This manuscript studies the problem of independence testing between two high-dimensional time series without assuming weak stationarity, that is, allowing their autocovariances to vary over time. To this end, we propose a bimodal weighted-average test statistic that removes the bias induced by temporal dependence under the null hypothesis, thereby avoiding the need to whiten the time series prior to hypothesis testing -- a procedure that is challenging in high-dimensional and nonstationary settings. To facilitate statistical inference, we develop a dependent wild bootstrap procedure. On the theoretical side, we derive a concentration inequality for quadratic forms of time series data stemming from a class of high-dimensional, nonlinear, and nonstationary processes. This result enables us to derive the asymptotic null distribution of the proposed test statistic and to establish the validity of the bootstrap algorithm. Numerical results show that the proposed test attains desired size and good power performance even when the dimension exceeds the sample size or when the data-generating process exhibits time-varying autocovariances. In contrast, tests based on whitening time series fail to maintain correct size in the presence of unstable autocovariance structures. Since nonstationary autocovariances commonly arise in real-life time series data, our work offers a robust procedure for independence testing.

The processes that determine the stellar initial mass function (IMF) and its connection to the core mass function (CMF) are among the major open questions in star formation. The definition of a core remains unclear, yet the way they are extracted from simulations and observations critically shapes the CMF. Nowadays, cores are mostly detected through their density or intensity only. We aim to explore a new way to define cores in 3D numerical simulations based on a direct application of the virial theorem, and break free from some limitations induced by density-based methods. We intend to improve the accuracy and the physical meaning of the extracted cores. We developed vibes, an innovative method that makes full use of the virial theorem to extract overdensities in simulation snapshots. It works by building structures iteratively around density peaks, and applying the virial theorem to the structure at each iteration. Then, the structure boundary is set from the evolution of the its energy as it spatially grows. We used STARFORGE simulations to test the sensitivity of the extraction process to the main working parameters (constraints on the structure shape, iteration step, and peak selection criteria). This sensitivity is observed to be low. We compared our extraction with two density-based extraction algorithms, hop and dendrogram, that are observed to be very sensitive to their input density threshold parameter. Vibes returns structures that are coherent to each other and physically motivated, and it appears much more stable than existing 3D extraction tools. By defining the boundary of the cores on a physical criterion rather than on a user-defined set of density parameters, we expect such extracted cores to be closer to their forsaken definition: gas reservoirs that will form a single star or a close multiple system.

This paper investigates the nonexistence of solutions to semilinear parabolic and hyperbolic inequalities with positive potentials on metric graphs, including both nonnegative solutions and sign-changing solutions. The Laplacian under consideration is of a nonstandard type, incorporating contributions from both the vertices and edges of the metric graph. We construct a new pseudo-metric and introduce suitable space-time test functions of either coupled or separated type. Under suitable weighted space-time volume growth conditions on the potential, we establish nonexistence results for very weak solutions. More precisely, we show that all such solutions to the inequality must be identically zero.

Bound states differ from scattering yet are not covered in textbooks on Quantum Field Theory. I discuss a perturbative method for QED and QCD based on canonical quantization. Fully fixing temporal gauge $A^0(t,\boldsymbol{x})=0$ imposes Gauss' law on physical states. As pointed out by Dirac, physical electrons have a longitudinal gauge field $\boldsymbol{A}_L$, whose energy is the instantaneous Coulomb potential. The situation is analogous for quarks and gluons in QCD. An instantaneous confining potential arises for color singlet $q\bar q$ states when a non-vanishing boundary condition on $\boldsymbol{A}_L^a(\boldsymbol{x}\to\infty)$ is specified in Gauss' constraint. As suggested by Gribov, $α_s(Q^2)$ may freeze at a perturbative value when the confining potential dominates. Hadrons can then be calculated perturbatively. At vanishing quark mass there is a $j^{PC}=0^{++}$ state with zero energy which can mix with the perturbative vacuum, giving rise to a spontaneous breaking of chiral symmetry.

