Therefore, in the next two sections, we show instead how statistically valid quantities, similar to PMFs, can be obtained for very different coarse grained variables.
Because we only have age at menarche measured in years, it is possible that very small effects of father absence, perhaps by shifting the timing of menarche byonly a few months, would be apparent had we used a more fine-grained variable.
Environmental coarse-grained variables were extracted from a geographic information system (GIS) at three spatial extents.
The success of this method attests to the accurate and sufficient description of the network by the chosen few coarse-grained variables.
Each iteration in this algorithm consists of a few steps; healing, microscopic evolution (direct integration of the full model), and the projection of the coarse-grained variables.
The framework is further enhanced through combination with data-mining algorithms that process detailed, fine-scale data to uncover underlying im- portant, coarse-grained variables (macroscopic system observables).
The first three PC coefficients for each dynamical variable are retained as the coarse-grained variables (truncating at is enough for general purposes, per the convergence results seen in Fig. 9).
This method, in which a forward Euler or other choice projection algorithm is directly applied to the time evolution of the coarse-grained variables, is the simplest demonstration of the applicability of equation-free computations.
It facilitates experimentation with a spectrum of coarse-grained variables, prototyping rare events (such as chemical reactions), or simulating nanocharacterization experiments such as terahertz spectroscopy, AFM, nanopore, and time-of-flight mass spectroscopy.
The approach is distinct from coarse-graining techniques in that it (1) avoids the need for conjecturing phenomenological governing equations for coarse-grained variables, (2) provides simulations with atomic resolution, (3) captures the cross-talk between disturbances at the atomic and the whole virus-like particle scale, and (4) achieves significant speedup over molecular dynamics.
