We study energy minimizers of the Ginzburg-Landau (GL) free energy, a fundamental model of superconductivity. We address the high-$κ$ regime, the regime of a large GL parameter, in which energy minimizers exhibit vortex structures whose finite element approximations require a fine mesh resolution. This difficulty is reflected in the error analysis of discrete minimizers, which relies on a second-order optimality condition. The spectrum of the energy's second Fréchet derivative must be bounded away from zero up to symmetry. In practice, the associated spectral gap decreases rapidly with the GL parameter. This degrades the quality of the approximations because the GL parameter directly enters as an additional factor in the error estimates. Although a polynomial dependence of the spectral gap on the GL parameter has been conjectured, its precise behavior remains unclear. As a first step toward addressing this issue, we compute the spectral gap based on a finite element approximation for a range of GL parameters, providing numerical evidence for the conjectured polynomial dependence.

We study PRODSAT-QSAT($k$): given rank-one $k$-local projectors, determine whether a quantum $k$-SAT instance admits a satisfying product state. We present a CDCL-style refutation framework that searches a finite partition of each qubit's Bloch sphere while a sound theory solver checks region feasibility using a geometric overapproximation of the projection amplitudes for each constraint. When the theory solver proves that no state in a region can satisfy a constraint, it produces a sound conflict clause that blocks that region; accumulated blocking clauses can yield a global result of product-state unsatisfiability (UN-PRODSAT). We formalise the problem, prove the soundness of the clause-learning rule, and describe a practical algorithm and implementation.

In the last decade research of quantum nonlocality has moved beyond the regime of standard Bell nonlocality to consider network-based experimental set-ups involving multiple independent sources. Notion of full network nonlocality has emerged as some truly network phenomena that cannot be realized in traditional Bell experiments. Present work manifests utility of such form of truly network non-classicality in designing a four partite network-based entanglement assisted quantum key distribution protocol. To be more precise, security of the protocol relies upon full network nonlocality detection via violation of some suitable trilocal inequality. Based on the quantum bit error rate and violation of trilocal inequality, arbitrary two qubit entangled states are characterized in accordance with their utility in successfully executing the protocol. Intuitively, owing to connected structure of entangled sources, any genuine form of network nonlocality may offer advantage over standard Bell nonlocality for designing secure key distribution protocols. To establish that as a fact, another QKD protocol relying upon Bell-CHSH nonlocality detection in all pairs of sender and a receiver party is designed. The former turns out to be more secure compared to the latter. Importantly, while the quantum bit error rate can be less than 14.6% exploiting Bell-CHSH nonlocality, it can be reduced below 13.7% by exploiting full network nonlocality.

Accurately estimating expectation values of quantum observables with as few measurements as possible is crucial to many quantum computing applications. We introduce a framework that covers many of existing measurement strategies and introduce heuristics that can be used to enhance randomized schemes, including those based on Pauli grouping with inverse probability weighting and variants of the classical shadow algorithm. We show how to maximize information gain from such schemes, while carefully optimizing the distribution of possible measurements, and show that simple grouping algorithms can get close to, and in some cases exceed, state-of-the-art accuracy for unbiased estimation of expectation values on a standard quantum chemistry benchmark. We show how these randomized methods may be compared to more recent measurement schemes, such as shadow grouping, derandomized shadow, and overlapped grouping measurement, we show how the same strategies can be used to augment these schemes, and we demonstrate that we can reduce measurement costs by up to a factor of two by allowing Clifford measurement circuits for otherwise Clifford-less methods.

We develop a predictor-feedback control design for a class of linear systems with state-dependent switching. The main ingredient of our design is a novel construction of an exact predictor state. Such a construction is possible as for a given, state-dependent switching rule, an implementable formula for the predictor state can be derived in a way analogous to the case of nonlinear systems with input delay. We establish uniform exponential stability of the corresponding closed-loop system via a novel construction of multiple Lyapunov functionals, relying on a backstepping transformation that we introduce. We validate our design in simulation considering a switching rule motivated by communication networks.

