361,554 research outputs found
Computational Performance Evaluation of Two Integer Linear Programming Models for the Minimum Common String Partition Problem
In the minimum common string partition (MCSP) problem two related input
strings are given. "Related" refers to the property that both strings consist
of the same set of letters appearing the same number of times in each of the
two strings. The MCSP seeks a minimum cardinality partitioning of one string
into non-overlapping substrings that is also a valid partitioning for the
second string. This problem has applications in bioinformatics e.g. in
analyzing related DNA or protein sequences. For strings with lengths less than
about 1000 letters, a previously published integer linear programming (ILP)
formulation yields, when solved with a state-of-the-art solver such as CPLEX,
satisfactory results. In this work, we propose a new, alternative ILP model
that is compared to the former one. While a polyhedral study shows the linear
programming relaxations of the two models to be equally strong, a comprehensive
experimental comparison using real-world as well as artificially created
benchmark instances indicates substantial computational advantages of the new
formulation.Comment: arXiv admin note: text overlap with arXiv:1405.5646 This paper
version replaces the one submitted on January 10, 2015, due to detected error
in the calculation of the variables involved in the ILP model
Clustering of solutions in hard satisfiability problems
We study the structure of the solution space and behavior of local search
methods on random 3-SAT problems close to the SAT/UNSAT transition. Using the
overlap measure of similarity between different solutions found on the same
problem instance we show that the solution space is shrinking as a function of
alpha. We consider chains of satisfiability problems, where clauses are added
sequentially. In each such chain, the overlap distribution is first smooth, and
then develops a tiered structure, indicating that the solutions are found in
well separated clusters. On chains of not too large instances, all solutions
are eventually observed to be in only one small cluster before vanishing. This
condensation transition point is estimated to be alpha_c = 4.26. The transition
approximately obeys finite-size scaling with an apparent critical exponent of
about 1.7. We compare the solutions found by a local heuristic, ASAT, and the
Survey Propagation algorithm up to alpha_c.Comment: 8 pages, 9 figure
Two Decades of Maude
This paper is a tribute to José Meseguer, from the rest of us in the Maude team, reviewing the past, the present, and the future of the language and system with which we have been working for around two decades under his leadership. After reviewing the origins and the language's main features, we present the latest additions to the language and some features currently under development. This paper is not an introduction to Maude, and some familiarity with it and with rewriting logic are indeed assumed.Universidad de Málaga. Campus de Excelencia Internacional AndalucÃa Tech
Steklov Spectral Geometry for Extrinsic Shape Analysis
We propose using the Dirichlet-to-Neumann operator as an extrinsic
alternative to the Laplacian for spectral geometry processing and shape
analysis. Intrinsic approaches, usually based on the Laplace-Beltrami operator,
cannot capture the spatial embedding of a shape up to rigid motion, and many
previous extrinsic methods lack theoretical justification. Instead, we consider
the Steklov eigenvalue problem, computing the spectrum of the
Dirichlet-to-Neumann operator of a surface bounding a volume. A remarkable
property of this operator is that it completely encodes volumetric geometry. We
use the boundary element method (BEM) to discretize the operator, accelerated
by hierarchical numerical schemes and preconditioning; this pipeline allows us
to solve eigenvalue and linear problems on large-scale meshes despite the
density of the Dirichlet-to-Neumann discretization. We further demonstrate that
our operators naturally fit into existing frameworks for geometry processing,
making a shift from intrinsic to extrinsic geometry as simple as substituting
the Laplace-Beltrami operator with the Dirichlet-to-Neumann operator.Comment: Additional experiments adde
Modeling vitreous silica bilayers
We computer model a free-standing vitreous silica bilayer which has recently
been synthesized and characterized experimentally in landmark work. Here we
model the bilayer using a computer assembly procedure that starts from a single
layer of amorphous graphene, generated using a bond switching algorithm from an
initially crystalline graphene structure. Next each bond is decorated with an
oxygen atom and the carbon atoms are relabeled as silicon. This monolayer can
be now thought of as a two dimensional network of corner sharing triangles.
Next each triangle is made into a tetrahedron, by raising the silicon atom
above each triangle and adding an additional singly coordinated oxygen atom at
the apex. The final step is to mirror reflect this layer to form a second layer
and then attach the two layers together to form the bilayer.
We show that this vitreous silica bilayer has the additional macroscopic
degrees of freedom to easily form a network of identical corner sharing
tetrahedra if there is a symmetry plane through the center of the bilayer going
through the layer of oxygen ions that join the upper and lower layers. This has
the consequence that the upper rings lie exactly above the lower rings, which
are tilted in general. The assumption of a network of perfect corner sharing
tetrahedra leads to a range of possible densities that we have previously
characterized in three dimensional zeolites as a flexibility window. Finally,
using a realistic potential, we have relaxed the bilayer to determine the
density, and other structural characteristics such as the Si-Si pair
distribution functions and the Si-O-Si bond angle distribution, which are
compared to the experimental results obtained by direct imaging
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