Papers

Personalized federated learning can improve estimation for high-dimensional time series while preserving client-specific dynamics. However, parameter heterogeneity creates a fundamental ambiguity between shared and personalized structure. We introduce the principle of personalization diversity, under which genuinely personalized effects recur in only a limited fraction of clients. Based on this principle, we propose PerFeCT-VAR, Personalized Federated Vector Autoregression via Frequency-Capped Thresholding, which decomposes each client-specific transition matrix into shared low-rank dynamics, shared sparse links, and personalized sparse departures. A cross-client frequency cap yields a sharp shared–personalized separation threshold and motivates frequency-capped thresholding for federated estimation. Our theory further accounts for heterogeneous client distributions through a distributional compatibility condition and establishes joint linear convergence of the shared and personalized components. Under sufficient personalization diversity, the shared dynamics retain federated total-sample-size gains while the personalized components achieve client-level accuracy. Simulations and an application to multi-store retail revenue data demonstrate the predictive and interpretive benefits of the proposed framework.

Serving an LLM means setting dozens of inference-time knobs, from per-layer KV retention to per-layer expert counts. Practice sets them with mechanism-specific heuristics that return a single operating point and do not scale to layer-wise search spaces. We recast inference configuration as constrained multi-objective black-box optimization and build InferOpt, a reusable search framework that requires only variable bounds, a deterministic resource cost, and an evaluation hook. InferOpt searches on a frozen sampled proxy set, rejects over-budget candidates before any model call, tightens the budget adaptively, and re-validates Pareto representatives on full-scale dataset. One pipeline covers a 28-dimensional continuous KV space (Qwen2.5-7B) and a 26-dimensional discrete MoE space (DeepSeek-V2-Lite). On KV, post-prefill pruning cuts the 16K cache by 64.4% and TPOT by 22.9–48.5%, and the searched layer-wise budget by InferOpt beats a matched uniform budget by 7.3% and 14.0% of the Full KV reference points. On MoE, a searched top-k schedule by InferOpt removes 43.0% of routed token–expert pairs while staying within 0.59 points of the default, closer than the matched-budget baselines. Against Random Search, NSGA-II, and MOTPE, InferOpt leads on both spaces, taking the best proxy hypervolume and the lowest retention on KV and staying closest to the uncompressed reference at the lowest experts on MoE.

Aviation accident and incident investigations generate extensive unstructured textual information containing evidence relevant to the causes and contributing factors of safety occurrences. Automatically extracting such information is challenging because causal evidence may be distributed across long and complex investigation narratives. This study proposes a semantic causal-factor inference framework combining natural language processing with a variational autoencoder (VAE) to learn the relationship between aviation investigation narratives and expert-reported probable causes. Investigation narratives and their corresponding probable causes are transformed into numerical representations, after which the encoder maps narrative representations to a probabilistic latent space. The decoder estimates representations of the corresponding probable causes and is trained using an objective that combines Kullback-Leibler divergence with cosine-similarity-based semantic reconstruction. The framework was evaluated using 20,919 finalized U.S. National Transportation Safety Board investigation reports from 2005 to 2020. On the held-out test set, the predicted and expert-reported probable-cause representations achieved a mean cosine similarity of 0.786 (SD = 0.120). The predicted representations also yielded interpretable terms associated with causal information in the reports. The results demonstrate the potential of probabilistic latent representation learning for AI-assisted extraction of causal information from aviation safety narratives while retaining expert investigation as the basis for formal causal determination.

The quest for a quantum theory of gravity remains a central challenge in modern physics, driven by the goal of unifying general relativity and quantum mechanics. Direct experimental access to quantum gravitational effects is notoriously difficult due to the inaccessibility of the Planck scale. Recent proposals, however, suggest that gravitationally induced quantum entanglement between two massive particles, realized through advanced quantum interferometric techniques, could provide empirical evidence for the quantum nature of gravity. We demonstrate that the geometrical configuration of an interferometer plays a decisive role in entanglement generation. Our analysis reveals that geometric optimization can substantially enhance the gravitationally induced phase shift, thereby improving the prospects for experimental detection of gravity-mediated entanglement. Moreover, we show that standard approximations employed in prior proposals may severely limit predictive accuracy and compromise experimental feasibility.

