Locally enhanced sampling in free energy calculations: Application of mean field approximation to accurate calculation of free energy differences

1992 ◽  
Vol 97 (10) ◽  
pp. 7838-7841 ◽  
Author(s):  
Gennady Verkhivker ◽  
Ron Elber ◽  
Wieslaw Nowak
Keyword(s):  
Free Energy ◽  
Mean Field ◽  
Field Approximation ◽  
Free Energy Calculations ◽  
Mean Field Approximation ◽  
Enhanced Sampling ◽  
Accurate Calculation ◽  
Energy Calculations ◽  
Locally Enhanced Sampling

scholarly journals The Possibility of Many Compensation Points in a Mixed-Spin Ising Ferrimagnetic System

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Hadey K. Mohamad
Keyword(s):  
Free Energy ◽  
Mean Field ◽  
Field Approximation ◽  
Spin Model ◽  
Mean Field Approximation ◽  
Zero Field ◽  
Mixed Spin ◽  
Simple Cubic ◽  
Simple Cubic Lattice ◽  
The Mean

The magnetic properties of a ferrimagnetic mixed spin-3/2 and spin-5/2 Ising model with different anisotropies are investigated by using the mean-field approximation (MFA). In particular, the effect of magnetic anisotropies on the compensation phenomenon, acting on A-atoms and B-ones for the mixed-spin model, has been considered in a zero field. The free energy of a mixed-spin Ising ferrimagnetic system from MFA of the Hamiltonian is calculated. By minimizing the free energy, we obtain the equilibrium magnetizations and the compensation points. The phase diagram of the system in the anisotropy dependence of transition temperature has been discussed as well. Our results of this model predict the existence of many (two or three) compensation points in the ordered system on a simple cubic lattice.

scholarly journals Accurate calculation of the absolute free energy of binding for drug molecules

2016 ◽  
Vol 7 (1) ◽  
pp. 207-218 ◽  
Author(s):  
Matteo Aldeghi ◽  
Alexander Heifetz ◽  
Michael J. Bodkin ◽  
Stefan Knapp ◽  
Philip C. Biggin
Keyword(s):  
Molecular Dynamics ◽  
Free Energy ◽  
Free Energy Calculations ◽  
Accurate Calculation ◽  
Energy Calculations ◽  
Thermodynamic Cycles ◽  
Drug Molecules ◽  
The Absolute ◽  
Free Energy Of Binding

Free energy calculations based on molecular dynamics and thermodynamic cycles accurately reproduce experimental affinities of diverse bromodomain inhibitors.

scholarly journals MEAN FIELD APPROACH TO THE GIANT WORMHOLE PROBLEM

1994 ◽  
Vol 03 (02) ◽  
pp. 421-430
Author(s):  
A. GAMBA ◽  
I. KOLOKOLOV ◽  
M. MARTELLINI
Keyword(s):  
Free Energy ◽  
Probability Density ◽  
Time Distribution ◽  
Mean Field ◽  
Field Approximation ◽  
Space Time ◽  
Mean Field Approximation ◽  
Field Approach

We introduce a gaussian probability density for the space-time distribution of worm-holes, thus taking effectively into account wormhole interaction. Using a mean-field approximation for the free energy, we show that giant wormholes are probabilistically suppressed in a homogenous isotropic “large” universe.

SEMICLASSICAL SHELL STRUCTURE OF MOMENTS OF INERTIA IN DEFORMED FERMI SYSTEMS

2010 ◽  
Vol 19 (04) ◽  
pp. 735-746 ◽  
Author(s):  
A. G. MAGNER ◽  
A. M. GZHEBINSKY ◽  
A. S. SITDIKOV ◽  
A. A. KHAMZIN ◽  
J. BARTEL
Keyword(s):  
Free Energy ◽  
Shell Structure ◽  
Mean Field ◽  
Field Approximation ◽  
Moment Of Inertia ◽  
Mean Field Approximation ◽  
Perfect Agreement ◽  
Periodic Orbit Theory ◽  
Shell Effects ◽  
The Moment

The collective moment of inertia is derived analytically within the cranking model in the adiabatic mean-field approximation at finite temperature. Using the nonperturbative periodic-orbit theory the semiclassical shell-structure components of the collective moment of inertia are obtained for any potential well. Their relation to the free-energy shell corrections are found semiclassically as being given through the shell-structure components of the rigid-body moment of inertia of the statistically equilibrium rotation in terms of short periodic orbits. Shell effects in the moment of inertia disappear exponentially with increasing temperature. For the case of the harmonic-oscillator potential one observes a perfect agreement between semiclassical and quantum shell-structure components of the free energy and the moment of inertia for several critical bifurcation deformations and several temperatures.

Active Inference, Belief Propagation, and the Bethe Approximation

2018 ◽  
Vol 30 (9) ◽  
pp. 2530-2567 ◽  
Author(s):  
Sarah Schwöbel ◽  
Stefan Kiebel ◽  
Dimitrije Marković
Keyword(s):  
Free Energy ◽  
Belief Propagation ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Active Inference ◽  
Inference Process ◽  
Bethe Approximation ◽  
Variational Free Energy ◽  
The Mean

When modeling goal-directed behavior in the presence of various sources of uncertainty, planning can be described as an inference process. A solution to the problem of planning as inference was previously proposed in the active inference framework in the form of an approximate inference scheme based on variational free energy. However, this approximate scheme was based on the mean-field approximation, which assumes statistical independence of hidden variables and is known to show overconfidence and may converge to local minima of the free energy. To better capture the spatiotemporal properties of an environment, we reformulated the approximate inference process using the so-called Bethe approximation. Importantly, the Bethe approximation allows for representation of pairwise statistical dependencies. Under these assumptions, the minimizer of the variational free energy corresponds to the belief propagation algorithm, commonly used in machine learning. To illustrate the differences between the mean-field approximation and the Bethe approximation, we have simulated agent behavior in a simple goal-reaching task with different types of uncertainties. Overall, the Bethe agent achieves higher success rates in reaching goal states. We relate the better performance of the Bethe agent to more accurate predictions about the consequences of its own actions. Consequently, active inference based on the Bethe approximation extends the application range of active inference to more complex behavioral tasks.

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