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Quantum Cluster Algebra Structure on the Quantum Grothendieck Ring K_(t-1)
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作者 Yahia Badawi Bashir Meny 马海涛 杨彦敏 《Chinese Quarterly Journal of Mathematics》 2015年第1期12-19,共8页
In this paper, we give a quantum cluster algebra structure on the deformed Grothendieck ring Kt-1 which is defined in section 2.
关键词 quantum cluster algebra deformed Grothendieck ring
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Traffic Clustering Algorithm of Urban Data Brain Based on a Hybrid-Augmented Architecture of Quantum Annealing and Brain-Inspired Cognitive Computing 被引量:6
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作者 Ning Wang Gege Guo +1 位作者 Baonan Wang Chao Wang 《Tsinghua Science and Technology》 SCIE EI CAS CSCD 2020年第6期813-825,共13页
In recent years,the urbanization process has brought modernity while also causing key issues,such as traffic congestion and parking conflicts.Therefore,cities need a more intelligent"brain"to form more intel... In recent years,the urbanization process has brought modernity while also causing key issues,such as traffic congestion and parking conflicts.Therefore,cities need a more intelligent"brain"to form more intelligent and efficient transportation systems.At present,as a type of machine learning,the traditional clustering algorithm still has limitations.K-means algorithm is widely used to solve traffic clustering problems,but it has limitations,such as sensitivity to initial points and poor robustness.Therefore,based on the hybrid architecture of Quantum Annealing(QA)and brain-inspired cognitive computing,this study proposes QA and Brain-Inspired Clustering Algorithm(QABICA)to solve the problem of urban taxi-stand locations.Based on the traffic trajectory data of Xi’an and Chengdu provided by Didi Chuxing,the clustering results of our algorithm and K-means algorithm are compared.We find that the average taxi-stand location bias of the final result based on QABICA is smaller than that based on K-means,and the bias of our algorithm can effectively reduce the tradition K-means bias by approximately 42%,up to approximately 83%,with higher robustness.QA algorithm is able to jump out of the local suboptimal solutions and approach the global optimum,and brain-inspired cognitive computing provides search feedback and direction.Thus,we will further consider applying our algorithm to analyze urban traffic flow,and solve traffic congestion and other key problems in intelligent transportation. 展开更多
关键词 cluster analysis intelligent transportation quantum annealing and brain-inspired clustering algorithm K-means
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Equilibrium and kinetic Si isotope fractionation factors and their implications for Si isotope distributions in the Earth's surface environments 被引量:3
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作者 Hong-tao He Siting Zhang +1 位作者 Chen Zhu Yun Liu 《Acta Geochimica》 EI CAS CSCD 2016年第1期15-24,共10页
Several important equilibrium Si isotope fractionation factors among minerals,organic molecules and the H_4SiO_4 solution are complemented to facilitate the explanation of the distributions of Si isotopes in Earth'... Several important equilibrium Si isotope fractionation factors among minerals,organic molecules and the H_4SiO_4 solution are complemented to facilitate the explanation of the distributions of Si isotopes in Earth's surface environments.The results reveal that,in comparison to aqueous H_4SiO_4,heavy Si isotopes will be significantly enriched in secondary silicate minerals.On the contrary,quadra-coordinated organosilicon complexes are enriched in light silicon isotope relative to the solution.The extent of ^(28)Si-enrichment in hyper-coordinated organosilicon complexes was found to be the largest.In addition,the large kinetic isotope effect associated with the polymerization of monosilicic acid and dimer was calculated,and the results support the previous statement that highly ^(28)Sienrichment in the formation of amorphous quartz precursor contributes to the discrepancy between theoretical calculations and field observations.With the equilibrium Si isotope fractionation factors provided here,Si isotope distributions in many of Earth's surface systems can be explained.For example,the change of bulk soil δ^(30)Si can be predicted as a concave pattern with respect to the weathering degree,with the minimum value where allophane completely dissolves and the total amount of sesquioxides and poorly crystalline minerals reaches their maximum.When,under equilibrium conditions,the well-crystallized clays start to precipitate from the pore solutions,the bulk soil δ^(30)Si will increase again and reach a constant value.Similarly,the precipitation of crystalline smectite and the dissolution of poorly crystalline kaolinite may explain the δ^(30)Si variations in the ground water profile.The equilibrium Si isotope fractionations among the quadracoordinated organosilicon complexes and the H_4SiO_4solution may also shed light on the Si isotope distributions in the Si-accumulating plants. 展开更多