Quantum-entangled measurements are known to enable multi-party behaviors that are impossible with unentangled measurements on nonlocal resources, even those that are super-quantum and bound only by the no-signaling principle. This advantage can be witnessed by the entanglement swapping protocol, along with corresponding impossibility results for "nonlocality swapping". However, the advantage assumes the absence of pre-existing nonlocal resources shared by the swapped-to parties; it no longer holds if all pairs of parties are allowed to share bipartite nonlocal resources. Here, we consider a resource-theoretic perspective in which bipartite nonclassical resources are free resources that can be shared by any pair of parties in a multipartite network, and ask whether quantum entangled measurements can still provide an advantage over certain basic measurements, known as wirings, of nonsignaling nonlocal resources. We resolve this question in the affirmative by demonstrating an explicit four-party behavior that can be achieved with bipartite quantum resources subject to entangled measurements, and cannot be achieved if the bipartite resources are allowed to be more general nonsignaling nonlocal "boxes" so long as the measurements are restricted to local wirings, even also allowing for globally shared classical randomness. Furthermore, the argument generalizes: the same separation can be witnessed for K+2 parties with access to K-partite nonlocal resources for any K > 2. We also examine these results in different contexts, such as the star network configurations and scenarios not admitting globally shared classical randomness, further enhancing understanding of the capabilities of entangled measurements in multi-party configurations.

Within a three-body system comprised of two celestial bodies and a spacecraft, the dynamical environment near a smaller primary is significantly perturbed, motivating a balance between global insight and model fidelity. While averaged dynamics offer an integrable model to classify solution landscapes, they inherently lack the accuracy of the unaveraged dynamics, such as the Hill Restricted Three-Body Problem and Circular Restricted Three-Body Problem. This work establishes a systematic bridge between the averaged and unaveraged regimes by explicitly linking averaged equilibria to symmetric periodic orbits in the unaveraged three-body systems. A unified frequency framework is introduced to characterize the mapping of invariant tori across the dynamical models. Leveraging the parity of the resonance ratio, an initialization scheme is developed to identify admissible apse configurations, enabling the a priori prediction of solution multiplicity and symmetry types. Furthermore, the global evolution of families derived from averaged equilibria is traced via bifurcation and frequency analysis. These findings are synthesized into archetypical bifurcation diagrams, providing a comprehensive atlas of the symmetric periodic orbit web within the HR3BP and CR3BP. The resulting framework not only clarifies the topological origins of complex periodic orbit families but also offers a versatile tool for trajectory design in cislunar and multi-body environments.

The Schrödinger cat state protocol (SCSP) makes use of a Schrödinger cat (SC) state generated with one-axis-twist squeezing (OATS) to enhance the sensitivity. In principle, the SCSP can magnify the phase shift by a factor N, the number of atoms under interrogation, accompanied by a quantum noise amplification by a factor of root-N, enabling an atomic sensor to reach the Heisenberg limit. However, the current SCSP can reach this benchmark only if the parity of N is known, which is almost impossible for a large ensemble. The reason is the orientation of the SC state generated with the conventional OATS depends on the parity of N. In this paper, we propose a modified OATS (MOATS) operation that generates the SC state aligned in a certain direction regardless of the parity of N.

The echo squeezing protocols (ESPs) are techniques that amplify the phase shift in a quantum sensor with one-axis-twist squeezing (OATS). For atomic sensors, spontaneous emission (SE) in the OATS operations is an important imperfection, which, however, is prohibitively difficult to study. SE can transfer atoms to all the Zeeman substates, making the number of relevant collective states excessively large. In this paper, we focus on a relatively simple isotope, namely Sr-88, which only has one Zeeman substate in each of the two ground states. Nevertheless, studying the effect of SE is still challenging because SE will populate all collective states, either symmetric or asymmetric, thus putting the ensemble into a mixed state. Based on analytical derivation and numerical simulations, we conclude that the GESP is more resistant to SE than the conventional echo squeezing protocol (CESP). This is another advantage of the GESP that has not been realized formerly. We also find that for the GESP employing Sr-88, the SE-induced reduction in the signal contrast is the same as that for a Ramsey protocol without squeezing and the quantum noise is suppressed by SE. This is an unexpectedly favorable result. The SE-induced suppression of quantum noise constitutes a previously unrecognized effect that challenges both earlier conclusions and intuitive expectations.

