drawn from the TIGRESS-NCR magnetohydrodynamic simulations, which follow the physics governing the ISM in Milky-Way-like conditions at high resolution. By integrating test-particle trajectories through time-dependent TIGRESS-NCR structures, we uncover transport behavior that contrasts sharply with conventional theoretical expectations. Notably, radial heating scales as $σ_R \propto t^{1/2}$ for initially cold orbits at early times, and $σ_R \propto t^{1/5}$ for warmer orbits at late times, contrary to the classic $σ_R \propto t^{1/3}$ prediction. The ISM drives substantial radial migration, accounting for $\gtrsim 30\%$ of that observed in the solar neighborhood (even without stellar spiral structure), and leads to a very low heating-to-migration ratio of $\mathrm{rms}\,δJ_R\,/\,\mathrm{rms}\,δJ_φ\approx 0.055$, where $J_R$ and $J_φ$ are the radial and azimuthal actions respectively. Vertical motion suppresses the amplitude of radial transport, but does not change the basic scalings. All our simulation results can be explained using quasilinear diffusion theory, accounting for the fact that the dominant ISM fluctuations have wavelengths of $λ_* \sim 600\,$pc and correlation timescales of $τ_* \sim 70\,$Myr. We provide simple fitting formulae for the corresponding diffusion coefficients. In Paper II, we study the ISM's role in vertical disk heating.

A rapid estimate of gravitational-wave (GW) detectability associated with astronomical transients is crucial for optimizing multi-messenger follow-up strategies and for constraining the physical origin of the transient itself. We introduce here the Targeted Detectability Range (TDR), designed to evaluate with minimal computational effort the detectability of compact binary coalescences under the hypothesis of association with an external messenger, such as an electromagnetic or neutrino signal. Unlike the standard GW range, which is based on averaged source parameters, the TDR incorporates prior information from observations of the external messenger, including sky localization, inclination constraints, and physically motivated bounds on component masses. We report the detectability range of all gamma-ray bursts, short and long duration, observed during the first three observing runs of the LIGO-Virgo-KAGRA collaboration. The method is validated by performing a systematic comparison with the 90$\%$ exclusion distances provided by modeled targeted GW searches.

It has been argued that supermassive black holes (BHs) coevolve with the central parts of galaxies, as a result of the common fuel for both the BH and star formation in the galaxy central region, as supported by the particularly significant relation between BH growth and the central mass density within 1 kpc found among star-forming galaxies. In the context of this scenario, one would naturally expect a close observational link between AGN activity and star formation activity in the central regions, e.g., the surface star formation rate density in the central 1 kpc region ($Σ_{\rm SFR, 1~kpc}$), as the manifestation of coeval growth. With ~3000 galaxies in the Mapping Nearby Galaxies at Apache Point Observatory (MaNGA) survey that have X-ray coverage from SRG/eROSITA, XMM-Newton, or Chandra, we studied how the X-ray AGN fraction varies with $Σ_{\rm SFR, 1~kpc}$. We found that the fraction of X-ray AGNs with relatively higher specific BH accretion rates increases with $Σ_{\rm SFR, 1~kpc}$, consistent with the expectation. Comparison of the mean star formation rate surface density ($Σ_{\rm SFR}$) profiles of the host galaxies of these AGNs and normal galaxies sharing similar properties reveals elevated $Σ_{\rm SFR}$ in AGN hosts across the entire central region. As for optically-selected AGNs, their hosts also tend to show high $Σ_{\rm SFR}$ in the central regions on average compared to normal galaxies, but are discrepant with X-ray AGNs in terms of the trend of AGN fraction vs. $Σ_{\rm SFR, 1~kpc}$, which can be explained by selection effects. While these general trends all support the coeval growth scenario, they do not contradict observational evidence for AGN feedback, as the time-averaged effects from local AGN feedback are modest in star-forming regions.

Type Ia supernovae (SNe Ia) play an important role throughout astrophysics, most notably as standardizable cosmological candles. Yet, their stellar progenitors and explosion mechanism remain areas of active investigation. For decades, the canonical model for normal brightness SNe Ia used in cosmology was a carbon-oxygen white dwarf (WD) accreting from a non-degenerate stellar companion, approaching the Chandrasekhar mass (M_Ch). Previously, all models of near-M_Ch SNe Ia invoked an ad hoc assumption on the critical process of detonation initiation, and could therefore be tuned to a variety of outcomes. Here, we present global 3D hydrodynamical simulations of near-M_Ch progenitors, which incorporate, for the first time, a laboratory-validated ab initio mechanism for the turbulence-driven deflagration-to-detonation transition (tDDT). The tDDT detonation mechanism is highly efficient, leading to detonation initiation which is prompt in comparison to most prior work. Despite spanning a factor of six in central ignition density and qualitatively distinct ignition topologies, all models converge on nearly identical synthetic spectra at peak luminosity, spectroscopically matched to the overluminous SN 1999aa. The turbulence-driven Chapman-Jouguet criterion drives each progenitor to a common detonation configuration from diverse initial conditions, providing a physical foundation for the ignition-insensitive detonation outcomes implicit in the empirical standardizability of SNe Ia. This provides the first physically motivated, self-consistent pathway for delayed detonation in SNe Ia simulations. Further work is necessary to understand how this mechanism might produce more delayed detonation initiation and potentially fail, thereby yielding SNe Iax.

