7,058 research outputs found
Packing ellipsoids with overlap
The problem of packing ellipsoids of different sizes and shapes into an
ellipsoidal container so as to minimize a measure of overlap between ellipsoids
is considered. A bilevel optimization formulation is given, together with an
algorithm for the general case and a simpler algorithm for the special case in
which all ellipsoids are in fact spheres. Convergence results are proved and
computational experience is described and illustrated. The motivating
application - chromosome organization in the human cell nucleus - is discussed
briefly, and some illustrative results are presented
Regularized Newton Methods for X-ray Phase Contrast and General Imaging Problems
Like many other advanced imaging methods, x-ray phase contrast imaging and
tomography require mathematical inversion of the observed data to obtain
real-space information. While an accurate forward model describing the
generally nonlinear image formation from a given object to the observations is
often available, explicit inversion formulas are typically not known. Moreover,
the measured data might be insufficient for stable image reconstruction, in
which case it has to be complemented by suitable a priori information. In this
work, regularized Newton methods are presented as a general framework for the
solution of such ill-posed nonlinear imaging problems. For a proof of
principle, the approach is applied to x-ray phase contrast imaging in the
near-field propagation regime. Simultaneous recovery of the phase- and
amplitude from a single near-field diffraction pattern without homogeneity
constraints is demonstrated for the first time. The presented methods further
permit all-at-once phase contrast tomography, i.e. simultaneous phase retrieval
and tomographic inversion. We demonstrate the potential of this approach by
three-dimensional imaging of a colloidal crystal at 95 nm isotropic resolution.Comment: (C)2016 Optical Society of America. One print or electronic copy may
be made for personal use only. Systematic reproduction and distribution,
duplication of any material in this paper for a fee or for commercial
purposes, or modifications of the content of this paper are prohibite
SEM image analysis in permeable recycled concretes with silica fume. A quantitative comparison of porosity and the ITZ
Recycled aggregates (RA) from construction and demolition can be used in permeable concretes (PC), improving the environment. PCs have a significant porous network, their cement paste and the interaction between the paste and the RA establishing their strength. Therefore, it is important to evaluate the porosity in the interfacial transition zones. The porosity of the cement paste, the aggregate and the interfacial transitional zones (ITZ) of a PC with recycled coarse aggregates (RCA) and silica fume (SF) is measured by means of image analysis–scanning electron microscope (IA)-(SEM) and by mapping the chemical elements with an SEM-EDS (energy dispersive spectrometer) detector microanalysis linked to the SEM and, as a contrast, the mercury intrusion porosimetry technique (MIP). In the IA process, a “mask” was created for the aggregate and another for the paste, which determined the porosity percentage (for the anhydrous material and the products of hydration). The results showed that using SF caused a reduction (32%) in the cement paste porosity in comparison with the PC with RA. The use of RA in the PC led to a significant increase (190%) in the porosity at different thicknesses of ITZ compared with the reference PC. Finally, the MIP study shows that the use of SF caused a decrease in the micropores, mesopores and macroporesPeer ReviewedPostprint (published version
A PTAS for the minimum dominating set problem in unit disk graphs
We present a polynomial-time approximation scheme (PTAS) for the minimum dominating set problem in unit disk graphs. In contrast to previously known approximation schemes for the minimum dominating set problem on unit disk graphs, our approach does not assume a geometric representation of the vertices (specifying the positions of the disks in the plane) to be given as part of the input. \u
Beyond developable: computational design and fabrication with auxetic materials
We present a computational method for interactive 3D design and rationalization of surfaces via auxetic materials, i.e., flat flexible material that can stretch uniformly up to a certain extent. A key motivation for studying such material is that one can approximate doubly-curved surfaces (such as the sphere) using only flat pieces, making it attractive for fabrication. We physically realize surfaces by introducing cuts into approximately inextensible material such as sheet metal, plastic, or leather. The cutting pattern is modeled as a regular triangular linkage that yields hexagonal openings of spatially-varying radius when stretched. In the same way that isometry is fundamental to modeling developable surfaces, we leverage conformal geometry to understand auxetic design. In particular, we compute a global conformal map with bounded scale factor to initialize an otherwise intractable non-linear optimization. We demonstrate that this global approach can handle non-trivial topology and non-local dependencies inherent in auxetic material. Design studies and physical prototypes are used to illustrate a wide range of possible applications
Building Clusters with Lower-Bounded Sizes
Classical clustering problems search for a partition of objects into a fixed number of clusters. In many scenarios however the number of clusters is not known or necessarily fixed. Further, clusters are sometimes only considered to be of significance if they have a certain size. We discuss clustering into sets of minimum cardinality k without a fixed number of sets and present a general model for these types of problems. This general framework allows the comparison of different measures to assess the quality of a clustering. We specifically consider nine quality-measures and classify the complexity of the resulting problems with respect to k. Further, we derive some polynomial-time solvable cases for k = 2 with connections to matching-type problems which, among other graph problems, then are used to compute approximations for larger values of k
Criticality for the Gehring link problem
In 1974, Gehring posed the problem of minimizing the length of two linked
curves separated by unit distance. This constraint can be viewed as a measure
of thickness for links, and the ratio of length over thickness as the
ropelength. In this paper we refine Gehring's problem to deal with links in a
fixed link-homotopy class: we prove ropelength minimizers exist and introduce a
theory of ropelength criticality.
Our balance criterion is a set of necessary and sufficient conditions for
criticality, based on a strengthened, infinite-dimensional version of the
Kuhn--Tucker theorem. We use this to prove that every critical link is C^1 with
finite total curvature. The balance criterion also allows us to explicitly
describe critical configurations (and presumed minimizers) for many links
including the Borromean rings. We also exhibit a surprising critical
configuration for two clasped ropes: near their tips the curvature is unbounded
and a small gap appears between the two components. These examples reveal the
depth and richness hidden in Gehring's problem and our natural extension.Comment: This is the version published by Geometry & Topology on 14 November
200
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