The author discusses 2-adjacency of two-component links and study the relations between the signs of the crossings to realize 2-adjacency and the coefficients of the Conway polynomial of two related links. By discussi...The author discusses 2-adjacency of two-component links and study the relations between the signs of the crossings to realize 2-adjacency and the coefficients of the Conway polynomial of two related links. By discussing the coefficient of the lowest m power in the Homfly polynomial, the author obtains some results and conditions on whether the trivial link is 2-adjacent to a nontrivial link, whether there are two links 2-adjacent to each other, etc. Finally, this paper shows that the Whitehead link is not 2-adjacent to the trivial link, and gives some examples to explain that for any given two-component link,there are infinitely many links 2-adjacent to it. In particular, there are infinitely many links 2-adjacent to it with the same Conway polynomial.展开更多
To address the problem in boundary tracing where there is no direct association between entities and boundary pixels-that is,determining which entity a boundary belongs to-a novel run data-based boundary tracing algor...To address the problem in boundary tracing where there is no direct association between entities and boundary pixels-that is,determining which entity a boundary belongs to-a novel run data-based boundary tracing algorithm is proposed.Unlike traditional t racing algorithms,this approach first extracts boundary pixels and then classifies them to ensure 100%extraction accuracy.A region labeling algorithm is introduced to establish a direct link between boundaries and objects.The concept of boundary run da ta is proposed to avoid errors in previous run data algorithms,particularly at corners.Furthermore,the proposed algorithm is parallelized using MPI to further improve its speed.Experiments conducted on the MPEG-7 CE standard dataset demonstrate that th e proposed algorithm achieves 100%accuracy,offers significant speed improvements over traditional algorithms,and exhibits further performance gains after parallelization.展开更多
基金supported by the Zhejiang Provincial Natural Science Foundation of China(No.LY12A01025)
文摘The author discusses 2-adjacency of two-component links and study the relations between the signs of the crossings to realize 2-adjacency and the coefficients of the Conway polynomial of two related links. By discussing the coefficient of the lowest m power in the Homfly polynomial, the author obtains some results and conditions on whether the trivial link is 2-adjacent to a nontrivial link, whether there are two links 2-adjacent to each other, etc. Finally, this paper shows that the Whitehead link is not 2-adjacent to the trivial link, and gives some examples to explain that for any given two-component link,there are infinitely many links 2-adjacent to it. In particular, there are infinitely many links 2-adjacent to it with the same Conway polynomial.
基金National Natural Science Foundation of China(42374152)Shandong Provincial Natural Science Foundation(ZR2020MD050)。
文摘To address the problem in boundary tracing where there is no direct association between entities and boundary pixels-that is,determining which entity a boundary belongs to-a novel run data-based boundary tracing algorithm is proposed.Unlike traditional t racing algorithms,this approach first extracts boundary pixels and then classifies them to ensure 100%extraction accuracy.A region labeling algorithm is introduced to establish a direct link between boundaries and objects.The concept of boundary run da ta is proposed to avoid errors in previous run data algorithms,particularly at corners.Furthermore,the proposed algorithm is parallelized using MPI to further improve its speed.Experiments conducted on the MPEG-7 CE standard dataset demonstrate that th e proposed algorithm achieves 100%accuracy,offers significant speed improvements over traditional algorithms,and exhibits further performance gains after parallelization.
