This study investigates Chinese teachers' continuance intention to use generative artificial intelligence (AI) by integrating the Expectation-Confirmation Model with Institutional Theory. A sequential explanatory mixed-methods design was employed. Questionnaire data from 437 teachers were analysed using structural equation modelling, followed by semi-structured interviews with 15 teachers to further interpret the findings. The results indicate that confirmation, perceived usefulness, and satisfaction play important roles in shaping teachers' continuance intention, while institutional pressures, including coercive, normative, and mimetic influences, also contribute to continued use. Qualitative findings further reveal that teachers often use generative AI pragmatically to support tasks such as lesson preparation and idea generation, while simultaneously exercising caution and critically evaluating the reliability of AI-generated content. These findings highlight the combined influence of individual evaluations and institutional contexts on teachers' sustained engagement with generative AI in education.

We studied McMillan's free energy of the lock-in transition in charge-density waves. The wave profiles near the critical value were obtained by numerical annealing. First, we demonstrated that our method reproduces the previous studies. The obtained wave profiles include discommensurations near the critical value. Then, we calculated possible wave profiles in the commensurate state. We found that discommensurations are able to be excited in the commensurate state, leading the system to turn out to an incommensurate state. We proposed that these wave profiles result from topological invariants. Moreover, excitation of the discommensurations is favorable for the direction to the original wavelength of the incommensurate state. This is attributed to the nature of McMillan's free energy. The current-induced incommensurations, which we discovered with the diffraction study of $o$-TaS$_3$ [Inagaki \textit{et al.}, J. Phys. Soc. Jpn. 77, 093708 (2008)], is consistent with this study.

For quantum field theory on curved spacetimes, a critical role is played by their foliation into spacelike time-slices at each value $t$ of a coordinate time, with corresponding metric in ADM form. We provide a general construction for the spacetime quantum Levi-Civita connection when each spatial slice is replaced by a quantum Riemannian geometry. This is then fully solved for a class of spatial algebras including fuzzy spheres and for any time-dependent spatial quantum metric, shift 1-form and lapse function. The result takes a particularly simple form if the spatial metric evolves in time according to a first order ODE which, in the case of a fuzzy sphere, requires the spatial metric to rotate in time according to the value at each $t$ of the shift vector. As an application, our results provide in principle fuzzy versions of most (pseudo)-Riemannian manifolds. We also fully solve the case of rotationally invariant spacetimes with angular directions replaced by a discrete circle, including a new $\Bbb Z_n$-FLRW model.

In this paper, we characterize the existence of perfect state transfer (PST) and fractional revival in continuous-time quantum walks on the zero-divisor graph $Γ(\mathbb{Z}_n)$. By using the canonical equitable partition of $Γ(\mathbb{Z}_n)$ induced by the proper divisors of $n$, we derive a sufficient condition on $n$ for PST to occur between a pair of vertices. We show that fractional revival is restricted to cells of size $2$ within the equitable partition. Furthermore, assuming $-1$ is not an eigenvalue of the quotient spectrum, we establish that two vertices in $Γ(\mathbb{Z}_n)$ are strongly cospectral if and only if they form a cell of size $2$ within the equitable partition that is either a set of false twins or true twins. Finally, we provide a characterization of fractional revival on bipartite $Γ(\mathbb{Z}_n)$ and prove the non-existence of fractional revival on $Γ(\mathbb{Z}_{p^2q})$.

Given a polarised maximal degeneration of compact Calabi-Yau manifolds, assuming there exists a canonical basis of the section ring for the polarisation line bundle, satisfying the valuative independence condition, we will prove the metric SYZ conjecture.