Ordinary differential equation models are widely used to understand and forecast complex dynamical systems, but their predictive value depends on reliable parameter estimation. Structural identifiability assesses whether parameters can be uniquely recovered from ideal observations, whereas practical identifiability depends on finite, noisy and partially observed data. We introduce the Practical Identifiability Index (PII), a marginal uncertainty-width metric based on the logarithmic span of confidence intervals. Expressed on an order-of-magnitude scale, the PII summarises how tightly individual positive-valued parameters are constrained by available observations, enabling comparison across parameters, models, error structures and observation designs. The PII is intended as a complementary diagnostic, not a standalone identifiability test, and should be interpreted alongside coverage, profile likelihoods, posterior summaries, sensitivity analysis or structural identifiability results. Using parametric bootstrap experiments across growth and compartmental epidemic models, we identify consistent principles: uncertainty decreases as calibration windows become more informative, increases with observation noise and parameter coupling, and remains high for latent or indirectly observed processes. Parameters governing early observable dynamics become constrained sooner, while additional observables can improve constraint for latent progression and recovery parameters. The PII provides a simple, reportable summary of marginal parameter uncertainty for dynamical modelling.

This paper considers a semiparametric difference-in-differences (DID) framework for identifying and estimating treatment effects on the treated (ATT) when outcomes are missing not at random (MNAR), and a fully observed shadow variable is available. The shadow variable is assumed to be associated with the outcome evolution but independent of the missingness process, conditional on covariates and the possibly unobserved outcome evolution. We establish the identification conditions, derive the corresponding identification results and estimation algorithm, and evaluate the finite-sample performance of the proposed estimator through simulation studies and a real data application.

Undirected graphical models provide a fundamental framework for representing conditional independence structures among high-dimensional random variables. While undirected graphical model selection has become a central problem in high-dimensional statistics, most existing methods are restricted to parametric settings. In this paper, we develop a nonparametric approach to undirected graphical model selection based on diffusion models. Recent work has shown that diffusion models can adapt to the unknown graph structure of the underlying distribution, yet utilizing these models for explicit graph estimation remains unexplored. To bridge this gap, we introduce a novel diffusion-based method for nonparametric undirected graphical model selection. We establish the model selection consistency of the proposed method and demonstrate its empirical performance through extensive simulations and two real data analyses.

Large Language Models (LLMs) have significantly advanced generative query recommendation. However, existing alignment methods primarily focus on standard chatbot scenarios, falling short in on-device intelligent assistants where users predominantly expect the rapid invocation of system-level tools. Moreover, directly aligning LLMs with real-world click logs introduces severe noise due to varying user activity levels and the failure to emphasize execution-oriented queries. To address these challenges, we propose ToolRec, a calibrated preference alignment framework tailored for on-device query recommendation. To ground query recommendation with executable actions, we first construct SysToolKit, a comprehensive repository of 708 system tools, paired with a context-aware tool retrieval mechanism to ensure recommendation relevance. We then propose a dual-level calibration mechanism to refine raw click data, effectively mitigating user behavioral noise by calibrating signals based on user activity levels, while simultaneously up-weighting click signals on system-level tool-invoking queries. Guided by these refined preference signals, we then align the model using a sample-level weighted Kahneman-Tversky Optimization (KTO). Extensive online A/B tests on our mobile assistant platform OPPO Xiaobu, which has over 150 million monthly active users, demonstrate that ToolRec can significantly improve Click-Through Rate (CTR) and total clicks volume over strong baselines while maintaining high query relevance.

Parsing underpins a vast range of software engineering tasks, from compilers and static analyzers to language servers and fuzz testing tools. Yet most parsers deployed in practice are deterministic (LL or LR), forcing developers not only to contort their grammars to fit the parser, but to simplify the very languages they design sacrificing expressiveness for the sake of parseability. General context-free parsers eliminate this constraint. Yet, despite decades of algorithmic development, no rigorous head-to-head comparison exists across the major families of parsing algorithms. We present the first unified, controlled benchmark of six generalized parsing algorithms: CYK, Valiant, Earley, GLL, RNGLR, and BRNGLR, plus deterministic LL(1) and LR(1) baselines, all implemented in Rust with shared data structures and parse-tree extraction, and evaluated across 22 grammars ranging from simple expressions to full C++ and Java. Our results show that the cost of generality is lower than widely assumed. On deterministic grammars, the GLR family incurs only a 3x median slowdown over LR(1), with a narrow and predictable variance. GLR is the clear performance winner among generalized parsers and a practical default choice for software engineering tools.

