We study the construction of mutually unbiased bases in Hilbert space for composite dimensions d which are not prime powers.We explore the results for composite dimensions which are true for prime power dimensions.We ...We study the construction of mutually unbiased bases in Hilbert space for composite dimensions d which are not prime powers.We explore the results for composite dimensions which are true for prime power dimensions.We then provide a method for selecting mutually unbiased vectors from the eigenvectors of generalized Pauli matrices to construct mutually unbiased bases.In particular,we present four mutually unbiased bases in C^(15).展开更多
Exports of Chinese satellites,joint construction of space infrastructure,and joint research and development of satellites...The recent years have seen substantial growth in China-Africa cooperation in the space sector...Exports of Chinese satellites,joint construction of space infrastructure,and joint research and development of satellites...The recent years have seen substantial growth in China-Africa cooperation in the space sector,which is bringing tangible benefits to both sides.展开更多
Affinity propagation(AP)is a widely used exemplar-based clustering approach with superior efficiency and clustering quality.Nevertheless,a common issue with AP clustering is the presence of excessive exemplars,which l...Affinity propagation(AP)is a widely used exemplar-based clustering approach with superior efficiency and clustering quality.Nevertheless,a common issue with AP clustering is the presence of excessive exemplars,which limits its ability to perform effective aggregation.This research aims to enable AP to automatically aggregate to produce fewer and more compact clusters,without changing the similarity matrix or customizing preference parameters,as done in existing enhanced approaches.An automatic aggregation enhanced affinity propagation(AAEAP)clustering algorithm is proposed,which combines a dependable partitioning clustering approach with AP to achieve this purpose.The partitioning clustering approach generates an additional set of findings with an equivalent number of clusters whenever the clustering stabilizes and the exemplars emerge.Based on these findings,mutually exclusive exemplar detection was conducted on the current AP exemplars,and a pair of unsuitable exemplars for coexistence is recommended.The recommendation is then mapped as a novel constraint,designated mutual exclusion and aggregation.To address this limitation,a modified AP clustering model is derived and the clustering is restarted,which can result in exemplar number reduction,exemplar selection adjustment,and other data point redistribution.The clustering is ultimately completed and a smaller number of clusters are obtained by repeatedly performing automatic detection and clustering until no mutually exclusive exemplars are detected.Some standard classification data sets are adopted for experiments on AAEAP and other clustering algorithms for comparison,and many internal and external clustering evaluation indexes are used to measure the clustering performance.The findings demonstrate that the AAEAP clustering algorithm demonstrates a substantial automatic aggregation impact while maintaining good clustering quality.展开更多
基金Project supported by Zhoukou Normal University,ChinaHigh Level Talents Research Start Funding Project (Grant No.ZKNUC2022010)+2 种基金Key Scientific Research Project of Henan Province (Grant No.22B110022)Key Research and Development Project of Guangdong Province (Grant No.2020B0303300001)the Guangdong Basic and Applied Basic Research Foundation (Grant No.2020B1515310016)。
文摘We study the construction of mutually unbiased bases in Hilbert space for composite dimensions d which are not prime powers.We explore the results for composite dimensions which are true for prime power dimensions.We then provide a method for selecting mutually unbiased vectors from the eigenvectors of generalized Pauli matrices to construct mutually unbiased bases.In particular,we present four mutually unbiased bases in C^(15).
文摘Exports of Chinese satellites,joint construction of space infrastructure,and joint research and development of satellites...The recent years have seen substantial growth in China-Africa cooperation in the space sector,which is bringing tangible benefits to both sides.
基金supported by Research Team Development Funds of L.Xue and Z.H.Ouyang,Electronic Countermeasure Institute,National University of Defense Technology。
文摘Affinity propagation(AP)is a widely used exemplar-based clustering approach with superior efficiency and clustering quality.Nevertheless,a common issue with AP clustering is the presence of excessive exemplars,which limits its ability to perform effective aggregation.This research aims to enable AP to automatically aggregate to produce fewer and more compact clusters,without changing the similarity matrix or customizing preference parameters,as done in existing enhanced approaches.An automatic aggregation enhanced affinity propagation(AAEAP)clustering algorithm is proposed,which combines a dependable partitioning clustering approach with AP to achieve this purpose.The partitioning clustering approach generates an additional set of findings with an equivalent number of clusters whenever the clustering stabilizes and the exemplars emerge.Based on these findings,mutually exclusive exemplar detection was conducted on the current AP exemplars,and a pair of unsuitable exemplars for coexistence is recommended.The recommendation is then mapped as a novel constraint,designated mutual exclusion and aggregation.To address this limitation,a modified AP clustering model is derived and the clustering is restarted,which can result in exemplar number reduction,exemplar selection adjustment,and other data point redistribution.The clustering is ultimately completed and a smaller number of clusters are obtained by repeatedly performing automatic detection and clustering until no mutually exclusive exemplars are detected.Some standard classification data sets are adopted for experiments on AAEAP and other clustering algorithms for comparison,and many internal and external clustering evaluation indexes are used to measure the clustering performance.The findings demonstrate that the AAEAP clustering algorithm demonstrates a substantial automatic aggregation impact while maintaining good clustering quality.
