It is well established that a general pair of twisted cubic curves in complex projective space has ten common secant lines. As an initial investigation, we show that the monodromy group of the ten common secant lines over the complex numbers is the full symmetric group demonstrating that the common secant lines have no special structure over the complex numbers. We then investigate a novel question in real algebraic geometry: describe the possible collections of ten common secant lines to a pair of real projective twisted cubic curves. In addition to distinguishing between real and nonreal secant lines, we introduce a refinement of this classification which takes intersection points into account yielding totally real, partially real, and minimally real secant lines. Using computational algebraic geometry as well as combinatorics, we show that for each $k$ between 0 and 10, there exist pairs of real twisted cubic curves with exactly $k$ common totally real secant lines. We also obtain examples of real twisted cubics whose sets of common real secants cover a wide range of possibilities within our admissible classification of common real secant lines.

We present high-resolution optical spectroscopy of interstellar comet 3I/ATLAS (C/2025 N1) obtained with the High Dispersion Spectrograph mounted on the Subaru Telescope on UT 2026 January 7, when the comet was on its outbound trajectory at a heliocentric distance of $r_{\mathrm{h}} = 2.87$ au. The spectra cover the forbidden atomic oxygen lines, [O~I], at 557.7, 630.0, and 636.4 nm. The [O~I] red-doublet intensity ratio $I_{630.0}/I_{636.4} = 2.91 \pm 0.21$ matches the optically thin branching ratio ($\sim$3; \citealt{StoreyZeippen2000}), indicating that optical-depth effects are small and that our relative flux calibration is reliable. We measure a green-to-red [O~I] intensity ratio of $G/R = I_{557.7}/(I_{630.0} + I_{636.4}) = 0.339 \pm 0.027$. This value is higher than those of most Solar System comets at similar heliocentric distances, but comparable to that of the interstellar comet 2I/Borisov. From the measured $G/R$ ratio in 3I/ATLAS, we estimate the CO$_2$/H$_2$O abundance ratio under the assumption that H$_2$O and CO$_2$ are the dominant parents of O($^1$S) and O($^1$D), with other oxygen-bearing species expected to have a smaller influence under typical conditions (e.g., \citealt{FestouFeldman1981}). The derived ratio is significantly lower than the extremely CO$_2$-rich composition reported from infrared observations on the inbound trajectory at $r_{\mathrm{h}} \sim 3.3$ au, yet higher than typical values measured for comets in the Solar System. Together with published pre- and post-perihelion measurements, our result indicates that the CO$_2$/H$_2$O ratio decreased substantially across perihelion.

The exploration of exotic hadrons provides a crucial testing ground for quantum chromodynamics in its non-perturbative regime. In this work, we perform a systematic study of the two-body strong decay properties of single-charm molecular pentaquarks in the $Y_c\bar{K}^{(*)}$ systems, where $Y_c = Λ_c$, $Σ_c$, $Ξ_c$, and $Ξ_c'$. Employing an effective Lagrangian approach combined with hadronic molecular wave functions derived from the one-boson-exchange model, we compute the decay widths and branching ratios for a series of predicted states with strangeness $|S| = 1$ and $|S| = 2$. Our calculations reveal distinctive decay patterns that serve as fingerprints for molecular identification. The total decay widths vary dramatically, from less than 1 MeV for the narrow $Σ_c\bar{K}$ $(I(J^P)=1/2(1/2^-))$ state to several tens of MeV for broader coupled-channel molecules like $Λ_c\bar{K}^*/Σ_c\bar{K}^*$. A key finding is the stability of the predicted branching ratios against variations in the binding energy. The decay dynamics are dominated by light meson (particularly pion) exchange, leading to a strong preference for final states containing a charmed baryon and a strange meson. Furthermore, coupled-channel effects and isospin-related interference play essential roles in both the formation and decay mechanisms of specific candidates. The results provide concrete, testable predictions for future experimental searches at facilities such as LHCb and Belle II.

Drawing on the theory of Minimal Model Program singularities for foliations, we define relative canonical and log-canonical singularities for algebraic stacks with finite generic stabilisers. We show that if a point has log-canonical singularities, its stabiliser group is a finite extension of an algebraic torus, thus, étale locally, the good moduli space exists. If the singularity is canonical, we further show that the locus of stable points is non-empty.