In the article by Michael Chmutov, Max Glick and Pavel Pylyavskii \cite{Chmutov} the action of the cactus group $C_N$ on the set of semi-standard Young tableaux filled with the numbers from $1$ to $N$ was defined. Namely, they constructed the set of generators (we rightfully call them Bender-Knuth generators) of the cactus group and a group homomorphism from $C_N$ to Berenstein-Kirillov group $BK_N$ (cf. \cite{Berenstein_Kirillov}), which sends these generators to the Bender-Knuth involutions on the set of semi-standard Young tableaux. In \cite{Henriques_Kamnitzer} Andre Henriques and Joel Kamnitzer defined a natural action of cactus group $C_N$ on the tensor product of $N$ normal crystals via commutors. By applying their result I defined the action of cactus group $C_N$ on the set of short semi-standard Young tableaux filled with the numbers $1, 2, \ldots, N$ in \cite{Svyatnyy}. A semi-standard Young tableau is called \textit{short} if the number of cells in the first two columns with the numbers $\leqslant N$ is less than or equal to $N$. The set of short semi-standard Young tableaux obviously forms a subset inside the set of semi-standard Young tableaux. The purpose of this paper is to explicitly compute the action of Bender-Knuth generators of cactus group $C_N$ on the set of short semi-standard Young tableaux defined in \cite{Svyatnyy} and compare it with their action on the set of semi-standard Young tableaux defined in \cite{Chmutov}.

We summarise known algebraic and model theoretic results on the ring $\mathscr{A}$ of integers modulo infinitely large primes for number theorists, and share topics in transcendental number theory with algebraists and model theorists. In particular, we extend transcendence criteria by Anzawa--Funakura and Matsusaka--Seki in order to show application of non-standard analysis to the study of transcendence.

Purpose: As interest in CEST-MRI grows, particularly in the preclinical setting, the necessity for standardized and easy-to-use acquisition and data analysis pipelines has become apparent. While vendors have increasingly introduced support for CEST acquisitions on both clinical and preclinical hardware, image post-processing and analysis pipelines remain siloed based on privately developed code. We aim to develop an easy-to-use, open-source graphical user interface toolbox for preclinical CEST-MRI data analysis (Preclinical CEST-MRI Analysis Tool; Pre-CAT), supporting multiple acquisition types, organ systems, and CEST contrast mechanisms. Methods: Pre-CAT was developed in Python and utilizes the Numpy, Scipy, and Matplotlib libraries for data analysis and plotting. Inbuilt data processing steps include image loading, reconstruction, post-processing, and segmentation. Pre-CAT also supports data analysis for QUESP, CEST-MRF, and field mapping experiments using consensus protocols and methods. Pre-CAT's web interface and GUI were developed using Streamlit, an open-source Python framework. Pre-CAT is hosted and accessible online and can be downloaded for local installation to complete the data analysis pipeline in roughly one minute using modern hardware. Results: Pre-CAT analysis pipelines for Z-spectroscopy, CEST-MRF, and quantitative CEST (QUESP/QUEST) are demonstrated. Conclusion: With the introduction of Pre-CAT, we aim to standardize the preclinical CEST-MRI data analysis pipeline, fostering collaboration across research sites and reducing methodological redundancy. Pre-CAT is open-source and relatively modular, encouraging the addition of new methods and protocols.

The purpose of the current work is the development of an approach to account for quasi-static mechanical equilibrium in empirical (i.e., data-based) models for the stress field employing neural approximations (NAs), which include neural networks (NNs) and neural operators (NOs), in particular Fourier NOs (FNOs). Rather than including such constraints from physics in the loss function as done in the (now standard) physics-informed approach, the current approach incorporates or "encodes" such constraints directly into the architecture of the NA. As a result, both NA training and output are physically constrained in the physics-encoded approach, in contrast to the physics-informed approach, in which only training is physically constrained. For the current constraint of divergence-free stress, a novel encoding approach based on a stress potential is proposed. As a "proof-of-concept" example application of the current approach, a physics-encoded FNO (PeFNO) is developed for a heterogeneous polycrystalline material consisting of isotropic elastic grains and subject to uniaxial extension. Stress field data for this purpose are obtained from the numerical solution of corresponding boundary-value problems for quasi-static mechanical equilibrium. For comparison with the PeFNO, this data is also employed to develop an analogous physics-guided FNO (PgFNO) and physics-informed FNO (PiFNO). As expected theoretically, and confirmed by this computational comparison, for comparable accuracy of the stress field itself as compared to the data, the stress field output by the trained and tested PeFNO is significantly more accurate in satisfying mechanical equilibrium than the output of either the PgFNO or the PiFNO.

