25,394 research outputs found
Algorithm engineering for optimal alignment of protein structure distance matrices
Protein structural alignment is an important problem in computational
biology. In this paper, we present first successes on provably optimal pairwise
alignment of protein inter-residue distance matrices, using the popular Dali
scoring function. We introduce the structural alignment problem formally, which
enables us to express a variety of scoring functions used in previous work as
special cases in a unified framework. Further, we propose the first
mathematical model for computing optimal structural alignments based on dense
inter-residue distance matrices. We therefore reformulate the problem as a
special graph problem and give a tight integer linear programming model. We
then present algorithm engineering techniques to handle the huge integer linear
programs of real-life distance matrix alignment problems. Applying these
techniques, we can compute provably optimal Dali alignments for the very first
time
Two-player envy-free multi-cake division
We introduce a generalized cake-cutting problem in which we seek to divide
multiple cakes so that two players may get their most-preferred piece
selections: a choice of one piece from each cake, allowing for the possibility
of linked preferences over the cakes. For two players, we show that disjoint
envy-free piece selections may not exist for two cakes cut into two pieces
each, and they may not exist for three cakes cut into three pieces each.
However, there do exist such divisions for two cakes cut into three pieces
each, and for three cakes cut into four pieces each. The resulting allocations
of pieces to players are Pareto-optimal with respect to the division. We use a
generalization of Sperner's lemma on the polytope of divisions to locate
solutions to our generalized cake-cutting problem.Comment: 15 pages, 7 figures, see related work at
http://www.math.hmc.edu/~su/papers.htm
Tuner: a tool for designing and optimizing ion optical systems
Designing and optimizing ion optical systems is often a complex and difficult
task, which requires the use of computational tools to iterate and converge
towards the desired characteristics and performances of the system. Very often
these tools are not well adapted for exploring the numerous degrees of freedom,
rendering the process long and tedious, as well as somewhat random due to the
very large number of local minima typically found when looking for a particular
optical solution. This paper presents a novel approach to finding the desired
solution of an optical system, by providing the user with an instant feedback
of the effects of changing parameters. The process of finding an approximate
solution by manually adjusting parameters is greatly facilitated, at which
point the final tune can be calculated by minimization according to a number of
constraints.Comment: 15 pages, 6 figures, to be published in Nuclear Instruments and
Methods
Molecular Dynamics of pancake vortices with realistic interactions: Observing the vortex lattice melting transition
In this paper we describe a version of London Langevin molecular dynamics
simulations that allows for investigations of the vortex lattice melting
transition in the highly anisotropic high-temperature superconductor material
BiSrCaCuO. We include the full electromagnetic
interaction as well as the Josephson interaction among pancake vortices. We
also implement periodic boundary conditions in all directions, including the
z-axis along which the magnetic field is applied. We show how to implement flux
cutting and reconnection as an analog to permutations in the multilevel Monte
Carlo scheme and demonstrate that this process leads to flux entanglement that
proliferates in the vortex liquid phase. The first-order melting transition of
the vortex lattice is observed to be in excellent agreement with previous
multilevel Monte Carlo simulations.Comment: 4 figure
Matrix Minor Reformulation and SOCP-based Spatial Branch-and-Cut Method for the AC Optimal Power Flow Problem
Alternating current optimal power flow (AC OPF) is one of the most
fundamental optimization problems in electrical power systems. It can be
formulated as a semidefinite program (SDP) with rank constraints. Solving AC
OPF, that is, obtaining near optimal primal solutions as well as high quality
dual bounds for this non-convex program, presents a major computational
challenge to today's power industry for the real-time operation of large-scale
power grids. In this paper, we propose a new technique for reformulation of the
rank constraints using both principal and non-principal 2-by-2 minors of the
involved Hermitian matrix variable and characterize all such minors into three
types. We show the equivalence of these minor constraints to the physical
constraints of voltage angle differences summing to zero over three- and
four-cycles in the power network. We study second-order conic programming
(SOCP) relaxations of this minor reformulation and propose strong cutting
planes, convex envelopes, and bound tightening techniques to strengthen the
resulting SOCP relaxations. We then propose an SOCP-based spatial
branch-and-cut method to obtain the global optimum of AC OPF. Extensive
computational experiments show that the proposed algorithm significantly
outperforms the state-of-the-art SDP-based OPF solver and on a simple personal
computer is able to obtain on average a 0.71% optimality gap in no more than
720 seconds for the most challenging power system instances in the literature
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