In this paper we consider one dimensional mean-field backward stochastic differential equations(BSDEs)under weak assumptions on the coefficient.Unlike[3],the generator of our mean-field BSDEs depends not only on the s...In this paper we consider one dimensional mean-field backward stochastic differential equations(BSDEs)under weak assumptions on the coefficient.Unlike[3],the generator of our mean-field BSDEs depends not only on the solution(Y,Z)but also on the law PY of Y.The first part of the paper is devoted to the existence and uniqueness of solutions in Lp,1<p≤2,where the monotonicity conditions are satisfied.Next,we show that if the generator/is uniformly continuous in(μ,y,z),uniformly with respect to(t,ω) and if the terminal valueξbelongs to Lp(Ω,F,P)with 1<p≤2,the mean-field BSDE has a unique Lp solution.展开更多
A new class of backward particle systems with sequential interaction is proposed to approximate the mean-field backward stochastic differential equations.It is proven that the weighted empirical measure of this partic...A new class of backward particle systems with sequential interaction is proposed to approximate the mean-field backward stochastic differential equations.It is proven that the weighted empirical measure of this particle system converges to the law of the McKean-Vlasov system as the number of particles grows.Based on the Wasserstein met-ric,quantitative propagation of chaos results are obtained for both linear and quadratic growth conditions.Finally,numerical experiments are conducted to validate our theoretical results.展开更多
We study mean-field BSDEs with jumps and a generalized mean-field operator that can capture higher-order interactions.We interpret the BSDE solution as a dynamic risk measure for a representative bank whose risk attit...We study mean-field BSDEs with jumps and a generalized mean-field operator that can capture higher-order interactions.We interpret the BSDE solution as a dynamic risk measure for a representative bank whose risk attitude is influenced by the system.This influence can come in a wide class of choices,including the average system state or average intensity of system interactions.Using Fenchel−Legendre transforms,our main result is a dual representation for the expectation of the risk measure in the convex case.In particular,we exhibit its dependence on the mean-field operator.展开更多
This paper considers a linear-quadratic(LQ) meanfield game governed by a forward-backward stochastic system with partial observation and common noise,where a coupling structure enters state equations,cost functionals ...This paper considers a linear-quadratic(LQ) meanfield game governed by a forward-backward stochastic system with partial observation and common noise,where a coupling structure enters state equations,cost functionals and observation equations.Firstly,to reduce the complexity of solving the meanfield game,a limiting control problem is introduced.By virtue of the decomposition approach,an admissible control set is proposed.Applying a filter technique and dimensional-expansion technique,a decentralized control strategy and a consistency condition system are derived,and the related solvability is also addressed.Secondly,we discuss an approximate Nash equilibrium property of the decentralized control strategy.Finally,we work out a financial problem with some numerical simulations.展开更多
Electrocatalysis is undergoing a renaissance due to its central importance for a sustainable energy economy,relying on green(electro-)chemical processes to harvest,convert,and store energy.Theoretical considerations b...Electrocatalysis is undergoing a renaissance due to its central importance for a sustainable energy economy,relying on green(electro-)chemical processes to harvest,convert,and store energy.Theoretical considerations by electronic structure methods are key to identify potential material motifs for electrocatalytic processes at the solid/liquid interface.Most commonly,heuristic concepts in the realm of materials screening by the compilation of volcano plots are used,which rely on a plethora of simplifications and approximations of the complex electrochemical interface.While the investigation of the catalytic processes at the solid/liquid interface mainly relies on descriptor-based approaches,in the present future article it is discussed that the inclusion of the liquid part of the interface by mean-field models is crucial to elevate screening approaches to the next level.展开更多
In this paper we consider general coupled mean-field reflected forward-backward stochastic differential equations(FBSDEs),whose coefficients not only depend on the solution but also on the law of the solution.The firs...In this paper we consider general coupled mean-field reflected forward-backward stochastic differential equations(FBSDEs),whose coefficients not only depend on the solution but also on the law of the solution.The first part of the paper is devoted to the existence and the uniqueness of solutions for such general mean-field reflected backward stochastic differential equations(BSDEs)under Lipschitz conditions,and for the one-dimensional case a comparison theorem is studied.With the help of this comparison result,we prove the existence of the solution for our mean-field reflected forward-backward stochastic differential equation under continuity assumptions.It should be mentioned that,under appropriate assumptions,we prove the uniqueness of this solution as well as that of a comparison theorem for mean-field reflected FBSDEs in a non-trivial manner.展开更多