Large language models (LLMs) remain vulnerable to jailbreak attacks that conceal harmful intent within complex adversarial prompts. Existing defenses primarily rely on input perturbation or harmful-output suppression, but they rarely model where malicious intent resides, resulting in brittle protection and excessive over-refusal. We propose SENTINEL, a plug-and-play, generation-time jailbreak defense that reframes mitigation as an intent extraction problem. Our key insight is that instruction-tuned LLMs exhibit strong input–output semantic consistency: regardless of jailbreak complexity, generated outputs tend to align with the attacker's true intent. SENTINEL exploits this property by matching semantically aligned input–output regions to extract intention-revealing subsequences, scores these subsequences using refusal-direction projections to estimate harmfulness, and halts generation when necessary. Experiments on HarmBench across multiple LLMs show that SENTINEL reduces jailbreak success rates to close to 5% while maintaining low over-refusal. We further demonstrate robustness to adaptive attacks and provide a mechanistic interpretation: SENTINEL re-distributes jailbreak features from alignment blind spots to aligned regions.

Self-evolving vision-language models (VLMs), a form of self-improvement in which a model generates its own training data from unlabeled images, are a promising route toward agents that expand their reasoning capability in an unsupervised manner, without relying on ever-larger annotation budgets. Existing methods pair a Questioner that proposes problems with a Solver that answers them, but reward both roles mainly by agreement among sampled answers. Agreement is a weak proxy for truth: it cannot tell whether a question is grounded in the image, whether the proposed reference answer is right, or whether a confident majority is wrong in the same way. We present Trinity, in which one VLM plays three roles, Questioner, Solver, and Verifier, and the Verifier is a self-verifier: an exponential moving average (EMA) of the policy itself, requiring neither labels nor an external judge. The Verifier screens every generated question for image grounding and answer correctness before it becomes supervision, scores Solver reasoning against the image, and adjudicates disputes between the reference answer and a strong Solver consensus, correcting the reference and penalizing the Questioner when the consensus is right. Trained on images alone, Trinity improves Qwen3-VL-8B on mathematical visual reasoning and on science benchmarks with biology content, for example, +8.6 points on the biology split of SciVQR and +12.8 on MathVerse, and its reward dynamics behave as a healthy self-play curriculum should. These results suggest that a self-evolving multimodal agent can strengthen its scientific reasoning from unlabeled scientific images alone, with the model itself serving as the verifier.

Status updates let a receiver track a changing process, but a sender that controls when they are sent can steer the receiver's estimate without misreporting. We study competition between two such senders with opposing preferences, who report on a binary continuous-time Markov chain using state-dependent Poisson rates under individual budgets. The receiver follows the reports through a zero-order-hold estimator only if this yields at least the long-run weighted correct-estimation utility of a prior-based default estimate. We model the interaction as a Stackelberg game in which the sender favored by this default leads, the opposing sender follows, and the receiver then selects its estimator. We characterize the pure-strategy equilibria in closed form. When the follower can obtain positive utility against a silent leader, limited state-$0$ reporting by the leader merely frees part of the follower's budget for state-$1$ reports, so every optimal leader policy is either silence or full-budget state-$0$ reporting, depending on explicit budget thresholds. A single sender with the same total budget leaves the receiver at its default utility, whereas the full-budget intervention outcome makes the receiver's participation constraint slack and strictly improves its utility. At the intervention threshold, silence and full-budget intervention yield identical sender payoffs but different receiver utilities. Numerical results illustrate these regimes and compare equilibrium performance with a receiver-optimal reporting benchmark.

Large language models (LLMs) remain highly vulnerable to jailbreak attacks that induce harmful behaviors and circumvent safety alignment. To defend against such attacks, adversarial training paradigms have been proposed to first simulate failure modes and then train the model to correct them, yielding promising improvements in safety alignment. However, these methods typically construct adversarial samples either by encouraging fixed harmful target completions or by performing targeted activation ablation derived from fixed benign–harmful data pairs. As a result, the generated adversarial samples tend to induce homogeneous harmful behaviors that poorly reflect the diversity of behaviors elicited by real-world jailbreak attacks. This behavior-level narrowness fundamentally limits their robustness. To address this issue, we propose a target-free adversarial training framework that generates adversarial samples in an unsupervised manner. By amplifying and diversifying behavior-level shifts in the model's latent space, our approach produces semantically diverse adversarial samples that induce a wide range of harmful behaviors. This expanded behavioral coverage exposes more diverse failure modes and thereby improves safety alignment. To quantify this effect, we use semantic entropy as an output-level measure of adversarial behavioral diversity. Empirically, our method elicits diverse harmful behaviors in the target model, substantially mitigating behavioral narrowness and improving robustness to jailbreak attacks.

