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Math Help - sigmoid function

  1. #1
    EITP
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    sigmoid function

    hi,
    I have some problem with the proof of the following problem

    sigmoid function ( r(s)= 1/(1+e^-^s))
    is antisymetric about the point (0,1/2)

    help me please!!!
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by EITP
    hi,
    I have some problem with the proof of the following problem

    sigmoid function ( r(s)= 1/(1+e^-^s))
    is antisymetric about the point (0,1/2)

    help me please!!!
    Anti-symmetric about (0,1/2) means that t(s)=r(s)-1/2 is anti-symmetric, that is:

    <br />
t(s)=-t(-s)<br />

    Now:

    <br />
t(s)=\frac{1}{1+e^{-s}}-\frac{1}{2}=\frac{1-e^{-s}}{2(1+e^{-s})}<br />
.

    Now multiply both top and bottom of the LHS by e^{s}:

    <br />
t(s)=\frac{e^s-1}{2(e^s+1)}=-t(-s)<br />

    QED

    RonL
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