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In the most fundamental sense, the maximum dimensionless excess temperature between the full system (the solid conducting wall and the cavity) and the surrounding is minimized with respect to four degrees of freedom.
We have shown that when a Hopf bifurcation in a (full) slow-fast system has a corresponding Hopf bifurcation in the layer problem (i.e. the equilibrium has eigenvalues λ = ±iω with ω = O(1)) the criticality can differ between the full system and the fast subsystem.
For example, in the case of a low abundance protein with only 10 molecules per cell, the genome cannot be reduced further than 10 times (minimum size for 10 molecules is 460 Kbp). Figure 3 shows that there is a strong correlation between the full system and the six subsystems in terms of occupancy biases.
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Both models are coupled to account for secretion and uptake of morphogens, the interface between the models, and the full system is shown in Figure 1C.
In addition, Figure 2 also shows that reducing the size of the system reduces the number of the lower outliers, and this might lead to mismatches between the results of the full system compared to the results of the subsystems.
The correlation between the occupancy bias of the full system and all the subsystems indicates that the peaks in the occupancy bias data are captured by all subsystems for both models (copy number and association rate models).
As discussed at the end of Section 3.3.1, we can thus expect an O(1) difference between the first Lyapunov coefficients for the Hopf bifurcations in the layer system and the full system, and there is no reason to expect the criticality of the Hopf bifurcations to be the same for the full system and the layer problem.
For example, when we reduce the size of the system from 4.6 Mbpto 46 Kbp for a TF with 100 molecules the ratio between the affinity and the occupancy of the subsystem deviates significantly from that of the full system.
The full system was installed in Sept. 2014.
The equilibrium of the full system (A3) is unstable.
Here, the performance of the full system is evaluated.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com