We establish a new type of backward stochastic differential equations(BSDEs)connected with stochastic differential games(SDGs), namely, BSDEs strongly coupled with the lower and the upper value functions of SDGs, wher...We establish a new type of backward stochastic differential equations(BSDEs)connected with stochastic differential games(SDGs), namely, BSDEs strongly coupled with the lower and the upper value functions of SDGs, where the lower and the upper value functions are defined through this BSDE. The existence and the uniqueness theorem and comparison theorem are proved for such equations with the help of an iteration method. We also show that the lower and the upper value functions satisfy the dynamic programming principle. Moreover, we study the associated Hamilton-Jacobi-Bellman-Isaacs(HJB-Isaacs)equations, which are nonlocal, and strongly coupled with the lower and the upper value functions. Using a new method, we characterize the pair(W, U) consisting of the lower and the upper value functions as the unique viscosity solution of our nonlocal HJB-Isaacs equation. Furthermore, the game has a value under the Isaacs’ condition.展开更多
Based on ab initio calculations,we utilize the mean-field potential approach with the quantum modification in conjunction with stress–strain relation to investigate the elastic anisotropies and sound velocities of hc...Based on ab initio calculations,we utilize the mean-field potential approach with the quantum modification in conjunction with stress–strain relation to investigate the elastic anisotropies and sound velocities of hcp and bcc Be under high-temperature(0–6000 K)and high-pressure(0–500 GPa)conditions.We propose a general definition of anisotropy for elastic moduli and sound velocities.Results suggest that the elastic anisotropy of Be is more significantly influenced by pressure than by temperature.The pressure-induced increase of c/a ratio makes the anisotropy of hcp Be significantly strengthen.Nevertheless,the hcp Be still exhibits smaller anisotropy than bcc Be in terms of elastic moduli and sound velocities.We suggest that measuring the anisotropy in shear sound velocity may be an approach to distinguishing the hcp–bcc phase transition under extreme conditions.展开更多
Self-normalizing neural networks(SNN)regulate the activation and gradient flows through activation functions with the self-normalization property.As SNNs do not rely on norms computed from minibatches,they are more fr...Self-normalizing neural networks(SNN)regulate the activation and gradient flows through activation functions with the self-normalization property.As SNNs do not rely on norms computed from minibatches,they are more friendly to data parallelism,kernel fusion,and emerging architectures such as ReRAM-based accelerators.However,existing SNNs have mainly demonstrated their effectiveness on toy datasets and fall short in accuracy when dealing with large-scale tasks like ImageNet.They lack the strong normalization,regularization,and expression power required for wider,deeper models and larger-scale tasks.To enhance the normalization strength,this paper introduces a comprehensive and practical definition of the self-normalization property in terms of the stability and attractiveness of the statistical fixed points.It is comprehensive as it jointly considers all the fixed points used by existing studies:the first and second moment of forward activation and the expected Frobenius norm of backward gradient.The practicality comes from the analytical equations provided by our paper to assess the stability and attractiveness of each fixed point,which are derived from theoretical analysis of the forward and backward signals.The proposed definition is applied to a meta activation function inspired by prior research,leading to a stronger self-normalizing activation function named‘‘bi-scaled exponential linear unit with backward standardized’’(bSELU-BSTD).We provide both theoretical and empirical evidence to show that it is superior to existing studies.To enhance the regularization and expression power,we further propose scaled-Mixup and channel-wise scale&shift.With these three techniques,our approach achieves 75.23%top-1 accuracy on the ImageNet with Conv MobileNet V1,surpassing the performance of existing self-normalizing activation functions.To the best of our knowledge,this is the first SNN that achieves comparable accuracy to batch normalization on ImageNet.展开更多
