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Archive for February, 2011

By the 1820s the Rothschilds had control of the British money supply.  They were instrumental in the founding of the US Federal Reserve as well after the panic of 1907 by 1913 after which by 1914 New York became the center of money power in the world.  They are an example of the holders of extraordinary powers in the financial markets whose resources outstrip anything one could consider “ordinary”.  Cabals of this order of financial power have such enormous control of resources that they are able to move entire markets at will, they are able to influence the construction of entire markets.  In finance theory, for example that of modern portfolio theory whose mathematical formulation is due to Nobel prize winner Harry Markowitz, there are assumptions of normal returns of asset.  Of course there have been tremendous work of testing other possible distributions such as parametric distributions but all of these have the same basic model of the market as determined by a large group of individuals with whatever characteristics as economic agents.  The Markowitz optimization on actual assets invariably produce negative allocations to some assets which would suggest that there is something dreadfully wrong with the Markowitz conception of the financial markets.  I suggest that essentially the problem is that a few very powerful players have enormous financial power and they neutralize the effectiveness of these models.  To a very large extent the global capital markets have most participants as noise traders while concentrated financial power coordinate movements in multiple markets.  The black swans, I suggest, are all intentional.

 

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warm bodies, I sense
are not machines that can only make money
past, perfect, tense
words for a feeling and all I’ve discovered
I’ll be along son with medicine supposed to,
designed to make you high
I’ll be along son
with words for a feeling and all I’ve discovered

–Live

In this dark age of the human race, where the entire planet is under a planetary Empire system, loneliness is virulent spiritual malaise.  This is a disease that I am intimately familiar with and for which I have found the unique solution.

Loneliness is the deceptive condition where the heart feels empty and one is tempted to seek fulfilment in the external world.  There is no such fulfillment to be found, and the unique solution is unconditional love within.  Only unconditional love can remove the emptiness of the heart that is accompanied by this malaise.  Wrong solutions abound.

Earth is hell, and one’s loneliness is like a black hole. For strong spirits it is not a big deal to handle, but the loneliness is like a vacuum that can destroy a weak spirit. Unconditional love is the only salve that will be lasting.

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Ideals of the Republic

TRUTH = BEAUTY (Keats)
TRUTH, LIBERTY, LOVE = ideals of Republic (Shelley)
DIVINE LOVE = JUSTICE (Myself)
Therefore: TRUTH=BEAUTY, LIBERTY, LOVE=JUSTICE ideals of REPUBLIC

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One the first approaches I am using for shape determination of proteins is a maximum likelihood approach.  I am sure many who read this are sophisticated mathematically.  Regardless, because I understand things very simply, I will speak of extremely simple ideas.  The sophistication comes only when the simplest pieces are clear.

So let’s consider the most elementary possible example in probability theory: coin tosses.  An unbiased coin tossed will have probability of 1/2, and successive tosses have nothing to do with each other, hence statistically independent.  So probabilities multiply.  The probability of seeing a head followed by a tail is (1/2)(1/2) = 1/4 and so on.

By analogy, consider sequence of 3D twists in a folded protein as a random event.  The sample space is now continuous, as a 3D rotation is parametrized by SO(3) rather than the two-value space {head, tail}.   One can discretize this space and ask for a finite space, so that the analogy with coin tosses is clearer.  But indeed proteins folded are far from random sequences.  This is where the second difference comes into play: successive rotations on amino acids in a folded protein are quite far from independent.  It is this LACK of independence that makes a probability maximization approach have any special merit: the probability densities of rotations conditioned on the previous rotation provide crucial information about protein shape construction.

Now for a basic idea of empirical facts.  I established in the last couple of days that using 9225 protein skeleta that unconditional rotation distributions concentrate on ~0.2% of a grid of a million points, and if we specify the amino acid of the twist, we have concentrations on 0.02% of the grid.  Interestingly, and positively, conditional probability distributions show evidence of good size sampling for the 0.2% points on which they concentrate (in the order of 200 points) and also show some concentration.  Thus maximization of probability of a sequence of twists in a row produces nontrivial probability maximization:  P(tN .. t1) = P(tN | t_{N-1}…t1) P(t_{N-1}…t1) and we want to pick twists t1, …, tN which maximizes the probability given the restriction that the pivot sequence is fixed.  This is a trivial problem if successive twists are independence.  Even a stepwise conditioning suddenly makes this maximization interesting.

 

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Pivot Amino Hit Count (in 1MM points)
ALA 234
ARG 213
ASN 170
ASP 185
CYS 57
GLN 156
GLU 236
GLY 210
HIS 86
ILE 185
LEU 288
LYS 230
MET 76
PHE 145
PRO 161
SER 180
THR 173
TYR 109
VAL 213

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I had obtained results on discreteness of angles between amino acids in folded proteins along the N-atom forming the peptide bonds in 2008.  Today I have a basic result for 3D twists in folded proteins.  Among 9,225 folded proteins if we histogram the twists in the 3-ball representation of the rotation space SO(3), and put them in a 100x100x100 cubic grid, and then consider only those grid points that were hit at least 5 times (noise level) we will note that only 2080 grid points have any value.  This implies that protein rotations are highly concentrated, and occur in only 0.2% of the space of rotations, and even then there is a great deal of concentration on pieces of this 2080 point space.

This is an interesting result in its own right because it points to very strong rigidity in folded protein shape, removing 99.7-8% of the rotations as having almost no chance of occurring.  This result is indicative rather than directly useful for protein folding algorithms, but it is certainly an enormous help for design of folding algorithms.

 

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