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Images are a convenient way for humans to obtain information and knowledge, but they are often destroyed throughout the collection or distribution process. Therefore, image processing evolves as the need arises, and color image processing is a broad and active field. A color image includes three distinct but closely related channels (red, green, and blue (RGB)). Compared to directly expressing color images as vectors or matrices, the quaternion representation offers an effective alternative. There are several papers and works on this subject, as well as numerous definitions, hypotheses, and methodologies. Our observations indicate that the quaternion representation method is effective, and models and methods based on it have rapidly developed. Hence, the purpose of this paper is to review and categorize past methods, as well as study their efficacy and computational examples. We hope that this research will be helpful to academics interested in quaternion representation.

In order to address the problem of data heterogeneity, in recent years, personalized federated learning has tailored models to individual user data to enhance model performance on clients with diverse data distributions. However, the existing personalized federated learning methods do not adequately address the problem of data heterogeneity, and lack the processing of system heterogeneity. Consequently, these issues lead to diminished training efficiency and suboptimal model performance of personalized federated learning in heterogeneous environments. In response to these challenges, we propose FedPRL, a novel approach to personalized federated learning designed specifically for heterogeneous environments. Our method tackles data heterogeneity by implementing a personalized strategy centered on local data storage, enabling the accurate extraction of features tailored to the data distribution of individual clients. This personalized approach enhances the performance of federated learning models when dealing with non-IID data. To overcome system heterogeneity, we design a client selection mechanism grounded in reinforcement learning and user quality evaluation. This mechanism optimizes the selection of clients based on data quality and training time, thereby boosting the efficiency of the training process and elevating the overall performance of personalized models. Moreover, we devise a local training method that utilizes global knowledge distillation of non-target classes, which combined with traditional federated learning can effectively address the issue of catastrophic forgetting during global model updates. This approach enhances the generalization capability of the global model and further improves the performance of personalized models. Extensive experiments on both standard and real-world datasets demonstrate that FedPRL effectively resolves the challenges of data and system heterogeneity, enhancing the efficiency and model performance of personalized federated learning methods in heterogeneous environments, and outperforming state-of-the-art methods in terms of model accuracy and training efficiency.

Cubic Hermite interpolation curve plays a very important role in interpolation curves modeling, but it has three shortcomings including low continuity, difficult shape adjustment, and the inability to accurately represent some common engineering curves. We construct a cubic trigonometric Hermite interpolation curve to make up the three shortcomings of cubic Hermite interpolation curve once and for all. The cubic trigonometric Hermite interpolation curve not only inherits the features of cubic Hermite interpolation curve but also achieves C2 continuity, has local and global adjustability, and can accurately represent elliptical arc, circular arc, quadratic parabolic arc, cubic parabolic arc, and astroid arc that often appear in engineering. In addition, we give the schemes for optimizing the shape of the cubic trigonometric Hermite interpolation curve based on internal energy minimization. The schemes include optimizing the shape of planar curve and spatial curve. Some modeling examples show that the proposed schemes are effective and the cubic trigonometric Hermite interpolation curve is more practical than cubic Hermite interpolation curve.

There is an emergent demand for high-flexibility, high-sensitivity and low-power strain gauges capable of sensing small deformations and vibrations in extreme conditions. Enhancing the gauge factor remains one of the greatest challenges for strain sensors. This is typically limited to below 300 and set when the sensor is fabricated. We report a strategy to tune and enhance the gauge factor of strain sensors based on Van der Waals materials by tuning the carrier mobility and concentration through an interplay of piezoelectric and photoelectric effects. For a SnS 2 sensor we report a gauge factor up to 3933, and the ability to tune it over a large range, from 23 to 3933. Results from SnS 2 , GaSe, GeSe, monolayer WSe 2 , and monolayer MoSe 2 sensors suggest that this is a universal phenomenon for Van der Waals semiconductors. We also provide proof of concept demonstrations by detecting vibrations caused by sound and capturing body movements. The Gauge factor (GF) enhancement in strain sensors remains a key challenge. Here the authors leverage the piezoelectric and photoelectric effects in a class of van der Waals materials to tune the GF, and obtain a record GF up to 3933 for a SnS 2 -based strain sensor.

The construction of trigonometric interpolatory splines plays a very important role in geometric modeling. This paper presents a quartic trigonometric interpolatory spline with local free parameters. The new spline not only automatically interpolates the given points and achieves C2 continuity, but also owns shape adjustability when the points remain fixed. Some examples show that the shape of the new spline can easily realize local and global adjustment by changing the free parameters.