Let $\mathcal O$ be an octonion algebra over a field $F$ of characteristic different from $2$, and let $A,B\in\mathcal O$, not both zero. We study the image of the generalized commutator $\Phi(x,y)=A(xy)-B(yx)$ on $\mathcal O$. We prove that $\Phi$ is surjective if and only if either one of $A$ and $B$ is invertible and $A\neq B$, or $A$ and $B$ are nonzero zero divisors and $A-B$ is invertible. In the remaining cases, the image of $\Phi$ is a hyperplane or a four-dimensional maximal totally isotropic subspace of $\mathcal O$, except when $A$ and $B$ are linearly independent zero divisors and $A-B$ is not invertible, in which case the image spans a six-dimensional subspace. Along the way, we show that every octonion of trace zero is a commutator. We also prove that the image of $Axy-Byx$ on any quaternion algebra over $F$ is a vector subspace, extending a result of Panja S., Saini P. and Singh A. (Images of polynomial maps with constants, Mathematika 71 (2025), no. 3, Paper No. e70031) for $2\times 2$ matrices over algebraically closed fields, and we give examples of other generalized polynomials whose images are not vector subspaces.

This paper addresses asymptotic tracking with prescribed transient and steady-state performance for a class of uncertain high-order nonlinear systems with uncertain dynamics. The proposed controller combines a barrier-type transformation of a filtered tracking error with a robust integral of the sign of the error (RISE) mechanism, yielding a continuous and low-complexity design. The proposed method does not employ neural, fuzzy, or other global approximation structures. It is shown that all closed-loop signals remain bounded, the prescribed performance funnel is preserved for all initial conditions in the funnel, and that the tracking error converges asymptotically to zero under appropriate gain selection. The analysis provides a continuous-feedback synthesis that integrates prescribed performance control (PPC) with the RISE methodology. Simulation results on a ship-steering example illustrate the effectiveness of the proposed approach.

Vickers hardness characterizes resistance to indentation but does not distinguish the magnitude of local densification from the volume of glass affected. Here, low-coherence holotomography reconstructs three-dimensional refractive-index (RI) images of Vickers-indented fused silica, borosilicate, and soda-lime glass across applied loads and nominal dwell times. Analysis of RI changes using the Lorentz-Lorenz relation quantifies densification, while segmentation measures the spatial extent of the densified region. Cracks are observed within the same reconstructed RI images. Densified volume increased with load even when peak densification plateaued, and glasses with similar hardness showed different densification responses. Longer nominal dwell times were associated with larger volumes above fixed RI thresholds and comparatively small changes in peak densification. Joint analysis of densification and crack morphology thus characterizes subsurface indentation damage beyond hardness alone. Densification is quantified as an optical estimate under the Lorentz-Lorenz assumptions; residual stress, polarizability, and reconstruction can also affect RI.

We prove sharp Hardy inequalities on $\mathbb{Q}_p^n$ for the quadratic form of the Vladimirov–Taibleson operator, the $L^q$ norm of its fractional derivative, and a nonlinear difference energy. Under the self-dual Fourier normalization, the sharp quadratic-form constant for $0<\alpha<n$ is $[(1-p^{-(n-\alpha)/2})/(1-p^{-(n+\alpha)/2})]^2$, with a remainder given by the ground state representation. For $1<q<\infty$, $q'=q/(q-1)$, and $0<s<n/q$, a weighted Schur estimate determines the exact $L^q$ norm of the weighted Riesz potential $\|\boldsymbol{x}\|_p^{-s}I_s$, giving the sharp linear Hardy constant $[\Gamma_{p}^{(n)}(n/q'+s)/\Gamma_{p}^{(n)}(n/q')]^q$. The two-point Picone inequality and shell decomposition give the sharp constant $2(1-p^{-n})\sum_{m\ge1}p^{-sqm}(1-p^{-(n/q-s)m})^q$ for the Gagliardo-type energy with kernel $\|\boldsymbol{x}-\boldsymbol{y}\|_p^{-n-sq}$. Annular truncations of the critical powers give explicit minimizing sequences with error estimates. Equality is attained only by the zero function in each stated class. For $q=2$, both $L^q$ inequalities reduce to the quadratic-form inequality. Uniform local constancy makes the difference energy finite for every Bruhat–Schwartz function and every $s>0$. The Hardy inequalities on the full test-function space therefore hold precisely when $sq<n$, without the restriction $s<1$.

