Evaluation for the performance of learning algorithm has been the main thread of theoretical research of machine learning. The performance of the regularized regression algorithm based on independent and identically d...Evaluation for the performance of learning algorithm has been the main thread of theoretical research of machine learning. The performance of the regularized regression algorithm based on independent and identically distributed（i.i.d.） samples has been researched by a large number of references. In the present paper we provide the convergence rates for the performance of regularized regression based on the inputs of p-order Markov chains.展开更多
We develop quantum mechanical Dirac ket-bra operator’s integration theory in Q-ordering or P-ordering to multimode case,where Q-ordering means all Qs are to the left of all Ps and P-ordering means all Ps are to the l...We develop quantum mechanical Dirac ket-bra operator’s integration theory in Q-ordering or P-ordering to multimode case,where Q-ordering means all Qs are to the left of all Ps and P-ordering means all Ps are to the left of all Qs.As their applications,we derive Q-ordered and P-ordered expansion formulas of multimode exponential operator e iPlΛlkQk.Application of the new formula in finding new general squeezing operators is demonstrated.The general exponential operator for coordinate representation transformation q1q2→A B C D q1q2is also derived.In this way,much more correpondence relations between classical coordinate transformations and their quantum mechanical images can be revealed.展开更多
基金Supported by the National Natural Science Foundation of China (10871226)the Natural Science Foundation of Zhejiang Province (Y6100096)
文摘Evaluation for the performance of learning algorithm has been the main thread of theoretical research of machine learning. The performance of the regularized regression algorithm based on independent and identically distributed（i.i.d.） samples has been researched by a large number of references. In the present paper we provide the convergence rates for the performance of regularized regression based on the inputs of p-order Markov chains.
基金supported by the National Natural Science Foundation of China (Grant No. 11175113)
文摘We develop quantum mechanical Dirac ket-bra operator’s integration theory in Q-ordering or P-ordering to multimode case,where Q-ordering means all Qs are to the left of all Ps and P-ordering means all Ps are to the left of all Qs.As their applications,we derive Q-ordered and P-ordered expansion formulas of multimode exponential operator e iPlΛlkQk.Application of the new formula in finding new general squeezing operators is demonstrated.The general exponential operator for coordinate representation transformation q1q2→A B C D q1q2is also derived.In this way,much more correpondence relations between classical coordinate transformations and their quantum mechanical images can be revealed.
