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## Why formal control theory applies for quasilinear parabolic PDE on graphs

Control theory applies formally to dynamical systems with a parameter described by a system of ordinary differential equations

$\dot{f}(t) = A(f(t), a(t))$

$f(t_0) = 0$

and the problem is to optimize over possible functions $a(t)$ a payoff functional and these are then addressed by solving the Bellman’s or Hamilton-Jacobi-Bellman’s PDE.  In particular control theory does not deal with control of partial differential equations at all.  However, quasilinear parabolic equations not involving a gradient such as $(\partial_t - \Delta) u = F(u)$ are actually simply ordinary differential equations since the graph Laplacian is simply a fixed matrix.  Therefore the control theory for quasilinear parabolic nonlinear PDE without any gradient terms is regular ordinary standard control theory.

Therefore purely formally, control theory for these PDE on graphs already exists.  Of course there is a great deal of flexibility in control parameters.  For the large problem of controlling global volatility it would be silly to make concrete the control parameters before having a clear idea of both the dynamics that fit the denoised volatility data on a concrete dataset and due consideration to the possible methods that could be implemented to impact the markets properly with tools that are available to humanity to affect controls.  For example, Shiller and Ackerloff’s book Animal Spirits tells us clearly that the Federal Reserve Board of the United States has impact on the American (and therefore the world) economy through the setting of short term interest rates that banks may use to borrow and was constructed in 1913 to solve a specific set of problems such as insecurity and crises of bank runs in the nineteenth century and occurred from a crisis of 1907 when Knickerbocker Trust in New York refused to pay in currency which destabilized the entire financial system causing panic in the interior.  Now this may or may not have been the best solution but John D. Rockefeller’s father-in-law Nelson Aldritch was the Chairman of the Monetary Committee in the Congress and went off for a couple of years to Europe to study the central banking there to return and meet with a few top New York bankers in an island far from the public eye and declare the solution of the private ‘banker’s bank’ which would apparently solve all the world’s problems etc.  This was not anything I would consider a grand scientific achievement by any standard.  There were more objective decisions I am sure by Augustus the Roman Emperor than this one.  Anyway, the issue of what options are truly available for solving a giant scientific problem of taming volatility storms cannot be decided in these ghetto manner of whose uncle is married to whose second cousin.  Let those poor villages being bombed in Afghanistan claim their ghetto manners if they choose.  We, the inheritors of Emerson and Onsager and Feynman and Planck and Einstein and others, should we not feel obligated to first study the problem objectively and then provide the sensible solution, whatever it might be, to the world for quelling these poisonous volatility storms?

Below are links to helpful papers when we return to the issue of control of volatility in a quantitative rigorous manner.  Note that this issue may seem like a more intractable problem by prejudices of the current culture of thought than our collective capacity is as a race of seven billion.  Let us not prejudice our imagination and intellectual freedom unnecessarily by pragmatic concerns that are tied to a political order whose rulers are neither enlightened nor benevolent.  Let us take speaking of scientific and mathematical truth to levels higher than politics of implementation when the rulers of the world who decided to destroy civilian cities of Hiroshima and Nagasaki and burn down Dresden literally burning the living flesh of the inhabitants of the city only to wax poetic in volumes of self-glorification.  If we do not do these things who will quell the volatility storms?  The rulers of the global empire being run from Washington do not have any incentive or interest because they never cared for benevolence to the oppressed humanity; Machiavelli studied Rome to find invariants in human affairs and we live in a much more sophisticated empire with a great lie of democracy.  There was never any democracy and there will never be any democracy.  Edward Bernays had produced the science of ruling democracy and standardized propaganda which is how democracy works, control of masses by aristocracy.  This is nothing new.  Petronius the greatest vizier of empire started his introduction to Satyricon with a critique of rhetoric which was already developed, matured and dead many times in the long history of Rome; compared to the mastery of rhetoric as a manipulation tool of Rome the modern approaches are mediocre because the school indoctrination has been much more successful in ensuring compliance and acceptance by the people and acceptance or not by people mean nothing if they do not own enough mass media;  I am proud to have taken a long shot risk at dissent in the internet and force many topics of free speech that jar and irritate and offend taking the blows without regret because that is what Emersonian Heroism demands of us.  We cannot merely be polite and decent when stakes for our people the human race are so great.