Designing clinical trials requires evaluating multiple operating characteristics (OCs), such as the likelihood of an early stopping decision, the probability of detecting a treatment effect, and the Type I error rate. In most cases, these evaluations are based on computationally intensive Monte Carlo simulations. As the complexity of clinical trials and the use of adaptive designs increase, the computational burden can quickly become prohibitive. We introduce a strategy for rapidly approximating OCs, called the Q-approximation. Our approach is based on quadratic approximations of the log-likelihood and asymptotic arguments. The Q-approximation approach can be applied to any trial design that uses data analysis methods coherent with the likelihood principle, including multistage designs with early stopping, adaptively randomized designs, and designs that leverage external data. We illustrate the approach with several examples and show that it provides an accurate approximation of important OCs while reducing the computation time compared to Monte Carlo simulations. In particular, in our experiments, the standard Monte Carlo approximation of OCs requires 150 to 1,900 times greater computing budget than Q-approximations to achieve comparable levels of accuracy.

I analyze the nonlinear Hamiltonian equations of motion for a one-dimensional chain of transverse magnetic nano-islands, seeking solutions for different types of static domain-walls (DWs) connecting uniform static states. The system of elongated magnetic islands oriented transverse ($y$-direction) to the chain direction ($x$-direction) experiences an applied magnetic field transverse to the chain. The macro-spin model includes dipole interactions between islands, their uniaxial and easy-plane anisotropies, and Oersted energy of the applied field. DWs can form most easily between pairs of degenerate uniform states, described by their local magnetizations as oblique, $y$-parallel, and $y$-alternating. The DWs between oblique states are well-described with scalar $φ^4$ theory. General DW structures are found via a numerical energy relaxation scheme. At some anisotropy and field parameters, nearest-neighbor dipole interactions drive antiferromagnetic order inside the DW itself. The variety of DWs present in the model might be exploited for their sensitivity to parameter changes in detectors or switching technology.

Recently, the U.S. Food and Drug Administration (FDA) released draft guidance \citep{FDA2026} signaling a paradigm shift that facilitates the use of Bayesian methodology as the primary analysis and decision framework for drug approval. The cornerstone and fundamental challenge of this framework is the specification and calibration of Bayesian success criteria to control decision errors, ensuring reliable clinical and regulatory outcomes. In this work, we systematically investigate various Bayesian decision-error metrics, their theoretical interrelationships, and their alignment with conventional Frequentist counterparts. This investigation provides critical theoretical insights and practical guidance on calibrating Bayesian success criteria and operating characteristics to ensure robust decision-making and the integrity of public health decisions. We illustrate this framework using a clinical trial evaluating revascularization strategies for cardiogenic shock. A Shiny application will be available at www.trialdesign.org to assist sponsors and regulators in evaluating calibration strategies consistent with recent regulatory perspectives.

This paper introduces a unified analytical and optimization framework for fluid antenna system-active reconfigurable intelligent surface (FAS-ARIS) communications in 6G. By combining the port reconfigurability of FAS with the signal amplification of ARIS, the proposed design enables more flexible control of the propagation environment and enhanced link reliability beyond what passive solutions can offer. We first derive the optimal ARIS amplification gain under a reflection power constraint to maximize the user's signal-to-noise ratio (SNR). Using a block-diagonal matrix approximation, we obtain a tractable outage expression and a tight independent-antenna equivalent upper-bound. Building on this, we establish the monotonic relationship between outage and effective channel gain, which enables a closed-form solution for ARIS phase optimization under limited channel state information (CSI). To further improve spectral efficiency, we propose a region-partitioned throughput optimization framework that achieves near-optimal performance without exhaustive search, thereby verifying its low computational complexity. Extensive simulations confirm the accuracy of the analysis and demonstrate consistent gains in outage and throughput compared to baselines.