In this paper, we prove a central limit theorem for inhomogeneous Diophantine approximation with a fixed shift, provided the shift is non-Liouville. This generalizes earlier work of Dolgopyat, Fayad, and Vinogradov~\cite{DFV}. This is achieved by translating the problem to one involving flows on homogeneous spaces. In this latter setting, we establish an effective multi-equidistribution result for diagonal translates of unipotent flows. This result is obtained by combining a recent result of Kim~\cite{Kim2024} with the height function construction of Shi~\cite{Shi20}. The central limit theorem is then deduced using the method of Björklund and Gorodnik~\cite{BG}.

Energy efficiency has emerged as a vital attribute of software quality, with significant implications for both environmental sustainability and operational costs. However, existing profiling tools operate only at runtime and coarse granularity, typically capturing energy at the process or method level. Such tools fail to expose how small code blocks, such as functions, loops, and conditionals, contribute to energy consumption, preventing developers from reasoning about and comparing the energy efficiency of programming constructs during design-time. To address this gap, we propose EnCoDe, a methodology for fine-grained, design-time energy estimation, with the following key contributions: (1) PowerLens, a novel measurement methodology that achieves reliable sub-millisecond energy readings for small code blocks; (2) Extensive empirical study on code blocks extracted from over 18,000 Python programs, uncovering linear and non-linear relationships between energy consumption and static code features such as structural, complexity, density, and contextual characteristics, resulting in a first-of-its-kind fine-grained dataset; and (3) Predictive modeling, in which machine learning models are trained on these features to accurately estimate and classify block-level energy consumption at design-time. Our results demonstrate stable, reproducible block-level estimations, with regressors achieving R^2 = 0.75 and classifiers achieving 80.6% accuracy in identifying energy hotspots, enabling developers to localize and address inefficient code regions early in the development process without execution.

Next-basket recommendation (NBR) is a type of recommendation that aims to predict a set of items a user will purchase based on their historical transaction basket sequences. It is governed by a dynamic interplay between two distinct user intents: habitual repurchase, which involves repeating past behaviors, and exploratory interest, which involves discovering new items. However, existing NBR methods generally suffer from two limitations: (1) they often entangle these conflicting motives within a single representation, causing habits to overshadow discovery, and (2) they rely on discrete sequential modeling that ignores continuous-time intervals and item-specific periodicities. In this paper, we propose a novel solution named Time-Interval Disentangled Experts (TIDE) to address these challenges. TIDE incorporates a Hawkes-enhanced Fourier Time Encoding to capture item-specific temporal periodicities and dynamic decay. To decouple user intentions, TIDE utilizes a dual-expert architecture that integrates a Habit Expert for recurring needs and a Pattern-Guided Exploration Expert for discovery. Combined with an item-aware gating mechanism, TIDE adaptively balances repurchase and exploration. Extensive experiments on four diverse real-world datasets demonstrate that TIDE consistently outperforms representative state-of-the-art NBR methods.