In pediatric chronic care, the triadic relationship among patients, caregivers, and healthcare providers introduces unique challenges for youth in managing their conditions. Diverging values, roles, and asymmetrical situational awareness across decision-maker groups often hinder collaboration and affect health outcomes, highlighting the need to support collaborative decision-making. We conducted co-design workshops with 6 youth with chronic kidney disease, 6 caregivers, and 7 healthcare providers to explore how digital technologies can be designed to support collaborative decision-making. Findings identify barriers across all levels of situational awareness, ranging from individual cognitive and emotional constraints, misaligned mental models, to relational conflicts regarding care goals. We propose design implications that support continuous decision-making practice, align mental models, balance caregiver support and youth autonomy development, and surface potential care challenges. This work advances the design of collaborative decision-making technologies that promote shared understanding and empower families in pediatric chronic care.

Hamilton-Jacobi (HJ) reachability provides formal safety guarantees for nonlinear systems. However, it becomes computationally intractable in high-dimensional settings, motivating learning-based approximations that may introduce unsafe errors or overly optimistic safe sets. In this work, we propose a hierarchical probabilistic verification framework for reachability learning that bridges offline global certification and online local refinement. We first construct a coarse safe set using scenario optimization, providing an efficient global probabilistic certificate. We then introduce an online local refinement module that expands the certified safe set near its boundary by solving a sequence of convex programs, recovering regions excluded by the global verification. This refinement reduces conservatism while focusing computation on critical regions of the state space. We provide probabilistic safety guarantees for both the global and locally refined sets. Integrated with a switching mechanism between a learned reachability policy and a model-based controller, the proposed framework improves success rates in goal-reaching tasks with safety constraints, as demonstrated in simulation experiments of two drones racing to a goal with complex safety constraints.

Grain boundary migration governs microstructural evolution in crystalline materials, directly influencing mechanical properties such as strength and thermal stability. Disconnections, which are line defects formed at grain boundaries in response to local curvature, have been identified as critical carriers of boundary migration. Here, we investigate the glide of unfaulted disconnections (UFDs) on a coherent twin boundary in aluminum at elevated temperatures using molecular dynamics simulations combined with the Nudged Elastic Band (NEB) method. Our results reveal a striking bifurcation in migration behavior depending on the disconnection core structure. UFDs with a pure edge Burgers vector migrate via a thermally activated double-kink mechanism, exhibiting a migration velocity that increases monotonically with temperature. In contrast, UFDs containing a screw dipole component possess an energy barrier approximately eight times lower, and their core structure undergoes a continuous transformation during glide, giving rise to stochastic, bidirectional motion with no systematic temperature dependence. These findings demonstrate that the disconnection core structure fundamentally dictates the migration mode and kinetics of twin boundaries, offering new mechanistic insights into disconnection-mediated grain boundary migration.

We present a search for neutrino counterparts to fast radio bursts (FRBs) using temporal and spatial cross-matching between the Second CHIME/FRB catalogue and the IceCube high-energy alert-track catalogue ICECAT1. Because current FRB--neutrino models do not provide a unique consensus on emission ordering, our primary significance test adopts a two-sided, order-agnostic temporal hypothesis. The analysis accounts for declination-dependent CHIME/FRB exposure and the look-elsewhere effect across multiple trials. No statistically significant FRB--neutrino association is found. The most significant pair is FRB\,20190630C--IC\,190629A, with a post-trial probability of $p=0.076$ ($1.43σ$), consistent with a chance coincidence. Within our statistical framework, a detectable physical association would require a time offset shorter than $\sim256$~s at $3σ$ or $\sim63$~ms at $5σ$. Using a population-level stacking analysis, we derive 90\% upper limits on the neutrino-to-radio luminosity ratio of FRBs, $ξ\lesssim 10^{8}-10^{11}$ for neutrino power-law spectral indices $γ=1.0-3.0$. These limits improve upon previous constraints by approximately two orders of magnitude and represent the most stringent bounds from FRB--neutrino coincidence searches to date. Although the current limits remain above the predictions of most magnetar-based models, they begin to constrain scenarios involving exceptionally efficient hadronic energy dissipation.

