Papers

Weight-space post-training quantization (PTQ) must choose finite formats, granularities, quantizer families, transformations, and bits before the completed quantized model reveals its output-distribution drift. Existing PTQ methods predict important pieces of this degradation, including reconstruction error, Hessian sensitivity, transformation effects, and downstream loss, but these pieces are usually scored after fixing the quantization geometry or inside separate configuration families. We formulate weight-space PTQ as pre-deployment configuration selection using priced layer-output error. Each admissible layer configuration is treated as an error generator with a deployment cost, which induces a layer-output error covariance $\boldsymbol{\Sigma}_l(\alpha_l)$, and the full-precision model prices that covariance by downstream curvature, $\widehat{\rho}_l(\alpha_l)=\frac{1}{2}\operatorname{Tr}\left(\widehat{\mathbf{H}}_l\,\widehat{\boldsymbol{\Sigma}}_l(\alpha_l)\right)$. The price follows from full-precision-to-quantized forward KL, whose first-order term cancels at the reference model. It turns reconstruction and diagonal scores into reduced proxies that drop price factors, while finite formats, codebooks, granularities, and equivalent transformations become comparable candidates through the covariances they induce and the costs they pay. A trace reduction then yields a calibration-time price table and a budgeted price-guided selector, making fixed-geometry bit allocation a special case rather than the organizing problem.

Chatterjee's estimator uses only two local comparisons per interior observation, leaving a finite-replication variance gap under fixed alternatives. We introduce BRACE, short for blockwise rank aggregation for correlation estimation, which replaces adjacent comparisons with local blocks and averages every within-block rank difference. The block size controls the variance cost of finite local replication. An L2 expansion separates the efficient first-order component of the response-rank statistic from an orthogonal finite-replication component. For an admissible diverging block size, the latter vanishes, so the direct rank estimator attains the information bound. The decomposition yields a consistent variance estimator and Wald confidence intervals under fixed alternatives. At independence, the efficient first-order term vanishes, and the proposed estimator enters a second-order regime in which the same factor controls its null variance.

Three-photon photoemission (3PPE) signals on NiTe$_{2}$ are observed for the first time upon ultraviolet excitations. In the energy range beyond two-photon excitations, an energy-momentum dispersive feature is clearly identified with characteristic light polarization dependence. Based on its dispersion, spectral width, as well as intensity as a function of the parallel momentum, this dispersive 3PPE feature could be ascribed to an image potential resonance overlapping with an unoccupied Ni $4s$ -Te $4d$/$5p$ bulk band in accordance with the electronic band structure. Our results underlie higher-order non-linear photoemission on metallic transition metal dichalcogenides and facilitate future ultrafast studies of coherent electron dynamics in anisotropic, two-dimensional systems.

We study a class of Dirichlet problems for coupled quasilinear elliptic systems driven by the $p$–Laplacian in a bounded domain, where the nonlinear terms split into a critical homogeneous part and a convex subcritical perturbation. Using variational methods, a nonlinear eigenvalue theory based on the Fadell–Rabinowitz $\mathbb Z_2$–cohomological index, and a refined linking construction, we prove the existence of a nontrivial solution for every parameter value under suitable dimensional assumptions. We also treat a nonhomogeneous version with small forcing terms by applying a recent abstract perturbation theorem, yielding the existence of two distinct nontrivial solutions.

Modern coherent imaging commonly treats defocus interference as an undesirable artifact to be suppressed. Here, we show that this interference is instead a deterministic projection shadow associated with broken time-reversal symmetry (TRS) under finite-aperture observation. The resulting non-unitary observation operator imposes irretrievable information loss, making this shadow an unavoidable coherent residual. We demonstrate that suppressing this residual beyond the measurement support can yield physically inconsistent reconstructions by assigning unconstrained components within the null space, thereby disrupting the propagation of the reconstructed complex field. We term this failure mode physical overfitting and introduce the complex-field TRS residual metric, R_TRS(z). By using the measured axial evolution of the projection shadow as a z-resolved physical reference, the metric extends fidelity assessment from two-dimensional (2D) detector-plane agreement to propagation-resolved three-dimensional (3D) complex-field consistency. These results establish a physical constraint on phase-space retrieval and wave-based inverse reconstruction.