We analyze the soft committee machine with Rectified Linear Unit (ReLU) activation by means of the replica method. In a realizable teacher--student setting, we compute the quenched free energy within a replica-symmetric ansatz and obtain the typical generalization behavior from the saddle-point equations for the macroscopic order parameters. The system exhibits a transition from an unspecialized symmetric phase to a specialized phase in which the permutation symmetry among hidden units is broken. We determine the critical training-set size as a function of the inverse training temperature and derive analytic expressions both near the transition and in the asymptotic large-sample regime. Unlike the corresponding model with sigmoidal activations, which undergoes a first-order transition, the ReLU soft committee machine shows a continuous specialization transition. These results show that the activation function plays a decisive role in the phase structure and generalization behavior of multilayer networks.

Mechanisms that dynamically relax the vacuum energy offer a concrete way to approach the cosmological constant problem, but because relaxation is not confined to the vacuum energy alone it can have consequences for the rest of low-energy physics. We explore this issue using the recently proposed 'yoga' relaxation models as an explicit framework and show how relaxation differentially suppresses 'slow' physics relative to a characteristic timescale set by the mass of the relaxon. It therefore need not alter e.g. Higgs & collider physics but can dramatically change how light scalar fields participate in cosmology. We revisit the QCD axion in this setting and show that the suppression of the axion's vacuum potential reshapes its behaviour on cosmological timescales while leaving fast, high-energy processes unaffected. The result is to alter the axion mass-coupling relation away from the standard QCD band, driving it into a regime already ruled out by observational constraints. In particular, suppression of the vacuum axion potential allows the QCD matter-induced potential to dominate even for matter densities relevant to cosmology and everyday matter, potentially driving the axion away from the CP-conserving minimum for QCD-motivated parameters. We conclude that conventional QCD axions are unlikely to remain viable in their standard form within vacuum-energy relaxation frameworks.

We present the first spatially resolved characterisation of the cool intragroup medium (IGrM) in a spectroscopically confirmed galaxy group at z=1.167. Using 30 independent sightlines towards the gravitationally lensed galaxy SGAS J0033+02, we combine background light from an extended gravitational arc and various sources in the field to map the distribution and kinematics of diffuse, metal-enriched gas pertaining to the group. We detect prominent MgII, FeII, CaII, and MgI absorption extending up to 62 kpc from a massive star-forming spiral galaxy and its interacting companion. Together with four other members, these form a compact group with a virial radius of 313 kpc. Down-the-barrel, blueshifted absorption indicates outflows. The distribution and two-dimensional kinematics of this gas suggest the influence of tidal stripping and star formation-driven winds. Intervening absorption across the field partly traces internal galaxy motions. A simple superposition of individual discs cannot reproduce the velocity field at large impact parameters or in counter-rotating regions, while a global IGrM halo with a rotational velocity of ~130 km/s provides a good match. Beyond individual galaxy envelopes, the data are consistent with a group-scale structure that co-rotates in concert with the galaxies. Assuming dynamical equilibrium, we estimate a total (cool+warm+hot) gas mass of 1.3-2.5x10^11 Msol, with large systematic uncertainties, corresponding to approximately 50% of all baryons, within one-quarter of the group's virial radius. These results point to a multiphase IGrM in which cool (~10^4 K) clouds are embedded within a dynamically coherent, group-wide halo. The gas appears gravitationally bound to the group rather than reaccreting onto individual galaxies.

