We study the Unitary Hitting Time Problem (UHTP) in quantum dynamics. Given computably described pure states |a>, |b> and a time-dependent unitary U(t), define the hitting time as the infimum of t > 0 such that the fidelity between U(t)|a> and |b> reaches a fixed threshold (with infinity if the threshold is never reached). We prove that there is no total algorithm that outputs this hitting time for all inputs; equivalently, the total UHTP is undecidable via a reduction from the halting problem. Operationally, we show a no-go theorem: for any fixed accuracy parameters, there is no universal finite-resource protocol that, for all computably described inputs, correctly outputs the hitting time while obeying uniform finite upper bounds on observation time and on dissipation/work. The proofs use reversible computation embedded into unitary dynamics, a fixed-target beacon construction, and a continuous-time lifting via piecewise-constant Hamiltonians. Our results target systems capable of embedding universal computation and complement prior undecidability results such as spectral-gap and quantum-control reachability. We distinguish logical time (inside the equations) from physical/operational time (of preparation, evolution, measurement), and show that universal time-step selection is impossible in both senses.

Density functional theory (DFT) in chemistry and materials science aims for "chemical accuracy," but this goal is challenged by the need to approximate the exact exchange-correlation (XC) energy functional. The r$^2$SCAN, meta-generalized gradient approximation to the XC functional fulfills 17 exact constraints of the XC energy, and has significantly boosted prediction accuracy for molecules and materials. However, r$^2$SCAN remains inadequate at predicting properties of open \textit{d} and \textit{f} transition-metal strongly correlated compounds, such as band gaps, magnetic moments, and oxidation energies. Prediction inaccuracies of r$^2$SCAN energies arise from functional and density-driven errors, mainly resulting from the DFT self-interaction error. We propose the r$^2$SCANY@r$^2$SCANX method to mitigate the self-interaction error of XC functionals for the accurate simulations of electronic, magnetic, and thermochemical properties of transition metal oxides. r$^2$SCANY@r$^2$SCANX uses different fractions of exact Hartree-Fock exchange: X for the electronic density and Y for the density functional approximation of the total energy, thereby simultaneously addressing functional-driven and density-driven inaccuracies. Building just on 1 (or maximum 2) parameters that apply unchanged to \emph{s-p}-bonded systems, we demonstrate that, r$^2$SCANY@r$^2$SCANX improves upon the r$^2$SCAN predictions for 20 highly correlated oxides and even outperforms the highly parameterized DFT(r$^2$SCAN)+\emph{U} method -- the state-of-the-art approach to predict strongly correlated materials. Prediction uncertainties for oxidation energies and magnetic moments of transition metal oxides are significantly reduced by r$^2$SCAN10@r$^2$SCAN50 and band gaps with r$^2$SCAN10@r$^2$SCAN. r$^2$SCAN10@r$^2$SCAN50 diminishes the density-driven error of the energy in r$^2$SCAN and r$^2$SCAN10.

The YORP effect plays an important role in the spin evolution of asteroids. Although craters are ubiquitous surface features, their influence on YORP torque has received limited attention. In this paper, we investigate the YORP torque of a circular crater on a spherical asteroid, focusing specifically on how lateral thermal conduction breaks symmetry to produce a net torque. Using three-dimensional finite element simulations, we calculate the resulting spin and obliquity accelerations and examine their dependence on the crater's location, depth, and thermal parameters. Our results show that the crater-induced spin torque is consistently positive, and craters at different latitudes drive the spin axis toward obliquity equilibria at 0, 90 or 180 degree. We demonstrate that the spin torque arises primarily from the lateral heat conduction inside the asteroid that occurs only in 3D model, while the contributions from self-heating and shadowing effects are negligible. While the YORP effect induced by internal heat conduction may be overtaken by torque components arising from shadowing and crater orientation, particularly on large asteroids, our numerical results show that for small craters, this spin torque amounts to approximately 10 to 100 percent of the normal YORP torque. Its persistent positivity may help explain the observed prevalence of positive spin accelerations in asteroids.

