Computations for Pyne et al. 251 bp 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 −02.

bBDNA bBDNA with gd-intras
Energy 39.6014 39.5334
Norm of the gradient 0.0082 0.0079
Min Hess eigenvalue 2.0416e-06 2.1203e-07
Max Hess eigenvalue 6.7709e+04 6.7768e+04
Median Hess eigenvalue 11.6407 11.6404
Number of negative eigenvalues 0 0
Hessian condition number 8.4430e+10 8.8909e+11
Number of links 25 25

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:
P251-3D-GUESS1-bBDNA.fig
P251-3D-GUESS1-bBDNAgd.fig
P251-2D-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 − 6. 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 16.4158 16.4159
Norm of the gradient 0.0332 0.0333
Min Hess eigenvalue 5.3207e-07 5.8142e-07
Max Hess eigenvalue 6.0911e+04 6.7323e+04
Median Hess eigenvalue 11.6002 11.6011
Number of negative eigenvalues 0 0
Hessian condition number 7.9421e+10 8.1229e+11
Number of links 24 24

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:
P251-3D-GUESS2-bBDNA.fig
P251-3D-GUESS2-bBDNAgd.fig
P251-2D-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 −02.

bBDNA bBDNA with gd-intras
Energy 17.0876 17.1798
Norm of the gradient 0.0232 0.0234
Min Hess eigenvalue 7.9233e-07 7.9302e-07
Max Hess eigenvalue 7.2311e+04 7.2308e+04
Median Hess eigenvalue 11.6631 11.6632
Number of negative eigenvalues 0 0
Hessian condition number 3.6720e+11 8.9902e+11
Number of links 24 24

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:
P251-3D-GUESS3-bBDNA.fig
P251-3D-GUESS3-bBDNAgd.fig
P251-2D-GUESS3.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 −02.

bBDNA bBDNA with gd-intras
Energy 16.6328 16.3974
Norm of the gradient 0.0572 0.0424
Min Hess eigenvalue 1.5211e-07 2.1331e-07
Max Hess eigenvalue 6.7081e+04 6.7083e+04
Median Hess eigenvalue 11.6248 11.6250
Number of negative eigenvalues 0 0
Hessian condition number 9.9887e+10 9.9887e+11
Number of links 24 24

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:
P251-3D-GUESS4-bBDNA.fig
P251-3D-GUESS4-bBDNAgd.fig
P251-2D-GUESS4.fig