A weakly nonlinear stability analysis is performed to investigate the influence of thermal buoyancy on phototactic bioconvection in a suspension of swimming microorganisms confined between horizontal boundaries and subjected to bottom heating or cooling. The objective is to examine how thermal forcing modifies the post-critical evolution of bioconvective instability through its influence on bifurcation behaviour and finite-amplitude convection. Linear stability theory is first employed to determine the critical conditions for the onset of convection. The corresponding direct and adjoint eigenvalue problems, together with the second-order resolvent system, are then solved numerically to derive the Stuart-Landau amplitude equation governing the nonlinear evolution of disturbances. A systematic analysis is carried out for varying thermal Rayleigh numbers. The results show that, as the thermal Rayleigh number approaches the classical Rayleigh-Benard critical value, the critical bioconvection Rayleigh number decreases to zero, indicating a gradual transition from phototaxis-dominated to thermally driven convection. The computed positive Landau coefficient predicts supercritical pitchfork and Hopf bifurcations for stationary and oscillatory instabilities, respectively. In parameter regimes with oscillatory onset, increasing the thermal Rayleigh number drives a transition from a supercritical Hopf bifurcation to a supercritical pitchfork bifurcation. The nonlinear dynamics are further characterized through amplitude evolution, phase portraits, potential functions, and finite-amplitude flow structures.

Quantum software testing (QST) is a central quality-assurance activity for checking whether quantum programs conform to their specifications. In the noisy intermediate-scale quantum (NISQ) era, gate, decoherence, and measurement errors distort observed outputs, making it difficult to distinguish program defects from noise. The existing noise-aware QST literature typically mitigates or models noise before applying a test oracle. However, these strategies can incur substantial cost and depend on calibration data, model training, or backend-specific information, limiting their applicability. We present Qomino, a dominance-guided QST approach for judging tests from noisy samples without a separate noise-estimation or mitigation phase. The approach combines decomposition-aware inverse construction, comparison of the expected outcome with the strongest observed competitor, and bounded retries for inconclusive decisions. We evaluate Qomino on 30 controlled buggy variants from six Qiskit programs and six simulated noisy backends, comparing it with six baselines spanning statistical, quantum-specific, and learning-based methods. Qomino achieves 85.65% accuracy over all six programs and 99.95% in the restricted two-program evaluation, significantly outperforming the corresponding baselines. Across the evaluated programs and backends under the stated settings, Qomino is faster than the compared quantum-specific and learning-based methods. Ablation and retry analyses support the contributions of its main components.

Let $X$ be the Cartwright–Steger surface with its real involution $c$ and Albanese map $\alpha:X\to E$, and put $Y=X/\langle c\rangle$. Every smooth real Albanese fiber has two ovals and is nondividing. The branch surface $B\cong\#_3\mathbb{RP}^2$ satisfies $j_*\pi_1(B)=4\mathbb Z\subset\pi_1(Y)\cong\mathbb Z$ and is nullhomologous modulo two. Every smoothly embedded $+1$-sphere representing the positive generator of $H_2(Y;\mathbb Z)$ meets $B$ in at least six points. Its lift has square two, pairs trivially with $K_X$, and has no connected embedded representative of genus zero or one. Circle surgery on an Albanese generator is homeomorphic to $\mathbb{CP}^2$ for either normal framing. Blowing down a positive sphere, if one exists, gives a $\mathbb Z[\mathbb Z]$-homology $S^1\times S^3$ homotopy equivalent to $S^1\times S^3$.

