Homogeneous ACM bundles on exceptional isotropic Grassmannians

In this paper, we characterize homogeneous arithmetically Cohen-Macaulay (ACM) bundles over exceptional isotropic Grassmannians in terms of their associated data. We show that there are only finitely many irreducible homogeneous ACM bundles by twisting line bundles over exceptional isotropic Grassmannians. As a consequence, we prove that some exceptional isotropic Grassmannians are of wild representation type.Comment: 18 pages. arXiv admin note: text overlap with arXiv:2206.0917

Data-driven model construction for anisotropic dynamics of active matter

The dynamics of cellular pattern formation is crucial for understanding embryonic development and tissue morphogenesis. Recent studies have shown that human dermal fibroblasts cultured on liquid crystal elastomers can exhibit an increase in orientational alignment over time, accompanied by cell proliferation, under the influence of the weak guidance of a molecularly aligned substrate. However, a comprehensive understanding of how this order arises remains largely unknown. This knowledge gap may be attributed, in part, to a scarcity of mechanistic models that can capture the temporal progression of the complex nonequilibrium dynamics during the cellular alignment process. The orientational alignment occurs primarily when cells reach a high density near confluence. Therefore, for accurate modeling, it is crucial to take into account both the cell-cell interaction term and the influence from the substrate, acting as a one-body external potential term. To fill in this gap, we develop a hybrid procedure that utilizes statistical learning approaches to extend the state-of-the-art physics models for quantifying both effects. We develop a more efficient way to perform feature selection that avoids testing all feature combinations through simulation. The maximum likelihood estimator of the model was derived and implemented in computationally scalable algorithms for model calibration and simulation. By including these features, such as the non-Gaussian, anisotropic fluctuations, and limiting alignment interaction only to neighboring cells with the same velocity direction, this model quantitatively reproduce the key system-level parameters--the temporal progression of the velocity orientational order parameters and the variability of velocity vectors, whereas models missing any of the features fail to capture these temporally dependent parameters.Comment: 20 pages, 14 figure

Research on the Mechanism of Entrepreneurship Education on College Students’ Entrepreneurial Willingness and Its Future Prediction

The strength of college students’ entrepreneurial willingness is a barometer for measuring the effectiveness of entrepreneurship education. It is also an important avenue for college students to expand their employment opportunities and enhance the quality of their employment in the face of new employment trends. Comprehensive universities offer a wide range of disciplines and great professional specialization. It is of great significance to explore the diversity results in college students’ entrepreneurship education indicators. According to the data on the relationship between entrepreneurial education and entrepreneurship willingness in comprehensive universities in Jiangsu province, various factors such as subject characteristics, work experience, educational background, and family environment significantly impact college students’ willingness to become entrepreneurs. The implementation of entrepreneurship education, including the awakening of entrepreneurial consciousness, the cultivation of entrepreneurial abilities, and the improvement of entrepreneurial willingness, has a direct impact on college students’ willingness to start their own businesses

DesignGPT: Multi-Agent Collaboration in Design

Generative AI faces many challenges when entering the product design workflow, such as interface usability and interaction patterns. Therefore, based on design thinking and design process, we developed the DesignGPT multi-agent collaboration framework, which uses artificial intelligence agents to simulate the roles of different positions in the design company and allows human designers to collaborate with them in natural language. Experimental results show that compared with separate AI tools, DesignGPT improves the performance of designers, highlighting the potential of applying multi-agent systems that integrate design domain knowledge to product scheme design

Lithium-Excess Research of Cathode Material Li2MnTiO4 for Lithium-Ion Batteries

Lithium-excess and nano-sized Li2+xMn1−x/2TiO4 (x = 0, 0.2, 0.4) cathode materials were synthesized via a sol-gel method. The X-ray diffraction (XRD) experiments indicate that the obtained main phases of Li2.0MnTiO4 and the lithium-excess materials are monoclinic and cubic, respectively. The scanning electron microscope (SEM) images show that the as-prepared particles are well distributed and the primary particles have an average size of about 20–30 nm. The further electrochemical tests reveal that the charge-discharge performance of the material improves remarkably with the lithium content increasing. Particularly, the first discharging capacity at the current of 30 mA g−1 increases from 112.2 mAh g−1 of Li2.0MnTiO4 to 187.5 mAh g−1 of Li2.4Mn0.8TiO4. In addition, the ex situ XRD experiments indicate that the monoclinic Li2MnTiO4 tends to transform to an amorphous state with the extraction of lithium ions, while the cubic Li2MnTiO4 phase shows better structural reversibility and stability