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Antonio Prestes GarcĂa edited figures/paper-20(LinearGraph-1)v2/caption.tex
over 8 years ago
Commit id: e3b33cae172a1bf28db11fa4665a00ce38a3f50a
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{\bf The simplified interaction graph}. This figure shows from left to right the snapshots for the temporal evolution of the linear graph representing our bacterial population. The cell types are $B^r$, $B^d$ and $B^t$ standing respectively for recipients, donors and transconjugants.
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\begin{equation}
\label{eq:slope}
\beta = \frac{|B^t|t_i - |B^t|t_{i-1}}{\Delta_t}, \forall i > 0
\end{equation}
\
where $|B^t|t_i$ and $|B^t|t_{i-1}$ are respectively the counting of $B^t$ cells at $t_i$ and $t_{i-1}$ and $\Delta_t = t_i - t_{i-1}$. The The intercept $\alpha$ is zero since at $t_0$ the number of $|B^t|$ cells are also zero. The choice of $|B^t|$ as the indicator of network flooding is just for the sake of generality but the same principles will also hold if instead of it the value of $T/(T+R)$ were used.