
1:15 PM (1 minute ago)



import cvxopt as opt
Posted in Uncategorized on May 31, 2015 Leave a Comment »

1:15 PM (1 minute ago)



import cvxopt as opt
Posted in Uncategorized on May 31, 2015 Leave a Comment »
Incompressible fluid dynamics is usually studied in physics in the mathematical setting space and time, where velocity and pressure follow a set of transport equations, which are and
which we can simplify with . Here is the Reynold’s number. The physicists’ intuition is that laminar flow is possible when is small but the solutions are turbulent when .
Weak solutions to NavierStokes on R^3 were proved to exist in 1933 (attached) and there is also a recent paper. As a curious novice in this direction, I am still confused about these weak solutions, especially with observed phase transition to turbulence. In turbulent flow, there does not seem to be any chance of C^infinity type behavior for the fluid and the physics literature provides many metrics. I know something about elliptic regularity in related context when weak smooth solutions of elliptic equations bootstrap to smoothness. But what are weak solutions with regularity that are turbulent? Apologies for airing my confusions. I will try to clarify for myself what a weak solution is exactly mathematically. Clearly this is a delicate issue worth investigating. John Nash, may he rest in peace, had always emphasized physical intuition even in his paper on parabolic kernels of uniformly elliptic operators and as a novice I would like to sharpen mine.
2 Attachments
Preview attachment weaksolutionsnavierstokes1933.pdf
Preview attachment regularityweaksolutionsnavierstokes.pdf

11:32 AM (1 minute ago) 


Historically, Leray’s introduction to his seminal paper of 1933 mentions that he believed in the irregularity development in finite time for Navier’s equations he calls the equations for velocity and pressure which I had been mangling for simplicity. These are actually equations for velocity u and also a pressure term
div(u) == 0 (incompressible)
The useful way according to Chorin to rewrite these is to introduce the ‘Reynold’s number’ R directly and put
d/dt u + R <u,grad u> = Laplacian(u) – d/dt pressure
We know generally that turbulence in this system can happen when R is much higher than 1. If we just set pressure to zero, we have the form that I was using for my exploratory thinking about the case of volatility on a graph instead of u:
(d/dt – Laplacian) u = – R<u,grad u> =: F(u)
In the intuition of physicists, laminar flow should result when R is small and there can be a phase transition to turbulence when R crosses some threshold. By early 1940s Onsager was using NavierStokes with high Reynold’s number to explain the formation of vortices, so I am trying to place the lack of singularity formation examples that Leray alluded to in his 1933 paper to the Onsager model around eight years later.
NavierStokes is a favourite of numerical analysis by computers for engineers, so I can look at this problem directly as well. The motivation for me ultimately is to understand financial market volatility with an exact model of this type if possible. I feel comfortable that the graph of the market will serve well as an xvariable for this problem now.
Posted in Uncategorized on May 31, 2015 Leave a Comment »
Inbox

x 

4:29 PM (34 minutes ago)



Preview attachment createreturnmatrix.py

4:43 PM (20 minutes ago)



Here is my analysis code again in R:
# code to generate the fundamental VOLATILITY data
V<read.table(‘volatility.csv’, sep=’,’,header=TRUE)
# we create a graph using volatilities correlated by subtracting diagonal
Posted in Uncategorized on May 30, 2015 1 Comment »
I’m sick and tired of population reductionists in the west. Go to hell. We should kill the ultrawealthy who are moronic fuckfaces who can make no decisions besides their sexual pleasures properly. Wipe out these lowlife insects.
Posted in Uncategorized on May 30, 2015 1 Comment »
Chaos has fascinated academic interest from the late 1980s. I happen to know this because as a poor kid living in Queens New York, I had a subscription to one of these book clubs that sent me among other technical and popular books Edward Witten’s two volumes on Superstring theory that I never understood and James Gleick’s Chaos: The Making of a New Science. Popularity of Mandelbrot and Chaos theory had generated a little cottage industry in academia and in finance too. The problem with it from my very limited honestly perspective about dynamical systems since I have no training at all in these things, is that it is too cool. I mean look at turbulence in actual hydrodynamics. It’s hard science. Onsager worked out the vortex creation problem in the depths of physics. NavierStokes equations with low viscosity is not a joke. Onsager, now there’s a man one can trust on this stuff. He actually knew a real system well enough to break new insights. Fluid dynamics is hard science. The fluffiness of the pretty pictures in dynamical systems is probably good for something, but it’s not good for a real science of volatility. Why am I so confident about this direction? Probably just because I am too arrogant and will fail in another mission impossible.
Here is my proposal for getting to a true real science of finance:
Study phase transitions of high dimensional nonlinear dynamical systems and their behavior with regards to phases of laminar versus turbulent behavior. The specific class of dynamical systems of interest to us is the NavierStokes type which on a graph becomes a delay differential equation since the Laplacian is just a numerical matrix. The guidance for this study should come from Kolmogorov’s ICM paper of 1954 which led Arnold and Moser to prove the famous KAM theorem. With any clear understanding of parameters and thresholds that divide laminar and chaotic phases, we use statistical technology to model the world’s volatility directly as an intrensic dynamical system.
Posted in Uncategorized on May 30, 2015 1 Comment »
n<dim(A)[1]
Posted in Uncategorized on May 29, 2015 Leave a Comment »
Finance needs a science. What does RISK mean to you? To me, who is now homeless after an unscrupulous Indian landlord got an eviction by default from maliciously blocking mail that could have let me defend myself in court to get richer clients almost throwing out my precious hundreds of books once again after I lost them in 2009 when I became homeless, for me THIS is risk of finance and volatility bubbles. The lowlife scumbag shithead Ken Patel could only do this because he has money and I don’t and he is like a thousand other cockroaches in San Francisco doing these things. The risk of finance is felt every day by seven billion people around the world, and this is real risk, not some lost few coins out of deep pockets. This is the lives of people all at risk by the manipulators of money and the trillionaires who own the west. This is the risk of living in their casino. So I find it funny that financial risk is considered by an entire civilization from the investor’s viewpoint and not the viewpoint of humanity. A true scientist would laugh at the hagiographies of risk metrics of financiers as science; they cannot produce a science of finance because of their greed and selfishness and their ego regarding their selfworth. They are criminals who feed the volatility storms from which the entire human race needs shelter and we are the pioneers who will conquer these storms with real science.