We realize the $\mathrm{SU}(3)$ Verlinde sums $V_n(m)$, up to an explicit factor, as the values at $n$ of the spectral zeta function of a higher-order Laplace operator on the triangular discrete torus on $m^2$ vertices. For fixed $m$, we express their generating function in terms of the logarithmic derivative of an associated even spectral polynomial and express this polynomial as an explicit iterated resultant. Exploiting permutation symmetry, we prove that this polynomial is a cube over $\mathbb{Q}$, apart from an explicit quadratic factor when $3\mid m$. This factorization yields shorter linear recurrences satisfied by $V_n(m)$ with constant coefficients. We also derive Binet-type formulas expressing $V_n(m)$ as finite linear combinations of powers of rescaled inverse squares of the roots of the spectral polynomial. These results provide an efficient algorithm for computing these Verlinde sums. Several fully developed examples demonstrating computational efficiency of the method are given, including expressions in terms of Fibonacci and Lucas numbers.

In [Be17], we introduced the notion of emergence to quantify the statistical complexity of a dynamical system. Roughly speaking, emergence measures the number of probability measures required to describe, up to a given precision $\epsilon$, the statistical behavior of most orbits. A system is said to have high emergence when this number grows super-polynomially as $\epsilon\to0$. We survey recent developments in a program aimed at understanding the prevalence of high emergence in differentiable dynamics. We review several notions of emergence and their connections with quantization, ergodic decompositions, and entropy, and discuss examples exhibiting high or maximal emergence in conservative, symplectic, analytic, and dissipative dynamics, as well as in constrained families such as unimodal, Hénon, and rational maps. We also present new results concerning variants of metric and topological emergence, convexity properties, local emergence, and variational principles, together with a collection of open problems on the typicality of high emergence.

The growth of large language model (LLM) inference and search services increases the scale of online linear programming problems, motivating computationally efficient algorithms. We develop resource-adaptive stochastic gradient descent (RASGD) for stochastic online linear programming. The algorithm uses one request and current inventory to update resource prices, requiring O(m) operations for m resources and memory per arrival and no LP or sample-average optimization. The central idea is to express the current-resource pricing logic of re-solving through a first-order SGD update: each arrival refreshes the remaining-inventory allowance in the dual objective, while the stepsize decreases for early learning and increases later to match the speed of inventory adjustment. Under standard non-degeneracy conditions, our algorithm is feasible on every sample path and achieves O(\log T) expected regret against the realized fractional hindsight optimum, which matches the lower bound, even for policies that know the distribution and have unrestricted computation. The analysis converts curvature around the fixed reference price into inventory stability without tracking optimal prices at changing resource levels. Numerical experiments show that RASGD achieves regret competitive with per-arrival LP re-solving and improves upon the tested first-order baselines, while retaining the computational efficiency of first-order methods. These results establish RASGD as a computationally efficient approach to achieving high allocation quality in large-scale OLP.

Deploying deep learning models on edge CPUs is bottlenecked by computational and memory constraints. Mixed-precision quantization promises to reduce inference latency while preserving accuracy. However, quantization affects different layer types in inconsistent ways, so identifying where accuracy loss is minimized and latency reduction is maximized is critical, as the effect accumulates over a full deployment into substantial savings or unacceptable task degradation. Such identification relies on sensitivity metrics, proxies that estimate layer-wise degradation without evaluating the task accuracy of every candidate policy. Nevertheless, widely used metrics fail systematically on modern architectures. We present a systematic empirical study of 13 sensitivity metrics for layer-wise INT8 quantization across four distinctly different neural networks, and validate the resulting policies on two ARM64 platforms. Gradient-based sensitivity methods fail on 4 out of 8 model-hardware configurations and weight-based statistics on 2. In contrast, the Jensen-Shannon Divergence achieves zero catastrophic failures, reliably isolating the layers that cannot be safely quantized. A sensitivity metric alone does not define a policy, and the fixed thresholds typically used for that step are fragile over the highly skewed distributions of modern architectures. We address this with K-Means clustering, achieving near-lossless accuracy and a mean speed-up of $1.81\times$ over the full-precision model. Finally, we reveal that excluding from quantization the layers whose speed-up is negligible, regardless of their sensitivity, can be counterproductive, as it induces computational graph fragmentation and disables operator fusion. Our results yield concrete allocation policies for practitioners and researchers deploying quantized vision models on heterogeneous edge CPUs, without GPU access or gradient computation.