This letter introduces a novel, full-wave, physics-compliant stochastic dyadic Green's function (SDGF) framework for modeling electromagnetic (EM) multiple-input-multiple-output (MIMO) channels under wavenumber uncertainty. Unlike conventional phenomenological fading models, the proposed approach provides what appear to be the simplest exact random field models of electromagnetic line-of-sight (LoS) propagation that are also exact solutions of Maxwell's equations. Hence, we dub them Maxwellian random field theoretic models. These physically consistent stochastic models, including an analytically tractable wavenumber Gaussian model and a more general stochastic plane wave (SPW) model, serve as fundamental baseline models for stochastic LoS channel characterization. By preserving the vectorial structure of Maxwell's equations and the dispersion relation, the framework naturally incorporates both propagating and evanescent modes. Our analysis of ergodic capacity and degrees of freedom (DoF) reveals that the key results of the complex SPW model can be reproduced by the simpler Gaussian model with limited variance. Furthermore, we provide examples using 2D continuous MIMO systems, illustrating how the model's Maxwell-consistent stochasticity explains observed increases in channel capacity and DoF over the deterministic MIMO capacity baseline. These idealized Maxwellian random field theoretic models offer a physically grounded reference point for understanding fundamental limits in stochastic LoS propagation environments.

Deep learning based approaches have shown great promise in cross-device disruption prediction for tokamaks, however, the robustness of these models heavily relies on massive amounts of training data. For the upcoming ITER, to ensure the safety of the first plasma and subsequent operations, experimental data should be entirely unavailable initially, and disruptive discharges should be strictly avoided thereafter. This extreme data scarcity inherently conflicts with the data-intensive nature of deep learning algorithms. To address this challenge, we utilize synthetic diagnostic signals from the target device to supplement the experimental data from existing devices for the zero-shot disruption prediction on a new device. The detailed implementation pipeline of this scheme is presented. For experimental validation, a predictive model trained on data from the EAST tokamak is deployed for a zero-shot cross-device experiment on the J-TEXT tokamak. A synthetic diagnostic framework, configured with the diagnostic parameters of the target device, is developed to process NIMROD magnetohydrodynamic (MHD) simulation data based on the target device's magnetic configuration, thereby achieving effective data augmentation. Ultimately, the results demonstrate that by integrating the target device's synthetic diagnostic data with Fourier Domain Adaptation, the zero-shot accurate early warning rate of the model on 1,596 J-TEXT discharges is improved from 50% to 57%, while exhibiting enhanced predictive robustness.

In this paper, we study thermal partition functions of free exotic conformal field theories, focusing on conformal higher-derivative and conformal higher-spin fields, in the semi-universal limit $|ω_i|\rightarrow 1$. It was recently conjectured in \cite{Anand:2025mfh} that, in this limit, the thermal partition function develops universal poles in $(1-|ω_i|)$, while the corresponding residue functions are theory-dependent. We analyze conformal higher-derivative scalar, fermionic, and vector fields in the semi-universal limit. We then extend the study to the Weyl graviton, the Weyl gravitino, and conformal higher-spin fields (CHS) on $S^1_β\times S^3$, using both spectral mode-sum and operator-counting methods. In all cases, we find the expected pole structure, with residue functions whose behavior depends on the presence or absence of negative-twist states. For four-dimensional conformal higher-spin fields, we further reproduce the same residue-pole structure from the one-loop partition function of massless higher-spin fields in thermal AdS$_5$. Finally, we show that the semi-universal limit provides a useful diagnostic of negative-twist states, which indicate violations of ANEC-type bounds in these theories, whereas the traditional high-temperature expansion is insensitive to them.

