2,624 research outputs found
Extending the scope of microscopic solvability: Combination of the Kruskal-Segur method with Zauderer decomposition
Successful applications of the Kruskal-Segur approach to interfacial pattern
formation have remained limited due to the necessity of an integral formulation
of the problem. This excludes nonlinear bulk equations, rendering convection
intractable. Combining the method with Zauderer's asymptotic decomposition
scheme, we are able to strongly extend its scope of applicability and solve
selection problems based on free boundary formulations in terms of partial
differential equations alone. To demonstrate the technique, we give the first
analytic solution of the problem of velocity selection for dendritic growth in
a forced potential flow.Comment: Submitted to Europhys. Letters, No figures, 5 page
Most Likely Separation of Intensity and Warping Effects in Image Registration
This paper introduces a class of mixed-effects models for joint modeling of
spatially correlated intensity variation and warping variation in 2D images.
Spatially correlated intensity variation and warp variation are modeled as
random effects, resulting in a nonlinear mixed-effects model that enables
simultaneous estimation of template and model parameters by optimization of the
likelihood function. We propose an algorithm for fitting the model which
alternates estimation of variance parameters and image registration. This
approach avoids the potential estimation bias in the template estimate that
arises when treating registration as a preprocessing step. We apply the model
to datasets of facial images and 2D brain magnetic resonance images to
illustrate the simultaneous estimation and prediction of intensity and warp
effects
Group-theoretic models of the inversion process in bacterial genomes
The variation in genome arrangements among bacterial taxa is largely due to
the process of inversion. Recent studies indicate that not all inversions are
equally probable, suggesting, for instance, that shorter inversions are more
frequent than longer, and those that move the terminus of replication are less
probable than those that do not. Current methods for establishing the inversion
distance between two bacterial genomes are unable to incorporate such
information. In this paper we suggest a group-theoretic framework that in
principle can take these constraints into account. In particular, we show that
by lifting the problem from circular permutations to the affine symmetric
group, the inversion distance can be found in polynomial time for a model in
which inversions are restricted to acting on two regions. This requires the
proof of new results in group theory, and suggests a vein of new combinatorial
problems concerning permutation groups on which group theorists will be needed
to collaborate with biologists. We apply the new method to inferring distances
and phylogenies for published Yersinia pestis data.Comment: 19 pages, 7 figures, in Press, Journal of Mathematical Biolog
A Global Approach for Solving Edge-Matching Puzzles
We consider apictorial edge-matching puzzles, in which the goal is to arrange
a collection of puzzle pieces with colored edges so that the colors match along
the edges of adjacent pieces. We devise an algebraic representation for this
problem and provide conditions under which it exactly characterizes a puzzle.
Using the new representation, we recast the combinatorial, discrete problem of
solving puzzles as a global, polynomial system of equations with continuous
variables. We further propose new algorithms for generating approximate
solutions to the continuous problem by solving a sequence of convex
relaxations
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