20,624 research outputs found
Optimization of supply diversity for the self-assembly of simple objects in two and three dimensions
The field of algorithmic self-assembly is concerned with the design and
analysis of self-assembly systems from a computational perspective, that is,
from the perspective of mathematical problems whose study may give insight into
the natural processes through which elementary objects self-assemble into more
complex ones. One of the main problems of algorithmic self-assembly is the
minimum tile set problem (MTSP), which asks for a collection of types of
elementary objects (called tiles) to be found for the self-assembly of an
object having a pre-established shape. Such a collection is to be as concise as
possible, thus minimizing supply diversity, while satisfying a set of stringent
constraints having to do with the termination and other properties of the
self-assembly process from its tile types. We present a study of what we think
is the first practical approach to MTSP. Our study starts with the introduction
of an evolutionary heuristic to tackle MTSP and includes results from extensive
experimentation with the heuristic on the self-assembly of simple objects in
two and three dimensions. The heuristic we introduce combines classic elements
from the field of evolutionary computation with a problem-specific variant of
Pareto dominance into a multi-objective approach to MTSP.Comment: Minor typos correcte
Land cover mapping at very high resolution with rotation equivariant CNNs: towards small yet accurate models
In remote sensing images, the absolute orientation of objects is arbitrary.
Depending on an object's orientation and on a sensor's flight path, objects of
the same semantic class can be observed in different orientations in the same
image. Equivariance to rotation, in this context understood as responding with
a rotated semantic label map when subject to a rotation of the input image, is
therefore a very desirable feature, in particular for high capacity models,
such as Convolutional Neural Networks (CNNs). If rotation equivariance is
encoded in the network, the model is confronted with a simpler task and does
not need to learn specific (and redundant) weights to address rotated versions
of the same object class. In this work we propose a CNN architecture called
Rotation Equivariant Vector Field Network (RotEqNet) to encode rotation
equivariance in the network itself. By using rotating convolutions as building
blocks and passing only the the values corresponding to the maximally
activating orientation throughout the network in the form of orientation
encoding vector fields, RotEqNet treats rotated versions of the same object
with the same filter bank and therefore achieves state-of-the-art performances
even when using very small architectures trained from scratch. We test RotEqNet
in two challenging sub-decimeter resolution semantic labeling problems, and
show that we can perform better than a standard CNN while requiring one order
of magnitude less parameters
Enumeration of octagonal tilings
Random tilings are interesting as idealizations of atomistic models of
quasicrystals and for their connection to problems in combinatorics and
algorithms. Of particular interest is the tiling entropy density, which
measures the relation of the number of distinct tilings to the number of
constituent tiles. Tilings by squares and 45 degree rhombi receive special
attention as presumably the simplest model that has not yet been solved exactly
in the thermodynamic limit. However, an exact enumeration formula can be
evaluated for tilings in finite regions with fixed boundaries. We implement
this algorithm in an efficient manner, enabling the investigation of larger
regions of parameter space than previously were possible. Our new results
appear to yield monotone increasing and decreasing lower and upper bounds on
the fixed boundary entropy density that converge toward S = 0.36021(3)
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