The stochastic gravitational-wave background is targeted by the millihertz observatories LISA, Taiji and TianQin, and its forecast precision rests on a Whittle approximation to the periodogram likelihood. The quoted scale is that of a joint fit a two-step forecast need not reach. We show that the residual risk of a two-step forecast lies in the estimator route rather than in the likelihood. At the exact Whittle form we separate the forecast error into a deterministic bias $\mathbf{b}$ and an efficiency gap $\mathbf{C}_b$, both in closed form. We find that this gap is governed by the span of the first-step nuisance fit. It decreases substantially as the span increases and vanishes when the first-step fit spans the entire band or when the response exhibits no within-bin structure. The gap does not arise as a cost of the prior. Across the LISA band the gap spans more than an order of magnitude, the amplitude and tilt inflation falling from about thirty and twenty to unity at a band-wide first step. A foreground from the released LDC2a population moves the mid-band gap by an order of magnitude. A two-step forecast should therefore report the span of its first-step fit with its intervals, since that span decides whether they sit at the Fisher scale or an order of magnitude above it.

In physics instruction, equations are often treated primarily as tools for obtaining numerical results. Yet physicists also use them to describe dependencies, explain why those dependencies hold, predict what happens in new situations, test expressions against physical knowledge, and explore consequences that are not immediately apparent. Although such uses appear throughout the physics education literature, they have not been brought together in a systematic account, and the terminology used to describe them remains inconsistent. Drawing on research in mathematics education on symbol sense and the function concept, we distinguish six epistemic functions of physics equations: calculating, describing, explaining, predicting, evaluating, and exploring. We then characterize six strategies through which these functions can be realized: dimensional analysis, order of magnitude analysis, covariational analysis, special case analysis, limiting case analysis, and formal analogies, illustrating each with examples from introductory physics. To examine how these strategies are viewed within the discipline, we surveyed 31 physicists at one university faculty about five of the strategies. Respondents regarded the strategies as indispensable to physics, judged limiting case analysis to be more difficult for students than dimensional analysis, and reported that their own courses could devote more time to them. By distinguishing what physicists use equations for from the strategies by which they do so, the paper provides a vocabulary for sensemaking of physics equations and specifies what explicit instruction in these strategies involves.

Vision Transformers (ViTs) achieve strong performance on image recognition and mobile vision applications, but their high-dimensional linear projections and attention computations still impose substantial storage and inference costs. Extremely low-bit quantization is a promising solution, yet ViTs often suffer severe accuracy degradation because conventional real-valued scalar codebooks are poorly matched to the directional geometry of Transformer projections. We present RPFQ-ViT, a Rotated Phase-Frame Quantization method that quantizes paired channels in two-dimensional phase planes, enabling low-bit codes to better preserve projection directions while recovering magnitude with lightweight scaling. RPFQ-ViT serves as a drop-in QAT replacement for nn.Linear and does not modify the standard real-valued attention, normalization, or activation computation graph. On ImageNet-1K, RPFQ-ViT-B/16 reaches 79.33% Top-1 / 94.48% Top-5 under W2/A4, Swin-T reaches 79.30% Top-1 / 94.79% Top-5 under W2/A8, and DeiT-S reaches 77.41% Top-1 / 93.11% Top-5 under W2/A8. Ablations, phase-geometry analysis, and direction-preservation metrics show that channel pairing, learnable rotation, phase-anchor learning, and residual phase refinement each improve quantization quality. We further deploy RPFQ-ViT image-classification models on native iOS and Android runtime stacks; with 2-bit packed weights, model size shrinks by roughly $5.4$-$7.1\times$ relative to FP32 and end-to-end on-device latency drops by $1.4$-$1.6\times$. All ImageNet results trained in our codebase use a matched 300-epoch recipe and are reported as mean accuracies over three independent runs. These results show that RPFQ-ViT provides a favorable trade-off among accuracy, compression, and practical mobile deployment for extremely low-bit ViTs.

