Physicists at the LHC are simultaneously studying thousands of distributions, and if you study enough of them, very likely some of them will show rare fluctuations like this.
Here, the escape of the particle is driven by large, rare fluctuations in the environment.
Further, in the case of two dimensional data shown in Figure 3 (as well as Figure S2), rare fluctuations represent a separation in the energetic properties (high to low or vice-versa).
The accumulation of deleterious mutations is driven by rare fluctuations that lead to the loss of all mutation free individuals, a process known as Muller's ratchet.
In the mutant, ligands that became trapped in the Xe1 cavity could only escape from this cavity upon rare fluctuations of the W29 side chain that opened the path into the distal pocket.
In particular, if we consider the function, (13) μ 1 (n, t ) μ 1 (M, t ) ≈ 1 − exp [ − n / N (t ) ] 1 − exp [ − M / N (t ) ], where M denotes a large clone size cut-off beyond which we can expect rare fluctuations to dominate, we expect (and indeed observe) μ 1 (n, t ) / μ 1 (M, t ) to depend only weakly on M for a range of M values.
However, a quick look at the long trajectory of any slow time scale process would indicate that proteins spend a significant amount of simulation time fluctuating within the basins associated with long-lived metastable states and a rare thermal fluctuation leads to the barrier-crossing event.
Besides, rare, single, fluctuations can be also revealed.
Because some of the cancers are rare, random fluctuations in rates may spuriously appear as significant trends, or alternatively it may seem that statistical power is insufficient to detect real trends.
However, on a longer time scale, a rare event (large fluctuation) will generate a path of escape from (mathbf{u}_{s}) to the boundary of Ω.
