In reply to WebHubTel, #29 and #32:

Ludescher et al's link strength is a highly derived quantity, and it is not at all easy to relate it back to physics. I believe that for correlations between slowly varying signals, it works in the opposite direction to what you'd expect, decreasing as the correlation increases.

Suppose the daily temperatures at two places are

$$ k t + N_1(t)$$

and

$$ k t + N_2(t)$$

where t is time, $k$ a constant, and the $N_i$ are independent daily fluctuations, and this holds for 365 + 200 days up to present time. If $k$ is large all the correlations at different time lags will be near 1, so the max/average they do results in a link strength a little above the minimum of 1. (You might get .99/.97 $\approx$ 1.02.) If $k$ is tiny, the noise dominates, and there is greater variation between correlations at different time lags, and max/average will be bigger.

So far as I can see, the highest values for the link strength occur when there is correlation on very short time scales. Eg if the two signals are $N_1(t)$ and $N_1(t+\tau)$. Then you get a correlation of 1 at one particular time lag, but very small correlations at other time lags, so max/average is large.

Ludescher et al's link strength is a highly derived quantity, and it is not at all easy to relate it back to physics. I believe that for correlations between slowly varying signals, it works in the opposite direction to what you'd expect, decreasing as the correlation increases.

Suppose the daily temperatures at two places are

$$ k t + N_1(t)$$

and

$$ k t + N_2(t)$$

where t is time, $k$ a constant, and the $N_i$ are independent daily fluctuations, and this holds for 365 + 200 days up to present time. If $k$ is large all the correlations at different time lags will be near 1, so the max/average they do results in a link strength a little above the minimum of 1. (You might get .99/.97 $\approx$ 1.02.) If $k$ is tiny, the noise dominates, and there is greater variation between correlations at different time lags, and max/average will be bigger.

So far as I can see, the highest values for the link strength occur when there is correlation on very short time scales. Eg if the two signals are $N_1(t)$ and $N_1(t+\tau)$. Then you get a correlation of 1 at one particular time lag, but very small correlations at other time lags, so max/average is large.