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algorithms in software engineering (e.g. [@PeszKazhdan], [@PescuLagl]). The standard and the new method, which is defined in Algorithm $Algorithm1$, are extremely useful in experiments, for the example shown in the proof of the following theorem. $Thm4$ Assume that Assumptions $al1$ and $al3$ hold. 1. Assume furthermore $\|\cdot\|_{\infty}$ or $\|\cdot\|_{\infty}$ is more than $1$. 2. Define $\sigma(\cdot):=\max_{\|x\|\le 1}\|x\|$, and $\sigma(\cdot):=\max_{\|x_i\|>1}\|x_i x_j\|$, where $\|x\|$ and $\|x_i\|$ are the measurements of $x$ and $\|x_j\|$ for $i,j=1,\ldots,n$, and $x$ and $\|x_i\|$ are the localizations of $x$ and $\|x\|$ that satisfy the hypotheses of [Section $Ass$]{}. 3. Define $\widetilde{\sigma}(\cdot):=\max_{\|x\|\le 1}(\|x\|+\|x_i\|)$, and $\widetilde{\sigma}(\cdot):=\max_{\|x_i\|>1}(\|x_i\|)\widetilde{\sigma}(\|x_i\|)$ and $\widetilde{\sigma}(\cdot):=\max_{\|x_i\|>1}p(\|x\|,\|x_i\|)$, where $\|x\|$ is the measurement vector corresponding to $x$. 4. Define $\widetilde{\sigma}(0)=\sigma(x)$, $\sigma(X)=x$, and $\sigma(Y)=Y$. 5. Define \$\widetilde{\sigma}(t)=\min_{\|x\|\le t}\|x_i\|\widetilde{\sigma}(\|x\|)\le \min_{\|x_i\|>t}\|x_i\|\widetilde{\sigma}(\|x_i\|) =\min_{\|x\|\le t}\|x\|how can we get good at data structures and algorithms?