In this work, we used numerical integration of the 4-body problem to study 3-body resonance chains (two planets and an asteroid in the innermost orbit) as a possible mechanism for white dwarf pollution. Two 3-body resonance chains were selected for study: the 6:3:2 and the 4:2:1. Asteroids in both a dynamically colder initial orbit in the 6:3:2 resonance and hotter initial orbits in both resonances were studied. An asteroid had up to a 1.08% chance of being delivered to the stellar Roche Limit of the white dwarf. This probability was strongly linearly correlated with the mass of the inner planet but was not correlated with the mass of the outer planet for both colder and hotter orbits. Average dynamical lifetimes ranged from 23 kyr to 1137 kyr for the dynamically colder orbit and from 12.9 kyr to 89.2 kyr and 10.8 kyr to 793.4 kyr for the dynamically hotter orbits in the 6:3:2 and 4:2:1 resonances, respectively. Average dynamical lifetime was exponentially anticorrelated with the outer planet mass and usually with the inner planet mass except in one case. The hotter 4:2:1 resonance delivered 1.1 times more asteroids to the stellar Roche Limit than the hotter 6:3:2 resonance. The hotter 6:3:2 resonance delivered 1.2 times more asteroids to the stellar Roche Limit than the colder 6:3:2 resonance. A typical accretion rate for a white dwarf star of 10^8 grams s^-1 could be explained by the accretion of an equivalent mass of one of our simulated asteroids every 13.8 Myr.

Automated program verifiers are often organized into a front-end, which encodes an input program into an intermediate verification language (IVL), and a back-end, which proves that the IVL program is correct. Soundness of such translational verifiers requires that the back-end verification is sound and that correctness of the IVL program implies correctness of the input program. Existing formalizations for translational verifiers based on separation logic target the former, but support the latter only under the strong assumption that there exists a separation logic for the input program with the same state model as the IVL. This assumption is unrealistic in practice, especially since the state model also defines the supported separation logic resources. We present the first formal framework for proving the soundness of translational separation logic verifiers with non-trivial state encodings. To be applicable to various front-ends and IVLs, our framework only assumes the existence of a homomorphic encoding relation between the front-end and IVL state models. At the core of our framework is a novel condition, backward satisfiability, which is crucial to guarantee the soundness of the front-end translation. We formalize our framework for front-end verifiers based on concurrent separation logic and separation logic IVLs, such as Raven, VeriFast, and Viper. We demonstrate its expressiveness by proving soundness for three common state encodings. Our framework and all proofs are formalized in Isabelle/HOL.

Dramatically increasing data volumes are forcing astronomers to adopt automated methods for the identification and classification of astronomical objects. Although deep-learning models are often well-suited to this task, obtaining a measure of uncertainty on their predictions is challenging. Here we consider the suitability of Monte Carlo conformal prediction (MCCP) set size and confidence as measures of model uncertainty for the astronomical classification of radio galaxies. We demonstrate this approach using model predictions from a pre-trained radio galaxy foundation model, fine-tuned on a smaller set of labelled radio galaxies. We calibrate the MCCP by obtaining annotator-derived soft label distributions, i.e. probability distributions over classes instead of single class assignments, for each of these labelled radio galaxies and compare the resulting set sizes and confidence scores to predictive entropy measures for each galaxy obtained using a supervised Bayesian deep-learning model trained using Hamiltonian Monte Carlo (HMC). The comparison reveals only a weak correlation between the measures.

This paper investigates the fundamental tradeoff between reconfigurable intelligent surfaces (RISs) and network-controlled repeaters (NCRs) in terms of achievable signal-to-noise ratio (SNR). Considering an uplink system with a multi-antenna base station (BS) and a single-antenna user equipment (UE), we derive closed-form SNR expressions for passive RIS-, active RIS-, and NCR-assisted communication under line-of-sight propagation between the BS-RIS/NCR and RIS/NCR-UE. Both narrowband and wideband transmissions are analyzed, with and without the presence of a direct BS--UE link. Our analysis reveals a key structural difference: while the SNR achieved with RISs grows unboundedly with the number of RIS elements, the SNR provided by an NCR is fundamentally limited by the UE--repeater channel due to noise amplification. Nevertheless, we show that NCRs can outperform both passive and active RISs when deployed close to the UE, provided that sufficient amplification is available. Numerical results based on realistic path loss models quantify the amplification levels required for NCRs to outperform RISs across different deployment geometries and system dimensions. These findings provide clear design guidelines for the practical integration of RISs and NCRs in future wireless networks.

