Dear Referee,
thank you for your comments.
The paper is extended by one page, but we had already asked the editors for one extra page before the 1st submission and they agreed. 
we are afraid that any reduction will remove significant information.
We have made all the requested modifications. However,we found some more (important) typos which we have also corrected, i.e.


1) page 3, 5 lines after Eq. 5: "Each data set consisted: a) of 15, on average, background reconstructed muons..."
2) Eq (7) was wrong, it has been corrected as ln(likelihood ratio)
3) page 3, 11 lines after Eq.7 : Your comment is right. The p-value was indeed evaluated for single sided gaussian (i.e. 2.83 E-7 at 5sigma).  The number 5.73E-7 is replaced by the correct number  in the text
4) page 4,  "...the angular signal PDF of Eq. 3.." is replaced by "P^disc_profile(r/d; cos(theta_z))..."
We changed the naming from  P^disc_ang(r/d; cos(theta_z)) to  P^disc_profile(r/d; cos(theta_z)). r is the deviation (in deg) from the center of the disc, and d the radius of the disc
5) page 4, : The disc of RXJ1713 was assumed to be 0.6 deg and not 0.65 deg


Comments:


the misalignment RMS in theta and phi, s_{theta} and s_phi respectively,  are the same due to the (azimuthal) symmetry of the muon emission around the parent neutrino direction. In the TRF the reconstructed muon track is perpendicular to the theta-phi plane. Consequently, the projection of the parrent neutrino direction in theta and phi should follow the same distribution. Anyway we have checked these distributions using simulated events and found that this true.


Recently we have repeated our analysis with a larger sample of simulated events. Whilst our results remained the same It was found that the statistical errors in the discovery times (5sigma-DT ans 3sigma-DT,) that we quoted  in the first version are underestimated (these errors reflect the uncertainty on the tails of the lambda parameter distribution for background only events and the interpolation/extrapolation of the discovery potential). We have updated the text and the table 1 with the new (more conservative) values. 


Table 1 looks fine with the official elsevier format. Thats why we didn't change it.


Regards

A. Leisos