Lefschetz Center for Dynamical Systems Seminar
Stochastic Systems Seminar
Brown Analysis Seminar
$ H^{o}[a,b] $ | |
Scientific Computing Seminar
Abstract:
A well known distance geometry problem is that of finding 3D coordinates
from the estimates of the interpoint distances. In this talk we impose the
constraint that some of the coordinates are known. This leads to a new
matrix minimization problem of considerable practical interest in biological
applications, such as determination of a 3D protein structure or a ligand/
receptor docking problem, where partial knowledge is frequently available.
A global minimum of a function of many variables is often attached a
considerable significance in biological applications. Furthermore, it is
regarded as one of the more challenging computational problems when the
number of local minima becomes very large. It is therefore essential to
find a problem reformulation that efficiently locates a global minimum.
One such reformulation for the problem stated above is based on the inertial
tensor associated with an unknown matrix. The entire solution space is then
characterized in terms of geometry of the intersection curves between the 3D
unit sphere and one parameter family of ellipsoids. Upon deriving tight
bilateral bounds on three moments of inertia of any possible solution, a
global search algorithm is constructed: it eliminates large portions of the
discretized solution space while searching for the candidate global minimum.
As a final check, the entire process is repeated on a finer discretization of
the search space. The effectiveness of this method is demonstrated on
realistic simulated and chemical test problems.
PDE Seminar
Department of Mathematics Colloquium
<--- 1997 Index