36 * This application can be used to solve the cycle clustering problem as described in
37 *
38 * "Mixed-Integer Programming for Cycle Detection in Non-reversible Markov Processes"@n
39 * by Isabel Beckenbach, Leon Eifler, Konstantin Fackeldey, Ambros Gleixner, Andreas Grever, Marcus Weber, and Jakob Witzig, @n
40 * <em> Multiscale Modeling and Simulation </em> , 2016 (accepted for publication, preprint available as <a href="https://opus4.kobv.de/opus4-zib/frontdoor/index/index/docId/6035">ZIB-Report 16-39</a> ).
41 *
42 * The input format is an \f$n \times n\f$ - matrix \f$Q\f$ of unconditional transition probabilities with a header of the form
43 * "# p nstates ncluster"; nstates is the size of the matrix, ncluster the desired number of clusters; the name of the file must end with ".spa".
44 *
45 * The cycle clustering problem is the following:
46 *
47 * Consider a set of states \f$ \mathcal B = \{1,\ldots,n\}\f$ and a set of clusters \f$\mathcal{C}=\{1,\ldots,m\}\f$.
48 * Let \f$Q \in \mathbb{R}^{n \times n}\f$ with entries \f$ q_{ij}\f$. Then the problem is given by the MINLP