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SEFD = {\frac{T_{sys}}{\frac{\eta_a A}{2k_B}}}  \end{equation}  where $T_{sys}$ is the system temperature including contributions from receiver noise, feed losses, spillover, atmospheric emission, galactic background and cosmic background, $k_B = 1.380 \times 10^{-23}$ Joule $K^{-1}$ is the Boltzmann constant, $A$ is the antenna collecting area (thus we could also write $\pi \cdot D^2$), and $\eta_a$ is the antenna efficiency with $\eta_a = \eta_{\text{surface efficiency}} \cdot \eta_{\text{aperture blockage}} \cdot \eta_{\text{feed spillover efficiency}} \cdot \eta_{\text{illumination taper efficiency}}$ (see \cite{antenna}).  If we assume N apertures with the same $SEFD$, obserbing the same bandwidth $\Delta\nu$, during the same correlator accumulation integration  time $\tau_{acc}$, $\t_{int}$,  then the weak-source limit in the sensitivity of a synthesis image of a single polarization is \begin{equation}\label{eq:sens}  \Delta I_m = {\frac{1}{\eta_s }}{\frac{SEFD}{\sqrt{(N(N-1) \Delta \nu \tau_{acc}}}} \t_{int}}}}  \end{equation}  in units of Janskys per synthesized beam area.   with $\eta_s$ most important factor being correlator efficiency $\eta_c = \frac{\text{correlator sensitivity}}{\text{sesitivity of a perfect analog correlator having the same } \tau_{acc}}$ (see \cite{sensitivity}).  Hence the  Thus if we are using vector $x = {\text{antenna diameter}, \text{antenna efficiency}, \}$, the antenna diameter, as the optimization variable the problem we would like to solve is:  \begin{equation*}  \begin{aligned}  & \underset{x}{\text{minimize}}  & & f(x) = {\frac{2k_B}{\eta_s \eta_a}}{\frac{T_{sys}}{\pi x^2 \sqrt{2 \Delta \nu \tau_{acc}}}}\\  & \text{subject to}  & & X_{ij} = M_{ij}, \; (i,j) \in \Omega, \\  &&& X \succeq 0.  \end{aligned}  \end{equation*} \cite{sensitivity2}).  \subsection{Minimize Operations Costs}  The operations cost is a complex problem divided in the sub-problems in this section.  \subsubsection{Maximize components reliability} 
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A commonly used rule of thumb for the cost of an antenna is that it is proportional to $D^{\alpha}$, where $\alpha \approx 2.7$ for values of $D$ from a few meters to tens of meters. (see \cite{moran})  \subsubsection{Cost of Antenna Electronics}  \subsubsection{Cost of Re-configuration Systems Construction}  \section{Mathematical Formulation}  Thus if we are using vector $x = {\text{antenna diameter}, \text{antenna efficiency}, \}$, the antenna diameter, as the optimization variable the problem we would like to solve is:  \begin{equation*}  \begin{aligned}  & \underset{x}{\text{minimize}}  & & f(x) = {\frac{2k_B}{\eta_s \eta_a}}{\frac{T_{sys}}{\pi x^2 \sqrt{2 \Delta \nu \tau_{acc}}}}\\  & \text{subject to}  & & X_{ij} = M_{ij}, \; (i,j) \in \Omega, \\  &&& X \succeq 0.  \end{aligned}  \end{equation*}  \section{Array Performance Data Generation - Python Implementation}  \section{Visualization Tool Notes}  \section{Conversation notes} 
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