The logical network is a framework that describes finite-valued networked *** can be applied to many fields,such as Boolean networks,networked evolutionary games,opinion dynamics,and finite automatons,to name but a fe...
详细信息
ISBN:
(数字)9789887581536
ISBN:
(纸本)9781665482561
The logical network is a framework that describes finite-valued networked *** can be applied to many fields,such as Boolean networks,networked evolutionary games,opinion dynamics,and finite automatons,to name but a few.A new kind of logical network,called the stochastic logical network,is proposed in this *** with probabilistic logical networks,stochastic logical networks can describe more extensive uncertain ***,we prove that a stochastic logical network can be modeled as a non-homogeneous Markov chain under independent conditions and a homogeneous Markov chain under conditionally independent conditions,***,a consistency condition is proposed for the non-equivalence between the independent model and the conditionally independent *** paper proves that a stochastic logical network can be modeled as a homogeneous Markov chain using a power-reducing operator,only under the consistency ***,connections between probabilistic logical networks and stochastic logical networks are *** is proved that a probabilistic logical network is a special case of stochastic logical ***,we point out that the reason why the transition matrix of the probabilistic logical network can be obtained using the power-reducing operator is that the probabilistic logical network satisfies the consistency condition.
We propose Monte Carlo Nonlocal physics-informed neural networks(MC-Nonlocal-PINNs),which are a generalization of MC-fPINNs in *** et al.(*** ***.400(2022),115523)for solving general nonlocal models such as integral e...
详细信息
We propose Monte Carlo Nonlocal physics-informed neural networks(MC-Nonlocal-PINNs),which are a generalization of MC-fPINNs in *** et al.(*** ***.400(2022),115523)for solving general nonlocal models such as integral equations and nonlocal *** to MC-fPINNs,our MC-Nonlocal-PINNs handle nonlocal operators in a Monte Carlo way,resulting in a very stable approach for high dimensional *** present a variety of test problems,including high dimensional Volterra type integral equations,hypersingular integral equations and nonlocal PDEs,to demonstrate the effectiveness of our approach.
In this paper,we consider the zero-viscosity limit of the 2D steady Navier-Stokes equations in(0,L)×R+with no-slip boundary *** estimating the stream-function of the remainder,we justify the validity of the Prand...
详细信息
In this paper,we consider the zero-viscosity limit of the 2D steady Navier-Stokes equations in(0,L)×R+with no-slip boundary *** estimating the stream-function of the remainder,we justify the validity of the Prandtl boundary layer ***,we show the global stability under the concavity condition of the Prandtl profile for an arbitrarily large constant L when the Euler flow is shear.
Sampled-data proportional（P） and proportional-integral（PI） control for first-order linear systems are studied in this *** claim that a process with linear first-order dynamics can achieve zero steady-state error t...
详细信息
ISBN:
(数字)9789887581536
ISBN:
(纸本)9781665482561
Sampled-data proportional（P） and proportional-integral（PI） control for first-order linear systems are studied in this *** claim that a process with linear first-order dynamics can achieve zero steady-state error through a sampled-data PI controller.A necessary and sufficient condition on the control gains is derived,in terms of the sampling period,to fulfill the tracking ***,given a control gain pair（k,k） whose analogy PI control system realizes zero steady-state error,we compute a critical sampling period T such that the state of the corresponding sampled-data PI control system still tends to the setpoint if and only if the sampling period T
This paper studies the stability of a class of first-order uncertain systemscontrolled by a simple recurrent neural network(RNN) *** convergence conditions are *** relationship between the parameters of RNN controlle...
详细信息
ISBN:
(数字)9789887581536
ISBN:
(纸本)9781665482561
This paper studies the stability of a class of first-order uncertain systemscontrolled by a simple recurrent neural network(RNN) *** convergence conditions are *** relationship between the parameters of RNN controller and its robustness is quantitatively analyzed for the linear uncertain *** examples are provided to verify the analysis results.
Solving Nash equilibrium (NE) is a fundamental problem in game theory. However, for general non-zero-sum games, computing NE remains challenging (in fact, it is PPAD-hard), and there are no known efficient algorithms ...
详细信息
The speeding-up and slowing-down(SUSD)direction is a novel direction,which is proved to converge to the gradient descent direction under some *** authors propose the derivative-free optimization algorithm SUSD-TR,whic...
详细信息
The speeding-up and slowing-down(SUSD)direction is a novel direction,which is proved to converge to the gradient descent direction under some *** authors propose the derivative-free optimization algorithm SUSD-TR,which combines the SUSD direction based on the covariance matrix of interpolation points and the solution of the trust-region subproblem of the interpolation model function at the current iteration *** analyze the optimization dynamics and convergence of the algorithm *** of the trial step and structure step are *** results show their algorithm’s efficiency,and the comparison indicates that SUSD-TR greatly improves the method’s performance based on the method that only goes along the SUSD *** algorithm is competitive with state-of-the-art mathematical derivative-free optimization algorithms.
The proximal alternating linearized minimization(PALM)method suits well for solving blockstructured optimization problems,which are ubiquitous in real *** the cases where subproblems do not have closed-form solutions,...
详细信息
The proximal alternating linearized minimization(PALM)method suits well for solving blockstructured optimization problems,which are ubiquitous in real *** the cases where subproblems do not have closed-form solutions,e.g.,due to complex constraints,infeasible subsolvers are indispensable,giving rise to an infeasible inexact PALM(PALM-I).Numerous efforts have been devoted to analyzing the feasible PALM,while little attention has been paid to the *** usage of the PALM-I thus lacks a theoretical *** essential difficulty of analysis consists in the objective value nonmonotonicity induced by the *** study in the present work the convergence properties of the *** particular,we construct a surrogate sequence to surmount the nonmonotonicity issue and devise an implementable inexact *** upon these,we manage to establish the stationarity of any accumulation point,and moreover,show the iterate convergence and the asymptotic convergence rates under the assumption of the Lojasiewicz *** prominent advantages of the PALM-I on CPU time are illustrated via numerical experiments on problems arising from quantum physics and 3-dimensional anisotropic frictional contact.
CHATGPT,one of the leading Large Language Models(LLMs),has acquired linguistic capabilities such as text comprehension and logical reasoning,enabling it to engage in natural conversations with humans.
CHATGPT,one of the leading Large Language Models(LLMs),has acquired linguistic capabilities such as text comprehension and logical reasoning,enabling it to engage in natural conversations with humans.
Sparsity of a parameter vector in stochastic dynamic systems and precise reconstruction of its zero and nonzero elements appear in many areas including systems and control[1-4],signal processing[5,6],statistics[7,8],a...
详细信息
Sparsity of a parameter vector in stochastic dynamic systems and precise reconstruction of its zero and nonzero elements appear in many areas including systems and control[1-4],signal processing[5,6],statistics[7,8],and machine learning[9,10]since it provides a way to discover a parsimonious model that leads to more reliable and robust *** system identification theory has been a well-developed field[11,12].It usually characterizes the identification error between the estimates and the unknown parameters using different criteria such as randomness of noises,frequency domain sample data。
暂无评论