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I am not sure whether to ask this in Physics, Math, or Computer Science, but I will try Math.

I read a paper "Nonlinear nonequilibrium statistical mechanics approach to C3 systems." Lester Ingber. 9th MIT/ONR Workshop on C3 Systems: Naval Postgraduate School, Monterey, CA, 2-5 June 1986. pp. 237-244. In this paper Ingber claims a method based on neural physiology to solve constraint-based problems, such as those found in military operations research. Without detailing all the twists and turns of the paper, the basic theory is that:

...learning and retrieval mechanisms can be developed by first determining expansion coefficients of eigenfunction expansions of the differential Fokker--Planck distributions, e.g., considering stationary states as Hermite polynomials in neighborhoods of minima.

The most relevant extract from the blizzard of math in this paper is the following segment:

enter image description here enter image description here

The idea being that one can solve a complex system of non-linear relationships which cannot be modelled as ODEs using the above Greek salad.

As a computer scientist I am unable to interpret the validity of these claims. I am hoping for an assessment of the validity of the paper before spending my time trying to understand it. Is this purported technique a potentially valid way to solve complex constraint systems, such as those found in operations research, or is it just a bunch of concocted BS?

Tyler Durden
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  • I have heavy suspicion at the very least. No proofs or citations for where these equations come from, little by way of explaining what they actually say, and what seems to me to be more than a little handwaving about brain structure, karate, and nuclear physics, none of which would seem to have much relation to decision-making processes in the military. – Zev Chonoles Dec 27 '16 at 22:16
  • As an aside, while PDEs and Riemannian geometry are not my area of expertise, I have a vague feeling that at least the latter half of that "Greek salad" is all standard formulas / definitions, which (in a cynical view) could have been included more for visual impressiveness. – Zev Chonoles Dec 27 '16 at 22:19
  • I would be happy to have an opportunity to learn more about this subject, and be shown to be incorrect in my doubts, if the author has an opportunity to comment here and provide more context to these equations. – Zev Chonoles Dec 27 '16 at 22:22

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