In this paper we study the following nonlinear BSDE：y（t） ＋ ∫1 t f（s,y（s）,z（s））ds ＋ ∫1 t [z（s） ＋ g 1 （s,y（s）） ＋ εg 2 （s,y（s）,z（s））]dW s=ξ,t ∈ [0,1],where ε is a small parameter.The coeffi...In this paper we study the following nonlinear BSDE：y（t） ＋ ∫1 t f（s,y（s）,z（s））ds ＋ ∫1 t [z（s） ＋ g 1 （s,y（s）） ＋ εg 2 （s,y（s）,z（s））]dW s=ξ,t ∈ [0,1],where ε is a small parameter.The coefficient f is locally Lipschitz in y and z,the coefficient g 1 is locally Lipschitz in y,and the coefficient g 2 is uniformly Lipschitz in y and z.Let L N be the locally Lipschitz constant of the coefficients on the ball B（0,N） of R d × R d×r.We prove the existence and uniqueness of the solution when L N ～ √ log N and the parameter ε is small.展开更多
The potential energy surfaces are calculated for neutron-deficient At isotopes from A - 190 to 207 in an axially deformed relativistic mean-field approach, using a quadratic constraint scheme for the first time. We fi...The potential energy surfaces are calculated for neutron-deficient At isotopes from A - 190 to 207 in an axially deformed relativistic mean-field approach, using a quadratic constraint scheme for the first time. We find several minima in the potential energy surface for each nucleus, shape-coexistence, and quadratic deform are discussed.展开更多
By using the mean-field Jordan-Wigner transformation analysis,this paper studies the one-dimensionalspin-1/2 XYZ antiferromagnetic chain in the transverse field with uniform long-range interactions among the z-compone...By using the mean-field Jordan-Wigner transformation analysis,this paper studies the one-dimensionalspin-1/2 XYZ antiferromagnetic chain in the transverse field with uniform long-range interactions among the z-components of the spins.The thermodynamic quantities,such as Helmholtz free energy,the internal energy,the specificheat,and the isothermal susceptibility,are obtained.Under degenerating condition,our results agree with numericalresults of the other literatures.展开更多
基金supported in part by the NSFC(11222110,11871037)Shandong Province(JQ201202)+1 种基金NSFC-RS(11661130148,NA150344)111 Project(B12023)。
文摘In this paper we consider one dimensional mean-field backward stochastic differential equations(BSDEs)under weak assumptions on the coefficient.Unlike[3],the generator of our mean-field BSDEs depends not only on the solution(Y,Z)but also on the law PY of Y.The first part of the paper is devoted to the existence and uniqueness of solutions in Lp,1<p≤2,where the monotonicity conditions are satisfied.Next,we show that if the generator/is uniformly continuous in(μ,y,z),uniformly with respect to(t,ω) and if the terminal valueξbelongs to Lp(Ω,F,P)with 1<p≤2,the mean-field BSDE has a unique Lp solution.
基金supported by the National Natural Science Foundation of China(No.12222103)the National Key R&D Program of China(No.2018YFA0703900).
文摘A new class of backward particle systems with sequential interaction is proposed to approximate the mean-field backward stochastic differential equations.It is proven that the weighted empirical measure of this particle system converges to the law of the McKean-Vlasov system as the number of particles grows.Based on the Wasserstein met-ric,quantitative propagation of chaos results are obtained for both linear and quadratic growth conditions.Finally,numerical experiments are conducted to validate our theoretical results.
文摘We study mean-field BSDEs with jumps and a generalized mean-field operator that can capture higher-order interactions.We interpret the BSDE solution as a dynamic risk measure for a representative bank whose risk attitude is influenced by the system.This influence can come in a wide class of choices,including the average system state or average intensity of system interactions.Using Fenchel−Legendre transforms,our main result is a dual representation for the expectation of the risk measure in the convex case.In particular,we exhibit its dependence on the mean-field operator.
基金supported by the National Key Research and Development Program of China(2022YFA1006103,2023YFA1009203)the National Natural Science Foundation of China(61925306,61821004,11831010,61977043,12001320)+2 种基金the Natural Science Foundation of Shandong Province(ZR2019ZD42,ZR2020ZD24)the Taishan Scholars Young Program of Shandong(TSQN202211032)the Young Scholars Program of Shandong University。
文摘This paper considers a linear-quadratic(LQ) meanfield game governed by a forward-backward stochastic system with partial observation and common noise,where a coupling structure enters state equations,cost functionals and observation equations.Firstly,to reduce the complexity of solving the meanfield game,a limiting control problem is introduced.By virtue of the decomposition approach,an admissible control set is proposed.Applying a filter technique and dimensional-expansion technique,a decentralized control strategy and a consistency condition system are derived,and the related solvability is also addressed.Secondly,we discuss an approximate Nash equilibrium property of the decentralized control strategy.Finally,we work out a financial problem with some numerical simulations.
