Computations for Kahn & Crothers sequence

In this page we show the minimizations results for each initial guess. In the table we show the energy, the norm of the gradient of the energy function with the obtained configuration, some data of the eigenvalues and the Hessian condition number. In particular what we can observe in this case is that all the solutions have only positive eigenvalues.

Solution for initial guess A:

We used fminunc Matlab function with Trust Region algorithm and tolerance for the first order optimality of 1.0e − 6. The absolute difference of the two configurations obtained with the two different initial guesses is of the order of 10e −03.

bBDNA bBDNA with gd-intras
Energy 23.2548 23.2543
Norm of the gradient 0.0767 0.0778
Min Hess eigenvalue 4.8661e-06 4.8346e-06
Max Hess eigenvalue 6.6359e+04 6.7084e+04
Median Hess eigenvalue 11.5859 11.5858
Number of negative eigenvalues 0 0
Hessian condition number 3.5723e+10 3.5927e+10
Number of links 15 15

3D plot of the configuration obtained with the bBDNA initial guess.


3D plot of the configuration obtained with the bBDNA with gd intras initial guess.


2D plot of the inter variables of the two solutions.
MATLAB figures saved variables:
KC-3D-GUESS1-bBDNA.fig
KC-3D-GUESS1-bBDNAgd.fig
KC-2D-GUESS4.fig

Solution for initial guess B:

We used fminunc Matlab function with Trust Region algorithm and tolerance for the first order optimality of 1.0e − 8. The absolute difference of the two configurations obtained with the two different initial guesses is of the order of 10e −02.

bBDNA bBDNA with gd-intras
Energy 56.1674 56.4639
Norm of the gradient 11.5856 11.5857
Min Hess eigenvalue 1.2581e-05 7.7524e-05
Max Hess eigenvalue 6.7400e+04 6.7375e+04
Median Hess eigenvalue 11.6828 11.5857
Number of negative eigenvalues 0 0
Hessian condition number 1.5657e+10 2.6192e+10
Number of links 14 14

3D plot of the configuration obtained with the bBDNA initial guess.


3D plot of the configuration obtained with the bBDNA with gd intras initial guess.


2D plot of the inter variables of the two solutions.
MATLAB figures and saved variables:
KC-3D-GUESS2-bBDNA.fig
KC-3D-GUESS2-bBDNAgd.fig
KC-2D-GUESS2.fig

Solution for initial guess C:

We used fminunc Matlab function with Trust Region algorithm and tolerance for the first order optimality of 1.0e − 6. The absolute difference of the two configurations obtained with the two different initial guesses is of the order of 10e −03.

bBDNA bBDNA with gd-intras
Energy 55.0552 55.0508
Norm of the gradient 0.0722 0.0663
Min Hess eigenvalue 1.1101e-05 1.1223e-05
Max Hess eigenvalue 7.8887e+04 6.2543e+04
Median Hess eigenvalue 11.4382 11.4355
Number of negative eigenvalues 0 0
Hessian condition number 7.1063e+09 5.5724e+09
Number of links 16 16

3D plot of the configuration obtained with the bBDNA initial guess.


3D plot of the configuration obtained with the bBDNA with gd intras initial guess.


2D plot of the inter variables of the two solutions.
MATLAB figures and saved variables:
KC-3D-GUESS4-bBDNA.fig
KC-3D-GUESS4-bBDNAgd.fig
KC-2D-GUESS4.fig

Solution for initial guess D:

We used fminunc Matlab function with Trust Region algorithm and tolerance for the first order optimality of 1.0e − 6. The absolute difference of the two configurations obtained with the two different initial guesses is of the order of 10e −03.

bBDNA bBDNA with gd-intras
Energy 23.3988 23.4270
Norm of the gradient 0.0562 0.1169
Min Hess eigenvalue 4.8661e-06 4.8346e-06
Max Hess eigenvalue 6.6359e+04 6.7084e+04
Median Hess eigenvalue 11.6873 11.6875
Number of negative eigenvalues 0 0
Hessian condition number 4.7163e+10 3.8725e+10
Number of links 15 15

3D plot of the configuration obtained with the bBDNA initial guess.


3D plot of the configuration obtained with the bBDNA with gd intras initial guess.


2D plot of the inter variables of the two solutions.
MATLAB figures and saved variables:
KC-3D-GUESS10-bBDNA.fig
KC-3D-GUESS10-bBDNAgd.fig
KC-2D-GUESS10.fig