The non-linear function of Hill-type, is an essential functional form in order to achieve a bistability response in the dynamics of the probed system [10], [57], [58], [59].
We study the system of root functions (SRF) of Hill operator Ly="−y″+vy with a singular (complex-valued) potential v∈H−1per and the SRF of 1D Dirac operator Ly= i(100−1)dydx+vy with matrix L2-potential v="(0PQ0), subject to periodic or anti-periodic boundary conditions.
The second phase of the work involved wind tunnel measurements of hill-top wind speed profiles as a function of surface roughness, hill shape, and hill slope.
Thus, the regulation function z j [ t] was modeled as the sigmoid function, which is one kind of Hill function, of y j [ t] (the protein activity profiles of transcription factor j) [ 3, 16, 30- 33] (2) where f j denotes the sigmoid function, μ j and σ j represent the mean and deviation of protein activity level of the TF j.
In our implementation, transfer functions are limited to a defined set of Hill functions, hence the use of the term "constrained" fuzzy logic.
Representing the behavior of a gene as a function of TF concentrations by a combination of Hill functions is very common and often matches experiments [ 92].
(B ) Optimization of Hill function by grid-search method.
In this case thus, an approximate model would employ the general form of Hill function: (1) (2) However, keep in mind that the parameters β and γ depend on the degree of multimerization of the TFs.
For the mean BrAC curves by gender and time, strong "sex differences were an increasing function of beers consumed" (Hill-Kapturczak 2014, p. 5)—that is, sex differences increased the more beer the participants had consumed.
Typically, Setty et al. [ 92] measured the mean RNA levels of the lac operon of E. coli as a function of cAMP and IPTG concentrations and interpreted their data in terms of Hill functions.
