### DISCO -- a MATLAB software for
distributed conformation of anchor-free graph realization problems

###
**
Kim-Chuan Toh
(corresponding author),
and
Ngai-Hang Z. Leung.
**

The software was first released on 25 Nov 2009. It was
last updated in Dec 2012
with some bugs corrected.
The software is designed to solve anchor-free graph realization
problems based on semidefinite programming (SDP)
relexation of the following nonconvex minimization problem:
\(
\qquad \min \big\{ \sum_{(i,j)\in {\cal E}} |\|x_i-x_i\|^2-d_{ij}^2| - \lambda \sum_{ij} \|x_i-x_j\|^2 \big\}
\)

where \(\lambda\) is a positive regularization parameter.
The given data is
\( \{ d_{ij} \mid (i,j) \in {\cal E} \}\)
with \( {\cal E}\) being a sparse subset of the set of all short-range distances given by
\( \{ (ij) :\mid \|x_i-x_j\| \leq R \}\),
and \(R\) is the cut-off radius.

For molecular conformation of protein molecules, \(R\) is typically set to
6 Angstrom.

Important note:
this is a research software.
It is not intended nor designed to be a general
purpose software.

For more details, see:
N.-H. Z. Leung and K.-C. Toh,
*
An SDP-based divide-and-conquer algorithm for large scale noisy
anchor-free graph realization*,
SIAM J. Scientific Computing, 31 (2009), pp. 4351--4372.
X.Y. Fang and K.C. Toh,
*
Using a distributed SDP approach to solve simulated protein molecular conformation problems,*
in Distance Geometry: Theory, Methods, and Applications, A. Mucherino, C. Lavor, L. Liberti, and N. Maculan eds., Springer, 2013, pp. 351--376.
A
**
movie
**
showing how the divide-and-conquer algorithm computes the
conformation of a protein molecule.

- Copyright:
This version of DISCO is distributed under the GNU General Public License 2.0.
For commercial applications that may be incompatible with this license,
please contact the authors to discuss alternatives.
**Download DISCO-1.4.zip**

Please read.
Welcome to DISCO-1.4!
- Firstly, unpack the software:

unzip DISCO-1.4.zip
- Run Matlab in the directory DISCO-1.4
- To see whether you have installed DISCO-1.4 correctly,
type:

>> discostartup

>> testdisco
- By now, DISCO is ready for you to use.

**
Sparse distance data generated from some protein molecules:
MolecularData.zip**.
The folder contains several problems such as
**1PTQ.mat** which
contains two structure arrays (called prob and probchem) each
encoding several sparse distance matrices such as
prob.Dmat30, prob.Lmat30, prob.Umat30.

**prob.Dmat30**
corresponds to the sparse distance matrix containing
30% of distances (without noise)
within the cut-off radius of 6.

**prob.Lmat30** is the corresponding lower bound
for the true distances.

**prob.Umat30** is the corresponding upper bound
for the true distances.

**prob.A** is the true coordinates of the atoms.

**probchem** is the same as `prob`
except that the pairwise distances between neighboring atoms on the backbone and
some pairwise distances of covalently bonded atoms on the side chains
are also included
in **probchem.Dmat30**, etc.