We assumed a priori that genetic background, resistance group, resistance mechanism, and the fitness cost of resistance could potentially affect the generality, sign, and magnitude of collateral networks in clinical E. coli strains.
We consider how those choices affect the generality of ABHH's results, consider an alternative theoretical explanation for those results, and suggest opportunities for future research that build on ABHH's work.
It was proven theoretically that for sensors of non-negligible length, the statistical properties of the signal obtained depend only on local holdup, local size distribution and sensor length; a new and easier method of deriving the appropriate mathematical expressions was found, based on a conceptual model which does not affect the generality of the expressions.
This does not affect the generality of the approach, and the method and results obtained for four spheres could be easily extended to six sphere phantoms.
To make the channel characteristics analyzable without affecting the generality of the channel, we further define as a random variable that takes the values +1 or −1 with equal probability.
To make the channel characteristics analyzable without affecting the generality of the channel, we further define as a random variable that takes the values +1 or with equal probability, and as a deterministic constant within the resolvable path time interval defined by [11], where and W is the signal bandwidth.
Although the backoff time is usually not uniformly distributed between [0,1] in the actual protocol (binary exponential backoff, for example), it is proved in [28] that assuming a uniform distribution for the time marks does not affect the generality of the model.
In contrast with this, the localization resulting from the use of small coin parameters survives to arbitrary dephasing strengths, albeit enhancing the probability to find the walker at positions far from the end-lattice ones with respect to the (hat{Z}_{c} -walk (Figure 4 only shows a specific instance that does not affect the generality of our conclusions).
Remark The condition Φ ( 0 ) = 0 imposed in the previous theorem is needed to ensure the uniqueness of the 0-monomial m 0. In fact, as D n f ( 0 ) = 0, we can consider, without affecting the generality, φ n + 1 ( 0 ) = 0 in inequality (4.1).
Importantly, we find that the assumption of independence does not greatly affect the generality of our method and modest SNP-SNP interactions in simulated data do not seem to significantly affect its predictability.
