The resolution of differential games often concerns the difficult problem of two points border value （TPBV）, then ascribe linear quadratic differential game to Hamilton system. To Hamilton system, the algorithm of s...The resolution of differential games often concerns the difficult problem of two points border value （TPBV）, then ascribe linear quadratic differential game to Hamilton system. To Hamilton system, the algorithm of symplectic geometry has the merits of being able to copy the dynamic structure of Hamilton system and keep the measure of phase plane. From the viewpoint of Hamilton system, the symplectic characters of linear quadratic differential game were probed; as a try, Symplectic-Runge-Kutta algorithm was presented for the resolution of infinite horizon linear quadratic differential game. An example of numerical calculation was given, and the result can illuminate the feasibility of this method. At the same time, it embodies the fine conservation characteristics of symplectic algorithm to system energy.展开更多
With the progress of plant genome research, more than 50 plant metallothionein_like (MT_L) genes have been found, but only several MT_L proteins have been detected and no experimental structural information for MT_L p...With the progress of plant genome research, more than 50 plant metallothionein_like (MT_L) genes have been found, but only several MT_L proteins have been detected and no experimental structural information for MT_L proteins has been reported so far. Since detailed knowledge of the protein tertiary structure is required to understand its biological function, a method is needed to determine the structure of these proteins. In this study, the structural data of known mammal MT was used to determine the interatomic distance constraints of the CXC and CXXC motifs and the metal_sulfur chelating cluster. Then several possible MT conformations were predicted using a distance geometry algorithm. The statistical analysis was used to select those with much lower target function values and lower conformation energies as the predicted tertiary structural models of the cysteine_rich (CR) domains of these proteins. A suitable prediction method for modeling the CR domain of the plant MT_L protein was constructed. The accurately predicted result for the known structure of an MT protein from blue crab suggests that this method is practicable. The tertiary structures of CR domains of rape MT_L protein LSC54 was then modeled with this method.展开更多
Adversarial approaches,which intentionally challenge machine learning models by generating difficult examples,are increasingly being adopted to improve machine learning interatomic potentials(MLIPs).While already prov...Adversarial approaches,which intentionally challenge machine learning models by generating difficult examples,are increasingly being adopted to improve machine learning interatomic potentials(MLIPs).While already providing great practical value,little is known about the actual prediction errors of MLIPs on adversarial structures and whether these errors can be controlled.We propose the Calibrated Adversarial Geometry Optimization(CAGO)algorithm to discover adversarial structures with userassigned errors.Through uncertainty calibration,the estimated uncertainty of MLIPs is unified with real errors.By performing geometry optimization for calibrated uncertainty,we reach adversarial structures with the user-assigned target MLIP prediction error.Integrating with active learning pipelines,we benchmark CAGO,demonstrating stable MLIPs that systematically converge structural,dynamical,and thermodynamical properties for liquid water and water adsorption in a metal-organic framework within only hundreds of training structures,where previously many thousands were typically required.展开更多
基金Project supported by the National Aeronautics Base Science Foundation of China (No.2000CB080601)the National Defence Key Pre-research Program of China during the 10th Five-Year Plan Period (No.2002BK080602)
文摘The resolution of differential games often concerns the difficult problem of two points border value （TPBV）, then ascribe linear quadratic differential game to Hamilton system. To Hamilton system, the algorithm of symplectic geometry has the merits of being able to copy the dynamic structure of Hamilton system and keep the measure of phase plane. From the viewpoint of Hamilton system, the symplectic characters of linear quadratic differential game were probed; as a try, Symplectic-Runge-Kutta algorithm was presented for the resolution of infinite horizon linear quadratic differential game. An example of numerical calculation was given, and the result can illuminate the feasibility of this method. At the same time, it embodies the fine conservation characteristics of symplectic algorithm to system energy.
文摘With the progress of plant genome research, more than 50 plant metallothionein_like (MT_L) genes have been found, but only several MT_L proteins have been detected and no experimental structural information for MT_L proteins has been reported so far. Since detailed knowledge of the protein tertiary structure is required to understand its biological function, a method is needed to determine the structure of these proteins. In this study, the structural data of known mammal MT was used to determine the interatomic distance constraints of the CXC and CXXC motifs and the metal_sulfur chelating cluster. Then several possible MT conformations were predicted using a distance geometry algorithm. The statistical analysis was used to select those with much lower target function values and lower conformation energies as the predicted tertiary structural models of the cysteine_rich (CR) domains of these proteins. A suitable prediction method for modeling the CR domain of the plant MT_L protein was constructed. The accurately predicted result for the known structure of an MT protein from blue crab suggests that this method is practicable. The tertiary structures of CR domains of rape MT_L protein LSC54 was then modeled with this method.
基金supported by the Research Council of Norway through the Centre of Excellence Hylleraas Centre for Quantum Molecular Sciences(Grant 262695)the Young Researcher Talent grants 344993 and 354100+2 种基金We acknowledge the EuroHPC Joint Undertaking for awarding this project access to the EuroHPC supercomputer LUMI,hosted by CSC(Finland)and the LUMI consortium through a EuroHPC Regular Access call(Grants EHPC-REG-2023R02-088,EHPC-REG-2023R03-146)Support was also received from the Centre for Advanced Study in Oslo,Norway,which funded and hosted the SLB Young CAS Fellow research project during the academic year of 23/24 and 24/25Part of the simulations were performed on resources provided by Sigma2—the Norwegian National Infrastructure for High-Performance Computing and Data Storage(grant numbers NN4654K and NS4654K).
文摘Adversarial approaches,which intentionally challenge machine learning models by generating difficult examples,are increasingly being adopted to improve machine learning interatomic potentials(MLIPs).While already providing great practical value,little is known about the actual prediction errors of MLIPs on adversarial structures and whether these errors can be controlled.We propose the Calibrated Adversarial Geometry Optimization(CAGO)algorithm to discover adversarial structures with userassigned errors.Through uncertainty calibration,the estimated uncertainty of MLIPs is unified with real errors.By performing geometry optimization for calibrated uncertainty,we reach adversarial structures with the user-assigned target MLIP prediction error.Integrating with active learning pipelines,we benchmark CAGO,demonstrating stable MLIPs that systematically converge structural,dynamical,and thermodynamical properties for liquid water and water adsorption in a metal-organic framework within only hundreds of training structures,where previously many thousands were typically required.