Photoacoustic (PA) imaging provides molecular and functional information about tissue, such as blood oxygen saturation (sO2), yet its clinical translation is hindered by inaccurate quantification. A major source of error is the spectral colouring effect, in which wavelength-dependent optical attenuation distorts the local optical fluence. Monte Carlo (MC) simulation is the gold standard for modelling light transport, but its computational demand precludes real-time use. Here, GenMC is presented, a deep generative framework based on a conditional generative adversarial network that estimates optical fluence distributions from tissue anatomy and literature-derived optical properties, with anatomical priors obtained from co-registered ultrasound images. Trained on MC-generated synthetic datasets, GenMC produces high-fidelity fluence maps in under 30 ms per frame, a four-orders-of-magnitude speed-up over conventional MC simulation, and reaches peak signal-to-noise ratios of up to 36.24 dB in vivo, outperforming UNet and Pix2Pix baselines. Validation in blood-mimicking phantoms and in 37 human volunteers spanning Fitzpatrick skin types III-V demonstrates improved accuracy, robustness, and physiological consistency of sO2 estimation. By enabling real-time, accurate, and reproducible quantification of tissue oxygenation, GenMC addresses a critical barrier to quantitative PA imaging and offers a general strategy for rapid, high-fidelity approximation of light transport in tissue.

We investigate a class of mixed-order quasilinear elliptic equations in \(\mathbb R^N\) driven by the \(q\)-biharmonic and \(p\)-Laplacian operators, \[ \Delta_q^2u-\Delta_pu = \lambda\frac{|u|^{r_\sigma-2}u}{|x|^\sigma} +|u|^{p^*-2}u +|u|^{q^{**}-2}u, \] where \(1<q<N/2\), \(1<p<q^*\), \(p\ne q\), \(q\ne p^*\), and the weighted exponent is determined by the natural scaling of the equation. We establish compact weighted embeddings compatible with this mixed scaling and develop the corresponding variational framework. As an application, we prove existence and multiplicity of nontrivial solutions under suitable assumptions on the parameters. We also establish a local regularity result for the more general equation $\Delta_q^2u-\Delta_pu=f(x,u),$ where \(f\) is a Carathéodory function with local critical growth. By combining nonlinear potential estimates, a regularity-lifting argument, and a finite bootstrap for an associated second-order system, we obtain higher local regularity of both \(u\) and the nonlinear flux \(|\Delta u|^{q-2}\Delta u\). This regularity result, which is also of independent interest, enables us to derive a Pohozaev-type identity for the equations under consideration.

We present a new Python package called FETA to compute fission observables. In comparison to existing fission event modeling codes on the market, FETA is a modular, flexible, and code-agnostic wrapper around a statistical reaction theory program. In this paper, we report on version 2.0 of FETA, which simulates the prompt decay of the fragments with the LLNL-developed Hauser-Feshbach code YAHFC. We discuss the design philosophy of FETA, present some validation results for the neutron-induced fission of 239Pu, and briefly outline the structure of the package.

