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Molecular embedding via a second order dissimilarity parameterized approach. (English) Zbl 1193.92039

Summary: We describe a computational approach to the embedding problem in structural molecular biology. The approach is based on a dissimilarity parameterization of the problem that leads to a large-scale non-convex bound constrained matrix optimization problem. The underlying idea is that an increased number of independent variables decouples the complicated effects of varying the location of individual atoms in coordinate-based formulations.
Numerical tests support this hypothesis and indicate that the optimization problem that results is relatively benign and easy to solve, despite being large and non-convex. We can solve problems with millions of independent variables in a few dozen to a few score optimization iterations. The non-convexity arises due to matrix rank constraints in the problem, and we focus on their efficient computational treatment. We present numerical results for a number of synthetic and real protein data sets and comment on features of real experimental data that can cause computational difficulties.

MSC:

92C40 Biochemistry, molecular biology
65K05 Numerical mathematical programming methods
92E10 Molecular structure (graph-theoretic methods, methods of differential topology, etc.)
90C90 Applications of mathematical programming

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