Deep learning models for crop leaf disease recognition routinely report near-perfect accuracy yet are typically trained and evaluated on a single dataset collected under controlled laboratory conditions, leaving their behavior under realistic cross-region domain shift poorly understood. We introduce MLD (Multi-crop Leaf Disease) dataset, a unified multi-region benchmark that combines six public crop-disease datasets from the USA, Asia, and Africa into a shared hierarchical taxonomy spanning 18 crops, 56 crop-disease classes (including one healthy class per crop) making 167,427 images. We define standardized single-source and pooled multi-source evaluation protocols that explicitly probe cross-region generalization. We also investigate whether exploiting the inherent crop-to-disease dependency via a hierarchical formulation (HiLeaD) that conditions disease prediction on the predicted crop improves recognition under cross-region shift. Under the HiLeaD, the model trained on PlantVillage achieves 99.07% in-domain disease F1 but collapses to 12.88% when tested on PlantDoc, exposing a severe cross-region domain gap. The model trained on the pooled MLD dataset partly recovers cross-region disease F1 from 12.88% to 39.64% on PlantDoc (HiLeaD), achieving a 26.76 percentage point improvement. The hierarchical formulation provides a consistent additional gain, ranging from 1.71 to 4.88 percentage points in disease F1 over the flat baseline under the MLD dataset indicating that progress in this area is currently limited more by data coverage and diversity than by model design.

We study the joint recovery of an unknown system matrix $A\in\mathbb R^{n\times n}$ and a rank-$r$ initial-state matrix $X_0\in\mathbb R^{n\times m}$ from partial observations of the state matrices $A^tX_0$, for $t=0,\ldots,T$. Each trajectory is observed at a fixed set of state coordinates, which may differ across trajectories. We derive necessary conditions for identifiability, including obstructions arising from incomplete spatial coverage and insufficient dynamical span, as well as lower bounds on the number of observations. We then characterize the Jacobian of the measurement map, account for the intrinsic symmetry of the low-rank factorization, and establish a rank-certificate principle yielding generic local identifiability. When the trajectories whose initial states form a basis of $\operatorname{range}(X_0)$ are fully observed, we obtain necessary and sufficient rank conditions for global recovery, together with explicit reconstruction formulas. We formulate the joint recovery problem as a nonlinear least-squares problem over the system matrix $A$ and the low-rank factors of $X_0$, and solve it using Adam. Numerical experiments on synthetic and real-world data evaluate the recovery performance under different spatial sampling rates and observation horizons.

Recently, Drifting Models and Wasserstein Gradient Flows have attracted substantial attention because they move iterative distributional refinement to training and amortize it into a generator, enabling fast inference. However, existing formulations have been developed largely for continuous Euclidean domains, such as image spaces, where particles admit unconstrained additive updates. On constrained spaces, these updates can leave the valid domain or ignore its geometry, making them unsuitable targets for training. Recent work has adapted updates to these spaces, but has focused on particular fields or offered limited empirical comparison. We derive and compare several geometry-aware fields within a common training framework for one-step generators. We test the method on data with different structures and obtain competitive one-step results in each setting. The best-performing field varies by task, showing why the choice of objective matters in practice.

Optical manipulation enables the control of microscopic particles using light and has become an active area of research in recent years. One particularly interesting aspect is the possibility of generating optical pulling forces with hyperbolic metamaterials (HMMs), which leads to unusual light-matter interactions. In this work, the pulling response of plasmonic, chiral, and dielectric nanorods is studied on an HMM substrate. The system is illuminated by a time-harmonic, plane-polarized laser beam propagating along the +Z to -Z direction. The analysis is carried out under two different configurations. In the first case, plasmonic, chiral, and dielectric nanorods are arranged in a heterogeneous cluster over the HMMs and analyzed for the optical force response under three environmental conditions: fully immersed in water, partially immersed (half air-half water), and fully in air. Full-wave simulations reveal that in all three environments, all the objects (plasmonic, chiral, dielectric) nanorods consistently experience an optical pulling force at the 1E(-20)N scales for clustered configuration. In the second case, each nanorod type was independently placed on the same HMMs substrate within a full-air medium and investigated their force behaviors, while the plasmonic experience 100 times more than others for the single setup, which is 1E(-19)N ranges. Like the case of the cluster, three nanorods alone demonstrate a stable optical pulling force, also getting the pulling force with the variation of length, radius, and distance between them, which makes this optical setup more practical. Plasmonic behavior changes a lot with the arrangement of the nanostructures. On the other hand, dielectric nanorods are affected more by their length than their position. In our results, optical pulling appears for all the nanorods even with a simple HMM structure...