Wide-orbit ($>$10 AU) gas giant planets shape the architecture of planetary systems, yet their occurrence rate remains poorly constrained. JWST has obtained the deepest mid-infrared images of nearby stars to date through substantial MIRI time-series observations of transiting planets, providing sensitive probes for wide-orbit companions. Here we leverage 15 micron observations from four programs targeting ten M-dwarf systems to search for such planets. By applying reference differential imaging for precise PSF subtraction, we achieve a 5$σ$ contrast of $8.9 \times 10^{-4} - 6.2 \times 10^{-3}$ (sensitivity in apparent magnitude of 14.8-15.8 mag) at a separation of 1" and $1.2 -9.1 \times 10^{-4}$ (16.5-17.9 mag) at separations $\gtrsim$3". The sensitivity is converted to planet detection probability for each system as a function of planet mass versus semimajor axis. Assuming solar metallicity and a clear atmosphere, we are sensitive to Jupiter-sized planets with an effective temperature of ${\sim}$233 K at separations beyond 20 AU in systems at 12.5 pc. Additionally, we catalog the nearby sources and estimate their possible impact on future observations assuming they are background sources. Our results demonstrate that archival MIRI time-series imaging data is a powerful window into the population of wide-orbit gas giants around M-dwarfs.

Understanding the formation and evolution of late type galaxies (LTG) requires deep imaging for tracing the faintest stellar components in their outskirts. Despite their crucial role in the buildup of stellar mass, these low surface brightness (LSB) features remain largely unexplored due to observational limitations. The VST-SMASH is designed to fill this gap, providing deep, wide field optical imaging for a volume limited sample of nearby LTG, overlapping with the Euclid Wide Survey in the South. This paper aims to introduce the VST-SMASH survey and showcase its scientific potential through the analysis of IC 5332, a LTG observed in the g, r, and i bands. The main goal is to demonstrate the depth, quality, and diagnostic power of the dataset in tracing LSB features and structural components in galactic outskirts. We carried out detailed surface photometry of IC 5332 to extract radial surface brightness and color profiles down to LSB regime. We performed multicomponent Sersic decompositions and constructed stellar mass surface density profiles. We identified and characterized faint stellar streams, estimating their colors and comparing them with adjacent galactic regions. While the internal (1Reff) negative colour gradients can be explained by dissipative collapses and SN outflows, the color profiles at larger radii reveal a significant gradient toward redder colors, consistent with the presence of accreted populations in the outskirts. We also find bluer r - i, which could be explained by strong Ha emission. These findings support a scenario of ongoing stellar mass assembly through accretion and highlight the capability of VST-SMASH to uncover faint structures in nearby galaxies.(abridged)

This work uses mostly model-theoretic methods to establish new proof-theoretic theorems about several axiomatic theories of truth over KP (Kripke-Platek set theory) and stronger theories, especially ZF (Zermelo-Fraenkel set theory).

Interacting transients probe mass loss in the final stages of stellar evolution; however, the geometry and timing of multi-episode mass loss remain poorly constrained. SN 2024abvb is a nearby interacting event with transitional Ibn/Icn spectroscopic properties and multi-epoch polarimetry, offering a rare opportunity to study structured circumstellar material (CSM). We aim to characterise the kinematics, composition and geometry of the CSM around SN 2024abvb and to identify plausible progenitor/ejection scenarios that can produce the observed spectro-polarimetric evolution. We present high-resolution (VLT/UVES and VLT/X-Shooter) optical/NIR spectroscopy across several epochs, complemented by broadband polarimetry and spectropolarimetry (VLT/FORS2 and NOT/ALFOSC). Line identifications, velocity decompositions and polarimetric time-series are used to trace multiple kinematic components and changes in scattering geometry. The high-resolution spectra reveal multiple narrow CSM components composed of He, C and O with absorption minima at $\sim150 - 400$ km s$^{-1}$ and additional faster material up to $\sim2000$ \kms. Low-velocity Balmer absorptions are present, indicating distant H-rich material, a first in SNe Ibn/Icn. Polarimetry shows a marked evolution ($P\sim1\%$ near peak, $\lesssim0.5\%$ after $\sim1$ week, rising to $\sim1.5\%$ at $\sim20$ d with $\sim50^\circ$ position-angle rotation and to $\sim4\%$ at $\sim30$ d, stronger in the blue), implying a time-variable, wavelength-dependent scattering/obscuration component. The combination of kinematics and polarimetric behaviour is consistent with multiple, concentric toroidal shells with differing orientations and partial dust content.