Task-agnostic model fingerprinting has recently gained increasing attention due to its ability to provide a universal framework applicable across diverse model architectures and tasks. The current state-of-the-art method, MetaV, ensures generalization by jointly training a set of fingerprints and a neural-network-based global verifier using two large and diverse model sets: one composed of pirated models (i.e., the protected model and its variants) and the other comprising independently trained models. However, publicly available models are scarce in many real-world domains, and constructing such model sets requires intensive training and massive computational resources, posing a significant barrier to deployment. Reducing the number of models can alleviate the overhead, but increases the risk of overfitting, a problem further exacerbated by MetaV's entangled design, in which all fingerprints and the global verifier are jointly trained. This overfitting issue compromises the generalization capability for verifying unseen models. In this paper, we propose LiteGuard, an efficient task-agnostic fingerprinting framework that attains enhanced generalization while significantly lowering computational cost. Specifically, LiteGuard introduces two key innovations: (i) a checkpoint-based model set augmentation strategy that enriches model diversity by leveraging intermediate model snapshots captured during training of each pirated and independently trained model, thereby alleviating the need to train a large number of such models, and (ii) a local verifier architecture that pairs each fingerprint with a lightweight local verifier, thereby reducing parameter entanglement and mitigating overfitting. Extensive experiments across five representative tasks show that LiteGuard consistently outperforms MetaV in both generalization performance and computational efficiency.

Understanding near-threshold strong interactions is essential for disentangling hadronic molecules and compact multiquark states in heavy-flavor spectroscopy. In this context, the doubly charmed tetraquark candidate $T_{cc}(3875)^+$ serves as a critical benchmark because it lies very close to the $D^*$-$D$ thresholds. Motivated by the interaction ambiguity reported recently [\href{https://doi.org/10.1103/kd4s-9rzr}{Phys.Rev.D 113, L031505 (2026)}], we evaluate the $D^*$-$D$ scattering lengths and femtoscopic correlation functions for the molecular and molecule-compact admixture assignments of the $T_{cc}(3875)^+$. We show that, although these scenarios yield similar invariant-mass line shapes, their corresponding femtoscopic correlation functions differ markedly and remain clearly distinguishable for typical particle-emitting sources created at the LHC. Our results indicate that femtoscopy can serve as a sensitive and complementary probe of the near-threshold dynamics of $T_{cc}(3875)^+$, providing vital theoretical references for future LHC femtoscopy measurements.

This paper is concerned with the stability of standing waves for the mass-critical Hartree equation with a focusing perturbation by the variational method. The profile decomposition theory is employed to prove the attainability of the cross constrained variational problem, and then the comparison of two cross constrained variational problems is derived. The sharp criteria of blowup, the orbital stability, and strong instability of standing waves without any frequency constraint are obtained. This improves the cross constrained variational argument proposed by Zhang (2005).

We investigate the interplay of in-plane magnetic and transverse electric fields in AB-stacked bilayer graphene. In prior work, we demonstrated that this configuration induces an insulator-metal (IM) transition with large impact on the magnetic response, albeit requiring impractically large magnetic fields. Here, we extend the analysis by incorporating previously neglected trigonal warping effects through interlayer skew couplings. In a restricted region of momentum space (on the order of 1/100 of the original Brillouin zone) trigonal warping produces a fine splitting of Dirac cones leading to a compensated semimetallic state in the absence of external fields. Application of a transverse electric field above a small threshold ($V_c\sim 0.6$ meV) reinstates the insulating gap, but this gap can be closed by a relatively small in-plane magnetic field, leading to an IM transition at a much smaller magnetic field ($\approx 10$ T) than previously predicted.

High-fidelity social simulation is pivotal for addressing complex Web societal challenges, yet it demands agents capable of authentically replicating the dynamic spectrum of human interaction. Current LLM-based multi-agent frameworks, however, predominantly adhere to static interaction topologies, failing to capture the fluid oscillation between cooperative knowledge synthesis and competitive critical reasoning seen in real-world scenarios. This rigidity often leads to unrealistic ``groupthink'' or unproductive deadlocks, undermining the credibility of simulations for decision support. To bridge this gap, we propose \textit{BEACOF}, a \textit{belief-driven adaptive collaboration framework} inspired by Perfect Bayesian Equilibrium (PBE). By modeling social interaction as a dynamic game of incomplete information, BEACOF rigorously addresses the circular dependency between collaboration type selection and capability estimation. Agents iteratively refine probabilistic beliefs about peer capabilities and autonomously modulate their collaboration strategy, thereby ensuring sequentially rational decisions under uncertainty. Validated across adversarial (judicial), open-ended (social) and mixed (medical) scenarios, BEACOF prevents coordination failures and fosters robust convergence toward high-quality solutions, demonstrating superior potential for reliable social simulation. Source codes and datasets are publicly released at: https://github.com/WUT-IDEA/BEACOF.