Robotic assembly in high-mixture settings requires adaptable systems that can handle diverse parts, yet current approaches typically rely on policies specialized to each insertion task. Although this can reach high success rates, it makes the process of deploying systems for new problems tedious and time consuming. We present a framework for generalizable insertion using world models that combine robot proprioceptive information with raw visual observations captured by a wrist-mounted camera. Our model-based approach trains a single world model on up to 90 insertion tasks with geometrically diverse parts, achieving 56% zero-shot success on unseen objects with unknown geometry compared to just 7% with a model-free baseline. Importantly, performance improves as more objects are included in the training dataset, demonstrating strong scalability. Lastly, finetuning the generalist model on held-out objects significantly enhances data-efficiency compared to training from scratch and, in some cases, achieves better asymptotic performance. To our knowledge, this is the first system capable of assembling unseen objects in an entirely data-driven manner, and thus represents a significant step toward scalable, generalizable robotic assembly systems.

Luminous young galaxies have been uncovered with relative ease by JWST, extending to z=14.5, so it is puzzling that deeper spectroscopy of fainter candidates now finds only interlopers. This redshift `ìmpasse" is underscored by the measured stellar ages of these high-z galaxies, which we show converge to zero by z=15, with a marked absence of earlier star-formation. Taken literally, such a late transition from the Dark Ages to luminous galaxies is unlike the gradual Cosmic Dawn of standard LCDM, but does confirm a key prediction of Wave Dark Matter, $\psi$DM, as a Bose-Einstein condensate. The de Broglie wave pressure resists gravity until a substantial Jeans mass of $4\times 10^9M_\odot$ is overcome at z$=$15, corresponding to a light boson $m_\psi=2.2_{-0.3}^{+0.4} \times 10^{-22}$eV, and similar to independent estimates from lensing anomalies and dwarf galaxies. Furthermore, the substantial luminosities of the highest redshift galaxies appear to converge to the initial Jeans scale of $\psi$DM, whereas LCDM predictions extend to lower luminosities and larger ages than observed. These contrasting predictions can be definitively tested as JWST observations accumulate, with diametric implications for Dark Matter as heavy particles beyond the Standard Model or ultra-light bosons motivated by the String Axiverse.

Vision-Language-Action models provide a strong foundation for general-purpose robot control, yet a vast majority of policies do not preserve and leverage episode-level information beyond the current observation. This limitation is consequential in history-dependent manipulation tasks that depend on information available only in past observations. Retaining past observations in context can aid in recovering this information, but at the significant cost of ever-growing, bloated context and inference latency. We thus introduce MemBodied, a fixed-size episodic memory with two complementary components: an associative state that records interactions across policy calls and an episode anchor that preserves a compact representation of the initial scene as a reference. At each policy call, the model conditions action generation on the current input and the memory components, rather than directly using past observations. Across five evaluated RMBench tasks requiring memory, MemBodied achieves $7.81\times$ the mean success rate of a stateless policy and $2.98\times$ of vanilla recurrent memory, while outperforming the strongest memory-augmented baseline by $1.3\times$ with $10\times$ fewer added parameters. On the fully observable LIBERO-Long suite, it reached 90.6%, a 5.4% improvement over the stateless $\pi_0$ policy. These findings support MemBodied as a practical alternative to expanding the policy context for history-dependent manipulation.

This paper proposes adaptive tensor tracking for angular trajectories (ATTRACT), a structure-aware alternating least squares algorithm for low-latency target tracking in reconfigurable intelligent surface (RIS)-assisted sensing. The received echo is represented as a dynamic third-order PARAFAC tensor that separates angular, delay, and Doppler information. Unlike batch tensor estimators, ATTRACT processes one data slice at a time and carries forward the preceding factor estimates, avoiding the need to collect an entire sensing window before updating the target state. Its distinguishing feature is the integration of delay and Doppler structure into each iterative update through the known transmitter-RIS channel, pilot signals, and RIS configurations. Numerical results show that, for a large enough RIS, ATTRACT achieves accuracy comparable to the offline tensor baseline at high signal-to-noise ratios while reducing computational overhead and providing slot-wise estimates.

For finite groups $G$, we discuss the enrichment of equivariant $KK$- and $E$-theory in genuine $G$-spectra.

