This paper studies non-convex programming problems. It is known that, in statistical inference, many constrained estimation problems may be expressed as convex programming problems. However, in many practical problems...This paper studies non-convex programming problems. It is known that, in statistical inference, many constrained estimation problems may be expressed as convex programming problems. However, in many practical problems, the objective functions are not convex. In this paper, we give a definition of a semi-convex objective function and discuss the corresponding non-convex programming problems. A two-step iterative algorithm called the alternating iterative method is proposed for finding solutions for such problems. The method is illustrated by three examples in constrained estimation problems given in Sasabuchi et al. （Biometrika, 72, 465472 （1983））, Shi N. Z. （J. Multivariate Anal., 50, 282-293 （1994）） and El Barmi H. and Dykstra R. （Ann. Statist., 26, 1878 1893 （1998））.展开更多
Endogenous biomolecules in cells are the basis of all life activities.Directly visualizing the structural characteristics and dynamic behaviors of cellular biomolecules is signiffcant for understanding the molecular m...Endogenous biomolecules in cells are the basis of all life activities.Directly visualizing the structural characteristics and dynamic behaviors of cellular biomolecules is signiffcant for understanding the molecular mechanisms in various biological processes.Singlemolecule localization microscopy(SMLM)can circumvent the optical diffraction limit,achieving analysis of the ffne structures and biological processes in living cells with nanoscale resolution.However,the large size of traditional imaging probes prevents SMLM from accurately locating ffne structures and densely distributed biomolecules within cells.In recent years,nucleic acid probes have emerged as potential tools to replace conventional SMLM probes by virtue of their small size and high speciffcity.In addition,due to their programmability,nucleic acid probes with different conformations can be constructed via sequence design,further extending the application of SMLM in bioanalysis.Here,we discuss the design concepts of different conformational nucleic acid probes for SMLM and summarize the application of SMLM based on nucleic acid probes in the ffeld of biomolecules.Furthermore,we provide a summary and future perspectives of the nucleic acid probe-based SMLM technology,aiming to provide guidance for the acquisition of nanoscale information about cellular biological processes.展开更多
基金the National Natural Science Foundation of China (Nos.10431010,10501005)Science Foundation for Young Teachers of NENU (No.20070103)
文摘This paper studies non-convex programming problems. It is known that, in statistical inference, many constrained estimation problems may be expressed as convex programming problems. However, in many practical problems, the objective functions are not convex. In this paper, we give a definition of a semi-convex objective function and discuss the corresponding non-convex programming problems. A two-step iterative algorithm called the alternating iterative method is proposed for finding solutions for such problems. The method is illustrated by three examples in constrained estimation problems given in Sasabuchi et al. （Biometrika, 72, 465472 （1983））, Shi N. Z. （J. Multivariate Anal., 50, 282-293 （1994）） and El Barmi H. and Dykstra R. （Ann. Statist., 26, 1878 1893 （1998））.
基金supported by the Natural Science Foundation of Hunan Province(2022JJ20005)National Natural Science Foundation of China(22174038,21925401,and 52221001),and Tencent Foundation.
文摘Endogenous biomolecules in cells are the basis of all life activities.Directly visualizing the structural characteristics and dynamic behaviors of cellular biomolecules is signiffcant for understanding the molecular mechanisms in various biological processes.Singlemolecule localization microscopy(SMLM)can circumvent the optical diffraction limit,achieving analysis of the ffne structures and biological processes in living cells with nanoscale resolution.However,the large size of traditional imaging probes prevents SMLM from accurately locating ffne structures and densely distributed biomolecules within cells.In recent years,nucleic acid probes have emerged as potential tools to replace conventional SMLM probes by virtue of their small size and high speciffcity.In addition,due to their programmability,nucleic acid probes with different conformations can be constructed via sequence design,further extending the application of SMLM in bioanalysis.Here,we discuss the design concepts of different conformational nucleic acid probes for SMLM and summarize the application of SMLM based on nucleic acid probes in the ffeld of biomolecules.Furthermore,we provide a summary and future perspectives of the nucleic acid probe-based SMLM technology,aiming to provide guidance for the acquisition of nanoscale information about cellular biological processes.