We study Gaussian fluctuations of differential observables of centered stationary random fields on the discrete $d$-dimensional torus of mesh $1/N$. Our main result is a Central Limit Theorem for the fields $f\mapsto N^{-d/2-m}\sum_x\phi_x^N(Pf)(x/N)$, where $P$ is a scalar homogeneous constant-coefficient differential operator of order $m\geq0$ with Fourier symbol $p$, e.g., $P=\Delta$ and $m=2$. Under suitable assumptions on the spectral scaling limit $\gamma$ of the covariance and the normalized cumulants of order $r\geq3$, we prove convergence in law in a negative Sobolev space to a centered Gaussian random distribution with covariance multiplier $|p(k)|^2\gamma(k)$. The two factors separate the effects of the operator and the field and, notably, differentiation can compensate a low-frequency spectral singularity. For the lattice Gaussian Free Field, this gives a projected white-noise limit for the gradient. The proofs use Fourier analysis and the method of moments and cumulants, together with a tightness argument. Finally, we give two sufficient criteria for the cumulant assumption, namely a tree–graph bound and the Dobrushin uniqueness condition for finite-range Gibbs fields, and recover the white-noise limits of the centered Ising magnetization and Potts colour fluctuation fields at high temperature.

In this paper, a complete characterization of the stability and the boundaries of the envelopes for trajectories of the Ćuk converter is provided in the cases of time and state-dependent switching. In particular, difference equations are developed and used to compute boundaries for the system's response envelopes as well as Lyapunov functions to show the system's stability in both continuous and discontinuous regimes of operation. Each case is illustrated by multiple simulations.

Nonreciprocal interactions have emerged as a fundamental driver of collective behavior far from equilibrium. Here, we show that nonreciprocal couplings between spin systems whose isolated dynamics favors ordered states, beyond the previously identified oscillatory (swap) phase, give rise to a richer nonequilibrium phenomenology, including a multistable regime where ordered and disordered states coexist, a scenario strictly forbidden in equilibrium. Crucially, we show that this nonequilibrium phenomenology is inherited directly from the critical properties of the underlying isolated model. In particular, tricriticality in the isolated system gives rise to multistability, hysteresis, and hard excitations in the oscillatory dynamics, while non-normal interactions further enrich the phase diagram by generating multistability. Moving beyond mean-field theory, we derive a universal field equation governing the onset of these nonreciprocal oscillations in finite dimensions. Our results establish a unified theoretical framework connecting critical phenomena, dynamical systems, and non-reciprocal collective dynamics, with applications ranging from opinion dynamics to active matter

Breakthrough Listen, humanity's most ambitious search for technosignatures, or evidence of extraterrestrial technology, is carrying out surveys across the sky and across the electromagnetic spectrum, in images, spectra, time series, catalogs, and alerts. Classical techniques still play a major role in the search, but the recent rapid growth in the capabilities of artificial intelligence is enabling new and more powerful algorithms and approaches to be deployed across enormous datasets. Surveys designed to look for technosignatures are still a major focus for the Breakthrough Listen program, but excitingly, the new strategies also enable comprehensive mining of archives and of general-purpose real-time data streams. We outline how artificial intelligence and machine learning are being used to scale up the search, including with the newly-commissioned Vera C. Rubin Observatory, in addition to radio telescopes around the planet. The chances of a detection have never been better.

The second-order Zarankiewicz number $z_2(m,n)$ and the biquadratic sum-of-squares rank $\mathrm{BSR}(m,n)$ are related by the unconditional hierarchy \[ \mathrm{BSR}(m,n)\ \ge\ z_2(m,n)\ \ge\ z_{SL}(m,n)\ \ge\ z_{RL}(m,n) \ \ge\ z_{wL}(m,n)\ \ge\ z(m,n). \] We introduce the second-order augmented Zarankiewicz number $z_{2A}(m,n)$, obtained from $z_2(m,n)$ by deleting the requirement that the configuration be limited, so that \[ \mathrm{BSR}(m,n)\ \ge\ z_{2A}(m,n)\ \ge\ z_2(m,n). \] Although the defining class is enlarged, $z_{2A}$ still obeys the universal cell bound of Löfberg and Qi, because that bound uses only the \(C_4\)-freeness of the one-edge graph. We prove \[ \mathrm{BSR}(4,4)\ \ge\ z_{2A}(4,4)\ =\ 11\ >\ 10\ =\ z_2(4,4) \ =\ z_{RL}(4,4), \] the first recorded separation between the second-order number and its augmented variant. This result also gives a better lower bound for $\mathrm{BSR}(4,4)$. The lower bound is witnessed by an explicit non-limited $4\times4$ configuration of displayed length $11$ whose recursive-line closure satisfies $(\mathrm{RW}3^+)$; the matching upper bound excludes $12$ by the universal cell bound together with an exact finite classification of the $161$ twelve-square configurations, and \(z_2(4,4)=z_{RL}(4,4)=10\) is the exact value of Xu and Yan.