Multi-agent LLM systems for medical question answering often treat consensus as a reliability signal: if multiple agents agree on an answer, it is presumed trustworthy. However, answer-level consensus does not entail reasoning-level alignment. We introduce CARA (Cross-Agent Reasoning Alignment), a family of automated metrics that measure whether agents who agree on an answer also agree on the reasoning. Applying CARA to a standard debate system on two medical QA benchmarks, MedQA-USMLE and MedThink-Bench, we identify the consistency illusion: a failure mode where debate reduces detectable contradictions between agents while simultaneously decreasing the semantic similarity of their reasoning chains; agents appear to agree more but reason less consistently. To improve this misalignment, we propose the Grounded Debate Protocol (GDP), a prompt-level intervention that requires agents to commit to named medical facts and take explicit stances on other agents' claims. GDP produces large, consistent alignment improvements, with Cohen's d ranging from +1.43 to +1.99, across two datasets and two backbone models, without adding LLM calls or modifying system architecture. Our results motivate cross-agent reasoning alignment as a quantity to audit alongside accuracy in safety-critical domains.

We study Frenet-Serret equations for timelike worldlines in Minkowski spacetime with proper-time-dependent curvature and torsion. This corresponds to relativistic motion with non-uniform proper acceleration and, when torsion is included, to trajectories whose Frenet-Serret frame rotates beyond the acceleration plane. Using the Gram-Schmidt construction of the tetrad from the four-velocity and its derivatives, we relate the intrinsic Frenet-Serret parameters to kinematic quantities such as proper acceleration, four-jerk, and four-snap. We then consider simple analytic cases for the jerk invariant and torsion, obtaining explicit curvature profiles and reduced Frenet-Serret equations. These examples clarify how non-constant acceleration and torsion modify the geometry of accelerated relativistic motion.

We plug two gaps in the constructive proof of Theorem 1 (respectively, Theorem 2) in <cite>dsb</cite>, showing that the property of C-connectedness (respectively, O-connectedness) of a subset S of R is equivalent to S containing the interval [a,b] (respectively, (a,b)) whenever a and b are in S and a < b.

Neutral-atom arrays combine scalable qubit registers, long coherence times, flexible optical control, and strong Rydberg-mediated entangling interactions, making them a promising platform for quantum information processing. However, physical error rates remain a challenge, and fault-tolerant quantum error correction (QEC) requires repeated mid-circuit measurement and reset of ancilla qubits without disturbing nearby data qubits. This requirement introduces significant control and architectural overhead, making qubit encoding an important architectural decision. Here, we propose a dual metastable-state qubit encoding for $^{171}\mathrm{Yb}$ atoms that utilizes two independent qubit subspaces in the $(6s6p)\,{}^3\mathrm{P}_0$ and $(6s6p)\,{}^3\mathrm{P}_2$ manifolds. The ${}^3\mathrm{P}_0$ manifold provides a long-coherence nuclear-spin (NS) qubit suitable for storage and arithmetic operations, while the ${}^3\mathrm{P}_2$ manifold provides a hyperfine-spin (HF) qubit, with $Δ_{\mathrm{HF}} = 2π\times 6.7~\mathrm{GHz}$, that enables fast Raman operations and direct state-selective imaging. Coherent shelving between the two metastable manifolds connects the qubit subspaces, allowing operations to be assigned to spectrally distinct processor zones. We simulate single-qubit and two-qubit gate fidelities in ${}^3\mathrm{P}_2$, as well as coherent shelving between the HF and NS qubit subspaces. We incorporate these physical-level estimates into an architectural resource estimation and logical-level simulation. Our approach integrates mid-circuit measurements and fast qubit operations within a single-species platform, providing a versatile framework for future fault-tolerant quantum computing with neutral-atom qubits.

Let $L_μ(G)=A(G)-μD(G)$ be the generalized $μ$-adjacency matrix of a finite graph $G$. Fan, Xing, Zhang, and Wang constructed pairs of non-degree-similar trees for which the Smith normal forms of the matrices $tI-L_μ(G)$ over $\mathbb{Q}(μ)[t]$ coincide, and conjectured that their construction remains valid when the attached rooted path is replaced by an arbitrary rooted tree. We prove this conjecture as a consequence of a more general coalescence theorem: if a finite graph $H$ has two vertices $u$ and $v$ that are cospectral for $L_μ(H)$, then, for every finite rooted graph $R$ with root $r$, the matrices \[ tI-L_μ(R(r)\odot H(u)) \quad\text{and}\quad tI-L_μ(R(r)\odot H(v)) \] have the same Smith normal form over $\mathbb{Q}(μ)[t]$, where $\odot$ denotes coalescence of rooted graphs. The proof uses an orthogonal intertwiner over a real closed extension field.

