Symmetry

Autoregressive Transformer translation relies on a target prefix and does not directly condition each prediction on an ungenerated target suffix. This study evaluates how complementary decoding directions, linguistic guidance, and pretrained source representations are integrated in a family of bidirectional translation configurations. BiDNMT uses an auxiliary right-to-left decoder; TeF-BiDNMT examines scheduled target replacement; KDS-BiDNMT combines keyword and dependency information; and XLK-BiDNMT links XLNet representations to serial–parallel cross-attention. These information-flow choices are of potential interest to translation involving less commonly taught languages, where contextual evidence may be uneven, but their effectiveness is evaluated here only on WMT17 Chinese–English and WMT14 English–German benchmarks. At beam size 5, BiDNMT records 22.42/29.96 BLEU and TeF-BiDNMT 26.02/25.65 on Chinese–English/English–German, respectively. KDS-BiDNMT is reported at 23.39/31.12 BLEU in its main comparison, and XLK-BiDNMT at 27.87, 23.61, and 27.12 across newstest2017, newstest2018, and cwmt2018. The length-stratified comparison shows both positive and negative differences, with the largest positive margin of 6.40 BLEU points in (70,80]. The evidence therefore characterizes condition-dependent architectural behavior; it does not establish improved performance on less commonly taught languages or uniform superiority on the evaluated language pairs.

Personalized learning requires systematic approaches for representing, analyzing, and quantifying learner characteristics and educational processes. This study presents a framework for analyzing and quantifying symmetry in personalized learning through standardized representations, criteria, and procedures. Symmetry is defined as the preservation of relevant relationships and personalization decisions under admissible transformations of learner profiles, whereas asymmetry represents appropriate changes when genuine educational differences exist. The proposed framework integrates standardization and symmetry into the analysis of learner profiles, educational data, predictive outputs, and personalization decisions. A novel Symmetry Index for Personalized Learning (SIPL) is introduced as a composite quantitative measure of symmetry across defined personalization processes. The SIPL encompasses five complementary components: data symmetry, learner-profile symmetry, prediction symmetry, content-selection symmetry, and transformation symmetry. These components provide a multidimensional basis for evaluating whether equivalent or sufficiently similar learner representations lead to consistent educational responses while preserving appropriate sensitivity to meaningful learner differences. The framework combines conventional predictive evaluation with symmetry-based measures. The proposed approach provides a methodological basis for more transparent, measurable, and comparable analysis of personalized learning processes and complements established evaluation perspectives by explicitly quantifying symmetry and asymmetry across interconnected stages of personalization.

To address the design requirements of structural lightweighting and multi-performance coordination for UAV frames, an optimization method combining topology optimization and the NSGA-III multi-objective evolutionary algorithm is proposed. Twelve kinds of topological structures are obtained by setting different parameters through the Altair Inspire platform. A three-objective optimization model considering mass, stiffness, and strength was constructed to identify the Pareto-optimal solutions. Numerical analysis shows that the optimized design achieves approximately 59% mass reduction, with a maximum displacement of 0.2891 mm and a maximum stress of 4.449 MPa, meeting structural performance requirements. The results indicate that the proposed method effectively improves both the design efficiency and structural performance of UAV frames. The optimized models indicate favorable mechanical behavior and potential manufacturability; however, experimental manufacturing and structural testing are still required for full validation. The proposed workflow can be extended to the structural design of multirotor and fixed-wing UAV platforms.