[quote][i]Originally posted by bur2000
> Both functions are sigmoidal...
> Is there any specific reason why Origin uses this special function instead of normal Boltzmann?
You have cited: (1) y = A2 + (A1-A2)/(1 + exp((x-x0)/dx)) (in Origin)
(2) y = A2 + (A1-A2)/(1 + exp(-E/k*x)) (the function you called "real" Boltzmann)
Your (2) is not sigmoidal. Though physical Boltzmann function usually regards the temperature as the independent variable, the sigmoidal version should regard the T as a parameter, and E is the independent variable. (I guess that this kind of interpretation may be more common in the Boltzmann machine in the machine learning - x as the mere input, y as the output.).)
Therefore, it should be expressed as: (2)' y(E) = A2 + (A1-A2)/(1 + exp(-E/k*T))
Origin as a general-purpose software, the formula has taken a more general form, I think, such as introducing the offsets of x and y. So, as k*T = -dx, you can get the temperature from Origin's formula by T=-dx/k .
Of course, k is the Boltzmann constant in physics, but can have various different meanings in other applications.
I'm not a physicist, and this is just what I thought.
--Hideo Fujii
OriginLab
P.S. When you fit your data with Boltzmann in Origin, if you need to set e.g., x0 to 0 as in your model, you can fix the parameter to 0 by entering 0 to the Value field, and turning ON the "Fixed" check box in the Parameter tab in NLFit tool.
P.P.S. You can define a derived parameter T in the Boltzmann's function definition in the Fitting Function Organizer (even though this is a built-in function) such as T=-dx/1.38E-23 .
Boltzmann Fit
Posted - 12/09/2013 : 03:58:41 AM