In this paper, we propose an operator learning method based on the multiscale Fourier neural operator (MscaleFNO) for inverse medium problems of Helmholtz equations. The MscaleFNO provides a neural surrogate model with reduced spectral bias for the Helmholtz equations, mapping highly oscillatory medium profiles to scattered wavefields. A plug-and-play inversion using elucidated diffusion model is introduced to regularize the inverse solver based on least squares of data misfits. Numerical results for partial aperture inversion of oscillatory two-dimensional media demonstrate the advantage and effectiveness of MscaleFNO for accurate reconstruction of highly oscillatory medium properties.

Large Language Models (LLMs) have become powerful tools for code generation, yet they remain prone to hallucinations-producing plausible but incorrect or fabricated outputs. Among these, package hallucination, where an LLM suggests non-existent dependencies, poses an emerging security risk to the software supply chain. While previous studies focus on popular languages like Python or JavaScript, in this work we present the first large-scale empirical study on crate hallucination in LLM-generated Rust code. We construct a multi-source dataset combining coding tasks from Stack Overflow, GitHub, and LLM-generated tasks, and evaluate both commercial and open-source models under various decoding settings. Our analysis reveals that, unlike prior findings in Python and JavaScript, hallucination behavior in Rust follows a distinct pattern: different models exhibit surprisingly consistent hallucination rates, and these rates show minimal sensitivity to model parameters. Furthermore, we investigate prompt engineering strategies to mitigate hallucinations without sacrificing code quality. This study provides new insights into the reliability and security implications of LLM-assisted Rust development, offering guidance for future research and safer model deployment in software engineering workflows.

We present a quantum algorithm for the Kravchuk transform that scales logarithmically in both the dimension and the inverse of the error parameter. The quantum Kravchuk transform maps computational basis states to states with amplitudes proportional to Kravchuk functions. We achieve this by combining two key techniques: the structural relationship between the Kravchuk transform and the Lie algebras $\mathfrak{su}(2)$, and a recent fast-forwarding simulation method for $\mathfrak{su}(2)$ operators in the oscillator representation. More precisely, we first establish the map from Kravchuk transform in computational basis to $\mathfrak{su}(2)$ in Fock basis. Then built on this connection, we apply the fast-forwarding to achieve an efficient quantum Kravchuk transform.

As physicians turn to AI-powered systems to help meet the dual demands of speed and care quality, they are met with hallucinations and sycophancy. Understanding how doctors reason through clinical problems in real-world settings is critical for design of effective AI reasoning systems. While recent advances in medical AI have emphasized performance benchmarks and diagnostic accuracy, comparatively little attention has been paid to the structure of clinicians' reasoning processes as they unfold over time, e.g., how they interact with electronic health records and operate under conditions of uncertainty and constraint. This study provides a comprehensive, empirically-grounded account of clinical reasoning and its relationship to current AI-mediated workflows through a mixed-methods design that combines qualitative interviews with structured survey data. Findings indicate that current AI systems are primarily deployed for encounter-level tasks such as documentation and summarization, and only partially align with physicians' underlying reasoning processes. In particular, AI-generated representations often omit temporal or interpretive structures central to clinical decision-making, while core aspects of reasoning, especially those spanning multiple encounters, remain largely implicit and physician-driven. By integrating fine-grained qualitative insights with broader quantitative patterns, this study offers a unified framework for understanding clinical reasoning as a context-sensitive, temporally extended process and identifies key mismatches between clinician cognition and current AI design. These results provide concrete directions for the development of AI systems that more effectively align with and augment real-world clinical reasoning.

This paper presents a systematic evaluation of five controller-free pointing techniques for 2D target selection in AR, using ISO 9241-411. We compared them across multiple depths (2 m, 6 m, 10 m) in terms of movement time, accuracy, throughput, and workload (NASA TLX). Head- and eye-based pointing significantly outperformed the hand-based methods (Finger, Wrist, and Arm); Head input was the most accurate and remained the most consistent across depth. Depth significantly impacted performance, with complex interactions with target size and distance. Our results offer a comprehensive empirical basis for selecting appropriate controller-free techniques in depth-varying AR tasks.

