# [Neuroscience] Re: Decay constants. What does "weighted" mean?

Bill via neur-sci%40net.bio.net (by connelly.bill from gmail.com)
Sat Jan 17 23:02:19 EST 2009

```Thanks Trevor, that explains it nicely (I geussed it was something
like that).

Why do people do it in that way? Wouldn't it make more sense if you
were comparing an intervention to do a 2-way ANOVA with Intervention
vs Slow Decay Constant vs Fast Decay Constant?

On Jan 16, 11:46 am, Trevor Lewis <t.le... from unsw.edu.au> wrote:
> Dear Bill,
>
> As explained, for a response that can be fitted with the sum of two
> exponentials -
>   f(t) = a exp(-t/t1) + b exp(-t/t2)
>
> where t1 and t2 are the time constants and a and b are the initial
> amplitudes of each component of the response at time t=0.
>
> In some instances, rather than just quote both of the time constants
> and their respective initial amplitudes, a single 'weighed' decay
> constant is reported. Some times this is because a comparison is
> being made between different synapses that may or may not have single
> exponential decays.
>
> To calculate the 'weighted' mean time constant, the individual
> initial amplitudes for each time constant are expressed as a fraction
> of the total initial amplitude. Lets call these fractions A and B,
> such that A = a / (a+b)  and B = b / (a+b)
> Lets then call the 'weighted' mean decay constant T, and this is given by:
> T = A * t1 + B * t2
>
> So you see, you get a indication of the exponential decay by
> 'weighting' the individual time constants according to the initial
> amplitude, to get a mean time constant. This is reasonable, given
> that the initial amplitude and the time constant of each component
> will determine the proportional contribution to the exponential decay
> that is being described.
>
> I hope this helps.
> Regards,
>
> Trevor

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