Google Page Rank is a prevalent algorithm for ranking the significance of nodes or websites in a network,and a recent quantum counterpart for Page Rank algorithm has been raised to suggest a higher accuracy of ranking...Google Page Rank is a prevalent algorithm for ranking the significance of nodes or websites in a network,and a recent quantum counterpart for Page Rank algorithm has been raised to suggest a higher accuracy of ranking comparing to Google Page Rank.The quantum Page Rank algorithm is essentially based on quantum stochastic walks and can be expressed using Lindblad master equation,which,however,needs to solve the Kronecker products of an O(N^(4))dimension and requires severely large memory and time when the number of nodes N in a network increases above 150.Here,we present an efficient solver for quantum Page Rank by using the Runge-Kutta method to reduce the matrix dimension to O(N^(2))and employing Tensor Flow to conduct GPU parallel computing.We demonstrate its performance in solving quantum stochastic walks on Erdos-Rényi graphs using an RTX 2060 GPU.The test on the graph of 6000 nodes requires a memory of 5.5 GB and time of 223 s,and that on the graph of 1000 nodes requires 226 MB and 3.6 s.Compared with QSWalk,a currently prevalent Mathematica solver,our solver for the same graph of 1000 nodes reduces the required memory and time to only 0.2%and 0.05%.We apply the solver to quantum Page Rank for the USA major airline network with up to 922 nodes,and to quantum stochastic walk on a glued tree of 2186 nodes.This efficient solver for large-scale quantum Page Rank and quantum stochastic walks would greatly facilitate studies of quantum information in real-life applications.展开更多
Purpose This study examined the effects of tournament load on neuromuscular function,perceived wellness and coach rat-ings of performance across two 6-day netball tournaments.Methods Thirty-nine female youth netballer...Purpose This study examined the effects of tournament load on neuromuscular function,perceived wellness and coach rat-ings of performance across two 6-day netball tournaments.Methods Thirty-nine female youth netballers(age=14.6±0.5 years,stature=165.9±4.7 cm,body mass=56.5±7.2 kg)were categorised as HIGH(10-11 matches,n=20)or LOW(6 matches,n=19)tournament load.Match load,jump height,perceived wellness and coach ratings of performance were monitored daily.Results HIGH tournament load resulted in greater reductions in jump height on match-day 4(-8.3%,±5.6%)when compared to LOW.HIGH tournament load resulted in greater reductions in perceived soreness(-0.9,±1.1 AU)and overall wellness(-2.6,±2.3 AU)on match-day 3,and a greater reduction in perceived sleep(-0.9,±1.1 AU)on match-day 4.HIGH tournament load was negatively associated with sleep quality and coach ratings of performance(effect size correlation=-0.34 to-0.47)when compared to LOW.Conclusion Our results indicate that a higher tournament load resulted in greater increases in neuromuscular fatigue,reduced perceived wellness,and lower ratings of performance.Practitioners should consider pre-tournament preparation and monitoring strategies to minimise the physiological disturbances during an intensified tournament.展开更多
基金supported by the National Key R&D Program of China(2019YFA0308700,and 2017YFA0303700)the National Natural Science Foundation of China(61734005,11761141014,11690033)+3 种基金the Science and Technology Commission of Shanghai Municipality(STCSM)(17JC1400403)the Shanghai Municipal Education Commission(SMEC)(2019SHZDZX01,2017-01-07-0002-E00049)supported by the National Natural Science Foundation of China(11904229)China Postdoctoral Science Foundation(2019T120334)。
文摘Google Page Rank is a prevalent algorithm for ranking the significance of nodes or websites in a network,and a recent quantum counterpart for Page Rank algorithm has been raised to suggest a higher accuracy of ranking comparing to Google Page Rank.The quantum Page Rank algorithm is essentially based on quantum stochastic walks and can be expressed using Lindblad master equation,which,however,needs to solve the Kronecker products of an O(N^(4))dimension and requires severely large memory and time when the number of nodes N in a network increases above 150.Here,we present an efficient solver for quantum Page Rank by using the Runge-Kutta method to reduce the matrix dimension to O(N^(2))and employing Tensor Flow to conduct GPU parallel computing.We demonstrate its performance in solving quantum stochastic walks on Erdos-Rényi graphs using an RTX 2060 GPU.The test on the graph of 6000 nodes requires a memory of 5.5 GB and time of 223 s,and that on the graph of 1000 nodes requires 226 MB and 3.6 s.Compared with QSWalk,a currently prevalent Mathematica solver,our solver for the same graph of 1000 nodes reduces the required memory and time to only 0.2%and 0.05%.We apply the solver to quantum Page Rank for the USA major airline network with up to 922 nodes,and to quantum stochastic walk on a glued tree of 2186 nodes.This efficient solver for large-scale quantum Page Rank and quantum stochastic walks would greatly facilitate studies of quantum information in real-life applications.
文摘Purpose This study examined the effects of tournament load on neuromuscular function,perceived wellness and coach rat-ings of performance across two 6-day netball tournaments.Methods Thirty-nine female youth netballers(age=14.6±0.5 years,stature=165.9±4.7 cm,body mass=56.5±7.2 kg)were categorised as HIGH(10-11 matches,n=20)or LOW(6 matches,n=19)tournament load.Match load,jump height,perceived wellness and coach ratings of performance were monitored daily.Results HIGH tournament load resulted in greater reductions in jump height on match-day 4(-8.3%,±5.6%)when compared to LOW.HIGH tournament load resulted in greater reductions in perceived soreness(-0.9,±1.1 AU)and overall wellness(-2.6,±2.3 AU)on match-day 3,and a greater reduction in perceived sleep(-0.9,±1.1 AU)on match-day 4.HIGH tournament load was negatively associated with sleep quality and coach ratings of performance(effect size correlation=-0.34 to-0.47)when compared to LOW.Conclusion Our results indicate that a higher tournament load resulted in greater increases in neuromuscular fatigue,reduced perceived wellness,and lower ratings of performance.Practitioners should consider pre-tournament preparation and monitoring strategies to minimise the physiological disturbances during an intensified tournament.