In this paper, we study how different Reddit communities discuss generative AI in high school education, focusing on learning, academic integrity, AI detection, and emotional framing. Using 3,789 posts from five education-related subreddits, we compare student, teacher, and mixed communities using a pipeline that combines keyword retrieval, human-validated relevance filtering, LLM-assisted annotation, and statistical tests of group differences. We find that stakeholder position strongly shapes discourse: teachers are more likely to articulate explicit pedagogical trade-offs, simultaneously framing AI as both beneficial and harmful for learning, whereas students more often discuss AI tactically in relation to accusations, grades, and enforcement. Across all groups, detector-related discourse is associated with significantly higher negative emotion, with larger effects for students and mixed communities than for teachers. These results suggest that AI detectors function not only as contested technical tools but also as governance mechanisms that impose asymmetric emotional burdens on those subject to institutional enforcement. Finally, we argue that detection-based enforcement should not serve as a primary academic-integrity strategy and that process-based assessment offers a fairer alternative for verifying authorship in AI-mediated classrooms.

Connected and automated vehicles require city-scale coordination under strict latency and reliability constraints. However, many existing approaches optimize communication and mobility separately, which can degrade performance during network outages and under compute contention. This paper presents QIVNOM, a quantum-inspired framework that jointly optimizes vehicle-to-vehicle (V2V) and vehicle-to-infrastructure (V2I) communication together with urban traffic control on classical edge--cloud hardware, without requiring a quantum processor. QIVNOM encodes candidate routing--signal plans as probabilistic superpositions and updates them using sphere-projected gradients with annealed sampling to minimize a regularized objective. An entanglement-style regularizer couples networking and mobility decisions, while Tchebycheff multi-objective scalarization with feasibility projection enforces constraints on latency and reliability. The proposed framework is evaluated in METR-LA--calibrated SUMO--OMNeT++/Veins simulations over a $5\times5$~km urban map with IEEE 802.11p and 5G NR sidelink. Results show that QIVNOM reduces mean end-to-end latency to 57.3~ms, approximately $20\%$ lower than the best baseline. Under incident conditions, latency decreases from 79~ms to 62~ms ($-21.5\%$), while under roadside unit (RSU) outages, it decreases from 86~ms to 67~ms ($-22.1\%$). Packet delivery reaches $96.7\%$ (an improvement of $+2.3$ percentage points), and reliability remains $96.7\%$ overall, including $96.8\%$ under RSU outages versus $94.1\%$ for the baseline. In corridor-closure scenarios, travel performance also improves, with average travel time reduced to 12.8~min and congestion lowered to $33\%$, compared with 14.5~min and $37\%$ for the baseline.

In heavy-ion collisions, an excess in photon production, together with a larger than expected positive elliptic flow, has been observed, a phenomenon commonly referred to as the direct photon puzzle. In this work we study the mechanism of photon production arising from gluon splitting and fusion during the pre-equilibrium stage in the presence of magnetic fields in peripheral heavy-ion collisions. We begin by analyzing the general tensor structure of the two-gluon one-photon vertex, computing it at the one-loop level for magnetic fields of arbitrary strength without resorting to additional approximations. Using these expressions, we calculate the contribution of gluon fusion and splitting to the photon yield, revealing that splitting dominates over fusion at low photon energies. Our results are compared with experimental data from the PHENIX collaboration. Finally, we incorporate a longitudinal anisotropy into the initial gluon distribution and find that it does not significantly alter the photon yield compared to an isotropic distribution.

