Mean-Field Theory for Batched TD(λ)

1997 ◽  
Vol 9 (7) ◽  
pp. 1403-1419 ◽  
Author(s):  
Fernando J. Pineda
Keyword(s):  
Field Theory ◽  
Fixed Point ◽  
Random Walk ◽  
Markov Process ◽  
Mean Field Theory ◽  
Mean Field ◽  
Independent Observation ◽  
Affine Map ◽  
Linear Representations ◽  
Linearly Independent

A representation-independent mean-field dynamics is presented for batched TD(λ). The task is learning to predict the outcome of an indirectly observed absorbing Markov process. In the case of linear representations, the discrete-time deterministic iteration is an affine map whose fixed point can be expressed in closed form without the assumption of linearly independent observation vectors. Batched linear TD(λ) is proved to converge with probability 1 for all λ. Theory and simulation agree on a random walk example.

scholarly journals Bistability of Feshbach resonance in optical cavity

Open Physics ◽  
2014 ◽  
Vol 12 (6) ◽  
Author(s):  
Xiao-Qiang Xu ◽  
You-Quan Li
Keyword(s):  
Field Theory ◽  
Fixed Point ◽  
Feshbach Resonance ◽  
Optical Cavity ◽  
Mean Field Theory ◽  
Mean Field ◽  
Quantum Model ◽  
Photon Interaction ◽  
Atoms And Molecules ◽  
Pump Cavity

AbstractWe consider Feshbach resonance in an optical cavity where photons interact with atoms and molecules dispersively. From mean-field theory we obtain multiple fixed-point solutions, which is strongly related to the phenomenon of bistability. Adiabatic evolutions demonstrate hysteretic behaviors by varying pump-cavity detuning from opposite directions. We also use the quantum model to check mean-field results which match perfectly. The analysis here may enrich the study of particle-photon interaction systems.

Mean field theory of n-layer unbinding

1993 ◽  
Vol 3 (3) ◽  
pp. 385-393 ◽  
Author(s):  
W. Helfrich
Keyword(s):  
Field Theory ◽  
Mean Field Theory ◽  
Mean Field

scholarly journals Evidence of exactness of the mean-field theory in the nonextensive regime of long-range classical spin models

2000 ◽  
Vol 61 (17) ◽  
pp. 11521-11528 ◽  
Author(s):  
Sergio A. Cannas ◽  
A. C. N. de Magalhães ◽  
Francisco A. Tamarit
Keyword(s):  
Field Theory ◽  
Long Range ◽  
Mean Field Theory ◽  
Mean Field ◽  
Spin Models ◽  
Classical Spin ◽  
The Mean ◽  
Classical Spin Models

scholarly journals Intrinsic dissipative Floquet superconductors beyond mean-field theory

2021 ◽  
Vol 104 (1) ◽  
Author(s):  
Qinghong Yang ◽  
Zhesen Yang ◽  
Dong E. Liu
Keyword(s):  
Field Theory ◽  
Mean Field Theory ◽  
Mean Field

scholarly journals Single Chain Mean-Field Theory Study on Responsive Behavior of Semiflexible Polymer Brush

Materials ◽  
2021 ◽  
Vol 14 (4) ◽  
pp. 778
Author(s):  
Yingli Niu ◽  
Xiangyu Bu ◽  
Xinghua Zhang
Keyword(s):  
Field Theory ◽  
Message Passing Interface ◽  
Mean Field Theory ◽  
Mean Field ◽  
Algorithmic Complexity ◽  
Ensemble Average ◽  
Single Chain ◽  
Metropolis Monte Carlo ◽  
Rigid Rod ◽  
Chain Conformations

The application of single chain mean-field theory (SCMFT) on semiflexible chain brushes is reviewed. The worm-like chain (WLC) model is the best mode of semiflexible chain that can continuously recover to the rigid rod model and Gaussian chain (GC) model in rigid and flexible limits, respectively. Compared with the commonly used GC model, SCMFT is more applicable to the WLC model because the algorithmic complexity of the WLC model is much higher than that of the GC model in self-consistent field theory (SCFT). On the contrary, the algorithmic complexity of both models in SCMFT are comparable. In SCMFT, the ensemble average of quantities is obtained by sampling the conformations of a single chain or multi-chains in the external auxiliary field instead of solving the modified diffuse equation (MDE) in SCFT. The precision of this calculation is controlled by the number of bonds Nm used to discretize the chain contour length L and the number of conformations M used in the ensemble average. The latter factor can be well controlled by metropolis Monte Carlo simulation. This approach can be easily generalized to solve problems with complex boundary conditions or in high-dimensional systems, which were once nightmares when solving MDEs in SCFT. Moreover, the calculations in SCMFT mainly relate to the assemble averages of chain conformations, for which a portion of conformations can be performed parallel on different computing cores using a message-passing interface (MPI).

Sign in / Sign up

Export Citation Format

Share Document