Dara,

I will have to look at what the SIGN model entails. Is this what is also refers to as a +/- signed bit model ? So all you know is the change of sign? This approach is often used in qualitative reasoning models.

So then one can come up with a correlation of unity if all (+)*(+) or (-)*(-) give a +1 value and 0 if random. The amplitude is out of the picture so then one doesn't have to worry about slight non-stationary amplitude variations, caused by noise, etc.

Good idea!

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I was thinking about what the modulated sinusoid means.

Say that a function is described as:

$ f(t) = sin(wt+sin(vt)) $

the first derivative of this

$ f'(t) = (w+v cos(vt)) cos(wt+sin(vt)) = (w+v cos(vt)) \cdot f(t+\pi/2) $

which indicates that a time-modulated interaction may be generating the resulting modulation, ala a Mathieu or [Hill differential equation](http://en.wikipedia.org/wiki/Hill_differential_equation).

This gets back to my original premise that these perturbed differential formulations may be very common in understanding climate to first-order.

I will have to look at what the SIGN model entails. Is this what is also refers to as a +/- signed bit model ? So all you know is the change of sign? This approach is often used in qualitative reasoning models.

So then one can come up with a correlation of unity if all (+)*(+) or (-)*(-) give a +1 value and 0 if random. The amplitude is out of the picture so then one doesn't have to worry about slight non-stationary amplitude variations, caused by noise, etc.

Good idea!

---

I was thinking about what the modulated sinusoid means.

Say that a function is described as:

$ f(t) = sin(wt+sin(vt)) $

the first derivative of this

$ f'(t) = (w+v cos(vt)) cos(wt+sin(vt)) = (w+v cos(vt)) \cdot f(t+\pi/2) $

which indicates that a time-modulated interaction may be generating the resulting modulation, ala a Mathieu or [Hill differential equation](http://en.wikipedia.org/wiki/Hill_differential_equation).

This gets back to my original premise that these perturbed differential formulations may be very common in understanding climate to first-order.