A dark matter axion with mass $m_a$ induces an oscillating electric field in a cylindrical sample placed under a magnetic field $B_0$ parallel to the cylinder axis. When the cylinder is made of a highly electrically conductive material, the induced oscillating current flows only at the surface. In contrast, if the cylinder is composed of a material with small conductivity, e.g. $σ= 10^{-3}\text{eV}$, the electric current flows inside the bulk of the cylinder. Within the QCD axion model, the current $I$ is estimated as $I(σ=10^{-3}\text{eV})\simeq 2.8\times 10^{-14}\text{A}g_γ\big(R/6\text{cm}\big)^2 \big(σ/10^{-3}\text{eV}\big)\big(B_0/15\text{T}\big)\big(10/ε\big)\big(ρ_a/0.3\rm GeVcm^{-3}\big)^{1/2}$ for $m_a=10^{-4}$eV, with radius $R$, permittivity $ε= 10$ of the cylinder and axion energy density $ρ_a$, where $g_γ$ is model dependent parameter; $g_γ(\text{KSVZ}) = -0.96$ and $g_γ(\text{DFSZ}) = 0.37$. Because the current is proportional to $R^2$, using large sample with $R=80$cm, we have large signal-noise ratio ( $>1$ ) even in temperature $T=4$K, $I(σ=10^{-3}\text{eV})/I_n({σ=10^{-3}\text{eV})}\times \sqrt{δωδt_{ob}/2π} \simeq 1.1g_γ(4\text{K}/T)^{1/2}(L/100\text{cm})^{1/2}(R/80\text{cm}) (B_0/7\mbox{T})(ρ_a/0.3\rm GeVcm^{-3})^{1/2} (δt_{ob}/10^3\,\text{s})^{1/2}$ for $m_a=10^{-4}\text{eV}$ with $ε=10$ and $σ=εm_a$, where thermal noise is $I_n=\sqrt{2Tδω/πR_c}$ with $δω=10^{-6}m_a$ and resistance $R_c=L/(σπR^2)$ of the cylinder with length $L$. Although a superconducting solenoid sufficiently large to accommodate such a sample is required, the detection of dark matter axions in our proposal may be feasible in the mass range $m_a =10^{-4}\text{-}10^{-3}\text{eV}$.

The motivic version of the $c_1$-spherical cobordism spectrum is constructed. A connection of this spectrum with other motivic Thom spectra is established. Using this connection, we compute the $\mathbb{P}^1$-diagonal of the homotopy groups of the special linear algebraic cobordism $π_{2*,*}(\mathrm{MSL})$ over a local Dedekind domain $k$ with $1/2\in k$ after inverting the exponential characteristic of the residue field of $k$. We discuss the action of the motivic Hopf element $η$ on this ring, obtain a description of the localization away from $2$ and compute the $2$-primary torsion subgroup. The complete answer is given in terms of the special unitary cobordism ring. An important component of the computation is the construction of Pontryagin characteristic numbers with values in the hermitian K-theory. We also construct Chern numbers in this setting, prove the motivic version of the Anderson-Brown-Peterson theorem and briefly discuss classes of Calabi-Yau varieties in the $\mathrm{SL}$-cobordism ring.

A quantitative understanding of cometary outbursts requires robust constraints on the size distribution of ejected particles, which governs outburst dynamics and underpins estimates of released gas and dust. In the absence of direct measurements of particle sizes, assumptions about the size distribution play a central role in modelling dust-trail formation, their dynamical evolution and observability, and the potential production of meteor showers following encounters with Earth. We analyse brightness amplitude variations associated with outbursts of comet 17P/Holmes from 1892 to 2021, with particular emphasis on the exceptional 2007 mega-outburst. During this event the comet underwent a rapid and substantial brightening: at its peak, the expanding coma reached a diameter exceeding that of the Sun and briefly became the largest object in the Solar System visible to the naked eye. We constrain the size distribution and total mass of porous agglomerates composed of ice, organics, and dust ejected during the outburst. The inferred particle size distribution is consistent with a power law of index q, yielding effective particle sizes between 10^-6 m for q = 4 and 5 x 10^-3 m for q = 2. Accounting for effective particle size, sublimation flux, and bulk density, we find that the total number of ejected particles increases with both q and sublimation flux. These results place constraints on the physical properties of outburst ejecta and provide physically motivated initial conditions for long-term dust-trail evolution modelling. They further indicate that cometary outburst brightness is determined primarily by the number of particles and their size distribution, rather than by the total ejected mass alone, with direct implications for the origin and evolution of meteoroid streams and the interplanetary dust population.

Motile bacteria shape microbial function by occupying space, yet how collective motion becomes population-scale architecture remains poorly resolved. Bacterial swarming is not merely surface motion, but a process by which motile populations commit to future macroscopic form. Here, in Enterobacter sp. SM3, a gut-associated swarmer linked to mucosal repair, we treat the advancing colony--environment interface as a morphodynamic state through which local motility becomes spatial order. We built SwarmEvo across thermal, hydration, and substrate-mechanical conditions and developed Morpher to resolve and propagate interface states. Counterintuitively, within the permissive assay range, condition labels only weakly separated future trajectories, whereas colony-specific interface geometry constrained later expansion, indicating that swarm fate is written into the interface rather than prescribed by condition identity. Boundary fidelity was decisive: a 0.67 percentage-point segmentation gap expanded into a 2.4--3.1 IoU-point forecasting loss. Preserving front displacement, protrusion continuity, and branch memory, Morpher predicted late-stage expansion with 95.42% mIoU, 10.61 px HD$_{95}$, and 3.93 px ASSD. These results identify the advancing interface as a state-bearing layer through which motility and environmental constraint are converted into future spatial form, enabling disease-relevant microbial organization to be read before endpoint architecture emerges.