We give an elementary exposition of the tilted sieve introduced by GPT-5.6~Sol \cite{GPT2026}, showing that one residue class modulo each prime $p \le x$ can cover an interval of length \begin{equation*} \gg \frac{x\log x}{(\log_{2} x)\log_{3} x}. \end{equation*} This improves the classical Erdős–Rankin bound by a factor of $(\log_{2} x)/(\log_{3} x)^{2}$. Although weaker than the strongest known bounds, it shows what the tilt and its associated covering of composite survivors achieve without Maynard sieve weights or a hypergraph covering theorem. The proof uses the prime number theorem, Mertens' reciprocal-prime formula, and elementary probability. The appendices provide a historical survey and self-contained proofs of the classical Erdős–Rankin bound.

Background: Wearable devices provide continuous, objective measures of daily activity and offer promise for assessing sleep disorders. However, the minimum monitoring duration needed to differentiate insomnia severity remains unclear. We investigated when wearable-derived behavioral features become informative for distinguishing Insomnia Severity Index (ISI) categories and examined the contribution of Activity Count (AC) and circadian-derived features. Methods: We analyzed wearable data from 2,305 participants in the Advancing Understanding of Recovery after Trauma (AURORA) study. Separate binary classifiers were developed for four ISI categories across six follow-up periods using AC and circadian-derived feature sets. Performance was evaluated using accuracy, F1-score, precision, recall, and AUROC. Results: Classification improved with longer monitoring. Across ISI categories, approximately eight weeks was the earliest time point at which wearable-derived features consistently achieved informative discrimination, with modest improvements thereafter. Participants without clinically significant insomnia were easiest to identify, reaching an AUROC of 0.693. Circadian-derived features performed comparably to, and in several cases better than, AC features, suggesting that the temporal organization of daily activity provides information beyond overall activity volume. Conclusions: Approximately eight weeks of longitudinal wearable monitoring may represent a practical minimum for differentiating ISI-defined insomnia categories. Longer monitoring provided only incremental improvements. Circadian behavioral features show promise as digital biomarkers for objective insomnia assessment.

We prove nonlinear Landau damping for the two-dimensional Vlasov–Poisson system in the unconfined Euclidean setting near the homogeneous Poisson equilibrium \[ \mu(v)=\frac{1}{2\pi}(1+|v|^2)^{-3/2}. \] For small, smooth, localized, and neutral perturbations we establish global existence, quantitative pointwise decay estimates for the electric field, and scattering to free transport. The result we prove here appears to be the first nonlinear Landau damping result for solution of the unconfined 2D Vlasov–Poisson system. The uniform Penrose stability bound degenerates at low spatial frequencies, giving rise to weakly damped plasma oscillations. We separate a faster-decaying regular field from oscillatory components with temporal factors $\cos(t)$ and $\sin(t)$. The proof combines a Volterra representation of the density, weighted estimates for the characteristic flow and nonlinear moments, and integration by parts in time. Neutrality supplies the spatial cancellation needed in the critical two-dimensional estimates.

At test time, large language models (LLMs) can encode historical information in activation memory (i.e., KV caches) and parametric memory (i.e., updated parameters). While activation memory is generally considered effective for factual recall and parametric memory for learning new tasks, their interplay remains unclear. In this work, we systematically investigate the role of memory in few-shot learning through controlled experiments. We find that activation memory is superior for recalling facts, whereas parametric memory does not consistently outperform activation memory in task learning. Moreover, our experiments show that the composite task, Conditional Arithmetic, requires the synergy of both memory types. Through neuron-level analysis, we find that the model activates distinct sets of neurons when accessing the same historical information through activation versus parametric memory. When both memory types are combined, the model recruits neurons from both sets, which is crucial for solving Conditional Arithmetic. These findings suggest that neither memory mechanism alone is sufficient for this composite task, highlighting the importance of their collaboration.

