In this paper,an adaptive cubic regularisation algorithm based on affine scaling methods(ARCBASM)is proposed for solving nonlinear equality constrained programming with nonnegative constraints on variables.From the op...In this paper,an adaptive cubic regularisation algorithm based on affine scaling methods(ARCBASM)is proposed for solving nonlinear equality constrained programming with nonnegative constraints on variables.From the optimality conditions of the problem,we introduce appropriate affine matrix and construct an affine scaling ARC subproblem with linearized constraints.Composite step methods and reduced Hessian methods are applied to tackle the linearized constraints.As a result,a standard unconstrained ARC subproblem is deduced and its solution can supply sufficient decrease.The fraction to the boundary rule maintains the strict feasibility(for nonnegative constraints on variables)of every iteration point.Reflection techniques are employed to prevent the iterations from approaching zero too early.Under mild assumptions,global convergence of the algorithm is analysed.Preliminary numerical results are reported.展开更多
This paper deals with Mckean-Vlasov backward stochastic differential equations with weak monotonicity coefficients.We first establish the existence and uniqueness of solutions to Mckean-Vlasov backward stochastic diff...This paper deals with Mckean-Vlasov backward stochastic differential equations with weak monotonicity coefficients.We first establish the existence and uniqueness of solutions to Mckean-Vlasov backward stochastic differential equations.Then we obtain a comparison theorem in one-dimensional situation.展开更多
In this article,we show the existence,uniqueness and stability of bounded solutions to the following quasilinear problems with mean curvature operator(φ'(x′(t)))′=f(t,x),t≥t_(0),lim_(t→∞)x(t)=ψ_(0),lim_(t→...In this article,we show the existence,uniqueness and stability of bounded solutions to the following quasilinear problems with mean curvature operator(φ'(x′(t)))′=f(t,x),t≥t_(0),lim_(t→∞)x(t)=ψ_(0),lim_(t→∞)x′(t)e^(t)=0,where t_(0) and ψ_(0) are real constants,φ(s)=s/√1−s^(2),s∈R with s∈(−1,1),f:[t_(0),∞)×R→R satisfies the Lipschitz or Osgood-type conditions.展开更多
The mechanistic target of rapamycin(m TOR) is a serine/threonine kinase that plays a pivotal role in cellular growth, proliferation, survival, and metabolism. In the central nervous system(CNS), the mTOR pathway regul...The mechanistic target of rapamycin(m TOR) is a serine/threonine kinase that plays a pivotal role in cellular growth, proliferation, survival, and metabolism. In the central nervous system(CNS), the mTOR pathway regulates diverse aspects of neural development and function. Genetic mutations within the m TOR pathway lead to severe neurodevelopmental disorders, collectively known as “mTORopathies”(Crino, 2020). Dysfunctions of m TOR, including both its hyperactivation and hypoactivation, have also been implicated in a wide spectrum of other neurodevelopmental and neurodegenerative conditions, highlighting its importance in CNS health.展开更多
The organization of biological neuronal networks into functional modules has intrigued scientists and inspired engineers to develop artificial systems.These networks are characterized by two key properties.First,they ...The organization of biological neuronal networks into functional modules has intrigued scientists and inspired engineers to develop artificial systems.These networks are characterized by two key properties.First,they exhibit dense interconnectivity(Braitenburg and Schüz,1998;Campagnola et al.,2022).The strength and probability of connectivity depend on cell type,inter-neuronal distance,and species.Still,every cortical neuron receives input from thousands of other neurons while transmitting output to a similar number of neurons.Second,communication between neurons occurs primarily via chemical or electrical synapses.展开更多
基金Supported by the National Natural Science Foundation of China(12071133)Natural Science Foundation of Henan Province(252300421993)Key Scientific Research Project of Higher Education Institutions in Henan Province(25B110005)。
文摘In this paper,an adaptive cubic regularisation algorithm based on affine scaling methods(ARCBASM)is proposed for solving nonlinear equality constrained programming with nonnegative constraints on variables.From the optimality conditions of the problem,we introduce appropriate affine matrix and construct an affine scaling ARC subproblem with linearized constraints.Composite step methods and reduced Hessian methods are applied to tackle the linearized constraints.As a result,a standard unconstrained ARC subproblem is deduced and its solution can supply sufficient decrease.The fraction to the boundary rule maintains the strict feasibility(for nonnegative constraints on variables)of every iteration point.Reflection techniques are employed to prevent the iterations from approaching zero too early.Under mild assumptions,global convergence of the algorithm is analysed.Preliminary numerical results are reported.
基金Supported by the National Natural Science Foundation of China(12001074)the Research Innovation Program of Graduate Students in Hunan Province(CX20220258)+1 种基金the Research Innovation Program of Graduate Students of Central South University(1053320214147)the Key Scientific Research Project of Higher Education Institutions in Henan Province(25B110025)。
文摘This paper deals with Mckean-Vlasov backward stochastic differential equations with weak monotonicity coefficients.We first establish the existence and uniqueness of solutions to Mckean-Vlasov backward stochastic differential equations.Then we obtain a comparison theorem in one-dimensional situation.
基金Supported by the National Natural Science Foundation of China(Grant Nos.12361040,12061064)the Na-tional Science Foundation of Gansu Province(Grant No.22JR5RA264)State Scholarship Fund(Grant No.20230862021).
文摘In this article,we show the existence,uniqueness and stability of bounded solutions to the following quasilinear problems with mean curvature operator(φ'(x′(t)))′=f(t,x),t≥t_(0),lim_(t→∞)x(t)=ψ_(0),lim_(t→∞)x′(t)e^(t)=0,where t_(0) and ψ_(0) are real constants,φ(s)=s/√1−s^(2),s∈R with s∈(−1,1),f:[t_(0),∞)×R→R satisfies the Lipschitz or Osgood-type conditions.
基金supported by grants from Simons Foundation (SFARI 479754),CIHR (PJT-180565)the Scottish Rite Charitable Foundation of Canada (to YL)funding from the Canada Research Chairs program。
文摘The mechanistic target of rapamycin(m TOR) is a serine/threonine kinase that plays a pivotal role in cellular growth, proliferation, survival, and metabolism. In the central nervous system(CNS), the mTOR pathway regulates diverse aspects of neural development and function. Genetic mutations within the m TOR pathway lead to severe neurodevelopmental disorders, collectively known as “mTORopathies”(Crino, 2020). Dysfunctions of m TOR, including both its hyperactivation and hypoactivation, have also been implicated in a wide spectrum of other neurodevelopmental and neurodegenerative conditions, highlighting its importance in CNS health.
基金supported in part by the Rosetrees Trust(#CF-2023-I-2_113)by the Israel Ministry of Innovation,Science,and Technology(#7393)(to ES).
文摘The organization of biological neuronal networks into functional modules has intrigued scientists and inspired engineers to develop artificial systems.These networks are characterized by two key properties.First,they exhibit dense interconnectivity(Braitenburg and Schüz,1998;Campagnola et al.,2022).The strength and probability of connectivity depend on cell type,inter-neuronal distance,and species.Still,every cortical neuron receives input from thousands of other neurons while transmitting output to a similar number of neurons.Second,communication between neurons occurs primarily via chemical or electrical synapses.