We study the equilibria of uniform price auctions where many asymmetric bidders have flat demands up to their respective quantity constraints. We present an iterative procedure that systematically finds an equilibrium outcome as well as an ascending auction that has this outcome as a dominant strategy equilibrium outcome. Demand reduction and low price equilibrium may occur since it is advantageous for a bidder to give up some of his/her demand and get the remaining demand at a low price rather than to get his/her entire demand at a higher price. We show that a low price equilibrium is the only possible equilibrium when no bidder's quantity constraint is large enough to cover the supply.

Gravitational effective theories are essential for characterizing the space of deviations from General Relativity (GR). Testing these theories against fundamental principles, such as causality and unitarity, can yield constraints on the corresponding parameters. In this paper, we perform such an analysis on the very interesting dynamical Chern-Simons (dCS) gravity. This is a parity violating correction to GR wherein a new scalar field couples to the Pontryagin density $^*R\,R$. It has generated significant interest, including possible new gravitational wave shapes for LIGO/Virgo and new phenomena from cosmic inflation. In this work, we begin by deriving the dispersion relation and wave packet speed on top of a gravitational wave background in dCS gravity. This alters the corresponding Shapiro time delay (which we compute to second order), potentially giving superluminality. Causality then demands a bound on the dCS coupling constant, which we find to be moderately sharper than, but compatible with, standard estimates. We then examine a UV completion in the form of a set of $N$ fermions with a (pseudo) Yukawa coupling. By imposing perturbativity and a gravitational species bound, we find that the dCS coupling constant is constrained significantly more, depending on the choice of scale of the species bound. We also identify higher order operators generated from the UV completion. Overall, we find that any dCS corrections to gravitational dynamics should likely be very small on macroscopic systems of observational interest, such as in late-time merging black holes.

We use a high signal-to-noise MIRI-LRS spectrum (5.45 - 11 $μ$m, R$_λ$ $\sim100$) of COCONUTS-2~b revealing prominent molecular features of H$_2$O, CH$_4$ and NH$_3$. This dataset is combined with spectra from Gemini/FLAMINGOS-2 and JWST/NIRSpec (G395H), as well as photometry from WISE and Spitzer, resulting in almost continuous wavelength coverage from 1 to 15 $μ$m. We analyze the data using five grids of self-consistent atmospheric models, spanning a wide range of T$_\text{eff}$, log(g), and [M/H]. We also investigate the use of Gaussian Processes to account for correlated noise either caused by the spectrograph or by systematic departures of models in the inversion framework. All models manage to fit the overall combined observations but predict fainter flux in Y- and N-bands. Classical model comparison suggests that the ATMO2020++ synthetic specra (with and without PH$_3$) are statistically preferred. Fitting for the correlated noise of the three spectroscopic instruments, ATMO2020++ models yields constraints consistent with previous studies and evolutionary models predictions: T$_\text{eff}$ $=496^{+5}_{-3}$ K, log(g) $=4.30^{+0.04}_{-0.02}$ dex, [M/H] $=-0.02^{+0.03}_{-0.02}$ dex, and R $=1.03^{+0.01}_{-0.02}$ R$_\text{jup}$. The extended wavelength coverage provided by MIRI (accounting for 41% of the bolometric flux) completes the SED, yielding a precise luminosity estimation of log(L/L$_{\odot}$) $=-6.166\pm0.002$ dex. Combined with a previous estimate of the system age ($414\pm23$ Myr), cooling models predict a mass of M $=7.3\pm0.3$ M$_\text{jup}$.

