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From the limited information, I can provide the following but I am not sure if this is what you are looking for. Also, I still don't see the statement where the author concludes we get the Linear regression model $E(q_i) = Aq_i + C$ which is odd notation since it says the expected value is a linear regression. In fact, if it is a linear regression, it should ...


5

The frequency fluctuations will be determined by a standard model of selection as found in any basic population genetics text. In this scenario they take a very basic form: during each long period $i$ the frequency of $A_1$ increases from $f_i$ to $f_i\cdot (1+s_1)^{n_1}$ and during each short period $j$ the frequency of $A_1$ decreases from $f_j$ to ...


2

Many systems have this property. The plot you are looking at is the plot of the transfer function for blood vessel diameter vs time. A trick in mathematics or engineering is to understand a system is to sometimes look at at different system with the same properties that you do understand. For instance, a mass springer damper system is similar to a RLC ...


2

Your logic looks correct to me. Essentially, what you are doing is uniformly distributing the regulator among the available mRNA. Note that even when using Hill functions to model transcription, the ratio of transcription factor (TF) concentration to the number of TF binding sites must be large - otherwise, you would have to consider binding ratios even at ...


2

Actually the derivation is pretty straightforward. It's easier to use the fact that $Cov(X,Y) = E(XY) - E(X)E(Y)$ to derive this result. Suppose $x_{j} = \sum_{i} s_{ij}$. \begin{align*} Cov (x_j, q_{j}) &= E (x_{j}q_{j}) - E (x_{j}) E (q_{j}) \\ &= \frac{1}{n}\sum x_{j} q_{j} - \frac{1}{n}\sum x_{j} q \\ ...



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