To address the limitations of existing Generative Fixed-Filter Active Noise Control (GFANC) methods, which rely on filter decomposition and recombination and require supervised learning with labeled data, this paper proposes a Transformer-based End-to-End Control-Filter Generation (E2E-CFG) framework. Unlike previous approaches that predict combination weights of sub control filters, the proposed method directly generates control filters in an unsupervised manner by integrating the co-processor and real-time controller into a fully differentiable ANC system, where the accumulated error signal is used as the training objective. By abandoning the decomposition--reconstruction process, the proposed design simplifies the control pipeline and avoids error accumulation, while the Transformer architecture effectively captures global and dynamic noise characteristics through its attention mechanism. Numerical simulations on real-recorded noises demonstrate that the proposed method achieves improved noise reduction performance and adaptability to different types of noises compared with the original GFANC framework.

We report on the longitudinal magnetoresistance (MR) in thin metal films on an Ising-type antiferromagnetic insulator, Na5Co15.5Te6O36 (NCTO). Steep changes in the MR spectra with hysteresis were observed at spin-flip transitions driven by magnetic fields applied along the easy axis of the NCTO crystal. The MR jumps almost follow step-like changes in magnetization at the spin-flip transition. At very low temperatures where Co moments are partially frozen, the MR anomalies exhibit a tunnel-magnetoresistance-like shape. The observed MR anomalies at the spin-flip transition are attributed to strain effects via magnetostriction upon the magnetic-structure change of the Co nets in NCTO, because similar MR jumps are observed in both Pt/NCTO and Cu/NCTO. Interestingly, we found that the high-field slopes of the MR spectra show opposite signs between Pt/NCTO and Cu/NCTO at low temperatures. Because the opposite signs of the high-field MR are prominent below the antiferromagnetic transition temperature of NCTO, the interaction between the interface spin accumulation and magnetization is likely to contribute to the MR effect in the induced ferromagnetic state.

We introduce a technology to formally verify that a software system satisfies a temporal specification of functional correctness, without revealing the system itself. Our method combines a deductive approach to model checking to obtain a formal certificate of correctness for the system, with zero-knowledge proofs to convince an external verifier that the system -- kept secret -- complies with its specification of correctness -- made public. We consider proof certificates represented as ranking functions, and introduce both an explicit-state and a symbolic scheme for model checking in zero knowledge. Our explicit-state scheme assumes systems represented as transition graphs. We use polynomial commitments to convince the verifier that the public proof certificates correspond to the secret transition relation. Our symbolic scheme assumes systems specified as linear guarded commands and uses piecewise-linear ranking functions. We apply Farkas' lemma to obtain a witness for the validity of the ranking function with public and secret components, and employ sigma protocols for matrix multiplication and range proofs to convince the verifier of the witness's existence. We built a prototype to demonstrate the practical efficacy of our two schemes on linear temporal logic verification examples. Our technology enables formal verification in domains where both the safety and the confidentiality of the system under analysis are critical.

As global fossil fuel reserves diminish, there's a growing impetus for nations to transition towards renewable energy sources. Sri Lanka, for instance, aims to generate 70% of its electricity from renewable sources by 2030. Achieving this target requires optimal use of the existing power transmission infrastructure, as expanding the grid is both time-consuming and expensive. Traditionally, Static Line Ratings (SLRs) are used to define line capacity, often resulting in underutilization. Dynamic Line Rating (DLR), which estimates line capacity in real time based on weather conditions, offers a more efficient solution. However, DLR prediction is highly sensitive to environmental variability and forecasting complexity. This study proposes a novel multivariate Long Short-Term Memory (LSTM) model enhanced with an attention mechanism for improved DLR forecasting. Unlike traditional models that treat weather variables independently, the proposed approach captures nonlinear interdependencies among key environmental features such as ambient temperature, cable temperature, wind speed, humidity, and solar irradiance. The attention mechanism dynamically prioritizes the most relevant inputs during forecasting, leading to improved performance. Experimental evaluation on real-world DLR data demonstrates that the proposed model achieves a prediction accuracy of 95.84%, surpassing the conventional LSTM model's 94.62%. This improvement highlights the model's superior ability to deliver accurate and robust DLR forecasts. The findings confirm that incorporating multivariate features with attention enhances forecasting precision, supporting more efficient transmission line utilization and higher renewable energy integration.