We show exactness of the homotopy sequence for the logarithmic fundamental group in the case of log smooth, finitely presented, proper and saturated morphisms of fs log schemes over a field. This generalizes earlier results of Hoshi in the log regular case. In passing, we also construct a "log Stein factorization" in some particular cases.

Localized surface plasmon resonances are self-sustained, collective oscillations of free electrons in metallic nanostructures. They have a wide range of applications. The most common plasmonic metals are noble metals, such as gold and silver. However, there are applications, such as surface-enhanced Raman spectroscopy, in which using non-noble metals is advantageous. This review summarizes the investigation of localized surface plasmons in non-noble metal nanoparticles, providing an overview of the plasmonic properties of non-noble metals. We cover the following metals: aluminium (Al), antimony (Sb), bismuth (Bi), chromium (Cr), copper (Cu), gallium (Ga), indium (In), lead (Pb), magnesium (Mg), molybdenum (Mo), nickel (Ni), potassium (K), selenium (Se), sodium (Na), tellurium (Te), tin (Sn), titanium (Ti), tungsten (W), and zinc (Zn). Our summary therefore compares the plasmonic properties of non-noble metals and briefly introduces their potential to the readers.

Water and methanol are key components of interstellar ices and gas in star- and planet-forming regions, but direct observations of water in low-mass protostars are challenging due to atmospheric absorption. We present high-resolution (R = 70,500) mid-infrared spectroscopy of the Class I protostar SVS13-A with EXES on board SOFIA at 26 $μ$m, targeting both H$_2$O and CH$_3$OH absorption lines. Several lines of each species are detected, tracing warm gas with rotational temperatures of $\sim$140--170 K. Remarkably, the methanol column density is a factor of $\sim$4 higher than that of water, well above typical interstellar ice ratios ($<$10\%). Comparison with previous millimeter observations indicates that absorption and emission probe distinct regions, with the mid-IR lines likely tracing cooler gas along the line of sight. The surprising observed CH$_3$OH/H$_2$O ratio may reflect selective sublimation due to the distribution of binding energies or ice stratification in the inner envelope. These observations probe the inner regions of the protostar, where planets are expected to form and inherit the chemical composition of their natal environment, providing a direct link between ice sublimation and gas-phase chemistry. Our results represent the first high-spectral-resolution mid-infrared view of both water and methanol toward a low-mass protostar, offering a unique window into the chemical composition of the innermost envelope and planet-forming region, and highlighting the diagnostic power of high-resolution mid-infrared spectroscopy to uncover hidden chemical layers and the ice-to-gas transition in embedded protostars.

The robust statistical description of dynamical systems under perturbations is a central problem in ergodic theory. In this paper, we investigate the statistical properties of skew-product maps driven by a subshift of finite type with contracting fiber maps, a setting that naturally encompasses Iterated Function Systems (IFS) and Random Dynamical Systems (RDS). Diverging from the classical perturbative frameworks that rely on the compact embedding of anisotropic Banach spaces, we employ a flexible operator approach based on the Lipschitz regularity of the invariant measure's disintegrations with respect to the Wasserstein metric. Our main results are threefold: first, we prove the quantitative statistical stability of the unique invariant measure under admissible deterministic perturbations, obtaining an explicit modulus of continuity of the form $O(R(δ) \log δ)$. Second, we establish the exponential decay of correlations on new pair of spaces of observables. Finally, leveraging this exponential decay and Gordin's method, we prove the Central Limit Theorem for the fluctuations of Birkhoff averages of Lipschitz observables.

