Typical Monte Carlo Results

Monte Carlo may be used to study the lateral distribution of lipid molecules in mixed bilayers. This of course is a very challenging problem, and, to date, the only way to obtain relevant information for this is to reduce the problem to a very simplistic two-dimensional lattice model. In this case, the lipid molecules occupy a given site and can be in one of the predefined number of different states. These pre-assigned states (usually about 10 are taken), are representative conformations of lipids in the gel or in the liquid state. Each state interacts in its own way with the neighbouring molecules (sitting on neighbouring sites). Typically, one is interested in the lateral phase behaviour near the gel-to-liquid phase transition of the bilayer [69,70]. For some recent simulations of mixtures of DMPC and DSPC, see the work of Sugar [71]. 

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The obvious lesson to be taken away from this amusing example is that how well a net learns the desired associations depends almost entirely on how well the database of facts is defined. Just as Monte Carlo simulations in statistical mechanics may fall short of intended results if they are forced to rely upon poorly coded random number generators, so do backpropagating nets typically fail to ac hieve expected re.sults if the facts they are trained on are statistically corrupt. 

A total of 10,000 iterations or calculations of dose were performed as part of this simulation, and Figure 4 shows the resulting distribution of average daily doses of chlorpyrifos as determined by the Monte Carlo simulation. Common practice in exposure and risk assessment is to characterize the 50th percentile as a "typical" exposure and the 95th percentile as the "reasonable maximum" exposure.4 The distributional analysis for these calculated doses... 

The absence of the subsampling problem in transmission Raman was demonstrated experimentally and computationally by Matousek and Parker [43]. The results of Monte Carlo simulations are shown in Fig. 3.7 re-location of a thin impurity layer from the sample surface to a depth of 3 mm within a typical tablet medium diminishes its conventional backscattering Raman signal by four orders of magnitude. In practical situations, such signal levels are... 

Typical trajectories calculated by this Monte Carlo method are shown in Fig. 8. The overall result is that about 7 x 10-5 of all antihydrogen atoms initially formed in the trap region can be transported to the H detector after S2. At expected formation rates of about 200/s [32] this would result in a count rate of 1 event per 2 minutes on resonance. This seems rather small, but is feasible since the antihydrogen atoms can be easily detected with unity efficiency from the annihilation of their constituents. 

Now a and the pressure (computed as the derivative of the free energy per unit area) will be calculated, using the procedure outlined in this article. For the Hamaker constant and the bending modulus, typical values from literature, namely, 1.0 x 10"20 and 1.0 x 10 l l J, respectively, will be used. For th and tc we employed the values obtained from X-rav data,1 th = 7.6 A and tc = 37.8 A for EPC and th = 7.6 A and tc = 36.4 A for DMPC, respectively. Because the hydrocarbon thicknesses tc of EPC and DMPC produced almost no difference (see eq 27), in the following only the results for the EPC are presented (tc = 37.8 A). For the degree of asymmetry a the value of 1.4, which is in agreement with the Monte Carlo simulations,17 was selected. 

FIG. 7 Radial distribution function of a typical suspension of charged spheres with screened Coulomb interaction. The exact results (open circles) from Monte Carlo computer simulations are compared with the theoretical predictions of the Ornstein-Zernike equation and different closure relations (lines). 

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