Transmission spectroscopy is a key technique in the characterization of exoplanet atmospheres and has been widely applied to planets undergoing hydrodynamic escape. While a robust analytic theory exists for transmission spectra of hydrostatic atmospheres, the corresponding interpretation for escaping atmospheres has so far relied on numerical modeling, despite the growing number of observations of planetary winds. In this work, a theory of transmission spectroscopy in hydrodynamically escaping atmospheres is developed by coupling the standard transmission geometry to a steady-state, spherically symmetric, isothermal outflow. This approach yields closed-form expressions for the chord optical depth and effective transit radius of a planetary wind and allows the optical depth inversion problem to be examined. The analytic solution reveals that transmission spectroscopy of planetary winds naturally separates into two regimes. In an opacity-limited regime, transmission depths retain sensitivity to the atmospheric mass-loss rate $\dot{M}$. Beyond a critical threshold, however, spectral-line cores become saturated and no longer provide a unique constraint on the escape rate. This transition is marked by a sharp analytic boundary of the form $σ(λ)\,\dot{M} \le C_{\rm sat}$, where $σ(λ)$ is the line absorption cross-section and $C_{\rm sat}$ is a constant set by the thermodynamic and geometric properties of the wind. This condition specifies when the inversion between transmission depth and mass-loss rate admits a real solution. Once it is violated, the effective transit radius is no longer controlled by opacity or mass loss, but by the geometric extent of the absorbing wind.

We present cuRAMSES, a suite of advanced domain decomposition strategies and algorithmic optimizations for the ramses adaptive mesh refinement (AMR) code, designed to overcome the communication, memory, and solver bottlenecks inherent in massive cosmological simulations. The central innovation is a recursive k-section domain decomposition that replaces the traditional Hilbert curve ordering with a hierarchical spatial partitioning. This approach substitutes global all-to-all communications with neighbour-only point-to-point communications. By maintaining a constant number of communication partners regardless of the total rank count, it significantly improves strong scaling at high concurrency. To address critical memory constraints at scale, we introduce a Morton-key hash table for octree-neighbour lookup alongside on-demand array allocation, drastically reducing the per-rank memory footprint. Furthermore, a novel spatial hash-binning algorithm in box-type local domains accelerates supernova and AGN feedback routines by over two orders of magnitude (an about 260 times speedup). For hybrid architectures, an automatic CPU/GPU dispatch model with GPU-resident mesh data is implemented and benchmarked. The multigrid Poisson solver achieves a 1.7 times GPU speedup on H100 and A100 GPUs, although the Godunov solver is currently PCIe-bandwidth-limited. The net improvement is about 20 per cent on current PCIe-connected hardware, and a performance model predicts about 2 times on tightly coupled architectures such as the NVIDIA GH200. Additionally, a variable-Nrank restart capability enables flexible I/O workflows. Extensive diagnostics verify that all modifications preserve mass, momentum, and energy conservation, matching the reference Hilbert-ordering run to within 0.5 per cent in the total energy diagnostic.

Left-right (LR) symmetric theories predict right-handed charged currents whose flavor structure encodes the realization of parity. While the right-handed quark mixing matrix closely tracks its left-handed counterpart, the leptonic sector with purely Dirac neutrinos has remained structurally unclear. We show that, in contrast to the quark case, parity in the Dirac leptonic sector admits a localized, branch-dependent enhancement band in which RH-LH misalignment becomes parametrically large despite small parity breaking. We derive analytic solutions of the LR consistency equation and demonstrate that the interplay between spontaneous parity violation and spectral near-degeneracies leads to a qualitatively new pattern of right-handed mixing. This establishes the Dirac leptonic sector of the minimal LR model as a predictive and structurally distinct regime.

We investigate reentrant topological transitions in a one-dimensional Su-Schrieffer-Heeger chain with generalized Bernoulli disorder in the intradimer hopping amplitudes. Owing to its independently tunable values and probabilities, the multivalued disorder distribution provides a direct way to control the topological phase diagram. We show that increasing the disorder strength can split the nontrivial regime into multiple disconnected topological windows, whose number, widths, and locations are determined by the distribution parameters. The phase boundaries are derived analytically from the zero-mode inverse localization length and are governed by a weighted geometric mean of the disordered hopping amplitudes, in agreement with numerical results from the reflection-matrix topological quantum number and the real-space winding number. We also show that the mean chiral displacement dynamically identifies these reentrant windows. These results demonstrate how multivalued random disorder can organize and tune reentrant topological behavior in one-dimensional chiral lattices.

We revisit the Gaussian broadcast channel (GBC) and explore the rate region achieved by purely discrete inputs with treating interference as noise (TIN) decoding. Specifically, we introduce a simple scheme based on superposition coding with identically and independently distributed (i.i.d.) inputs drawn from discrete constellations, e.g., pulse amplitude modulations (PAM). Most importantly, we prove that the resulting achievable rate region under TIN decoding is within a constant gap to the capacity region of the GBC, where the gap is independent of all channel parameters. In addition, we show via simulation that the weak user can achieve a higher rate with PAM than with Gaussian signaling in some cases.