Radio map (RM) estimation is a key enabler for environment-aware optimization in 6G wireless networks. In practice, RM construction increasingly relies on crowdsourced received signal strength (RSS) feedback that is inherently sparse and noisy. A further and often overlooked challenge is location drift, whereby privacy constraints and user mobility cause reported sampling coordinates to deviate from the true measurement locations. Unlike additive measurement noise, location drift perturbs the sensing operator itself, since each RSS sample effectively queries the underlying RM at an incorrect spatial coordinate. This operator uncertainty, compounded with sparse noisy sensing, renders the inverse problem severely ill-posed and limits conventional estimators that rely on analytically specified priors. This paper proposes RadioDiff-Inv2, a differentiable diffusion inversion framework that estimates RMs from sparse noisy measurements under location drift. A Gaussian resampling scheme is introduced to construct a differentiable, drift-aware measurement operator on grid-based maps, and the probability-flow ordinary differential equation (ODE) is exploited to cast the diffusion sampler as a deterministic, differentiable mapping from an initial noise code to the estimated RM. By optimizing the noise code via backpropagation against a drift-marginalized data-fidelity objective, RadioDiff-Inv2 produces reconstructions that are both prior-plausible and measurement-consistent without costly posterior sampling. Extensive experiments show that RadioDiff-Inv2 outperforms the best competing baseline by 4 to 14 dB in PSNR across varying sparsity and drift levels. The advantage is most pronounced in low-SNR regimes, where the learned diffusion prior maintains near-constant reconstruction fidelity while conventional methods degrade severely.

Numerous machine learning-based sound field interpolation methods have been proposed. In particular, physics-informed neural networks (PINNs) can accurately interpolate sound fields from a small number of microphones. However, their high computational cost and long training time pose practical challenges for applications requiring real-time processing or online learning. To address this, we propose a hybrid framework that combines PINN-based pre-training with a physics-informed extreme learning machine (PIELM) tailored for acoustic fields. By replacing iterative PINN fine-tuning for each target sound field with closed-form output-layer adaptation using hidden-layer weights pre-trained by PINN, the proposed method efficiently interpolates unknown sound fields from limited observations. Simulation results under simplified one-dimensional free-field conditions demonstrate that, given a pre-trained model, the proposed method achieves interpolation accuracy comparable to that of PINN-based fine-tuning while reducing the adaptation time by more than three orders of magnitude.

The shift to renewable-dominated power systems has produced low-inertia grids, undermining system stability. In this context, grid-forming inverters (GFMs) have emerged as a promising solution. However, GFMs challenge conventional analysis techniques, especially those relying on small-signal or root-mean-square (RMS) models. Such models rely on linearization and sinusoidal steady-state assumptions, which fail in large-signal cases. Stability of GFM-based systems therefore becomes operating-point dependent, and a feasible operating point may not even exist. While large-signal analyses are available, decentralized certification of operating-point convergence with explicit transient guarantees, such as rate and overshoot, remains rare. This paper proposes an algebraic, decentralized contraction-based framework. The proposed contraction stability analysis certifies system stability and convergence to desired operating points. The method works in the time domain and captures nonlinear, large-signal behavior of synchronization and power-sharing mechanisms. Moreover, the contraction rate provides an explicit bound on transient time: trajectories converge exponentially to the new operating point at a controlled rate, yielding computable contraction regions that certify stability and large-signal convergence across operating-point changes. These regions directly guide parameter tuning for heterogeneous GFMs.

This paper studies neural ordinary differential equations (neural ODEs) from a control-theoretic perspective using controllability and observability concepts. The neural ODE is represented in a control-affine form to facilitate analysis using tools from nonlinear and linear time-varying (LTV) systems. Controllability is examined through trajectory linearization, where the LTV controllability Gramian provides a local, first-order measure of input influence along a nominal trajectory. Observability is analyzed through output linearization, where the LTV observability Gramian characterizes the local ability to reconstruct system states from output measurements. Koopman-based lifting is considered to extend the analysis to a higher-dimensional representation, and its limitations under multiple equilibria and basin-dependent behavior are discussed. The proposed framework is illustrated on a series RLC circuit. The learned neural ODE reproduces system trajectories and generalizes to unseen initial conditions. The computed Gramians are numerically full rank along the tested trajectories, indicating local controllability and observability of the linearized dynamics.