Population simulation

Caprio MA, Tabashnik BE. 1992. Gene flow accelerates local adaptation among finite populations simulating the evolution of insecticide resistance. J Econ Entomol 85 611-620. 

Fig. 1.7 (a) Observed and model fitted percent responders in Phase II trials. (b)Predicted dose-response of response (% responders) in a Phase III population based on a population simulation of the Phase II model. The dotted lines are the 5th and 95th percentiles of the prediction distribution and represent uncertainty in the model parameters. 

Evolutionary algorithms are metaheuristics that typically maintain populations of potential solutions. These populations simulate the evolution of individual strutures through the processes of selection, reproduction, recombination, and mutation. Each individual structure, more commonly referred to simply as an individual, in a population represents one possible solution to the problem at hand. Generally, each individual is considered to have a chromosome... 

In general, the phonon density of states g(cn), doi is a complicated fimction which can be directly measured from experiments, or can be computed from the results from computer simulations of a crystal. The explicit analytic expression of g(oi) for the Debye model is a consequence of the two assumptions that were made above for the frequency and velocity of the elastic waves. An even simpler assumption about g(oi) leads to the Einstein model, which first showed how quantum effects lead to deviations from the classical equipartition result as seen experimentally. In the Einstein model, one assumes that only one level at frequency oig is appreciably populated by phonons so that g(oi) = 5(oi-cog) and, for each of the Einstein modes. is... 

Knowledge of the underlying nuclear dynamics is essential for the classification and description of photochemical processes. For the study of complicated systems, molecular dynamics (MD) simulations are an essential tool, providing information on the channels open for decay or relaxation, the relative populations of these channels, and the timescales of system evolution. Simulations are particularly important in cases where the Bom-Oppenheimer (BO) approximation breaks down, and a system is able to evolve non-adiabatically, that is, in more than one electronic state. 

To add non-adiabatic effects to semiclassical methods, it is necessary to allow the trajectories to sample the different surfaces in a way that simulates the population transfer between electronic states. This sampling is most commonly done by using surface hopping techniques or Ehrenfest dynamics. Recent reviews of these methods are found in [30-32]. Gaussian wavepacket methods have also been extended to include non-adiabatic effects [33,34]. Of particular interest here is the spawning method of Martinez, Ben-Nun, and Levine [35,36], which has been used already in a number of direct dynamics studies. 

The two /3-turn structures, pc and Pe are the most stable among those considered. This is in accord with the unconstrained nanosecond simulations of linear DPDPE, which converged to these conformers [14]. Because the cyclic form is relatively rigid, it is assumed that the conformation it adopts in solution is the biologically active one, responsible for its high affinity and specificity towards the 5 opioid receptor. The relatively low population of the cyclic-like structure for the linear peptide thus agrees qualitatively with the... 

For the selection of descriptors, GA simulated evolution of a population. Each individual of the population represents a subset of descriptors and is defined by a chromosome of binary values. The chromosome has as many genes as there are possible descriptors (92 for the aromatic group, 119 for non-rigid aliphatic,... 

A number of molecular properties can be computed. These include ESR and NMR simulations. Hyperpolarizabilities and Raman intensities are computed using the TDDFT method. The population analysis algorithm breaks down the wave function by molecular fragments. IR intensities can be computed along with frequency calculations. 

This is not an uncommon problem. For a target population with a relative sampling variance of 50 and a desired relative sampling error of 5%, equation 7.7 predicts that ten samples are sufficient. In a simulation in which 1000 samples of size 10 were collected, however, only 57% of the samples resulted in sampling errors of less than 5% By increasing the number of samples to 17 it was possible to ensure that the desired sampling error was achieved 95% of the time. 

In this problem you will collect and analyze data in a simulation of the sampling process. Obtain a pack of M M s or other similar candy. Obtain a sample of five candies, and count the number that are red. Report the result of your analysis as % red. Return the candies to the bag, mix thoroughly, and repeat the analysis for a total of 20 determinations. Calculate the mean and standard deviation for your data. Remove all candies, and determine the true % red for the population. Sampling in this exercise should follow binomial statistics. Calculate the expected mean value and expected standard deviation, and compare to your experimental results. 

The energy laws of Bond, Kick, and Rittinger relate to grinding from some average feed size to some product size but do not take into account the behavior of different sizes of particles in the mill. Computer simulation, based on population-balance models [Bass, Z. Angew. Math. Phys., 5(4), 283 (1954)], traces the breakage of each size of particle as a function of grinding time. Furthermore, the simu-... 

Finally, an alchemical free energy simulation is needed to obtain the free energy difference between any one substate of system A and any one substate of system B, e.g., Ai- In practice, one chooses two substates that resemble each other as much as possible. In the alchemical simulation, it is necessary to restrain appropriate parts of the system to remain in the chosen substate. Thus, for the present hybrid Asp/Asn molecule, the Asp side chain should be confined to the Asp substate I and the Asn side chain confined to its substate I. Flat-bottomed dihedral restraints can achieve this very conveniently [38], in such a way that the most populated configurations (near the energy minimum) are hardly perturbed by the restraints. Note that if the substates AI and BI differ substantially, the transfomnation will be difficult to perform with a single-topology approach. 

Hence values of K and K/ generated by the GA are inserted into equation (10.102) and the control u kT) used to drive the discrete plant equation (10.101). The fitness function J is updated at each sampling instant to give an overall value at the end of each simulation. For a population of 10 members, 10 simulations are required per generation. 

Colloidal crystals . At the end of Section 2.1.4, there is a brief account of regular, crystal-like structures formed spontaneously by two differently sized populations of hard (polymeric) spheres, typically near 0.5 nm in diameter, depositing out of a colloidal solution. Binary superlattices of composition AB2 and ABn are found. Experiment has allowed phase diagrams to be constructed, showing the crystal structures formed for a fixed radius ratio of the two populations but for variable volume fractions in solution of the two populations, and a computer simulation (Eldridge et al. 1995) has been used to examine how nearly theory and experiment match up. The agreement is not bad, but there are some unexpected differences from which lessons were learned. 

The model contains a surface energy method for parameterizing winds and turbulence near the ground. Its chemical database library has physical properties (seven types, three temperature dependent) for 190 chemical compounds obtained from the DIPPR" database. Physical property data for any of the over 900 chemicals in DIPPR can be incorporated into the model, as needed. The model computes hazard zones and related health consequences. An option is provided to account for the accident frequency and chemical release probability from transportation of hazardous material containers. When coupled with preprocessed historical meteorology and population den.sitie.s, it provides quantitative risk estimates. The model is not capable of simulating dense-gas behavior. 

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