基金funding by the Ministry of Culture and Science of the Federal State of North Rhine-Westphalia(NRW Return Grant)funded by the CRC/TRR247:“Heterogeneous Oxidation Catalysis in the Liquid Phase”(Project number 388390466-TRR 247)+2 种基金the RESOLV Cluster of Excellence,funded by the Deutsche Forschungsgemeinschaft under Germany’s Excellence Strategy–EXC 2033–390677874–RESOLVthe Center for Nanointegration(CENIDE)supported by COST(European Cooperation in Science and Technology)。
文摘Electrocatalysis is undergoing a renaissance due to its central importance for a sustainable energy economy,relying on green(electro-)chemical processes to harvest,convert,and store energy.Theoretical considerations by electronic structure methods are key to identify potential material motifs for electrocatalytic processes at the solid/liquid interface.Most commonly,heuristic concepts in the realm of materials screening by the compilation of volcano plots are used,which rely on a plethora of simplifications and approximations of the complex electrochemical interface.While the investigation of the catalytic processes at the solid/liquid interface mainly relies on descriptor-based approaches,in the present future article it is discussed that the inclusion of the liquid part of the interface by mean-field models is crucial to elevate screening approaches to the next level.
基金supported in part by theNSFC(11871037)Shandong Province(JQ201202)+3 种基金NSFC-RS(11661130148NA150344)111 Project(B12023)supported by the Qingdao Postdoctoral Application Research Project(QDBSH20220202092)。
文摘In this paper we consider general coupled mean-field reflected forward-backward stochastic differential equations(FBSDEs),whose coefficients not only depend on the solution but also on the law of the solution.The first part of the paper is devoted to the existence and the uniqueness of solutions for such general mean-field reflected backward stochastic differential equations(BSDEs)under Lipschitz conditions,and for the one-dimensional case a comparison theorem is studied.With the help of this comparison result,we prove the existence of the solution for our mean-field reflected forward-backward stochastic differential equation under continuity assumptions.It should be mentioned that,under appropriate assumptions,we prove the uniqueness of this solution as well as that of a comparison theorem for mean-field reflected FBSDEs in a non-trivial manner.
基金supported by the NSF of China(11071144,11171187,11222110 and 71671104)Shandong Province(BS2011SF010,JQ201202)+4 种基金SRF for ROCS(SEM)Program for New Century Excellent Talents in University(NCET-12-0331)111 Project(B12023)the Ministry of Education of Humanities and Social Science Project(16YJA910003)Incubation Group Project of Financial Statistics and Risk Management of SDUFE
文摘We establish a new type of backward stochastic differential equations(BSDEs)connected with stochastic differential games(SDGs), namely, BSDEs strongly coupled with the lower and the upper value functions of SDGs, where the lower and the upper value functions are defined through this BSDE. The existence and the uniqueness theorem and comparison theorem are proved for such equations with the help of an iteration method. We also show that the lower and the upper value functions satisfy the dynamic programming principle. Moreover, we study the associated Hamilton-Jacobi-Bellman-Isaacs(HJB-Isaacs)equations, which are nonlocal, and strongly coupled with the lower and the upper value functions. Using a new method, we characterize the pair(W, U) consisting of the lower and the upper value functions as the unique viscosity solution of our nonlocal HJB-Isaacs equation. Furthermore, the game has a value under the Isaacs’ condition.
基金supported by the National Natural Science Foundation of China(Grant Nos.U23A_(2)0537,U2230401,and 52371174)Funding of National Key Laboratory of Computational Physics.
