# Talk:Chromosome structure via Euclidean Distance Matrices

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-                                                                                            %%% 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.