The increasing availability of generative artificial intelligence (GenAI) tools, such as ChatGPT and code-completion assistants, raises questions about how learners integrate these tools into learning activities, particularly in MOOCs that attract diverse participant populations. This study examines the use of GenAI in two programming MOOCs taught in Estonian that differ in duration, workload, topic complexity, and assignment volume: About Programming (4 weeks, 26 expected hours, n = 187) and Introduction to Programming (8 weeks, 78 expected hours, n = 182). Post-course questionnaire data were analyzed using non-parametric statistical methods to examine self-reported adoption, usage frequency, and purposes of GenAI use across courses and learner backgrounds. The results show that GenAI adoption was widespread in both MOOCs, with no statistically significant differences by gender, age, education level, or prior programming experience. However, participants in the longer, more extensive MOOC reported significantly higher usage frequency and were more likely to use GenAI for debugging and idea generation. Reported usage frequency for code explanation and debugging was also higher in the longer course. Exploratory analyses found limited relationships between GenAI use and learning-related outcomes. The findings suggest that course context may play a greater role than learner characteristics in shaping how GenAI tools are used. These results provide implications for instructional design and guidance in programming education.

Magnetic flux quanta in type-II superconductors are topological excitations of the order parameter whose sensitivity to the local environment makes them probes of current density, magnetic fields, and pinning landscapes. Yet, in planar thin films, individual vortices are difficult to manipulate, often requiring intricate nanopatterning or demanding scanning-probe instrumentation. Here, we show that shaping a superconducting thin film into a three-dimensional curved geometry enables controllable vortex trapping under a spatially uniform applied magnetic field. Employing a conformal formulation of the time-dependent Ginzburg-Landau equation, we simulate vortex dynamics in a cap-shaped superconducting membrane and compare it with a planar reference. Curvature converts the uniform applied magnetic field into a nonuniform local normal component, creating a reconfigurable asymmetric rim-pinning potential tunable by magnetic-field orientation. Rotating the magnetic field therefore controls the number and positions of vortices trapped along the rim. Moreover, the asymmetric pinning produces a superconducting diode effect through current-direction-dependent vortex capture. Three-dimensional curvature thus provides a route to engineer local vortex pinning and realize fluxonic devices with magnetic-field-programmable vortex trapping and transport.

Requirement changes can affect connected stakeholders, constraints, components, and tests. We present World Requirement Model (WRM), which encodes this engineering context as a typed artifact graph and predicts consequences at shared artifact identifiers. Relation-aware attention and typed propagation contextualize nodes; world and decision representations support learned dynamics. Shared readouts score impact, conflict, violation, and defect risk; auxiliary objectives supervise successor adjacency and latent prediction. On 28 scored cases from 282 synthetic cases in six domains, WRM obtains impact mean average precision (MAP) of 0.724 versus 0.623 for a hashed-text multilayer perceptron (MLP), a 16.2% relative gain and paired difference of 0.101 (conditional 95% interval [0.044,0.159]). Lowest-quarter mean AP improves by 32.4%, and equal-domain MAP by 13.3%. Four 47-case comparisons on an expanded corpus show MAP gains of 15.6–29.1% and higher means on all five reported metrics. The recorded advantage thus extends across score summaries and annotation/training settings. Checkpoints were selected on scored cases, and backbones are unmatched, so these results characterize selected systems. Our analysis establishes candidate-coverage bounds and shows that the current linear impact head cannot rerank a fixed world's artifacts across decisions. WRM contributes an artifact-addressed world-model formulation, comparative evidence for contextual consequence scoring, and explicit conditions for evaluating requirement-world prediction.