Although AlphaZero has achieved superhuman performance in board games, recent studies reveal its limitations in handling scenarios requiring a comprehensive understanding of the entire board, such as recognizing long-sequence patterns in Go. To address this challenge, we propose ResTNet, a network that interleaves residual and Transformer blocks to bridge local and global knowledge. ResTNet improves playing strength across multiple board games, increasing win rate from 54.6% to 60.8% in 9x9 Go, 53.6% to 60.9% in 19x19 Go, and 50.4% to 58.0% in 19x19 Hex. In addition, ResTNet effectively processes global information and tackles two long-sequence patterns in 19x19 Go, including circular pattern and ladder pattern. It reduces the mean square error for circular pattern recognition from 2.58 to 1.07 and lowers the attack probability against an adversary program from 70.44% to 23.91%. ResTNet also improves ladder pattern recognition accuracy from 59.15% to 80.01%. By visualizing attention maps, we demonstrate that ResTNet captures critical game concepts in both Go and Hex, offering insights into AlphaZero's decision-making process. Overall, ResTNet shows a promising approach to integrating local and global knowledge, paving the way for more effective AlphaZero-based algorithms in board games. Our code is available at https://rlg.iis.sinica.edu.tw/papers/restnet.

Currently, a dynamic programming (DP) algorithm CDSfold has been proposed to design a CDS by minimizing the minimum free energy (MFE) of its secondary structure. However, it has been questioned recently that such a DP algorithm is difficult to be modified to design a CDS when attempting to jointly optimize its secondary structure stability and codon adaptation index (CAI). In this study, we successfully modify the DP algorithm of CDSfold to exactly solve this kind of CDS design problem in $\mathcal {O}(L^{3})$ time and $\mathcal {O}(L^{2})$ space, where $L$ is the CDS length. We further accelerate this DP algorithm by beam search, enabling it to design a high-quality approximate CDS in $\mathcal {O}(L)$ time, and implement it as the program LinearCDSfold. Our experimental results show that when running with exact search, LinearCDSfold has comparable accuracy to two state-of-the-art CDS design tools LinearDesign and DERNA in terms of both MFE and CAI. In terms of running time, however, LinearCDSfold is slower than LinearDesign, but significantly faster than DERNA, even though they all run in $\mathcal {O}(L^{3})$ time and $\mathcal {O}(L^{2})$ space. Moreover, LinearCDSfold using beam search can design an approximate CDS in very short time with very high quality in terms of both MFE and CAI.