Using the short-wavelength instability method, we investigate the linear instability of an exact solution describing upward-propagating mountain waves, derived in A. Constantin, \emph{J. Phys. A: Math. Theor.} (2023), under the assumption of a dry adiabatic flow. Within this approach, the stability problem reduces to analysing a system of ordinary differential equations along fluid trajectories. Our results show that the flow becomes unstable when the wave steepness exceeds the critical threshold of $\frac{1}{3}$. Given the representation of the solution in Lagrangian coordinates, the instability analysis will show the existence of an unstable layer beneath the tropopause, where instability may occur, finally leading to a chaotic 3-dimensional fluid motion.

We present an observation of the Rossiter-McLaughlin effect for the TOI-1710 system with the NEID spectrograph on the WIYN 3.5 m telescope. The system hosts a warm Neptune ($P\sim24$ days), and our observations reveal that it orbits in the opposite direction to the stellar spin, with a sky-projected obliquity $λ=179\pm19^{\circ}$. Combined with information about the rotation period of the host star, we measure a true obliquity $ψ=158_{-13}^{+11}\,^{\circ}$. The host star has an M-dwarf companion at a separation of $\sim3600$ au, but this companion is too distant to be solely responsible for misaligning the warm Neptune. The host star also shows a long-term radial velocity trend, indicative of a companion at intermediate separations. We show that such a companion can dynamically couple the warm Neptune to the distant M dwarf, enabling the transfer of inclination from the wide binary orbit to the planetary orbit. Assuming this scenario is correct, we predict the intermediate companion is a $\sim5\,M_J$ planet on a $\sim15$ au orbit that is nearly aligned with the transiting planet's orbit.

Amplitude damping fundamentally limits qubit lifetimes by irreversibly leaking energy and information into the environment. Standard Wiseman--Milburn feedback offers only modest improvement because it acts on a single measured quadrature and its corrective drive is degraded by loop delay. We introduce a compact hybrid upgrade with two components: (i) a coherently coupled \emph{ancilla} qubit that receives the homodyne current and feeds back \emph{quantum-coherently} on the system, recovering information from \emph{both} field quadratures and intentionally engineered to decay much faster than the system; and (ii) a lightweight supervised predictor that forecasts the near-future homodyne current, phase-aligning the correction to overcome hardware latency. A Lindblad treatment yields closed-form effective decay rates: the ancilla suppresses the emission channel by a cooperativity factor, while the predictor further suppresses the residual decay in proportion to forecast quality. Using IBM-scale parameters (baseline \(T_1 = 50~μ\mathrm{s}\)), numerical simulations surpass the W--M limit, achieving \(\sim 3\!-\!4\times\) longer \(T_1\) together with improved population retention and integrated energy. The method is modular and hardware-compatible: ancilla coupling and supervised prediction can be added to existing W--M loops to convert leaked information into a precise, time-advanced corrective drive. We also include a detailed, student-friendly derivation of the effective rates for both ancilla-assisted and prediction-enhanced feedback, making the impact of each design element analytically transparent.

Automating C-to-Rust migration is critical for improving software security without sacrificing performance. Traditional rule-based methods struggle with diverse C idioms, often producing rigid and unidiomatic Rust code. Large Language Models (LLMs), trained on massive code corpora, offer a promising alternative by leveraging cross-language generalization to generate more idiomatic and maintainable Rust code. However, several challenges remain. First, existing LLM-based approaches fail to handle cross-file dependencies effectively, either ignoring them or including entire files as context, which limits accurate dependency modeling. Second, complex dependencies and structured inputs and outputs make it difficult to verify syntactic correctness and functional equivalence at the repository level. Third, the lack of large-scale C-Rust parallel data constrains model performance. We propose DepTrans, a framework that combines model capability enhancement with structured inference. DepTrans introduces Reinforcement-Aligned Syntax Training to improve generation quality through multi-task fine-tuning and feedback-driven reinforcement learning. It further applies Dependency-Guided Iterative Refinement to capture fine-grained cross-file dependencies and iteratively refine generated Rust code. We construct a dataset of 85k training samples and a benchmark of 145 repository-level instances. Experiments show that DepTrans achieves a 60.7 percent compilation success rate and 43.5 percent computational accuracy, outperforming the strongest baseline by 22.8 and 17.3 percentage points. It also successfully builds 7 of 15 industrial C projects, demonstrating its practical potential.

