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The estimation of stochastic limit buckling loads of imperfection sensitive structures is a natural extension of this method.

Recently, Medvedev [18] has used this approach to understand in more detail the synchronisation of linearly coupled stochastic limit cycle oscillators.

Using a 2-μm-diameter beam, as in many XFEL measurements, would reduce the current density to 20 MA/cm2, well above the stochastic limit (≈2,000 A/cm2) for a continuous beam.

This means that a microscopic model, which is close to the limit presently corresponding to a large number of neurons in a large number of populations can be assumed to be close to the limiting processes in structure and pathwise dynamics as indicated by the quality of the stochastic limit.

The associated current density is J ≈ (eN p/D 2 T −1 = 1.6 × 1012 A/cm2, exceeding the estimated stochastic limit (Figure 3b) even when reduced (for 100-fs pulses) by a factor of 300. Figure 5 Particle/beam geometry for TEM serial crystallography.

These results show the stochastic limit to the deterministic behaviour, confirming the qualitative intuition of a stochastic lower limit to the wave pinning mechanism.

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The method also treats the detection limit as a fixed and non-stochastic limit, which is appropriate for many economic applications but may not be correct for radiological assessment equipment with an inherent machine error at this lower boundary.

Then we performed the biological significance validation for the randomly assigned results as the stochastic lower limit of the performance of the validation methods.

Despite the many complexities included in our global model, many uncertainties and stochastic events limit our ability to predict what will actually happen in an unprecedented post-OPV era and which may lead to a wide range of potential consequences.

In order to prove that the doses of 20 mSv measured above lead aprons do not exceed the stochastic dose limit, it was decided to provide additional personal dosimeters to the radiologists performing interventional procedures at the AMC.

In this paper we review these four random-motion models–henceforth termed "fractional motions" –via a unified physical setting that is based on Langevin's equation, the Einstein Smoluchowski paradigm, and stochastic scaling limits.

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