The Von Neumann entropy of reduced states is a measure of bipartite entanglement. Despite its name, the entanglement entropy cannot by itself be used as a resource for creating thermodynamic heat flows. In order to extract heat from an entangled pure state, it first needs to be converted into a stochastically mixed state by a process of quantum state reduction. Here we show that even in a system with only two degrees of freedom, for which bipartite entanglement is the sole form of entanglement available, the entanglement entropy cannot be converted into thermodynamic entropy in a one-to-one fashion. Moreover, we show that the stochastic dynamics which is necessarily present in any realistic model of quantum state reduction, allows for multiple definitions of entropy. We indicate why quantum state reduction does not allow construction of a perpetuum mobile, despite some measures of entropy evolving non-monotonically during its dynamics. Finally, we relate the different measures of entropy to the information they contain about quantum entanglement and extractable heat, and show that models of quantum state reduction based on physical, correlated stochastic driving forces give rise to observable thermodynamic signatures of quantum state reduction that can be unambiguously distinguished from environment-induced dephasing.

We study extreme wave formation for the Korteweg-de Vries equation on the torus with random initial data of average size $ε$. We establish a large deviations principle for the supremum of the solution over arbitrarily long polynomial timescales $t \leq ε^{-n}$ for any fixed natural number $n$. This identifies the leading-order asymptotics of the probability of observing unusually large amplitudes. In this integrable setting, the dynamics evolves on invariant tori where Fourier moduli are almost conserved, ruling out mechanisms for extreme wave formation based on resonant energy exchange. As a result, large amplitudes can only arise through coherent structures or dispersive focusing, which corresponds to the quasi-synchronization of many phases. We show that the latter is dominant in the weakly nonlinear regime. Our approach combines a Birkhoff normal form analysis with probabilistic arguments, exploiting the stability of the integrable dynamics to control the probability of phase quasi-synchronization over long timescales.

We study the existence of Hamiltonian semisprays on Lie algebroids. This work is motivated by a problem studied by Vaisman for tangent bundles, and we extend this question to the setting of arbitrary Lie algebroids and provide a general solution. More precisely, given a Lie algebroid and a regular Lagrangian, we construct a family of Poisson brackets on the algebroid such that the Hamiltonian vector field associated with the corresponding energy function is a semispray. Our approach is based on the symplectic geometry of the prolongation of a Lie algebroid and a cohomological analysis of its vertical subbundle. The results provide a geometric framework for second-order Hamiltonian dynamics on Lie algebroids, extending some known facts in the classical tangent bundle case and revealing new interactions between Poisson geometry and algebroid structures.

Surface-bound electric charge on polymer materials can strongly influence droplet behaviour and solid-liquid charge transfer, but the mechanisms and the means to control these effects remain unclear. In this work, we systematically controlled the surface charge on polymer surfaces, including polytetrafluoroethylene (PTFE) and Nylon-66, by first neutralising the surfaces with an anti-static ion blower and then applying charge using an ion gun. We find that droplets pick up pre-deposited surface ions during the first wetting of the surface, and that the transferred charge directly correlates with the deposited charge encountered by the wetted area for moderate deposited densities (|σ_d |<40 μC/m2) independent of material properties. We also demonstrate that the deposited charge reduces contact angle and increases contact-line mobility in a manner consistent with an increase in effective solid surface energy. For higher surface charge densities, we observe instabilities such as droplet splitting or detachment. This work demonstrates an effective approach to control solid-liquid electrification, enabling amplification or suppression of surface charge and the directed manipulation of fluid motion on surfaces.