The interstellar scintillation observed in radio pulsars arises from interference between electromagnetic waves scattered by electron density fluctuations in the turbulent interstellar plasma, providing a critical tool for probing the small-scale structure of the ionized interstellar medium and the pulsar system itself. The primary aim of this work is to study long-term scintillation variations for a bright and nearby pulsar, PSR J0814$+$7429, carried out from 2013 September to 2023 September with the LOw-Frequency ARray (LOFAR) High Band Antennae in the frequency range of 120 - 170 MHz. We derive the basic scintillation parameters, scintillation bandwidth ($Δν_{\rm d}$) and scintillation timescale ($Δτ_{\rm d}$), from the two-dimensional (2D) auto-covariance function of the dynamic spectra that are a 2D matrix of pulse intensity as a function of time and frequency. We present the long-term monitoring of $Δν_{\rm d}$ and $Δτ_{\rm d}$ for PSR J0814$+7429$, which shows a strong annual variation in the time series of the $Δτ_{\rm d}$. From our modeling of the annual variations of scintillation velocities, the scattering screen is anisotropic and located at $0.23\pm0.02$ kpc from the Earth, likely corresponding to the boundary of the Local Bubble.

Radio relics are diffuse, extended synchrotron sources located at the outskirts of merging galaxy clusters. Their origin has been linked with shock waves injected into the intracluster medium, but the acceleration mechanism at the shock front is still under debate. Some clusters, like MACS J1752.0+4440, host a double relic system, with two relics found on opposite sides with respect to the cluster center. To investigate the acceleration mechanism that generates radio relics, we study the morphological and spectral properties of the double relic system in MACS J1752. We present new wideband radio continuum observations made with uGMRT and JVLA, and LOFAR data. We perform a detailed, high-resolution spectral analysis of the double relic system in MACS J1752, observing and characterizing substructures, particularly for the brighter relic. We find a double-peaked surface brightness and spectral index profile for the NE relic and identify a "bright bar" substructure. Moreover, we observed surprisingly flat integrated spectral indices for both relics, at $α_{\mathrm{int}}^{\mathrm{NE}} = -0.91 \pm 0.06$ and $α_{\mathrm{int}}^{\mathrm{SW}} = -0.83 \pm 0.05$. We study the spatial variation of the spectral index, observing a coherent trend with the observed substructures. We estimate an injection Mach number of $\mathcal{M}_{\mathrm{NE}} = 3.1^{+0.1}_{-0.1}$ and $\mathcal{M}_{\mathrm{SW}} = 3.2^{+0.1}_{-0.1}$. By performing a spectral curvature analysis for both relics, generating color-color plots and a spectral curvature maps, we observe two "concave" spectra represented by positive spectral curvature, in contrast with particle population ageing models. The observed properties of the NE relic are not consistent with a simple scenario with a single shock front. Multiple shock surfaces, re-acceleration, and projection effects likely play a role in shaping the morphology of the relic.

Non-Hermitian systems exhibit spectral and topological phenomena absent in Hermitian physics; however, their geometric characterization remains subtle due to the intrinsic ambiguity of biorthogonal eigenspaces. Since left and right eigenvectors are not related by Hermitian conjugation, the associated Berry connection is generally nonunique, leading to complex geometric phases and ambiguously defined holonomies. Here we formulate a covariant geometric framework for non-Hermitian quantum systems based on the metric structure of the underlying Hilbert space. We show that, in the quantum regime with continuous state evolution, the conventional Berry connection and the associated Berry holonomy over closed parameter-space loops can be consistently defined only in the pseudo-Hermitian limit, where the spectrum is real. For generic non-Hermitian Hamiltonians with complex spectra, the relevant geometric object is instead the Aharonov--Anandan holonomy associated with cyclic evolution in projective Hilbert space. Within the pseudo-Hermitian regime, we construct a unique Hermitian Berry connection that is covariant under arbitrary ${\rm GL}(N,\mathbb C)$ frame transformations and reduces to the standard Berry connection in the Hermitian limit. The resulting formalism separates the intrinsic geometry of the Hamiltonian eigenspace from contributions arising from the parameter dependence of the Hilbert-space metric, revealing that the conventional biorthogonal formulation generally mixes these distinct geometric effects. Consequently, geometric phases, synthetic gauge fields, and topological characteristics commonly attributed to non-Hermitian eigenspace geometry may, in part, originate from the underlying metric structure. Our framework therefore provides a consistent geometric foundation for Berry phases, non-Abelian holonomies, and topological invariants in non-Hermitian quantum systems.