The SWUF-3D drone fleet is used in the atmospheric boundary layer (ABL) for in situ turbulence measurements of complex flows, such as in mountainous terrain or wind turbine wakes. Previous calibrations for measuring vertical wind speed $w$ using the drones' avionics data were performed on field data, limiting applicability to low winds ($\leq 8~\mathrm{m}\,\mathrm{s}^{-1}$) and being prone to high uncertainties. To overcome these limitations, we calibrate $w$ measurement in a wind tunnel and validate it in field measurements. Calibration is performed in a wind tunnel with an active grid used to deflect horizontal flow into the vertical. This wind is measured with a multi hole probe, while wind forces acting on the drone are determined from the avionics data, allowing an empirical relationship between these quantities. For validation, we conduct comparative fleet measurements with up to 10 drones simultaneously around an array of meteorological masts equipped with sonic anemometers. The results show high accuracy for turbulence statistics: the variance determination for $w$ has a root mean square error (RMSE) of 0.12~$\mathrm{m^2\,s^{-2}}$ and a normalized RMSE (nRMSE) of 17.0~\%, for the horizontal wind components the RMSEs are $\sim$0.3~$\mathrm{m^2\,s^{-2}}$ and nRMSEs $\sim$25~\%. The RMSEs for the covariances of the components are $<\,$0.3~$\mathrm{m^2\,s^{-2}}$. The variance spectra of $w$ measured with drones and reference sensors agree in all frequency ranges, the RMSE for covariances between different measurement points is $\sim$0.1~$\mathrm{m^2\,s^{-2}}$. Accurate $w$ retrieval at all wind speeds sustainable by the drone enables studies of strongly three-dimensional flows, supports eddy-covariance flux estimation, enables resolving diurnal turbulence evolution in the ABL, and improves spatial turbulence characterization.

This paper studies how platform design shapes strategic behavior in decentralized electricity trading. We develop a finite-horizon dynamic game in which photovoltaic- and battery-equipped players ("prosumers") trade on a platform that maps aggregate imports and exports into internal buy and sell prices. We establish existence of a perfect conditional epsilon-equilibrium and characterize a Cournot-like market-power mechanism in an observable-types benchmark of the game: because the producer price is decreasing in aggregate exports, strategic prosumers withhold supply and underutilize storage relative to the price-taking benchmark. To quantify these effects, we use a multi-agent computational framework that exploits the differentiable structure of the platform's clearing rule to compare planner, price-taking, and strategic outcomes under alternative pricing mechanisms. In our baseline calibration, strategic play raises grid settlement cost by about 6 percent relative to price-taking. The magnitude of the distortion depends strongly on platform design: some designs can largely eliminate strategic incentives, while increased competition in storage ownership sharply reduces withholding, with most of the distortion disappearing once storage is split across more than three owners. We also find that information disclosure can improve competitive coordination but also increase the market power effects. Despite these distortions, the platform remains highly valuable overall, reducing a passive consumer's annual electricity bill by roughly 40 percent relative to exclusive grid settlement, with strategic behavior clawing back only about 8 percent of that saving. The results show that pricing rules, information disclosure, and ownership structure determine how much of the gains from decentralized electricity trading are realized.

Estimating the number of migrants who die or go missing along dangerous routes such as the Central Mediterranean remains challenging as available records are incomplete. Some incidents are never documented, and fatalities associated with such unobserved incidents are absent from observed totals. We propose a Bayesian approach for probabilistic estimation of total migrant fatalities in such settings. Building on recent developments in multiple-systems estimation, we develop a time-stratified latent-class framework that accommodates missing fatality counts for unobserved incidents. We apply the method to recoded incident-level data from the Missing Migrants Project for the Central Mediterranean route from 2014 to 2025, encompassing 25,712 fatalities across 1,562 incidents. Our model yields 95% credible intervals of 30,426-39,172 fatalities and 2,200-2,591 deadly incidents, indicating that approximately 66%-85% of fatalities and 60%-71% of incidents are reflected in the available data. We estimate that unreported fatalities were concentrated between 2014 and 2016. Furthermore, we document that reporting likelihood increases with incident severity, implying that smaller incidents are most likely to remain undetected. While contingent on modeling assumptions and incomplete data, our method provides a broadly applicable and principled alternative to naive data adjustment methods.