Metastable quantum materials often occupy narrow composition windows with local symmetries distinct from competing equilibrium structures. These features open pathways for realizing qualitatively new electronic properties within a similar chemical subspace while at the same time complicating their deterministic synthesis. Here we illustrate a post-growth solid-state dealloying process using epitaxial ternary thin films in the La–Ag–Ge chemical space to realize a diffraction-averaged centrosymmetric superconducting structure. The process converts polar $P6_3mc$-LaAgGe into diffraction-averaged centrosymmetric AlB$_2$-type $P6/mmm$ La-Ag-Ge through net Ag loss during annealing at 800–900 $^\circ$C. Atomic-resolution electron microscopy reveals local Ag–Ge displacements of both signs relative to the planar configuration, consistent with local inversion-symmetry-breaking distortions. The converted films exhibit composition-dependent superconductivity with critical temperatures below 1 K and in-plane upper critical fields that exceed the weak-coupling Pauli-field estimate by a factor of approximately 6 in the thinnest superconducting films. These results establish epitaxial solid-state dealloying as a route to phase-selective synthesis of metastable phases, offering control over atomic-scale structural configurations and their interplay with emergent electronic properties.

We present hyperbolix, an open-source library for hyperbolic deep learning in JAX, built on Flax NNX. To our knowledge, it is the first comprehensive, general-purpose hyperbolic deep learning library in JAX. It includes six manifolds with a common interface: Euclidean space, the Poincaré ball, the hyperboloid, the $\kappa$-stereographic model, mixed-curvature product spaces, and the proper velocity space. We implement layer families that cover linear layers, convolutions, attention, normalization, positional encoding, regression, and vector quantization. These building blocks span methods ranging from Ganea's original hyperbolic neural networks to recent fully hyperbolic architectures such as Hypformer and Lorentzian ResNet. Additionally, hyperbolix contains Riemannian optimizers implemented as optax transformations, wrapped distributions, and hyperbolic dimensionality-reduction techniques. Its API uses idiomatic JAX: Manifolds are stateless, with curvature being passed at call time, while manifold operations act on single points, with vmap enabling batch operations. The precision of every checked operation is tested against a closed-form NumPy/SciPy transcription from the source paper or a finite difference, for both float32 and float64. On the hyperboloid, standard formulas for two-point operations, such as the distance, lose precision far from the origin, because they subtract two large, nearly equal terms. hyperbolix replaces these subtractions with cancellation-free formulas that stay accurate in float32 at distances where prior implementations return NaN. hyperbolix is available under the MIT license at https://github.com/timoklein/hyperbolix .

Large Language Models (LLMs) introduce an exciting new paradigm for planning and navigation in robotics, but fail on even simple multi-robot tasks as team sizes grow. We propose COMPASS, a scalable, decentralized multi-robot architecture for controlling large collectives of agentic robots with reasoning space feedback control. Feedback is generated locally on each robot by a spatial transformer which aggregates multi-hop messages across the fleet into a learned feedback token. Our experiments find that collectives of language models demonstrate performance gains from structured diversity of the input command, which can cancel biases; an advantage that is held across scale. Compared against a centralized frontier LLM policy and a language-only communication ablation, we find that the coupled design of COMPASS decisively produces cohesive flocking formations that accurately fly the commanded intent. We show that reasoning feedback works best when composed with a compact learned token. Our ablations show that hand engineered feedback with raw state appearing in the language channel obliterates cohesion. COMPASS generalizes zero-shot to unseen instructions of ambiguous meaning while commanding flocks up to 16 times its training scale, flying up to 1024 robots under natural language commands.