The stochastic simulation algorithm (SSA) is widely used to perform exact forward simulation of discrete stochastic processes in biology. However, the computational cost, driven by sequential event-by-event sampling across large ensembles, remains a computational barrier. We investigate whether reduced-precision floating-point arithmetic can accelerate SSA without degrading statistical fidelity, drawing on the success of reduced-precision methods in weather and climate modelling. We evaluate two strategies across five canonical models (birth--death, Schlögl, Telegraph, dimerisation, repressilator): (i) mixed precision, computing propensities in 16-bit while maintaining accumulators in 32-bit; and (ii) uniform precision, performing all arithmetic in 16-bit. Mixed-precision SSA produces ensemble statistics that closely match the 64-bit reference for all models, as measured by Kolmogorov--Smirnov tests and Wasserstein distances. Under uniform precision, deterministic rounding introduces systematic biases across several models, with catastrophic failures in some cases. Stochastic rounding (SR) and propensity normalisation eliminate these biases, restoring distributional fidelity across all models tested (KS $p > 0.05$). Our results establish mixed-precision SSA with SR as a viable acceleration strategy for mathematical biology: 16-bit formats shrink per-variable data size by $2$--$4\times$ relative to \texttt{fp32}/\texttt{fp64}, yielding comparable reductions in memory footprint and up to $\sim 1.5\times$ wall-clock speedup on CPU hardware that lacks native 16-bit arithmetic. As a hardware-level acceleration, mixed-precision SSA complements algorithmic methods such as tau-leaping and maps naturally onto modern GPU and TPU architectures with native 16-bit arithmetic.

We study the root-averaged density of states for the Anderson model on the Bethe lattice in the strong-disorder regime. Here the density of states means the root-averaged spectral measure, not a finite-volume eigenvalue counting limit. We assume that the single-site distribution has compact support and has a locally analytic density on an interval $I^\sharp$ containing a given interval $I$. Combining the random-walk expansion on the tree with a complex-analytic argument for the single-site Stieltjes transforms, we prove that the scaled averaged diagonal resolvent has a holomorphic continuation to a complex neighborhood of $I$ for all sufficiently large $λ$. By the Stieltjes inversion formula, the root-averaged density of states measure is absolutely continuous on the scaled energy window $λI$, and its density is real analytic and has a finite-order strong-disorder expansion there. In the scaled form $E=λξ$, the leading coefficient is the local density of the single-site distribution. All odd coefficients vanish, and the higher coefficients are finite sums determined by occupation profiles of short closed walks on the tree. For the uniform single-site distribution, we compute the first nonzero correction term explicitly.

Superconductors that spontaneously break time-reversal symmetry host complex order parameters and are widely regarded as a hallmark of unconventional superconductivity. Whether such symmetry breaking can also arise in superconductors with nominally isotropic spin-singlet pairing remains an open question. Here we report a zero-field Josephson diode effect in noncentrosymmetric 2H-TaS2/2H-NbSe2 van der Waals junctions. The diode efficiency shows no systematic correlation with supercurrent amplitude, TaS2 thickness, or normal-state resistance, arguing against simple extrinsic, purely interfacial, or transparency-driven mechanisms. Time-reversal-symmetric scenarios are further tested using symmetry-controlled and molecule-intercalated control devices, in which the nonreciprocal response is absent or strongly reduced. Normal-state Hall transport in TaS2 exhibits a nonlinear response consistent with multiband correlated electronic states. Within a Josephson framework, our modelling shows that interband scattering acts as a phase-locking mechanism generating an intrinsic anomalous phase difference and a nonsinusoidal asymmetric current-phase relation, leading to finite zero-field rectification. Together, zero-field Josephson nonreciprocity and nonlinear Hall transport provide complementary evidence for a multiband superconducting phase structure in 2H-TaS2, consistent with intrinsic time-reversal-symmetry breaking.