关键词 Si isotopes Equilibrium fractionation factor quantum chemistry calculation Cluster model Kinetic isotope effect
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Recursive formulas for the Kronecker quantum cluster algebra with principal coefficients 被引量:1
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作者 Ming Ding Fan Xu Xueqing Chen 《Science China Mathematics》 SCIE CSCD 2023年第9期1933-1948,共16页
We use the quantum version of Chebyshev polynomials to explicitly construct the recursive formulas for the Kronecker quantum cluster algebra with principal coefficients.As a byproduct,we obtain two barinvariant positi... We use the quantum version of Chebyshev polynomials to explicitly construct the recursive formulas for the Kronecker quantum cluster algebra with principal coefficients.As a byproduct,we obtain two barinvariant positive ZP-bases with one being the atomic basis. 展开更多
关键词 quantum cluster algebra cluster variable positive basis
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Bases of the Quantum Cluster Algebra of the Kronecker Quiver 被引量:1
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作者 Ming DING Fan XU 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2012年第6期1169-1178,共10页
We construct bar-invariant Z[q ±1/2]-bases of the quantum cluster algebra of Kronecker quiver which are quantum analogues of the canonical basis, semicanonical basis and dual semicanonical basis of the correspond... We construct bar-invariant Z[q ±1/2]-bases of the quantum cluster algebra of Kronecker quiver which are quantum analogues of the canonical basis, semicanonical basis and dual semicanonical basis of the corresponding cluster algebra. As a byproduct, we prove positivity of the elements in these bases. 展开更多
关键词 quantum cluster algebra Z[q ±1/2]-basis POSITIVITY
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A quantum analogue of generic bases for affine cluster algebras
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作者 DING Ming XU Fan 《Science China Mathematics》 SCIE 2012年第10期2045-2066,共22页
We construct quantized versions of generic bases in quantum cluster algebras of finite and affine types.Under the specialization of q and coefficients to 1,these bases are generic bases of finite and affine cluster al... We construct quantized versions of generic bases in quantum cluster algebras of finite and affine types.Under the specialization of q and coefficients to 1,these bases are generic bases of finite and affine cluster algebras. 展开更多
关键词 cluster variable quantum cluster algebra tame quiver
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Quantum Private Comparison of Equality Based on Five-Particle Cluster State
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作者 Yan Chang Wen-Do Zhang +7 位作者 Shi-Bin Zhang Hai-Chun Wang Li-Li Yan Gui-Hua Han Zhi-Wei Sheng Yuan-Yuan Huang Wang Suo Jin-Xin Xiong 《Communications in Theoretical Physics》 SCIE CAS CSCD 2016年第12期621-628,共8页
A protocol for quantum private comparison of equality(QPCE) is proposed based on five-particle cluster state with the help of a semi-honest third party(TP). In our protocol, TP is allowed to misbehave on its own but c... A protocol for quantum private comparison of equality(QPCE) is proposed based on five-particle cluster state with the help of a semi-honest third party(TP). In our protocol, TP is allowed to misbehave on its own but can not conspire with either of two parties. Compared with most two-user QPCE protocols, our protocol not only can compare two groups of private information(each group has two users) in one execution, but also compare just two private information. Compared with the multi-user QPCE protocol proposed, our protocol is safer with more reasonable assumptions of TP. The qubit efficiency is computed and analyzed. Our protocol can also be generalized to the case of 2N participants with one TP. The 2N-participant protocol can compare two groups(each group has N private information)in one execution or just N private information. 展开更多
关键词 quantum private comparison of equality five-particle cluster state semi-honest third party
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