JWST has revealed a substantial population of "Little Red Dots" (LRDs) at $z>4$, challenging conventional AGN frameworks. However, the low-redshift regime remains largely unexplored. In the second paper of the (LRDs)$^2$ series, we present a systematic selection from DESI DR1 and identify 27 LRDs at $z=0.2-0.9$, yielding a number density lower limit of $7.5 \times 10^{-10}$ cMpc$^{-3}$. We conducted near-IR spectroscopic follow-up observations for 18 of them, revealing their full SED shapes and emission lines. These low-$z$ LRDs share the hallmark properties of their high-$z$ counterparts: compact morphology, V-shaped UV-optical continua, broad Balmer emission with extreme decrements (median H$α$/H$β\sim 16$), frequent Balmer absorption (67%), and blackbody-like optical-to-near-IR continua. All have low metallicity, occupy the same regions in the BPT diagram as high-$z$ LRDs, and have softer ionizing spectra than typical AGNs. The consistency between low-$z$ and high-$z$ LRD properties indicates the same physical processes at work. The correlation between broad-line Balmer luminosity and $L_{5100}$ deviates from that of local type-1 AGNs, limiting the direct application of local BH mass calibrations. Ionized [O III] outflows are ubiquitous (78%). One LRD at $z=0.196$, J1717+3807, shows robust long-term variability in $i$ and WISE bands. The optical-to-NIR continua of LRDs reveal a wide range of temperatures $\sim 2000-4700$ K (peak $0.6-1.5$ $μ$m), with a subset showing cooler and larger envelopes than those at high $z$. Low-$z$ LRDs serve not only as proximate laboratories for probing the nature of LRDs, but also trace the cosmic evolution of this population from the cosmic dawn to the present day.

In this work, we delve into the physics of charged black holes modified by Weyl corrections, a framework that emerges from the subtle non--minimal coupling between spacetime curvature and electromagnetism. We begin by revisiting the thermodynamics of these cases, where we derive the Hawking temperature, entropy, and heat capacity to see how the Weyl correction parameter reshapes the landscape of thermal stability and phase transitions. Then, we apply the winding number method to classify the thermodynamic states of the system from a topological perspective and show the effect of the Weyl modifications on the universal classification of the Wey--corrected black hole. Moving beyond pure theory and into the realm of astrophysics, we study the motion of massless particles affected by the Weyl correction for the two photon polarization, and by exploring the shadow, we find constraints of the black hole parameters. Also, we study the null trajectories for the two photon polarization of the Weyl--corrected black hole. Finally, we model the accretion disk around these black holes. By calculating the energy flux, spectral luminosity, and differential luminosity, we show how these corrections leave a detectable trace on the light we might observe.

Quantum purity amplification (QPA) is the task of coherently transforming $n$ copies of a mixed state into high-fidelity copies of a chosen eigenstate. We solve QPA in the general setting of $n$ input copies, $m$ output copies, arbitrary target eigenstates, arbitrary local dimension $d$, and generic input spectra. We characterize the optimal channel and derive its all-site and one-site performance laws across output regimes. For the asymptotic analysis, we use a path-graph parametrization to show that, when the target eigenvalue has a constant spectral gap $D_{k,\mathrm{min}}$, achieving all-site error $\varepsilon$ requires a number of input copies independent of $d$ and scaling as $O(m/(\varepsilon D_{k,\mathrm{min}}^2))$. When $m/n$ approaches a constant, the performance exhibits phase-like regimes, which we characterize explicitly. For the nonasymptotic analysis, we develop a theory of generalized Young diagrams that yields tight sample complexity bounds and provides the first dimension-uniform guarantee for optimal QPA. We also provide asymptotically efficient implementations of the optimal protocol. Together, these results establish QPA as a rigorous example of coherent quantum information processing with dimension-uniform sample complexity, supplying the technical foundation for the coherent-incoherent separation developed in the companion work.

Large language models are increasingly used for mental health support, yet little is known about whether their responses are psychologically safe across different help-seeking styles. We examine a foundational distinction in emotional disclosure, venting vs. advice-seeking, and whether LLMs respond in ways that regulate or amplify distress. Using 178,800 Reddit posts, we first show the two help-seeking styles are linguistically distinguishable at scale. We then introduce a measurement framework grounded in interpersonal emotion regulation theory that captures Regulation and Escalation as empirically independent dimensions. Across persona conditions (default, friend, therapist), GPT-5.3 responses systematically mirror help-seeking style: venting elicits more regulation, but also more escalation. Therapist personas reduce escalation while maintaining regulation, whereas friend personas increase both. A crowdsourced human study finds no user experience penalty for the safer therapist condition, but reveals that lay raters cannot reliably detect escalation without expert knowledge. Responses that feel supportive may simultaneously intensify distress in ways standard safety evaluation cannot see, and empathy metrics alone cannot replace a framework that measures both.