We investigate the origin of non-Markovianity in stochastic inflation and its implications for nonlinear perturbation theory. In the Schwinger--Keldysh formulation, the noise terms sourcing the infrared (IR) Langevin equations are determined by ultraviolet (UV) modes evolving on top of the stochastic IR background. Since the UV-mode evolution generally depends on the past history of the IR sector, the resulting stochastic dynamics is intrinsically non-Markovian. Working perturbatively, we derive the UV-mode solutions up to second order and decompose the corresponding noise contributions into two parts. The first is a ``deterministic'' contribution, generated by the functional Taylor expansion of the first-order UV solution around the background trajectory. The second is a genuinely ``stochastic'' contribution, originating from terms in the UV-mode equations that are quadratic in the noise variables and are usually neglected in the standard formulation of stochastic inflation. Under this conventional truncation, the deterministic contribution reduces to a Markovian correction in attractor backgrounds, whereas it could become history dependent in non-attractor phases and gives rise to non-Markovian terms involving integrals over first-order IR perturbations. We finally show that the stochastic contribution is of the same perturbative order as the deterministic one, which indicate that the conventional truncation is generically inconsistent and quadratic-noise terms may be required for a consistent treatment of nonlinear perturbations in stochastic inflation. Our analysis clarifies the perturbative structure of non-Markovianity and provides the basis for a systematic treatment of quadratic-noise effects beyond the standard formulation.

As software systems grow in scale, developers face increasing difficulty in selecting appropriate Application Programming Interfaces (APIs) from numerous options. Efficiently identifying APIs that satisfy functional requirements has become a key challenge. To evaluate the semantic understanding of existing query-based API recommendation methods, this paper constructs Q-ARE (Query-based API Recommendation Evaluation), a dataset based on open-source Java projects from GitHub. Methods and their invocation chains are analyzed to identify third-party APIs directly or indirectly invoked by target methods, recursively expanding multi-level invocations to unify hierarchical call structures into API recommendation target sets. Furthermore, we introduce two metrics: API Call Depth, measuring the invocation distance between a query method and a target API, and Invocation Density, quantifying the proportion of code lines associated with the target API in the invocation chain. Based on Q-ARE, we systematically evaluate several query-based API recommendation methods and general Large Language Models (LLMs). Results show that performance drops significantly as API Call Depth increases and invocation density decreases, indicating that existing methods still struggle with multi-level method invocation structures. Q-ARE and its metrics provide a new benchmark for assessing semantic understanding in API recommendation and offer insights for improving future algorithms.

We develop a Fisher-consistent redescending robust estimator for the spatial scalar-on-function regression model, where a scalar response depends on both a functional predictor and a spatial autoregressive lag. Existing estimation procedures for this model are typically based on likelihood methods or monotone-loss robust M-estimators. They may be highly sensitive to vertical outliers, leverage points in the functional predictor, and numerical instability induced by strong spatial dependence. To address these issues, we propose a new estimation framework that first applies robust functional principal component analysis to obtain a contamination-resistant finite-dimensional representation of the functional predictor and then estimates the resulting spatial regression model through a bias-corrected system of M-estimating equations. The proposed method allows redescending loss functions, including Andrews' sine and Danish losses, and jointly estimates the regression coefficients, spatial dependence parameter, and scale parameter within a unified Fisher-consistent framework. For computation, we develop a hybrid IRLS-Newton algorithm that combines weighted least-squares updates for the regression parameters with a Newton-Raphson update for the spatial parameter. We establish Fisher consistency, consistency, asymptotic normality, and the asymptotic distribution of the reconstructed slope function. Monte Carlo experiments show that the proposed estimators remain competitive under clean data and substantially outperform classical and Huber-type robust competitors under contamination, particularly in severe outlier settings. An application to French air-quality data further demonstrates improved predictive performance and stable estimation of spatial dependence. Our method has been implemented in the fcsar R package.

