deletions | additions       diff --git a/section_Requirements_We_want_the__.tex b/section_Requirements_We_want_the__.tex  index 18bbb8b..ca93929 100644  --- a/section_Requirements_We_want_the__.tex  +++ b/section_Requirements_We_want_the__.tex 
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\item{{\bf Maintain the smoothness requirement, while the uncertainties may be underestimated or overestimated, and fill gaps with simple extrapolations: linear or nearly linear, so as to not to over-interpret the data:} The smoothness requirement can be enforced by minimizing the second derivative of the fit.}  \end{enumerate}  I choose a square exponential kernel ({\tt ExpSquaredKernel} in {\tt george}) $$k(d)=θ_1^2 \sum { \left| \exp(\frac{−d^2}{θ_2^2})\right| }$$. \exp(\frac{−d^2}{θ_2^2})$$.  In order to choose the hyperparameters $θ_1^2$ and $θ_2^2$ I minimize the objective function: $\chi^2(m) ~*~ \sum { \left|  \sqrt{\frac{d^2 m}{dt^2} }\right|  }$, where $m$ is the magnitude, and the fit is done in log time. This works remarkably well in general, with some ``pathological'' exceptions.