Traditional projection-based reduced-order modeling approximates the full-order model by projecting it onto a linear subspace. With a fast-decaying Kolmogorov $n$-width of the solution manifold, the resulting reduced-order model (ROM) can be an efficient and accurate emulator. However, for parametric partial differential equations with slowly decaying Kolmogorov $n$-width, the dimension of the linear subspace required for a reasonable accuracy becomes very large, which undermines computational efficiency. To address this limitation, quadratic manifold methods have recently been proposed. These data-driven methods first identify a quadratic mapping by minimizing the linear projection error over a large set of snapshots, often with the aid of regularization techniques to solve the associated minimization problem, and then use this mapping to construct ROMs. In this paper, we propose and test a novel enhancement to this quadratic manifold approach by introducing a first-of-its-kind double-greedy algorithm on the regularization parameters coupled with a standard greedy algorithm on the physical parameter. Our approach balances the trade-off between the accuracy of the quadratic mapping and the stability of the resulting nonlinear ROM, leading to a highly efficient and data-sparse algorithm. Numerical experiments conducted on equations such as linear transport, acoustic wave, advection-diffusion, and Burgers' demonstrate the accuracy, efficiency, and stability of the proposed algorithm.

For extremely large-scale arrays (XL-arrays), the discrete Fourier transform (DFT) codebook, conventionally used in the far-field, has recently been employed for near-field beam training. However, most existing methods rely on the line-of-sight (LoS) dominant channel assumption, which may suffer degraded communication performance when applied to the general multi-path scenario due to the more complex received signal power pattern at the user. To address this issue, we propose in this paper a new hybrid learning-and-optimization-based beam training method that first leverages deep learning (DL) to obtain coarse channel parameter estimates, and then refines them via a model-based optimization algorithm, hence achieving high-accuracy estimation with low computational complexity. Specifically, in the first stage, a tailored U-Net architecture is developed to learn the non-linear mapping from the received power pattern to coarse estimates of the angles and ranges of multi-path components. In particular, the inherent permutation ambiguity in multi-path parameter matching is effectively resolved by a permutation invariant training (PIT) strategy, while the unknown number of paths is estimated based on defined path existence logits. In the second stage, we further propose an efficient particle swarm optimization method to refine the angular and range parameters within a confined search region; in the meanwhile, a Gerchberg-Saxton algorithm is used to retrieve multi-path channel gains from the received power pattern. Last, numerical results demonstrate that the proposed hybrid design significantly outperforms various benchmarks in terms of parameter estimation accuracy and achievable rate, yet with low computational complexity.

Modern deep recommender models are trained under a continual learning paradigm, relying on massive and continuously growing streaming behavioral logs. In large-scale platforms, retraining models on full historical data for architecture comparison or iteration is prohibitively expensive, severely slowing down model development. This challenge calls for data-efficient approaches that can faithfully approximate full-data training behavior without repeatedly processing the entire evolving data stream. We formulate this problem as \emph{streaming dataset distillation for recommender systems} and propose \textbf{DIET}, a unified framework that maintains a compact distilled dataset which evolves alongside streaming data while preserving training-critical signals. Unlike existing dataset distillation methods that construct a static distilled set, DIET models distilled data as an evolving training memory and updates it in a stage-wise manner to remain aligned with long-term training dynamics. DIET enables effective continual distillation through principled initialization from influential samples and selective updates guided by influence-aware memory addressing within a bi-level optimization framework. Experiments on large-scale recommendation benchmarks demonstrate that DIET compresses training data to as little as \textbf{1-2\%} of the original size while preserving performance trends consistent with full-data training, reducing model iteration cost by up to \textbf{60$\times$}. Moreover, the distilled datasets produced by DIET generalize well across different model architectures, highlighting streaming dataset distillation as a scalable and reusable data foundation for recommender system development.

Closed-loop shallow geothermal systems are one of the key technologies for decarbonizing the residential heating and cooling sector. The primary type of these systems involves vertical borehole heat exchangers (BHEs). During the planning phase, it is essential to find the optimal design for these systems, including the depth and spatial arrangement of the BHEs. In this work, we have developed a novel approach to find the optimal design of BHE fields, taking into account constraints such as temperature limits of the heat carrier fluid. These limits correspond to the regulatory practices applied during the planning phase. The approach uses a finite line source model to simulate temperature changes in the ground in combination with an analytical model of heat transport within the boreholes. Our approach is demonstrated using realistic scenarios and is expected to improve current practice in the planning and design of BHE systems.

Okounkov [36] proved a remarkable formula relating $n$-point GUE (Gaussian unitary ensemble) correlators of a fixed genus to Witten's intersection numbers of the same genus. The partition function of GUE correlators is a tau-function for the Toda lattice hierarchy. In this note, based on the knowledge of these two statements we give a new proof of the Witten--Kontsevich theorem, that relates Witten's intersection numbers to the KdV (Korteweg--de Vries) integrable hierarchy.

