1,317 research outputs found
\v{C}ech-Delaunay gradient flow and homology inference for self-maps
We call a continuous self-map that reveals itself through a discrete set of
point-value pairs a sampled dynamical system. Capturing the available
information with chain maps on Delaunay complexes, we use persistent homology
to quantify the evidence of recurrent behavior. We establish a sampling theorem
to recover the eigenspace of the endomorphism on homology induced by the
self-map. Using a combinatorial gradient flow arising from the discrete Morse
theory for \v{C}ech and Delaunay complexes, we construct a chain map to
transform the problem from the natural but expensive \v{C}ech complexes to the
computationally efficient Delaunay triangulations. The fast chain map algorithm
has applications beyond dynamical systems.Comment: 22 pages, 8 figure
Colored fused filament fabrication
Fused filament fabrication is the method of choice for printing 3D models at
low cost and is the de-facto standard for hobbyists, makers, and schools.
Unfortunately, filament printers cannot truly reproduce colored objects. The
best current techniques rely on a form of dithering exploiting occlusion, that
was only demonstrated for shades of two base colors and that behaves
differently depending on surface slope.
We explore a novel approach for 3D printing colored objects, capable of
creating controlled gradients of varying sharpness. Our technique exploits
off-the-shelves nozzles that are designed to mix multiple filaments in a small
melting chamber, obtaining intermediate colors once the mix is stabilized.
We apply this property to produce color gradients. We divide each input layer
into a set of strata, each having a different constant color. By locally
changing the thickness of the stratum, we change the perceived color at a given
location. By optimizing the choice of colors of each stratum, we further
improve quality and allow the use of different numbers of input filaments.
We demonstrate our results by building a functional color printer using low
cost, off-the-shelves components. Using our tool a user can paint a 3D model
and directly produce its physical counterpart, using any material and color
available for fused filament fabrication
Accelerated Parameter Estimation with DALE
We consider methods for improving the estimation of constraints on a
high-dimensional parameter space with a computationally expensive likelihood
function. In such cases Markov chain Monte Carlo (MCMC) can take a long time to
converge and concentrates on finding the maxima rather than the often-desired
confidence contours for accurate error estimation. We employ DALE (Direct
Analysis of Limits via the Exterior of ) for determining confidence
contours by minimizing a cost function parametrized to incentivize points in
parameter space which are both on the confidence limit and far from previously
sampled points. We compare DALE to the nested sampling algorithm
implemented in MultiNest on a toy likelihood function that is highly
non-Gaussian and non-linear in the mapping between parameter values and
. We find that in high-dimensional cases DALE finds the same
confidence limit as MultiNest using roughly an order of magnitude fewer
evaluations of the likelihood function. DALE is open-source and available
at https://github.com/danielsf/Dalex.git
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