Arbitrated quantum signature (AQS) schemes aim at ensuring the authenticity of a message with the help of an arbitrator. Moreover, they aim at preventing repudiation, both from a sender that denies the origin of a message, and from a receiver who disavows its reception. Such protocols use quantum communication and are often designed to protect quantum messages. In this paper, we study four recently submitted AQS schemes and propose attacks on their security. Firstly, we look at Zhang, Sun, Zhang and Jia's AQS scheme which aims at signing quantum messages with chained CNOT encryption. We show that the sender can repudiate her messages and make false allegation of reception. Moreover, we show that a dishonest receiver can forge signatures. Secondly, we analyse Ding, Xin, Yang and Sang's AQS protocol to sign classical messages based on GHZ states. We show that both the sender and the receiver have simple repudiation strategies. Thirdly, we study Lu, Li, Yu and Han's AQS scheme that uses controlled teleportation to protect quantum messages. We expose forgeries, false allegation attacks and the possibility of repudiation by both parties. Fourthly, we focus on the AQS scheme by Zhang, Xin, Sun, Li and Li designed to sign classical messages without entangled states. We show that one can disavow the reception of messages, and that information-theoretic security is not achieved for other security goals.

Model risk arises from the misspecification of probabilistic models used for pricing and hedging derivatives. While model risk for European-style claims has been widely studied, much less attention has been given to American-style derivatives and the associated optimal stopping problems. This paper analyzes model risk in the optimal exercise of an American put option using the benchmark methodology of Hull and Suo [2002]. The true data-generating process is assumed to follow a Heston stochastic volatility model. We compare the optimal exercise strategy of an investor who correctly uses the Heston model with those of investors who instead use misspecified Black--Scholes or Dupire local volatility models. Optimal exercise boundaries are computed numerically via finite difference methods. Stochastic volatility dynamics and return--volatility correlation are found to have a substantial impact on optimal exercise behavior across models, creating a source of model risk. As this behavior is not transmitted to exercise strategies determined by misspecified models, even if such models are fully calibrated to European option prices, calibration fails to mitigate model risk in this context. This issue persists under frequent recalibration of a misspecified model.

Observations of the binary system DX Cha (HD 104237) reveal a compact, asymmetric ring structure with a radius of 0.43\,au. This ring is just outside the binary orbit, which has semi-major axis $a_{\rm b} = 0.22$\,au and eccentricity $e_{\rm b} = 0.665$; placing the ring at $\approx 1.2$ times the binary apocenter distance. The inner regions of circumbinary disks, $\approx 2-3\,a_{\rm b}$, are typically evacuated by strong gravitational torques from the binary, resulting in a deep gap between the binary and the disk. Accordingly, previous numerical simulations of DX Cha have found an eccentric inner cavity with almost no material inside $\approx 1$\,au, and we find similar results when making the same assumption that the circumbinary disk orbits in the same direction as the binary. However, the disk can exist much closer to the binary if it is retrograde. For DX Cha we find that the inner edge of a retrograde disk occurs at $\approx 2a_{\rm b}$, and moreover takes the form of one or two arcs, in agreement with observations. We therefore suggest that the circumbinary disk in the DX Cha system could be orbiting retrograde to the binary star system in the center. We conclude that compact circumbinary disks observed in young stellar systems are important targets for future observations; if the disks are prograde then their properties are likely to be significantly different from current estimates, while if they are retrograde then this will have profound implications for our understanding of star and planet formation.