Hammerhead ribozymes have found extensive applications in gene expression regulation across diverse biological systems including Escherichia coli , yeast, plants, and mammalian cells. However, their implementation in parasitic nematodes remains unexplored. Strongyloides stercoralis emerges as a particularly valuable model organism for studying developmental transitions in parasitic nematodes due to its unique life cycle alternating between parasitic and free-living stages. To expand the experimental toolkit for investigating developmental, evolutionary, and behavioral processes in this species, we established a conditional gene regulation system through transgenic integration of synthetic ribozyme constructs and demonstrated efficacy in regulating both exogenous ( mrfp ) and endogenous ( unc-22 ) gene expression through targeted RNA processing mechanisms. Focusing on the insulin/IGF-1 signaling pathway, a critical regulator of parasitic nematode development and longevity, we implemented ribozyme-mediated post-transcriptional control to dissect functional divergence between two isoforms of the insulin receptor homolog Ss -DAF-2. Comparative analysis revealed isoform-specific characteristics: while both isoforms maintain conserved signaling functions, isoform B exhibits specific binding affinity for human insulin and demonstrates significant transcriptional upregulation during parasitic transition phases. This ligand selectivity profile suggests that isoform B may serve as a molecular interface for host-derived insulin signaling coordination during parasitism. This study established a programmable ribozyme tool in S. stercoralis , functionally discriminated the two Ss -DAF-2 isoforms through precision RNA engineering, and identified isoform-specific ligand preferences with implications for host-parasite signaling. Our findings not only validate ribozyme-based approaches for genetic manipulation in parasitic nematodes but also lay the groundwork for future implementation of synthetic RNA switches in helminth research.

Molecular dynamics simulation was used to better understand a single, non-crystalline cellulose molecular chain and its response to high-temperature treatment. The system temperature was varied from 430 K to 510 K, and the temperature interval was 20 K. Under the polymer consistent force field (PCFF), the dynamics simulation of each temperature was completed under the constant pressure/constant temperature dynamics (NPT). The experimental results showed that the mechanical properties of cellulose heat-treated at high temperature in a vacuum environment initially increased and then decreased with the increase of temperature. When the temperature was at 450 K, the mechanical properties reached an optimal state. Moreover, its mechanical properties were noticeably related to the connection of hydrogen bonds in the cellulose molecular chain and the thermal motion of the molecular chain.

As a critical impurity in the production of solar-grade silicon, the concentration of phosphorus (P) significantly affects photoelectric conversion efficiency. To address the challenge of P removal in solar-grade silicon production, this study proposes a combined process of Si-Fe solvent refining and SiO2-TiO2-CaO-CaF2 slag treatment. Under conditions utilizing collaborative refining with an alloy composition of Si-10 wt. %Fe and a slag composition of 32 wt. %SiO2-48 wt. %CaO-10 wt. %TiO2-10 wt. %CaF2, the removal rate of P in silicon can reach up to 96.8%. This paper investigates the effectiveness of combining solvent refining with slag making under fixed conditions of a Si-10 wt. %Fe alloy paired with various slag systems (no slag addition, binary slag SiO2-TiO2, ternary slag SiO2-CaO-TiO2, and quaternary slag SiO2-TiO2-CaO-CaF2). Based on the experimental results, the optimal TiO2 content in the slag system for maximizing P removal was analyzed and determined. Finally, leveraging both theoretical analysis and experimental findings, the mechanism of P removal was elucidated as a dual process: P is oxidized into Ca3(PO4)2 within the slag phase, and residual P is captured by the Fe-Si-Ti ternary phase.

The rapid advancement of AI-generated content (AIGC) has significantly improved the realism and accessibility of synthetic images. While large image generation models offer immense potential in creative industries, they also introduce serious challenges, including copyright infringement, content authentication, and the traceability of generated images. Digital watermarking has emerged as a promising approach to address these concerns by embedding imperceptible yet detectable signatures into generated images. This survey provides a comprehensive review of three core areas: (1) the evolution of image generation technologies, highlighting key milestones such as the transition from GANs to diffusion models; (2) traditional and state-of-the-art digital image watermarking algorithms, encompassing spatial domain, transform domain, and deep learning-based approaches; (3) watermarking methods specific to AIGC, including ownership authentication of AI model and diffusion model, and watermarking of AI-generated images. Additionally, we examine common performance evaluation metrics used in this field, such as watermark capacity, watermark detection accuracy, fidelity, and robustness. Finally, we discuss the unresolved issues and propose several potential directions for future research. We look forward to this paper offering valuable reference for academics in the field of AIGC watermarking and related fields.

In this paper, we aim at smoothing two connected ball Bézier curves from Cr−1 to Crr≥1 by minimizing the energies of the curves. We propose the algorithms based on internal energy minimization and curve attractor minimization. Then, we combine the internal energy and the curve attractor and give the algorithm based on combined energy minimization. All algorithms are established by solving bi-objective minimizations. Some numerical examples show that the proposed algorithms are effective, making them useful for smoothing 3D objects constructed by connected ball Bézier curves.