5,081 research outputs found
Joint Image Reconstruction and Segmentation Using the Potts Model
We propose a new algorithmic approach to the non-smooth and non-convex Potts
problem (also called piecewise-constant Mumford-Shah problem) for inverse
imaging problems. We derive a suitable splitting into specific subproblems that
can all be solved efficiently. Our method does not require a priori knowledge
on the gray levels nor on the number of segments of the reconstruction.
Further, it avoids anisotropic artifacts such as geometric staircasing. We
demonstrate the suitability of our method for joint image reconstruction and
segmentation. We focus on Radon data, where we in particular consider limited
data situations. For instance, our method is able to recover all segments of
the Shepp-Logan phantom from angular views only. We illustrate the
practical applicability on a real PET dataset. As further applications, we
consider spherical Radon data as well as blurred data
Adoption and non-adoption of a shared electronic summary record in England: a mixed-method case study
Publisher version: http://www.bmj.com/content/340/bmj.c3111.full?sid=fcb22308-64fe-4070-9067-15a172b3aea
Deterministic Modularity Optimization
We study community structure of networks. We have developed a scheme for
maximizing the modularity Q based on mean field methods. Further, we have
defined a simple family of random networks with community structure; we
understand the behavior of these networks analytically. Using these networks,
we show how the mean field methods display better performance than previously
known deterministic methods for optimization of Q.Comment: 7 pages, 4 figures, minor change
Entropy evaluation sheds light on ecosystem complexity
Preserving biodiversity and ecosystem stability is a challenge that can be
pursued through modern statistical mechanics modeling. Here we introduce a
variational maximum entropy-based algorithm to evaluate the entropy in a
minimal ecosystem on a lattice in which two species struggle for survival. The
method quantitatively reproduces the scale-free law of the prey shoals size,
where the simpler mean-field approach fails: the direct near neighbor
correlations are found to be the fundamental ingredient describing the system
self-organized behavior. Furthermore, entropy allows the measurement of
structural ordering, that is found to be a key ingredient in characterizing two
different coexistence behaviors, one where predators form localized patches in
a sea of preys and another where species display more complex patterns. The
general nature of the introduced method paves the way for its application in
many other systems of interest.Comment: 13 pages, 5 figure
Extremal Optimization at the Phase Transition of the 3-Coloring Problem
We investigate the phase transition of the 3-coloring problem on random
graphs, using the extremal optimization heuristic. 3-coloring is among the
hardest combinatorial optimization problems and is closely related to a 3-state
anti-ferromagnetic Potts model. Like many other such optimization problems, it
has been shown to exhibit a phase transition in its ground state behavior under
variation of a system parameter: the graph's mean vertex degree. This phase
transition is often associated with the instances of highest complexity. We use
extremal optimization to measure the ground state cost and the ``backbone'', an
order parameter related to ground state overlap, averaged over a large number
of instances near the transition for random graphs of size up to 512. For
graphs up to this size, benchmarks show that extremal optimization reaches
ground states and explores a sufficient number of them to give the correct
backbone value after about update steps. Finite size scaling gives
a critical mean degree value . Furthermore, the
exploration of the degenerate ground states indicates that the backbone order
parameter, measuring the constrainedness of the problem, exhibits a first-order
phase transition.Comment: RevTex4, 8 pages, 4 postscript figures, related information available
at http://www.physics.emory.edu/faculty/boettcher
A computationally efficacious free-energy functional for studies of inhomogeneous liquid water
We present an accurate equation of state for water based on a simple
microscopic Hamiltonian, with only four parameters that are well-constrained by
bulk experimental data. With one additional parameter for the range of
interaction, this model yields a computationally efficient free-energy
functional for inhomogeneous water which captures short-ranged correlations,
cavitation energies and, with suitable long-range corrections, the non-linear
dielectric response of water, making it an excellent candidate for studies of
mesoscale water and for use in ab initio solvation methods.Comment: 6 pages, 5 figure
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