Simple soft thresholding peak-counts for rotation distributions

If we consider twist decompositions of proteins, the relative rotations between amino acids are elements of the rotation group SO(3) whose elements have the representation by an axis, unit vector in three dimensional space and a rotation angle, which means S^1 x S^2. Simple protein folding algorithms can be constructed if we had a uniformly … More Simple soft thresholding peak-counts for rotation distributions

Typical example of relative rotation: case of GLN-SER-GLY

What you will find below is a table of sphere grid points (x,y,z) and counts, counts soft thresholded by the standard deviation as noise. Out of 1864 points, only 145 points have nonzero counts, and of these, 18 points contain almost 60% of the mass concentrated on them. This is a typical situation with rotation … More Typical example of relative rotation: case of GLN-SER-GLY

Cleaner version of sparsity of rotation twists by amino triples

The simple (and coarse) peak-selection criterion is by thresholding by 1.5 x mean(count). The second column is peak count, the third is number of grid points on the 2-sphere with nonzero count. BILE-ILE-LYS.txt 1 15 ILE-ILE-LYS.txt 3 19 ILE-ILE-MET.txt 0 10 ILE-ILE-VAL.txt 0 12 ILE-ILE-ALA.txt 0 10 ILE-LEU-ILE.txt 553 2974 ILE-LEU-LYS.txt 506 3839 ILE-LEU-MET.txt 64 … More Cleaner version of sparsity of rotation twists by amino triples

Sparsity of rotations pivoted on amino triples

This is a quick estimate of “peak counts” in rotation distributions on a fixed grid with a point labeled a peak if it is 1.5 x mean(count) of the grid points hit — for rotations pivoted on amino triples of folded proteins. One can gauge immediately the enormous concentration of rotations leading to the natural … More Sparsity of rotations pivoted on amino triples

Sparsity of protein twists – April 17 2011 – a simple example

In order to have fast solutions to the protein folding problem, the path we have chosen is to seek a deconvolution of twist distribution for triples of amino acids. The general idea is exceedingly simple: we want to model twists in SO(3) ~ S^1 x S^2. I have shown previously that the angle of rotation, … More Sparsity of protein twists – April 17 2011 – a simple example

Observations about the ideal of Truth

Absolute truth is a topic of interest to all sentient beings for obvious reasons. Some truths are absolute truth, like mathematical truths, my favorite example is 2+2=4. There are slightly deeper mathematical truths, for example square-integrable functions on the circle can be uniquely decomposed into a series of sines and cosines of different frequencies. These … More Observations about the ideal of Truth