# Talk:Chromosome structure via Euclidean Distance Matrices

(Difference between revisions)
 Revision as of 22:46, 6 August 2008 (edit) (New page:
%%% Ronan Fleming, E.coli molecule data  %%% -Jon Dattorro, August 2008 clear all load ecoli  frame = 12;                                         % 1 through 12 G = her49imfs12movful...)← Previous diff                                         Revision as of 22:56, 6 August 2008 (edit) (undo) (New section: E.coli realization)Next diff →
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plot3(Xs(1,:), Xs(2,:), Xs(3,:), '.')                                                                                                  plot3(Xs(1,:), Xs(2,:), Xs(3,:), '.')

+ + == E.coli realization == + + I regard the autocorrelation data you provided as a Gram matrix. + + Then the conversion to an EDM is straightforward - Chapter 5.4.2 of Convex Optimization & Distance Geometry. + + The program calculates the first 20 eigenvalues of the projection of the EDM on the positive semidefinite (PSD) cone. + + You can see that there are many significant eigenvalues; which means, the Euclidean body lives in a space higher than dimension 3, assuming I have interpreted the E.coli data correctly. + + To get a picture corresponding to physical reality, you have to project on the PSD cone, rank 3 subset.

## Revision as of 22:56, 6 August 2008

```%%% Ronan Fleming, E.coli molecule data
%%% -Jon Dattorro, August 2008
clear all

frame = 12;                                         % 1 through 12
G = her49imfs12movfull(frame).cdata;                % uint8
G = (double(G)-128)/128;                            % Gram matrix
N = size(G,1);

D = diag(G)*ones(N,1)' + ones(N,1)*diag(G)' - 2*G;  % EDM D

clear her49imfs12movfull G;

Vn = [-ones(1,N-1); speye(N-1)];
VDV = (-Vn'*D*Vn)/2;

clear D Vn

[evec evals flag] = eigs(VDV, [], 20, 'LR');
if flag, disp('convergence problem'), return, end;

close all

Xs = sqrt(real(evals(1:3,1:3)))*real(evec(:,1:3))'; % Projection of -VDV on PSD cone rank 3
plot3(Xs(1,:), Xs(2,:), Xs(3,:), '.')
```

## E.coli realization

I regard the autocorrelation data you provided as a Gram matrix.

Then the conversion to an EDM is straightforward - Chapter 5.4.2 of Convex Optimization & Distance Geometry.

The program calculates the first 20 eigenvalues of the projection of the EDM on the positive semidefinite (PSD) cone.

You can see that there are many significant eigenvalues; which means, the Euclidean body lives in a space higher than dimension 3, assuming I have interpreted the E.coli data correctly.

To get a picture corresponding to physical reality, you have to project on the PSD cone, rank 3 subset.