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Created the introduction and structure for:

## Comments

In the forum, we are analyzing some articles on climate networks.

K. Yamasaki, A. Gozolchiani, and S. Havlin, Climate networks around the globe are significantly effected by El Niño, June 2013.

Josef Ludescher, Avi Gozolchiani, Mikhail I. Bogachev, Armin Bunde, Shlomo Havlin, and Hans Joachim Schellnhuber, Improved El Niño forecasting by cooperativity detection,

Proceedings of the National Academy of Sciences, 30 May 2013.Here is the forum thread for Yamasaki et al.

Here is the forum thread for Ludescher et al.

`In the forum, we are analyzing some articles on climate networks. * K. Yamasaki, A. Gozolchiani, and S. Havlin, [Climate networks around the globe are significantly effected by El Niño](http://arxiv.org/abs/0804.1374), June 2013. * Josef Ludescher, Avi Gozolchiani, Mikhail I. Bogachev, Armin Bunde, Shlomo Havlin, and Hans Joachim Schellnhuber, [Improved El Niño forecasting by cooperativity detection](http://www.pnas.org/content/early/2013/06/26/1309353110.full.pdf+html), _Proceedings of the National Academy of Sciences_, 30 May 2013. Here is the [forum thread](http://forum.azimuthproject.org/discussion/1357/paper-yamasaki-et-al-climate-networks-around-the-globe-are-significantly-effected-by-el-nino/) for Yamasaki et al. Here is the [forum thread](http://forum.azimuthproject.org/discussion/1360/paper-ludescher-et-al-improved-el-nino-forecasting-by-cooperativity-detection/) for Ludescher et al.`

Another paper:

`Another paper: * Y. Berezin, A. Gozolchiani, O. Guez & S. Havlin, [Stability of climate networks with time](http://www.nature.com/srep/2012/120918/srep00666/full/srep00666.html), 2012, Scientific Reports.`

I have filled the details for the definitions of cross-correlations. This need checking!

`I have filled the details for the definitions of cross-correlations. This need checking!`

The paper by Ludescher

et althat caused the stir is now available for free at a certain location:• Josef Ludescher, Avi Gozolchiani, Mikhail I. Bogachev, Armin Bunde, Shlomo Havlin, and Hans Joachim Schellnhuber, Very early warning of next El Niño,

Proceedings of the National Academy of Sciences, February 2014.I've updated various links to point to this free version.

`The paper by Ludescher _et al_ that caused the stir is now available for free at a certain location: • Josef Ludescher, Avi Gozolchiani, Mikhail I. Bogachev, Armin Bunde, Shlomo Havlin, and Hans Joachim Schellnhuber, <a href="http://www.climatelinc.eu/fileadmin/UG_ADVANCED/Publications/BIU_-_Avi__Halvin__et_al-Very_early_warning_of_next_El_Nino.pdf">Very early warning of next El Niño</a>, <i>Proceedings of the National Academy of Sciences</i>, February 2014. I've updated various links to point to this free version.`

I added the following to the wiki. I am trying to understand what the link strengths used by Ludescher actaully measure. I think its pretty weird!

## Understanding the link strength

The link strength defined above by Yamasaki

et alhas some surprising behaviour. The following graphs are all based on simulated data. There are two time series of length 565, called "signal 1" and "signal 2" in the graphs, which consist of quadratics $q_1$ and $q_2$ plus independent gaussian noise. The noise has the same amplitude (standard deviation) in all cases, but $q_1$ and $q_2$ are multiplied by 1000 (leftmost column), 9 (second column), 3 (third column) and 1 (fourth column).Examples of the signals themselves are shown in the top two rows, the value of $ c^{(t)}_{i,j}(\tau) $ is in the third row, and the fourth row shows an estimated density of the link strength derived from 100 replicates (different samplings of noise).

In the first column, the $q_1$ and $q_2$ overwhelm the guassian noise, so you can see their shapes. In particular, note that have positive correlation for all delays: it varies between about 0.87 and 0.97. The other three columns are intended to be more realistic signals which roughly resemble climate data. One would expect that as the multiplier for $q_1$ and $q_2$ decreases, the link strength would also decrease, but the opposite is the case.

`I added the following to the wiki. I am trying to understand what the link strengths used by Ludescher actaully measure. I think its pretty weird! #### Understanding the link strength The link strength defined above by Yamasaki *et al* has some surprising behaviour. The following graphs are all based on simulated data. There are two time series of length 565, called "signal 1" and "signal 2" in the graphs, which consist of quadratics $q_1$ and $q_2$ plus independent gaussian noise. The noise has the same amplitude (standard deviation) in all cases, but $q_1$ and $q_2$ are multiplied by 1000 (leftmost column), 9 (second column), 3 (third column) and 1 (fourth column). Examples of the signals themselves are shown in the top two rows, the value of $ c^{(t)}_{i,j}(\tau) $ is in the third row, and the fourth row shows an estimated density of the link strength derived from 100 replicates (different samplings of noise). In the first column, the $q_1$ and $q_2$ overwhelm the guassian noise, so you can see their shapes. In particular, note that have positive correlation for all delays: it varies between about 0.87 and 0.97. The other three columns are intended to be more realistic signals which roughly resemble climate data. One would expect that as the multiplier for $q_1$ and $q_2$ decreases, the link strength would also decrease, but the opposite is the case. <img src = "http://www.azimuthproject.org/azimuth/files/linkstrength.png" alt = ""/>`