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<p style="margin-top:0;margin-bottom:0">Hi Michel, </p>
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<p style="margin-top:0;margin-bottom:0">Thank you for your informative comments and helpful suggestions in your earlier post (which I happened to have deleted by accident). In any case I have a copy of the post so I can answer your questions raised therein.</p>
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<p style="margin-top:0;margin-bottom:0">(<b>1</b>) I am defining the Planckian information, I_P, as the<span style="color: rgb(255, 0, 0);"> information required </span><span style="color: rgb(255, 0, 0);">to transform a symmetric, Gaussian-like equation (GLE)</span>,
into the Planckian distribution. which is the Gaussian distribution with the pre-exponential factor replaced with a free parameter, A, i.e., y = A*exp(-(\m - x)^2/2\s^2), which was found to overlap with PDE (Planckian Distribution Equation) in the rising
phase. So far we have two different ways of quantifying I_P: (i) the Plamck informaiton of the fist kind, i_PF = log_2 [AUC(PDE)/AUC(GLE)], where AUC is the area under the curve, and (ii) the Planckian information of the second kind, I_PS = -log_2[(\m -mode)/ \s],
which applies to right-skewed long-tailed histograms only. To make it apply also to the left-skewed long-tailed histograms, it would be necessary to replace (\m - mode) with its absolute value, i.e., |\m - mode|.</p>
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<p style="margin-top:0;margin-bottom:0">(<b>2</b>) There can be more than two kinds of Planckian information, including what may be called the Planckian information of the third kind, i.e., I_PT = - long_2 (\chi), as you suggest. (By the way, how do you define
\chi ?).</p>
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<p style="margin-top:0;margin-bottom:0">(<b>3</b>) The definition of Planckian information given in (<b>1</b>) implies that I_P is associated with
<span style="color: rgb(255, 0, 0);">asymmetric distribution</span> generated by distorting the symmetric Gaussian-like distribution by transforming the x coordinate non-linearly while keeping the y-coordinate of the Gaussian distribution invariant [1]. </p>
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<span style="font-size:12.0pt;font-family:"Times New Roman",serif"><o:p> </o:p></span></p>
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<span style="font-size:12.0pt;font-family:"Times New Roman",serif"><span style="mso-spacerun:yes">
</span><span style="mso-spacerun:yes"> </span><span style="color: rgb(255, 0, 0);">GP</span><span style="mso-spacerun:yes">
</span>definition<o:p></o:p></span></p>
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<span style="font-size:12.0pt;font-family:"Times New Roman",serif"><span style="mso-spacerun:yes">
</span><b style="mso-bidi-font-weight:
normal">Gaussian-like Distribution</b> ------------->
<b>PDE</b> --------------------> <b style="mso-bidi-font-weight:normal">I<sub>P</sub><span style="mso-spacerun:yes">
</span><o:p></o:p></b></span></p>
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<b style="mso-bidi-font-weight:normal"><span style="font-size:12.0pt;
font-family:"Times New Roman",serif">Figure 1.</span></b><span style="font-size:12.0pt;font-family:"Times New Roman",serif"><span style="mso-spacerun:yes">
</span>The definitions of the <span style="color: rgb(255, 0, 0);">Gaussian process</span> (<span style="color: rgb(255, 0, 0);">GP</span>) and the Planckian information (I<sub>P</sub>) based on PDE, Planckian Distribution Equation. GP is the physicochemical
process generating a long-tailed histogram fitting PDE.<o:p></o:p></span></p>
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<p style="margin-top:0;margin-bottom:0"><span style="font-size: 12pt;">(</span><b style="font-size: 12pt;">4</b><span style="font-size: 12pt;">) I am assuming that the PDE-fitting asymmetric histograms will always have non-zero measures of asymetry.</span><br>
