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....transduction were still present in the modified model. The one di#erence was a shift in the direction of signal propagation from the N S direction (along the protofilament) to the NW SE direction (around the helix) The lattice dynamics were simulated using a standard Monte Carlo technique (Binder 1988). For a given time step, the energy of the present state and of the opposite state were calculated. Whether a change of state occurs is a random event whose probability is determined by the availability of stored lattice energy, the temperature, and the threshold to reaction. An important ....

Binder, K. 1988 Monte Carlo simulation in statistical physics: an introduction. New York: Springer.

....has a random state each individual dimer can be found in the up or down state in a rather arbitrary fashion. At lower temperatures, the interaction energy dictates the dipole arrangement and the lattice becomes ordered. The lattice dynamics are simulated using a standard Monte Carlo technique[20]. For a given timestep, the energy of the present state and the opposite state are calculated. Whether a change of state occurs is a random event whose probability is determined by the availability of stored lattice energy, the temperature, and the threshold to reaction. There are two numbers ....

K. Binder. Monte Carlo simulation in statistical physics : an introduction. Springer-Verlag, New York, 1988.

....the move is accepted with probability exp [ DE k B T ] where DE is the energy difference between the newly added bond and the last bond of the other end of the chain. This last bond is removed, provided the move is accepted. By means of the probability exp [ DE k B T ] Metropolis criterion [32]) temperature is introduced into the simulation [33] 2.2 A Brief Review of the Model s Properties The above mentioned competition between the internal energy and the packing constraints of the polymers prevents the melt from crystallizing so that it may easily be supercooled. During the ....

K. Binder, and D. W. Heermann, Monte Carlo Simulation in Statistical Physics: An Introduction, Springer, Heidelberg (1992).

....commonly used chooses a single split of the data into k folds, thus approximating complete k fold cross validation with k estimates having disjoint test sets. Executing cross validation multiple times, each time with a different split into the k folds, can viewed as a Monte Carlo estimation (Binder Heerman 1988) to complete k fold cross validation, which is usually too expensive to run. 3 Repeating crossvalidation multiple times will not change the bias inherent in the method but it might change the variance of the estimates. 3 One reviewer asked if we ever tried running complete cross validation to ....

Binder, K. & Heerman, D. W. (1988), Monte Carlo Simulation in Statistical Physics : an Introduction, Springer-Verlag.

....only in a few special cases. Furthermore, approximation methods like e.g. low and high temperature expansions, are often useful only within a limited domain of the parameters of the model. Therefore computer simulations turn out to be an important tool to make contact with experimental data [2] [3] [4] 5] For large simulations, e.g. for simulations performing very many sweeps on a big lattice, a multiprocessor system of the MIMD type 3 with distributed memory seems to be the most appropriate computer system, because (ideally) 3 For an excellent overview on the various models of ....

.... systems (SISD computers) 13] 14] 15] 16] on vector computers (SIMD computers) 17] 18] 19] and on multiprocessor systems (MIMD computers) 20] 21] 7 Considering effects due to the finiteness of the lattice, it may be necessary to average over the absolute value of O(fsg i ) see [3] 8 We choose a 1 bit to represent spin up and a 0 bit to represent spin down 9 In models, where the interaction between neighbouring spins may be described by logical operations, e.g. Lattice Gases, one bit is sufficient. 10 Working in natural units (setting the Boltzmann constant k ....

K. Binder, D.W.Heermann, Monte Carlo Simulation in Statistical Physics: An Introduction, Springer Series in Solid--State Sciences, Vol. 80 (Springer-- Verlag, Berlin, Heidelberg 1988).

....materials makes it impossible to have just one generic tool comprising all possible situations. It is possible to develop simulation methods that in principle are able to handle the simulation of models for the design of materials. Examples are the Monte Carlo and the molecular dynamics method [1, 2], as well as methods derived from these two methods. In practice there are insurmountable problems if one tries to apply the bare or generic methods. In most cases a modification of the basic simulation method and or the model is necessary to surmount the difficulties. Unfortunately most of the ....

K. Binder and D.W. Heermann, Monte Carlo Simulation in Statistical Physics: An Introduction, Springer Verlag, Heidelberg, 1988

....s i s j ; s i = Sigma1 (1) where hiji are nearest neighbour pairs of lattice sites. The exchange coupling J is restricted to be positive (ferro magnetic) The dynamics of the system is specified by the transition probability of the Markov chain which will be realized by a Monte Carlo algorithm [3, 4, 5]. We used two transition probabilities ffl Metropolis P (s i s 0 i ) minf1; expf Gamma DeltaE)g ffl Glauber P (s i s 0 i ) 1 2 f1 Gamma s i tanh(E i =k b T )g; E i = J P i;j s j Time t in this context is measured in Monte Carlo steps per spin. One Monte Carlo step (MCS) per ....

K. Binder and D.W. Heermann, Monte Carlo Simulation in Statistical Physics: An Introduction Springer Verlag, Heidelberg, 1988

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K. Binder, D. Heermann, Monte Carlo simulation in statistical physics: an introduction (Springer, 1992)

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K. Binder, D. Heermann, Monte Carlo simulation in statistical physics: an introduction (Springer, 1992)

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Binder, K.; Heermann, D. W. Monte Carlo Simulation in Statistical Physics: An Introduction, Springer-Verlag: New York, 1998, 3rd ed.

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Binder, K., Heermann, D. W. Monte Carlo simulation in statistical physics: an introduction, New York: Springer, 1997.

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K. Binder and D. W. Heermann, Monte Carlo Simulation in Statistical Physics -- An Introduction, 2nd ed., (Springer-Verlag, 1992).

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K. Binder, Monte Carlo Simulation in Statistical Physics : An Introduction (Springer-Verlag, New York, 1988).

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Binder, K., Heermann, D.W. (1988) Monte Carlo simulation in statistical physics: an introduction. Berlin: Springer-Verlag.

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Binder, K., Heermann, D.W. (1988) Monte Carlo simulation in statistical physics: an introduction. Berlin: Springer-Verlag.

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