23,907 research outputs found
Multiple Shape Registration using Constrained Optimal Control
Lagrangian particle formulations of the large deformation diffeomorphic
metric mapping algorithm (LDDMM) only allow for the study of a single shape. In
this paper, we introduce and discuss both a theoretical and practical setting
for the simultaneous study of multiple shapes that are either stitched to one
another or slide along a submanifold. The method is described within the
optimal control formalism, and optimality conditions are given, together with
the equations that are needed to implement augmented Lagrangian methods.
Experimental results are provided for stitched and sliding surfaces
Distribution on Warp Maps for Alignment of Open and Closed Curves
Alignment of curve data is an integral part of their statistical analysis,
and can be achieved using model- or optimization-based approaches. The
parameter space is usually the set of monotone, continuous warp maps of a
domain. Infinite-dimensional nature of the parameter space encourages sampling
based approaches, which require a distribution on the set of warp maps.
Moreover, the distribution should also enable sampling in the presence of
important landmark information on the curves which constrain the warp maps. For
alignment of closed and open curves in , possibly with
landmark information, we provide a constructive, point-process based definition
of a distribution on the set of warp maps of and the unit circle
that is (1) simple to sample from, and (2) possesses the
desiderata for decomposition of the alignment problem with landmark constraints
into multiple unconstrained ones. For warp maps on , the distribution is
related to the Dirichlet process. We demonstrate its utility by using it as a
prior distribution on warp maps in a Bayesian model for alignment of two
univariate curves, and as a proposal distribution in a stochastic algorithm
that optimizes a suitable alignment functional for higher-dimensional curves.
Several examples from simulated and real datasets are provided
Digital Alchemy for Materials Design: Colloids and Beyond
Starting with the early alchemists, a holy grail of science has been to make
desired materials by modifying the attributes of basic building blocks.
Building blocks that show promise for assembling new complex materials can be
synthesized at the nanoscale with attributes that would astonish the ancient
alchemists in their versatility. However, this versatility means that making
direct connection between building block attributes and bulk behavior is both
necessary for rationally engineering materials, and difficult because building
block attributes can be altered in many ways. Here we show how to exploit the
malleability of the valence of colloidal nanoparticle "elements" to directly
and quantitatively link building block attributes to bulk behavior through a
statistical thermodynamic framework we term "digital alchemy". We use this
framework to optimize building blocks for a given target structure, and to
determine which building block attributes are most important to control for
self assembly, through a set of novel thermodynamic response functions, moduli
and susceptibilities. We thereby establish direct links between the attributes
of colloidal building blocks and the bulk structures they form. Moreover, our
results give concrete solutions to the more general conceptual challenge of
optimizing emergent behaviors in nature, and can be applied to other types of
matter. As examples, we apply digital alchemy to systems of truncated
tetrahedra, rhombic dodecahedra, and isotropically interacting spheres that
self assemble diamond, FCC, and icosahedral quasicrystal structures,
respectively.Comment: 17 REVTeX pages, title fixed to match journal versio
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