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<div>(<b>5</b>) I have shown in [1] that the human decision-making process is an example of the Planckian process that can be derived from a Gaussian distribution based on the drift-diffusion model well-known in the field of decision-making psychophysics.</div>
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<div>Reference:</div>
<div> [1] Ji, S. (2018). The Cell Language theory: Connecting Mind and Matter. World Scientific Publishing, New Jersey. Figure 8.7, p. 357.</div>
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<div>All the best.</div>
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<div>Sung</div>
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<div id="divRplyFwdMsg" dir="ltr"><font face="Calibri, sans-serif" style="font-size:11pt" color="#000000"><b>From:</b> Fis <fis-bounces@listas.unizar.es> on behalf of Michel Petitjean <petitjean.chiral@gmail.com><br>
<b>Sent:</b> Monday, May 7, 2018 2:05 PM<br>
<b>To:</b> fis<br>
<b>Subject:</b> Re: [Fis] Are there 3 kinds of motions in physics and biology?</font>
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<div class="PlainText">Dear Karl,<br>
In my reply to Sung I was dealing with the asymmetry of probability<br>
distributions.<br>
Probability distributions are presented on the Wikipedia page:<br>
<a href="https://na01.safelinks.protection.outlook.com/?url=https%3A%2F%2Fen.wikipedia.org%2Fwiki%2FProbability_distribution&data=02%7C01%7Csji%40pharmacy.rutgers.edu%7C171407db4122453fe72a08d5b4465e1f%7Cb92d2b234d35447093ff69aca6632ffe%7C1%7C0%7C636613136684543650&sdata=mMWRW6FO6hrflqQRGhXtoTkhDqt0FTspjtT9YGgNn2c%3D&reserved=0" id="LPlnk577552" class="OWAAutoLink" previewremoved="true">https://na01.safelinks.protection.outlook.com/?url=https%3A%2F%2Fen.wikipedia.org%2Fwiki%2FProbability_distribution&data=02%7C01%7Csji%40pharmacy.rutgers.edu%7C171407db4122453fe72a08d5b4465e1f%7Cb92d2b234d35447093ff69aca6632ffe%7C1%7C0%7C636613136684543650&sdata=mMWRW6FO6hrflqQRGhXtoTkhDqt0FTspjtT9YGgNn2c%3D&reserved=0</a><br>
Don't read all this page, the beginning should suffice.<br>
Then, the skewness is explained on an other wiki page:<br>
<a href="https://na01.safelinks.protection.outlook.com/?url=https%3A%2F%2Fen.wikipedia.org%2Fwiki%2FSkewness&data=02%7C01%7Csji%40pharmacy.rutgers.edu%7C171407db4122453fe72a08d5b4465e1f%7Cb92d2b234d35447093ff69aca6632ffe%7C1%7C0%7C636613136684543650&sdata=HQh0OOxgyE5fXZMMEfZF6mG5S0yKOPNjoEPO%2FNo28rA%3D&reserved=0" id="LPlnk933529" class="OWAAutoLink" previewremoved="true">https://na01.safelinks.protection.outlook.com/?url=https%3A%2F%2Fen.wikipedia.org%2Fwiki%2FSkewness&data=02%7C01%7Csji%40pharmacy.rutgers.edu%7C171407db4122453fe72a08d5b4465e1f%7Cb92d2b234d35447093ff69aca6632ffe%7C1%7C0%7C636613136684543650&sdata=HQh0OOxgyE5fXZMMEfZF6mG5S0yKOPNjoEPO%2FNo28rA%3D&reserved=0</a><br>
Possibly the content of these two pages is unclear for you.<br>
In order to avoid a huge of long and non necessary explanations, you<br>
may tell me what you already know about probability distributions and<br>
what was unclear from my post, then I can explain more efficiently.<br>
However, I let Sung explain about his own post :)<br>
Best regards,<br>
Michel.<br>
<br>
2018-05-07 19:55 GMT+02:00 Michel Petitjean <petitjean.chiral@gmail.com>:<br>
> Dear Karl,<br>
> Yes I can hear you.<br>
> About symmetry, I shall soon send you an explaining email, privately, because I do not want to bother the FISers with long explanations (unless I am required to do it).<br>
> However, I confess that many posts that I receive from the FIS list are very hard to read, and often I do not understand their deep content :)<br>
> In fact, that should not be shocking: few people are able to read texts from very diverse fields (as it occurs in the FIS forum), and I am not one of them.<br>
> Even the post of Sung was unclear for me, and it is exactly why I asked him questions, but only on the points that I may have a chance to understand (may be).<br>
> Best regards,<br>
> Michel.<br>
><br>
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