In this paper, we investigate the performance of a fluid antenna relay (FAR)-assisted downlink communication system utilizing non-orthogonal multiple access (NOMA). The FAR, which integrates a fluid antenna system (FAS), is equipped on an autonomous aerial vehicle (AAV), and introduces extra degrees of freedom to improve the performance of the system. The transmission is divided into a first phase from the base station (BS) to the users and the FAR, and a second phase where the FAR forwards the signal using amplify-and-forward (AF) or decode-and-forward (DF) relaying to reduce the outage probability (OP) for the user maintaining weaker channel conditions. To analyze the OP performance of the weak user, Copula theory and the Gaussian copula function are employed to model the statistical distribution of the FAS channels. Analytical expressions for weak user's OP are derived for both the AF and the DF schemes. Simulation results validate the effectiveness of the proposed scheme, showing that it consistently outperforms benchmark schemes without the FAR. In addition, numerical simulations also demonstrate the values of the relaying scheme selection parameter under different FAR positions and communication outage thresholds.

This paper studies the convexity properties of nonsmooth extended-real-valued weakly convex functions, a class of functions that is central to modern optimization and its applications. We establish new characterizations of convexity using second-order generalized derivative tools, including subgradient graphical derivatives, second subderivatives, and second-order subdifferentials. These tools allow us to derive necessary and sufficient conditions for convexity in the nonsmooth framework.

Fermionic linear optics (FLO) with Gaussian resources is efficiently classically simulable. We show that this is no longer the case for such quantum circuits for fermions with internal degrees of freedom, equipped with mid-circuit number monitoring and classical feedforward. In our architecture, the measurement record routes the selected blocks into a fixed-order Bell-fusion pairing geometry. On the level of classical description, this implies realizing a situation in which the permutation sum no longer collapses to a single determinant or Pfaffian. Each post-selected branch expands as a signed sum of path-ordered products of typically non-commuting dressed blocks, and branch amplitudes are matrix elements of the resulting non-commutative trace polynomials. Numerically, we observe Porter-Thomas statistics as the output distribution and a rapid growth of the minimal order-respecting matrix product operator bond dimension. These results thus establish mid-circuit measurement-induced non-commutativity as a route to sampling hardness for noninteracting fermions under reasonable complexity assumptions, without introducing coherent two-body interactions into the FLO evolution.

Model correction is essential for reliable PDE learning when the governing physics is misspecified due to simplified assumptions or limited observations. In the machine learning literature, existing correction methods typically operate in parameter space, where uncertainty is often quantified via sampling or ensemble-based methods, which can be prohibitive and motivates more efficient representation-level alternatives. To this end, we develop a latent-space model-correction framework by extending our previously proposed LVM-GP solver, which couples latent-variable model with Gaussian processes (GPs) for uncertainty-aware PDE learning. Our architecture employs a shared confidence-aware encoder and two probabilistic decoders, with the solution decoder predicting the solution distribution and the correction decoder inferring a discrepancy term to compensate for model-form errors. The encoder constructs a stochastic latent representation by balancing deterministic features with a GP prior through a learnable confidence function. Conditioned on this shared latent representation, the two decoders jointly quantify uncertainty in both the solution and the correction under soft physics constraints with noisy data. An auxiliary latent-space regularization is introduced to control the learned representation and enhance robustness. This design enables joint uncertainty quantification of both the solution and the correction within a single training procedure, without parameter sampling or repeated retraining. Numerical experiments show accuracy comparable to Ensemble PINNs and B-PINNs, with improved computational efficiency and robustness to misspecified physics.