Milky Way analogues (MWAs) are usually selected from structural and kinematic properties, but robust SED-based similarity criteria are limited by heterogeneous photometry and incomplete wavelength coverage. We present a homogeneous, aperture-photometry SED of the Milky Way near-twin NGC~3521 from the ultraviolet to the radio decameter range. Fluxes are measured within a fixed elliptical isophotal aperture using GALEX, SDSS, WISE, Spitzer/MIPS, Herschel/PACS+SPIRE, and VLA data, and supplemented by meter/decameter constraints. We report new observations obtained in Jan-Feb 2022 with the Ukrainian T-shape radio telescope and derive, for the first time, an upper limit in the 24--32~MHz band. The UV-to-decameter SED (27 points) is modelled with \textsc{CIGALE}, including a dedicated low-frequency radio prescription (\texttt{radio_extra}) that accounts for emission and absorption effects. Using ZTF and NEOWISE data (2014--2025), we detect genuine nuclear variability; optical trends at $\sim2^{\prime\prime}$ primarily trace the compact nucleus, while NEOWISE variability reflects a mix of nuclear changes and warm-dust emission within the larger aperture. The preferred fit yields $M_\star \simeq 6.0\times10^{10},M_\odot$, ${\rm SFR}\simeq1.65,M_\odot,{\rm yr}^{-1}$, $M_{\rm dust}\simeq1.3\times10^{8},M_\odot$, and an effective dust temperature of $\sim23$~K. The decameter constraint gives $S_{28,{\rm MHz}}<11.22$~Jy, consistent with expectations for a Milky Way-like system placed at 10.7~Mpc. We conclude that an integrated, homogeneous SED, especially below 100~MHz, provides a complementary diagnostic for identifying and validating MWAs and for interpreting how Milky Way properties would appear to an external observer.

We define a class of Bernstein-Szegő measures on $\mathbb{R}^2$ and we establish their spectral properties, providing a natural extension of the one-dimensional theory. We also derive conditions involving finitely many moments, which are new in the two-dimensional setting, and which completely characterize these measures. A key ingredient in the theory on the real line stems from the fact that a measure $μ$ on $\mathbb{R}$ determines a unique sequence of orthonormal polynomials which gives a simple formula for $dμ/dx $ in the Bernstein-Szegő family. Since there is no canonical way to introduce orthonormal polynomials in the plane, our extension is based on a new identity which connects a Fejér-Riesz factorization of the weight to a polynomial depending on three variables associated with $μ$. Using recent results in the bivariate trigonometric Fejér-Riesz factorization problem, we define a nontrivial two-dimensional extension of the Szegő mapping which provides explicit orthonormal bases of the spaces associated with Bernstein-Szegő measures on $\mathbb{R}^2$. An important part of the paper is devoted to a self-contained development of the Bernstein-Szegő theory for matrix-valued functionals. The proofs combine techniques from real analysis, complex analysis and algebra.

We report a triple black hole candidate with a close binary black hole (BBH) in the blue quasar SDSS J153231.80+420342.7 (=SDSS J1532) at a redshift of 0.209. It shows double-peaked profiles in all narrow emission lines, which can be a signature of a dual AGN. If the double-peaked features are produced by a dual AGN, the estimated physical separation between the two cores is about 3 kpc. Alternative interpretations to the double-peaked profiles involving rotating disk-like narrow line region (NLR) and AGN-driven outflow models are also discussed for the double-peaked features. Besides, SDSS J1532 shows optical quasi-periodic oscillations (QPO) of about 0.6 yr from the ZTF and CSS light curves, with time duration longer than 14 years, which may indicate a binary black hole with about 1 mpc separation. Two alternative explanations, the disk precession and the jet precession models, are also discussed. The current results cannot completely rule out alternative models for the characteristics of spectrum and light curves. As a candidate for triple black hole with two cores in kpc scale and a close BBH in milli-pc scale in SDSS J1532, it may be going through a critical period in its evolution.

Although Approximate Nearest Neighbor (ANN) search has been extensively studied, large-k ANN queries that aim to retrieve a large number of nearest neighbors remain underexplored, despite their numerous real-world applications. Existing ANN methods face significant performance degradation for such queries. In this work, we first investigate the reasons for the performance degradation of quantization-based ANN indexes: (1) the inefficiency of existing top-k collectors, which incurs significant overhead in candidate maintenance, and (2) the reduced pruning effectiveness of quantization methods, which leads to a costly re-ranking process. To address this, we propose a novel bucket-based result collector (BBC) to enhance the efficiency of existing quantization-based ANN indexes for large-k ANN queries. BBC introduces two key components: (1) a bucket-based result buffer that organizes candidates into buckets by their distances to the query. This design reduces ranking costs and improves cache efficiency, enabling high performance maintenance of a candidate superset and a lightweight final selection of top-k results. (2) two re-ranking algorithms tailored for different types of quantization methods, which accelerate their re-ranking process by reducing either the number of candidate objects to be re-ranked or cache misses. Extensive experiments on real-world datasets demonstrate that BBC accelerates existing quantization-based ANN methods by up to 3.8x at recall@k = 0.95 for large-k ANN queries.