For smooth convex–concave minimax optimization, the higher-order lower bound of Chen et al. (2026) applies to a restricted tensor-algorithm class with prescribed regularized Taylor-model updates. We establish the same bound for arbitrary adaptive deterministic and randomized algorithms, matching, up to logarithmic factors, the upper bound of Zhang et al. (2026). Fix an integer $p\ge 2$ and let $L_p>0$ bound the Lipschitz constant of the objective's $p$-th derivative on a compact convex product domain of diameter at most $D_Z>0$. Each feasible query returns the objective value and all derivatives through order $p$. For accuracy $\epsilon>0$, set $Q_{\mathrm{tan}}=L_pD_Z^p/\epsilon$ for tangent residual and $Q_{\mathrm{gap}}=L_pD_Z^{p+1}/\epsilon$ for saddle gap. Let $T_E^{\mathrm{det}}(\epsilon)$ and $T_E^{\mathrm{rand}}(\epsilon)$ denote the high-dimensional minimax query complexities for criterion $E\in\{\mathrm{tan},\mathrm{gap}\}$, with randomized success probability at least $2/3$ on every instance. Our lower bounds and the existing upper bound give $c_pQ_E^{2/(3p-1)}\le T_E^{\mathrm{rand}}(\epsilon)\le T_E^{\mathrm{det}}(\epsilon)\le C_pQ_E^{2/(3p-1)}[1+\log(3+Q_E)]^{6(p-1)}$ for sufficiently large $Q_E$, where $c_p,C_p>0$ depend only on $p$. Thus the same accuracy exponent holds beyond tensor update rules, even for randomized queries and arbitrary feasible outputs. The proof constructs a scalar convex–concave chain with exactly flat gates that hide complete derivative information. Direct product-domain error witnesses and adaptive transcript arguments establish the lower bounds for both criteria.

Large language models (LLMs) have shown strong performance in creative text generation, yet their ability to produce culturally grounded and stylistically constrained literary forms remains underexplored. Prior work has focused largely on modern language varieties and poetry, while classical prose traditions such as maqama remain largely unstudied. The maqama is a classical literary genre characterized by rhymed prose (saj), dense rhetorical ornamentation, and episodic narrative structure, making it a challenging testbed for evaluating whether LLMs can move beyond surface fluency toward deeper literary competence. In this paper, we present the first controlled evaluation study of maqama generation with LLMs, comparing five models under zero-shot, few-shot, and rule-based prompting, and evaluating outputs through both human annotation and an LLM-as-a-judge framework across dimensions such as rhetorical richness, saj density, structural coherence, and stylistic authenticity. Our results show that prompting strategy plays a strong role in stylistic quality: few-shot prompting most consistently improves saj density, while its effects on rhetoric and coherence vary by model, with the strongest models (GPT-4o and GPT-5.4-mini) benefiting most from rule-based prompting on these dimensions, though zero-shot prompting yields the highest aggregate scores across all five models. We further observe systematic differences between models in stylistic alignment with Arabic maqama conventions, and corroborate our findings with a second independent LLM judge, paired statistical significance testing, and non-LLM proxy measures of saj.

This paper presents the design and experimental evaluation of a fully solderless realization of a 400 V, 2.5 kW GaN-based variable speed drive (VSD), using screw-clamped resin molds and rubber compression pads instead of soldered interconnections. The power stage uses 650 V GaN power transistors and is operated at a switching frequency of 200 kHz. The solderless demonstrator is compared to a soldered reference realization using an identical printed circuit board (PCB). Over 120 thermal cycles with heatsink temperatures up to 90 {\deg}C, the solderless contacts show no degradation in effective on-state resistances (including contact resistances). Separately, open-loop vibration sweeps from 5 Hz to 2 kHz with acceleration amplitudes above 10 g were performed on the solderless assembly and left the continuously powered demonstrator electrically intact; subsequent resistance and nominal-power checks likewise indicate no contact degradation. An initial life-cycle assessment (LCA) indicated a higher embodied carbon footprint for the solderless realization due to 3D-printed resin molds, whereas a prospectively evaluated injection-molding scenario reduces the carbon footprint to near that of the soldered reference. The solderless assembly furthermore enables non-destructive component replacement, as demonstrated after a power transistor failure, as well as component re-use. These results support the feasibility of repair-oriented, industrially relevant kilowatt-class solderless power converters.