In arXiv:2508.14768, a variant of Goodstein's original process was recently introduced which, given a set $B\subseteq \mathbb{N}$ of bases, writes each $n\in\mathbb{N}$ in $B$-normal form, namely $n=b^ea+r$, where $b\in B$ the greatest base below $n$. The numbers $e$ and $r$ are then recursively written in $B$-normal form, and finally each base of $B$ is replaced by a corresponding base of some other set $C\subseteq \mathbb{N}$. The resulting process was shown to terminate and to be independent of $\mathsf{KP}$, but the proofs relied on two different ordinal assignments: one monotone but not tight enough to establish independence, and another suitable for independence but not monotone and thus ineffective for proving termination. We introduce a new ordinal assignment that simultaneously yields termination and independence, thereby revealing the `true' ordinals associated with the numbers in the process. This assignment allows us to investigate which restrictions to impose on the process in order for the proof-theoretic strength of its termination to lie between the systems $\mathsf{RCA}_0$, $\mathsf{ACA}_0$, $\mathsf{ATR}_0$ and $\mathsf{KP}$.

The Quantum Approximate Optimization Algorithm (QAOA) and its advanced variant, the Quantum Alternating Operator Ansatz (QAOA), are major research topics in the current era of Noisy Intermediate-Scale Quantum (NISQ) computing. However, the problem of initializing their parameters remains unresolved. Motivated by the combinatorial optimization task in the 6th MindSpore Quantum Computing Hackathon (2024), this paper proposes Stone-in-Waiting, a cloud-based accelerator for obtaining high-quality initial parameters for QAOA. Internally, the accelerator builds on state-of-the-art theories and methods for parameter determination and integrates four self-developed algorithms for QAOA parameter initialization, mainly based on Bayesian methods, nearest-neighbor methods, and metric learning. Compared with the Baseline Algorithm, the generated parameters improve the score by 40.19%. Externally, the accelerator offers both a web interface and an API, providing flexible and convenient access for users to test and develop related experiments and applications. This paper presents the design principles and methods of Stone-in-Waiting, demonstrates its functional characteristics, compares the strengths and weaknesses of the four proposed algorithms, and validates the overall system performance through experiments.

Active small bodies in extrasolar systems, the extrasolar analogues of Solar System comets, provide insights into the orbital evolution and physical processes shaping planetary systems. Since the discovery of exocomets around $β$ Pictoris, these small, icy bodies have shown the potential to become key probes for understanding planetary formation and migration. This review presents an overview of current observational techniques used to detect exocomets, focusing on individual systems and large-scale searches. We discuss photometric methods that identify exocomet transits through asymmetric light curves and spectroscopic techniques revealing cometary gases via time-variable absorption lines. Despite progress, significant open questions remain regarding the physical properties, occurrence rates, and similarities between exocomets and their Solar System counterparts. This review explores future opportunities in observational exocomet research, highlighting advancements required to further our understanding of these active small bodies and their role in the context of planetary system evolution.

Gaussian processes provide a flexible framework for spatial prediction, but their computational cost limits applicability to large-scale data with large sample size $n$. Predictive processes (PPs), a popular low-rank approximation, mitigate this burden by projecting the original process onto a reduced set of $m\ll n$ inducing points. However, existing theory requires $m$ to grow with $n$, creating a trade-off between accuracy and computational efficiency. We address this challenge by introducing an ensemble of PPs based on spatial partitioning, and propose a novel partitioning and patching scheme with desirable properties. By generalizing the convergence results of PPs, it becomes possible to explicitly balance scalability and accuracy: increasing the number of ensemble components slows down the convergence but substantially improves computational efficiency. We further show theoretically that, despite the limited approximation accuracy of PPs with fixed $m$, they are asymptotically robust to data contamination. Motivated by this insight, we finally introduce a multi-resolution ensemble that combines PPs with fixed $m$ with multiple ensembles defined over possibly overlapping coarse to fine partitions. Simulations and large-scale geostatistical applications demonstrate that our approach delivers accurate, robust predictions with computational gains, providing a practical and broadly applicable solution for spatial prediction.