文摘Based on ab initio calculations,we utilize the mean-field potential approach with the quantum modification in conjunction with stress–strain relation to investigate the elastic anisotropies and sound velocities of hcp and bcc Be under high-temperature(0–6000 K)and high-pressure(0–500 GPa)conditions.We propose a general definition of anisotropy for elastic moduli and sound velocities.Results suggest that the elastic anisotropy of Be is more significantly influenced by pressure than by temperature.The pressure-induced increase of c/a ratio makes the anisotropy of hcp Be significantly strengthen.Nevertheless,the hcp Be still exhibits smaller anisotropy than bcc Be in terms of elastic moduli and sound velocities.We suggest that measuring the anisotropy in shear sound velocity may be an approach to distinguishing the hcp–bcc phase transition under extreme conditions.
基金National Key R&D Program of China(2018AAA0102600)National Natural Science Foundation of China(No.61876215,62106119)+1 种基金Beijing Academy of Artificial Intelligence(BAAI),ChinaChinese Institute for Brain Research,Beijing,and the Science and Technology Major Project of Guangzhou,China(202007030006).
文摘Self-normalizing neural networks(SNN)regulate the activation and gradient flows through activation functions with the self-normalization property.As SNNs do not rely on norms computed from minibatches,they are more friendly to data parallelism,kernel fusion,and emerging architectures such as ReRAM-based accelerators.However,existing SNNs have mainly demonstrated their effectiveness on toy datasets and fall short in accuracy when dealing with large-scale tasks like ImageNet.They lack the strong normalization,regularization,and expression power required for wider,deeper models and larger-scale tasks.To enhance the normalization strength,this paper introduces a comprehensive and practical definition of the self-normalization property in terms of the stability and attractiveness of the statistical fixed points.It is comprehensive as it jointly considers all the fixed points used by existing studies:the first and second moment of forward activation and the expected Frobenius norm of backward gradient.The practicality comes from the analytical equations provided by our paper to assess the stability and attractiveness of each fixed point,which are derived from theoretical analysis of the forward and backward signals.The proposed definition is applied to a meta activation function inspired by prior research,leading to a stronger self-normalizing activation function named‘‘bi-scaled exponential linear unit with backward standardized’’(bSELU-BSTD).We provide both theoretical and empirical evidence to show that it is superior to existing studies.To enhance the regularization and expression power,we further propose scaled-Mixup and channel-wise scale&shift.With these three techniques,our approach achieves 75.23%top-1 accuracy on the ImageNet with Conv MobileNet V1,surpassing the performance of existing self-normalizing activation functions.To the best of our knowledge,this is the first SNN that achieves comparable accuracy to batch normalization on ImageNet.
文摘In this paper we study the following nonlinear BSDE：y（t） ＋ ∫1 t f（s,y（s）,z（s））ds ＋ ∫1 t [z（s） ＋ g 1 （s,y（s）） ＋ εg 2 （s,y（s）,z（s））]dW s=ξ,t ∈ [0,1],where ε is a small parameter.The coefficient f is locally Lipschitz in y and z,the coefficient g 1 is locally Lipschitz in y,and the coefficient g 2 is uniformly Lipschitz in y and z.Let L N be the locally Lipschitz constant of the coefficients on the ball B（0,N） of R d × R d×r.We prove the existence and uniqueness of the solution when L N ～ √ log N and the parameter ε is small.
基金The project supported by National Natural Science Foundation of China under Grant Nos. 10475116, 10535010, and 10235030, and Asia-Europe Link in Nuclear Physics and Astrophysics under Grant No. CN/ASIA-LINK/008 （094-791） and by Major State Basic Research Development Program of China under Grant No. 2007CB815000
文摘The potential energy surfaces are calculated for neutron-deficient At isotopes from A - 190 to 207 in an axially deformed relativistic mean-field approach, using a quadratic constraint scheme for the first time. We find several minima in the potential energy surface for each nucleus, shape-coexistence, and quadratic deform are discussed.
基金the Open Fund of Jiangsu Laboratory of Advanced Functional Materials under Grant No.06KFJJ004
文摘By using the mean-field Jordan-Wigner transformation analysis,this paper studies the one-dimensionalspin-1/2 XYZ antiferromagnetic chain in the transverse field with uniform long-range interactions among the z-components of the spins.The thermodynamic quantities,such as Helmholtz free energy,the internal energy,the specificheat,and the isothermal susceptibility,are obtained.Under degenerating condition,our results agree with numericalresults of the other literatures.
