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Milestoning with coarse memory
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View: Figures


Image of FIG. 1.
FIG. 1.

(a) A schematic representation of a trajectory x(t) that crosses milestones H 1, H 2, H 3, H 4. Each milestone is divided into 3 numbered regions (clusters), distinguished by their opacity. (b) The piecewise continuous function i(t) that tracks the index of the milestone the trajectory in (a) last crossed. Its value is the first index in the ordered pair above each continuous portion of i(t). The 2nd index of each ordered pair denotes the cluster the trajectory sampled when it transitioned to the current milestone. These ordered pairs define the MCM state of the molecular system. This figure has been previously published in a Ph.D. dissertation. 30

Image of FIG. 2.
FIG. 2.

A fixed height histogram in which the set of initial configurations on milestone i, {x i }, is binned along u(x). Each short line is a value of u(x) assumed by a sample initial configuration (i.e., a first hitting point) at x. The height of each bin is fixed at 3 samples, and the intervals between the thick lines define the clusters on the milestone. This figure has been previously published in a Ph.D. dissertation. 30

Image of FIG. 3.
FIG. 3.

The reversal of a polymer, as monitored by the z coordinate of the polymer's end-to-end vector, q(x) = z N z 1.

Image of FIG. 4.
FIG. 4.

Figures (a) and (b) give the MFPT, τ, and the MTT, t of polymer reversal as a function of the pore radius (in units of bond length, σ), respectively. In MCM calculations, 40 MCM states were defined on milestone 1 (noting that it only has one reachable milestone), and 80 MCM states were defined on each subsequent milestone.

Image of FIG. 5.
FIG. 5.

The runtime, t run, for calculations of the MFPT as a function of pore radius. Circles are the runtimes of Milestoning calculations, and squares are the runtimes of the brute force MD calculations. For the brute force MD calculations, we performed 4 independent trials, in which 162 reversal events were observed in each trial at each radius. 64 processors (16 Opteron quad-core 64 bit processors with core frequency of 2.3 GHz) were run in parallel with a master-slave load balancing algorithm. On the same hardware, the MCM calculations were obtained by requiring that all allowed transitions between the M1TM states were sampled by a minimum of 600 trajectories. Figure 4 was generated from the same data used in these calculations. This figure has been previously published in a Ph.D. dissertation. 30

Image of FIG. 6.
FIG. 6.

(a) The MFPT, τ, of reversal for a 35 bead polymer in a pore of radius 2.46σ, as a function of n m (see main text for definition). The ordinate is here normalized by the MFPT found from MD simulations, τ MD . (b) The ratio of the standard deviation of the MFPT, to τ MD , as a function of n m . The standard deviation was computed by 32 independent calculations of the MFPT. A total of 6 milestones were used in all calculations. Blue triangles correspond to conventional Milestoning calculations. For circles, 16 MCM states are defined on milestone 1, 32 MCM states are defined on subsequent milestones. For red squares, 4 MCM states are defined on milestone 1, 8 MCM states are defined on subsequent milestones. This figure has previously been published in a Ph.D. dissertation. 30


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Milestoning with coarse memory