Given a symmetrizable Kac-Moody algebra $\mathfrack{g}$, we study its $π$-systems, which are subsets of real roots, the pairwise differences of whose elements are not roots. Such systems arise as simple systems of regular subalgebras of $\mathfrack{g}$, and were originally studied by Dynkin, Morita and Naito. We show that the binary relation introduced by Morita defines a partial order on the set of $\mathfrack{g}$ of finite, untwisted affine or hyperbolic type. We also formulate general principles for constructing $π$-systems as well as for finding forbidden diagrams that cannot occur as Dynkin diagrams of $π$-systems of a given $\mathfrack{g}$. Among other applications, we use this to determine the set of maximal hyperbolic Dynkin diagrams in ranks $3$-$10$ relative to the Morita partial order.

While vertical GaN-on-silicon architectures promise a transformative leap in cost-effective power electronics and high-resolution micro-LEDs, their deployment remains bottlenecked by the high electrical resistance of conventional epitaxial buffer layers. Here, a universal and straightforward sputtering-based strategy is presented to realize high quality GaN epitaxial films on Si(111) substrates characterized by exceptionally low vertical resistance, ohmic behavior, and robust thermal stability. This technique centers on the in-situ formation of a sub nanometer (0.5 nm) silicide-based template via rapid thermal annealing method demonstrating unprecedented versatility across 25 different metallic species. Scanning transmission electron microscopy (STEM) reveals that a unique amorphous like interlayer (AL-IL) effectively accommodates lattice mismatch and relaxes epitaxial strain. These AL-IL templates further serve as high performance platforms for metalorganic chemical vapor deposition (MOCVD) overgrowth, successfully bridging the gap between scalable, low-cost fabrication and device-grade vertical performance.

We carry the deadline-resolved Information Leakage Score (ILS-dl) framework of Nechepurenko (2026a, 2026b) from a single-case proof of concept to a population-scale evaluation across 12,708 Polymarket markets, October 2020 to April 2026. We frame the paper as a scope-discovery study: scaling reveals that the framework's effective domain is materially narrower than initial framing suggested, and the principal obstacle is not score computation but resolution semantics. We report four findings. First, only 88 of 12,708 candidate markets (0.7%) yield computable ILS-dl values; only 1 of 32 markets in the ForesightFlow Insider Cases (FFIC) inventory is in scope, and 14 of 32 FFIC markets are flagged unclassifiable due to genuine resolution-criterion ambiguity. Second, only 12 of the 88 computed markets (13.6%) satisfy anchor-sensitivity, and an independent-second-pass T_event validation reaches 57.8% exact-date agreement, below the 90% ex-ante criterion. Third, raw ILS-dl medians are negative across all six (sub-bucket by period) cells, but a hazard-decay baseline correction we introduce yields a heterogeneous result: regulatory_formal post-2024 shifts to near-zero (-0.21 to -0.02), while regulatory_announcement post-2024 retains a 95% bootstrap CI entirely below zero. Fourth, the constant-hazard exponential of Nechepurenko (2026b) is rejected in favor of Weibull on the pooled post-2024 cell, but a per-subcategory check confirms the preference reflects category mixture rather than within-cell duration dependence. The implication is that detection of informed flow requires methodological refinement on the resolution-typology and score-baseline axes, not only on the score-computation axis where prior work concentrated.

We propose a Deep-Picard iteration framework for high-dimensional nonlinear space-time fractional diffusion equations.The method is based on a nonlinear fractional Feynman--Kac fixed-point formulation, which replaces direct discretization of the Caputo memory term and the nonlocal fractional Laplacian by Monte Carlo simulation of the associated fractional dynamics. Each Picard update is approximated by stochastic label generation and realized through supervised neural-network regression, thereby avoiding residual minimization involving fractional differential operators. The fractional trajectories are generated by coupling a discretized beta-stable subordinator with a walk-on-spheres-type simulation of the rotationally symmetric alpha-stable Lévy process. Numerical experiments on two-dimensional and high-dimensional test problems ddemonstrate stable Picard convergence and accurate approximation, with tests reported up to dimension d=100.