The Ideal Membership Problem (IMP) asks whether a polynomial f belongs to an ideal <p_1, ..., p_m> of Q[x_1, ..., x_n]. Polynomial Calculus (PC) certifies membership by deriving f from the generators, and a degree-d derivation needs at most n^O(d) steps. We write PC-IMPd for the problem of producing a degree-bounded PC certificate, and call it solvable when one is guaranteed to exist and can be found in time n^O(d). Over Q, unlike over finite fields, a derivation may need exponentially many bits. We study PC-IMPd on instances arising from constraint satisfaction problems, and ask for which constraint languages L it is solvable. Our main contribution is a reduction framework for PC-IMPd, based on pp-definitions, pp-interpretations, and pp-encodings, that mirrors the algebraic approach to CSP complexity. Solvability is preserved by these constructions and, in the language of algebras, by passing to subalgebras, finite direct powers, and homomorphic images. We obtain new tractable classes over ternary and larger domains: every language closed under the median operation on a finite chain has solvable PC-IMPd, by reduction to the Boolean majority algebra, and in particular so does every language over {0, 1, 2} closed under a fixed-value majority. This also places IMPd(L) in P for such languages, advancing the classification of IMPd over ternary domains. In the process, we settle the last open case of the Boolean dichotomy for IMPd(L) and complete the Boolean classification of PC-IMPd(L) with an unconditional lower bound for an instance of PC-IMP1. A recent PC-to-SoS simulation reduces degree-automatability of Sum-of-Squares (the open problem of finding a degree-d SoS proof in time n^O(d) when one exists) to solvability of PC-IMPd. Each new tractable class therefore yields a family of constraint systems on which SoS proofs are degree-automatable.

We study the nonparametric statistical inverse problem of recovering the space-dependent permittivity in a coupled Fokker-Planck-Darcy system from discrete, noisy observations of the Fokker-Planck solution. We consider the coupled parabolic-elliptic system on a bounded domain with the physically natural no-flux boundary condition for the Fokker-Planck equation and homogeneous Dirichlet boundary conditions for the Darcy equation. The inverse problem is indirect, since the unknown coefficient enters only through the elliptic equation and is observed only through its effect on the density in the parabolic equation. We first develop the analytical theory of the forward problem required for the statistical analysis, establishing well-posedness and a priori bounds uniform over the admissible set of permittivities. We then derive two stability estimates for the inverse problem, namely a Lipschitz-type forward estimate and a generalized backward estimate. Placing a rescaled Gaussian process prior on the log-shifted permittivity, we show that the posterior contracts around the truth at an explicit polynomial rate in the number of observations, with the posterior mean converging at the same rate. Numerical experiments in one and two dimensions, using preconditioned Crank-Nicolson and ensemble Kalman filter algorithms, complement our theoretical results.

Encrypted quantum cloning distributes an unknown $k$-qubit state among $m$ individually concealed signals, each permitting exact recovery when combined with a common quantum key. While canonical constructions rely on maximally entangled resources, they do not establish which multipartite states are necessary or sufficient for this task. Here we derive necessary and sufficient conditions characterizing all pure resources compatible with a prescribed sector-wise two-Pauli encoder for $m\geq 2$, with necessity holding for arbitrary completely positive trace-preserving recovery maps. The classification reveals a sharp parity dependence: even $m$ requires maximal signal–key entanglement, whereas odd $m$ admits nonmaximally entangled resources when their residual signal correlations belong to an encoder-selected commuting algebra. Beyond this architecture, we show that exact recovery from every authorized subsystem under arbitrary unitary encoders acting on the input and signals while leaving the key untouched necessarily implies perfect individual concealment, requires at least $(m-1)k$ ebits of signal–key entanglement, and imposes spectral constraints on the resource. For graph states, the classification reduces to an exact cut-kernel criterion, enabling binary certification and constructive Clifford recovery. In particular, a rank-deficient three-output resource in the YZ/ZY branch attains the general entanglement lower bound with two ebits rather than three. We also exclude the entire Dicke family, including $W$ states, within the two-Pauli architecture. Together, these results distinguish fundamental entanglement requirements from encoder-dependent correlation constraints, providing an exact characterization of resource admissibility and a constructive recovery framework for graph states.