Computations for Pyne et al. 339 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 run fminunc Matlab function with Quasi-Newton 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. We then run the fminunc Matlab function again with Trust Region algorithm and first order optimality of 1.0e −6, but having as starting point the solutions obtained with the first Quasi-Newton run. Doing that we obtained an absolute difference of the two configurations with the two different initial guesses of the order of 10e −04.

bBDNA bBDNA with gd-intras
Energy 15.5709 15.5434
Norm of the gradient 0.0232 0.0113
Min Hess eigenvalue 2.1046e-07 1.2818e-07
Max Hess eigenvalue 6.7081e+04 6.7083e+04
Median Hess eigenvalue 11.6687 11.6688
Number of negative eigenvalues 0 0
Hessian condition number 8.2116e+11 1.3584e+12
Number of links 33 33

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:
P339-3D-GUESS1tr-bBDNA.fig
P339-3D-GUESS1tr-bBDNAgd.fig
P339-2D-GUESS4tr.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 20.4514 20.4059
Norm of the gradient 0.0876 0.0539
Min Hess eigenvalue 2.8500e-07 2.8502e-07
Max Hess eigenvalue 6.8838e+04 6.8732e+04
Median Hess eigenvalue 11.6586 11.6585
Number of negative eigenvalues 0 0
Hessian condition number 6.4429e+11 1.0332e+12
Number of links 32 32

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:
P339-3D-GUESS3-bBDNA.fig
P339-3D-GUESS3-bBDNAgd.fig
P339-2D-GUESS3.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 21.2955 21.1221
Norm of the gradient 0.0767 0.0557
Min Hess eigenvalue 6.4206e-08 1.1106e-07
Max Hess eigenvalue 6.6768e+04 6.6768e+04
Median Hess eigenvalue 11.6666 11.6665
Number of negative eigenvalues 0 0
Hessian condition number 2.7352e+12 1.5177e+12
Number of links 32 32

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:
P339-3D-GUESS6-bBDNA.fig
P339-3D-GUESS6-bBDNAgd.fig
P339-2D-GUESS6.fig

Solution for initial guess D:

We run fminunc Matlab function with Quasi-Newton 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 604.9322 604.1401
Norm of the gradient 35.8213 37.0695
Min Hess eigenvalue -7.8645e-04 -8.2728e-04
Max Hess eigenvalue 6.4288e+04 6.4294e+04
Median Hess eigenvalue 11.6202 11.6187
Number of negative eigenvalues +5 +5
Hessian condition number 2.3881e+8 2.3640e+8
Number of links 28 28

3D plot of the configuration obtained in Beaud's thesis versus the one obtained with the bBDNA initial guess and Quasi-Newton method.


3D plot of the line linking the Watson phospate with the bBDNA initial guess.


We then run Trust Region method using as initial point the ”optimum” found with Quasi-Newton method and a tolerance for the first order optimality of 1.0e −6. In particular we obtain a solution similar to the one obatained with initial guess 1. Furthermore, the absolute difference of the two solutions becomes of the order of 10e −04.

bBDNA bBDNA with gd-intras
Energy 15.6406 15.6078
Norm of the gradient 0.2485 0.0364
Min Hess eigenvalue 2.9066e-07 1.5568-07
Max Hess eigenvalue 6.7428e+04 6.7428e+04
Median Hess eigenvalue 11.6693 11.6692
Number of negative eigenvalues 0 0
Hessian condition number 7.9021e+11 1.0208e+12
Number of links 33 33

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


3D plot of the line linking the Watson phospate with the bBDNA initial guess.


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


3D plot of the line linking the Watson phospate with the bBDNA initial guess.


2D plot of the inter variables of the two solutions.
MATLAB figures and saved variables:
P339-3D-GUESS9-bBDNA.fig
P339-3D-GUESS9-bBDNAgd.fig
P339-2D-GUESS9.fig