scholarly journals Automatic Moment-Closure Approximation of Spatially Distributed Collective Adaptive Systems

2016 ◽  
Vol 26 (4) ◽  
pp. 1-22 ◽  
Author(s):  
Cheng Feng ◽  
Jane Hillston ◽  
Vashti Galpin
Keyword(s):  
Adaptive Systems ◽  
Moment Closure ◽  
Closure Approximation ◽  
Spatially Distributed ◽  
Moment Closure Approximation

scholarly journals Evidence accumulation and change rate inference in dynamic environments

2016 ◽  
Author(s):  
Adrian E Radillo ◽  
Alan Veliz-Cuba ◽  
Kresimir Josic ◽  
Zachary Kilpatrick
Keyword(s):  
Rate Of Change ◽  
Ideal Observer ◽  
Moment Closure ◽  
Dimensional System ◽  
Change Rate ◽  
Observer Model ◽  
Low Dimensional ◽  
State Of The Environment ◽  
Rate Correlation ◽  
Moment Closure Approximation

In a constantly changing world, animals must account for environmental volatility when making decisions. To appropriately discount older, irrelevant information, they need to learn the rate at which the environment changes. We develop an ideal observer model capable of inferring the present state of the environment along with its rate of change. Key to this computation is updating the posterior probability of all possible changepoint counts. This computation can be challenging, as the number of possibilities grows rapidly with time. However, we show how the computations can be simplified in the continuum limit by a moment closure approximation. The resulting low-dimensional system can be used to infer the environmental state and change rate with accuracy comparable to the ideal observer. The approximate computations can be performed by a neural network model via a rate-correlation based plasticity rule. We thus show how optimal observers accumulates evidence in changing environments, and map this computation to reduced models which perform inference using plausible neural mechanisms.

Analysis of the Closure Approximation for a Class of Stochastic Differential Equations

2017 ◽  
Vol 10 (2) ◽  
pp. 299-330
Author(s):  
Yunfeng Cai ◽  
Tiejun Li ◽  
Jiushu Shao ◽  
Zhiming Wang
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Open Systems ◽  
Numerical Study ◽  
Computational Cost ◽  
Nonlinear Problems ◽  
Exact Result ◽  
Moment Closure ◽  
Closure Approximation ◽  
The Moment

AbstractMotivated by the numerical study of spin-boson dynamics in quantum open systems, we present a convergence analysis of the closure approximation for a class of stochastic differential equations. We show that the naive Monte Carlo simulation of the system by direct temporal discretization is not feasible through variance analysis and numerical experiments. We also show that the Wiener chaos expansion exhibits very slow convergence and high computational cost. Though efficient and accurate, the rationale of the moment closure approach remains mysterious. We rigorously prove that the low moments in the moment closure approximation of the considered model are of exponential convergence to the exact result. It is further extended to more general nonlinear problems and applied to the original spin-boson model with similar structure.

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