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As prompts become central to Large Language Models (LLMs), optimizing them is vital. Textual Stochastic Gradient Descent (TSGD) offers a data-driven approach by iteratively refining prompts using LLM-suggested updates over minibatches. We empirically show that increasing training data initially improves but can later degrade TSGD's performance across NLP tasks, while also raising computational costs. To address this, we propose Textual Stochastic Gradient Descent with Momentum (TSGD-M)—a scalable method that reweights prompt sampling based on past batches. Evaluated on 9 NLP tasks across three domains, TSGD-M outperforms TSGD baselines for most tasks and reduces performance variance. 

Abstract BackgroundThermomechanical testing of nanomaterials is essential to assess their performance in applications where thermal and mechanical loads occur simultaneously. However, developing a multi-physics testing platform for nanomaterials that integrates temperature control, displacement control, and force sensing remains challenging due to the interference between heating and mechanical testing components. ObjectiveThis work aims to develop a novel microelectromechanical system-based platform for in situ thermomechanical testing of nanomaterials with displacement control and precise temperature regulation. MethodsThe platform integrates a high-stiffness thermal actuator, Joule heating elements, and a capacitive displacement sensor, along with sample stage heaters featuring thermal insulation and thermal expansion compensation structures. Finite element analysis was used to optimize the design and minimize thermomechanical interference. Heating performance was characterized using Raman spectroscopy and resistance measurements. ResultsDisplacement control and precise localized temperature control are achieved, overcoming limitations of transient heat transfer and thermal drift observed in previous systems. Its performance is demonstrated through in situ thermomechanical tensile testing of silver nanowires, showcasing its capability for nanoscale material characterization. ConclusionsThe developed microelectromechanical system platform enables thermomechanical investigation of size-dependent phenomena in nanomaterials, such as phase transitions and temperature-dependent fracture. Its displacement control and localized temperature regulation, combined with in-situ observation, provide a powerful tool for understanding nanoscale deformation and fracture mechanisms. 

Abstract In this paper, we design a tunable phase-modulated metasurface composed of periodically distributed piezoelectric patches with resonant-type shunt circuits. The electroelastic metasurface can control the wavefront of the lowest antisymmetric mode Lamb wave (A₀mode) in a small footprint due to its subwavelength features. The fully coupled electromechanical model is established to study the transmission characteristics of the metasurface unit and validated through numerical and experimental studies. Based on the analysis of the metasurface unit, we first explore the performance of electroelastic metasurface with single-resonant shunts and then extend its capability with multi-resonant shunts. By only tuning the electric loads in the shunt circuits, we utilize the proposed metasurface to accomplish wave deflection and wave focusing ofA₀mode Lamb waves at different angles and focal points, respectively. Numerical simulations show that the metasurface with single-resonant shunts can deflect the wavefront of 5 kHz and 6 kHz flexural waves by desired angles with less than $2\mathrm{\%}$deviation. In addition, it can be tuned to achieve nearly three times displacement amplification at the designed focal point for a wide range of angles from $-{75}^{\circ }$to 75^∘. Furthermore, with multi-resonant shunts, the piezoelectric-based metasurface can accomplish anomalous wave control over flexural waves at multiple frequencies (i.e. simultaneously at 5 kHz and 10 kHz), developing new potentials toward a broad range of engineering applications such as demultiplexing various frequency components or guiding and focusing them at different positions. 

Summary The ingenious approach of Chatterjee (2021) to estimate a measure of dependence first proposed by Dette et al. (2013) based on simple rank statistics has quickly caught attention. This measure of dependence has the appealing property of being between 0 and 1, and being 0 or 1 if and only if the corresponding pair of random variables is independent or one is a measurable function of the other almost surely. However, more recent studies (Cao & Bickel 2020; Shi et al. 2022b) showed that independence tests based on Chatterjee’s rank correlation are unfortunately rate inefficient against various local alternatives and they call for variants. We answer this call by proposing an improvement to Chatterjee’s rank correlation that still consistently estimates the same dependence measure, but provably achieves near-parametric efficiency in testing against Gaussian rotation alternatives. This is possible by incorporating many right nearest neighbours in constructing the correlation coefficients. We thus overcome the ‘ only one disadvantage’ of Chatterjee’s rank correlation (Chatterjee, 2021, § 7). 

Summary We propose and investigate an additive regression model for symmetric positive-definite matrix-valued responses and multiple scalar predictors. The model exploits the Abelian group structure inherited from either of the log-Cholesky and log-Euclidean frameworks for symmetric positive-definite matrices and naturally extends to general Abelian Lie groups. The proposed additive model is shown to connect to an additive model on a tangent space. This connection not only entails an efficient algorithm to estimate the component functions, but also allows one to generalize the proposed additive model to general Riemannian manifolds. Optimal asymptotic convergence rates and normality of the estimated component functions are established, and numerical studies show that the proposed model enjoys good numerical performance, and is not subject to the curse of dimensionality when there are multiple predictors. The practical merits of the proposed model are demonstrated through an analysis of brain diffusion tensor imaging data. 

ABSTRACT Long-period comets are planetesimal remnants constraining the environment and volatiles of the protoplanetary disc. We report the discovery of hyperbolic long-period comet C/2022 E3 Zwicky Transient Facility (ZTF), which has a perihelion ∼1.11 au, an eccentricity ≳1 and an inclination ∼109°, from images taken with the Palomar 48-inch telescope during morning twilight on 2022 March 2. Additionally, we report the characterization of C/2022 E3 (ZTF) from observations taken with the Palomar 200-inch, the Palomar 60-inch, and the NASA Infrared Telescope Facility in early 2023 February to 2023 March when the comet passed within ∼0.28 au of the Earth and reached a visible magnitude of ∼5. We measure g–r = 0.70 ± 0.01, r–i = 0.20 ± 0.01, i–z = 0.06 ± 0.01, z–J = 0.90 ± 0.01, J–H = 0.38 ± 0.01, and H–K = 0.15 ± 0.01 colours for the comet from observations. We measure the A(0°)fρ (0.8 μm) in a 6500 km radius from the nucleus of 1483 ± 40 cm, and CN, C3, and C2 production of 5.43 ± 0.11 × 1025, 2.01 ± 0.04 × 1024, and 3.08 ± 0.5 × 1025 mol s−1, similar to other long-period comets. We additionally observe the appearance of jet-like structures at a scale of ∼4000 km in wide-field g-band images, which may be caused by the presence of CN gas in the near-nucleus coma.