Heuristic sampling

In practice it is helpful to know the order of magnitude of the sample size N needed to reach a reasonably accurate free energy. The inaccuracy model described above presents an effective way to relate the sample size N and the finite sampling error through perturbation distribution functions. Alternatively, one can develop a heuristic that does not involve distribution functions and is determined by exploring the common behavior of free energy calculations for different systems [25]. Although only FEP calculations are considered in this section, the analysis extends to NEW calculations. 

Overall sampling quality — heuristic analysis. If the system of interest can be thought of as fluctuating about one primary structure (e.g., a native protein), use qualitative tools, such as projections onto a small number of PCA modes or all-to-all RMSD plots to simplify visualization of trajectory quality. Such... 

To make these heuristic ideas precise we define a stochastic function 7(x) whose sample functions are the y(x). Take n different points xv in the interval (0, L) and label them in increasing order... 

Today it is recognized that all three approaches (heuristics-based selection, geometric representation, and optimization methods) are useful, and indeed required, for complex process synthesis strategies. This follows because different applications lend themselves to quite different representations. This volume addresses a variety of these synthesis strategies for process subsystems, but represents only a sampling of the state-of-the-art of process synthesis research. The five chapters in this volume address quite different process subsystems and application areas but still combine basic concepts related to a systematic approach. 

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