This study investigates the X-ray characteristics of jet-associated radio-quiet AGNs across distinct optical/UV to X-ray correlation phases. Quasi-simultaneous optical/UV/X-ray observations of NGC 4051 from May-June 2009, obtained through Swift and XMM-Newton, reveal a temporal dichotomy: a strong optical/UV to X-ray correlation dominates the initial observation phase (before May 27), followed by an optical/UV flare event concurrent with X-ray flux suppression in the latter period. Our multi-method analysis of XMM-Newton data, incorporating short-term X-ray variability assessment, spectral decomposition, and RGS spectral analysis, identifies significant inter-phase X-ray emission disparities. During optical/UV flaring episodes, compared to the correlated phase, we observe: attenuated short-term X-ray variability amplitudes, enhanced soft X-ray absorption, suppressed intrinsic hard X-ray flux, and more prominent RGS emission-line features. Notably, these X-ray characteristics during optical/UV flaring intervals show no statistically significant deviations from pre-flare low-state X-ray emission patterns. These non-synchronous optical/UV-X-ray variations contradict predictions from both reprocessing models, starburst-driven emission scenarios, and the simplistic absorption models. While potential jet-related mechanisms remain ambiguous, our findings demonstrate strong consistency with predictions from the inhomogeneous accretion disk perturbation framework.

The traditional definition of the circumstellar habitable zone (HZ) focuses on liquid water, but neglects the crucial role of ultraviolet (UV) radiation in prebiotic chemistry. Low-mass stars typically emit insufficient UV radiation for photochemistry throughout the liquid water HZs during quiescent states. However, frequent flares can provide substantial UV fluxes, potentially fostering habitable conditions. We refine the concept of a UV habitable zone (UV-HZ) by incorporating a temperature-dependent model for RNA precursor synthesis. Furthermore, we explore a parameterized spectral energy distribution model and adopt an empirical flare frequency distribution for flares on different stars to quantify their UV contribution. Applying this framework to different flaring stars, we find the UV-HZ around low-mass stars can extend to inner regions, and overlap with the traditional HZ in wide ranges. Apply the analysis to 9 planets around Kepler flaring stars, three planets are located within both the refined UV-HZ and liquid water habitable zone (LW-HZ) without causing ozone depletion. Our findings highlight the significant role of flares in expanding the potential for life around low-mass stars, offering a revised perspective on exoplanet habitability criteria.

We compute the one-loop contribution to the semiclassical partition function of near-extremal, asymptotically AdS black holes in five-dimensional Einstein-Gauss-Bonnet gravity. In the absence of an exact analytic rotating solution at finite Gauss-Bonnet coupling $α$, we restrict to static, charged configurations and evaluate the contribution to $Z_{\text{1-loop}}$ arising from tensor, vector, and $U(1)$ gauge fluctuations. The analysis is based on the spectrum of a generalized Lichnerowicz operator governing linearized perturbations on the near-horizon geometry of the extremal solution, including its deformation by the coupling $α$. In the canonical ensemble, the low-temperature behavior of the one-loop partition function leads to logarithmic corrections to the entropy of the form $\log(T/T_0)$, where the scale $T_0$ depends on both the fluctuation sector and the Gauss-Bonnet coupling. These corrections are controlled by the structure of zero modes of the deformed operator and their splitting at small but finite temperature. Our explicit computation yields a universal low-temperature scaling $Z_{\text{1-loop}}\sim 5 \log T$, where the coefficient arises from the combined contributions of tensor, vector, and $U(1)$ gauge modes, reflecting the corresponding counting of zero modes in each sector.

We study the perfectoid pure threshold with respect to $p$, an invariant of singularities in mixed characteristic $(0,p)$ arising from perfectoid purity. In this paper, we compute perfectoid pure thresholds for lifts of rational double points. We show that the set of such thresholds is contained in $\mathbb{Q}$ and satisfies the ascending chain condition. In characteristic $2$, all reciprocals of positive integers occur, and $0$ is the unique accumulation point.

Microalgae are an abundant bioorganic material source and play a significant role in life on Earth by conducting photosynthesis for carbon dioxide (CO2) capture and its conversion to oxygen (O2). In this study, a combination of microalgae as a negative-CO2-emitting sacrificial agent with the traditional photocatalytic water-splitting process using brookite TiO2, as a model photocatalyst, is introduced as a new strategy to maximize green hydrogen (H2) production while converting microalgae to valuable products, like methane (CH4) and carbon monoxide (CO). The process, under optimal conditions, produces up to 0.990 mmol/g.h of H2 without cocatalyst addition and 3.200 mmol/g.h with platinum (Pt) cocatalyst, which is 13 times higher than the production rate without microalgae. The strategy of using microalgae in photocatalysis has high potential in green H2 production, as it not only eliminates valuable hole sacrificial agents, like alcohol, but also produces other useful compounds, like CH4 and CO. Moreover, this sustainable process contributes to CO2 capture and conversion during microalgae cultivation.