Ciliated organs transport viscous fluids through confined ducts, yet how duct morphology and ciliary activity jointly set the limits of flow rate and sustainable pressure remains unclear. Here, we model dense arrays of beating cilia lining duct walls as an active porous medium driven by prescribed metachronal waves, and identify two key morphological parameters that govern transport: the ciliary confinement ratio and the mean ciliary fraction. The resulting flows are described by the incompressible Navier-Stokes-Brinkman equations, which we solve numerically using a spectral method in the low-Reynolds-number regime. We also develop a complementary mean-field analytical model. The active porous medium framework provides an intermediate description between classical envelope theories and filament-resolved simulations and enables a systematic investigation of how fluid transport is shaped by confinement and packing of ciliary material. We find that transport is characterized by a decreasing linear relationship between flow rate and pressure generation, marking a fundamental trade-off between throughput and sustainable adverse pressure. These results provide a unified physical interpretation of the morphological diversity of ciliated ducts, from high-throughput ciliary carpets to pressure-generating ciliary flames, and offer guiding principles for the design of bio-inspired microfluidic pumps.

We develop an optimization framework for high-efficiency quantum cycles implemented with a trapped Bose-Einstein condensate, whose control parameters are the trap stiffness and the interaction strength tuned via a Feshbach resonance. Optimal driving protocols for each stroke of the cycle are obtained from a variational description of the condensate dynamics combined with Nelson's stochastic quantization, which maps the quantum evolution onto an effective Ornstein-Uhlenbeck process. The optimal protocol is obtained by minimizing a user-defined cost functional that selects the best trade-off between protocol duration and arbitrary physical constraints (such as the expended work or the proximity to an adiabatic evolution), and exhibits remarkable stability over repeated cycles. The method also provides a systematic route to optimal control for generic nonlinear Schrödinger equations, paving the way to optimal control strategies in fields as diverse as nonlinear optics, quantum fluids, and quantum plasmas.

This work proposes a variable neighbourhood search (FTS) that uses a fractal-based local search primarily designed for images. Searching for specific content in images is posed as an optimisation problem, where evidence elements are expected to be present. Evidence elements improve the odds of finding the desired content and are closely associated to it in terms of spatial location. The proposed local search algorithm follows the fashion of a chain of triangles that engulf each other and grow indefinitely in a fractal fashion, while their orientation varies in each iteration. The authors carried out an extensive set of experiments, which confirmed that FTS outperforms state-of-the-art metaheuristics. On average, FTS was able to locate content faster, visiting less incorrect image locations. In the first group of experiments, FTS was faster in seven out of nine cases, being >8% faster on average, when compared to the second best search method. In the second group, FTS was faster in six out of seven cases, and it was >22% faster on average when compared to the approach ranked second best. FTS tends to outperform other metaheuristics substantially as the size of the image increases.

Let $θ$ be a non-constant inner function and let $ϕ=\overline{u}v$, where $u$ and $v$ are inner functions such that $v$ divides $θ$. In this paper we characterize the partially isometric truncated Toeplitz operators $A_ϕ$ and dual truncated Toeplitz operators $D_ϕ$ with symbols of the form $ϕ=\overline{u}v$. Along with that, we obtain a few more characterization results, including the space of extremal vectors for non-zero partially isometric truncated and dual truncated Toeplitz operators.

We investigate the gravitational field of an extended spherically symmetric body within the framework of Extended Relativity (ER), a Lorentz-covariant formulation of relativistic gravity on a Minkowski background. Using a relativistic superposition principle for retarded gravitational fields, we derive an explicit metric for an extended body by integrating the contributions of its mass elements. The resulting metric reproduces the standard gravitational time dilation of a point source and agrees with the classical tests of General Relativity in the appropriate limits. However, unlike the exact Newtonian shell theorem and the Schwarzschild exterior solution, the external field depends weakly on the internal mass distribution through higher-order corrections. These corrections decay rapidly with distance but become significant near compact objects. We analyze the corresponding admissible-velocity geometry, derive the motion equations for test particles, and compare the predictions of extended-body and point-source models. For neutron stars, the corrections noticeably modify the local light-velocity structure near the surface. For the Earth, the corrections are small but produce measurable differences in round-trip light travel times to the International Space Station. The formalism provides a transparent relativistic description of extended gravitational sources and offers a framework for studying relativistic corrections due to internal structure in strong-field and precision-measurement regimes.

Inspired by the well-known result stating that if any iterate of a mapping is a Banach contraction on a complete metric space, then the mapping itself possesses a unique fixed point, we investigate that claim for a Chatterjea contraction but by retaining the left-hand side of the inequality as per the mapping itself. With an additional assumption of k- continuity, the existence and uniqueness of a fixed point is obtained for a new class of contractions, m-Chatterjea contraction, on a complete metric space. Several examples are given in order to substantiate many theoretical claims such as discontinuity at the unique limit point of the iterative sequence, as well as examples demonstrating that this new class strictly contains the class of Chatterjea mappings.