78,478 research outputs found
SPEDEN: Reconstructing single particles from their diffraction patterns
Speden is a computer program that reconstructs the electron density of single
particles from their x-ray diffraction patterns, using a single-particle
adaptation of the Holographic Method in crystallography. (Szoke, A., Szoke, H.,
and Somoza, J.R., 1997. Acta Cryst. A53, 291-313.) The method, like its parent,
is unique that it does not rely on ``back'' transformation from the diffraction
pattern into real space and on interpolation within measured data. It is
designed to deal successfully with sparse, irregular, incomplete and noisy
data. It is also designed to use prior information for ensuring sensible
results and for reliable convergence. This article describes the theoretical
basis for the reconstruction algorithm, its implementation and quantitative
results of tests on synthetic and experimentally obtained data. The program
could be used for determining the structure of radiation tolerant samples and,
eventually, of large biological molecular structures without the need for
crystallization.Comment: 12 pages, 10 figure
Trifocal Relative Pose from Lines at Points and its Efficient Solution
We present a new minimal problem for relative pose estimation mixing point
features with lines incident at points observed in three views and its
efficient homotopy continuation solver. We demonstrate the generality of the
approach by analyzing and solving an additional problem with mixed point and
line correspondences in three views. The minimal problems include
correspondences of (i) three points and one line and (ii) three points and two
lines through two of the points which is reported and analyzed here for the
first time. These are difficult to solve, as they have 216 and - as shown here
- 312 solutions, but cover important practical situations when line and point
features appear together, e.g., in urban scenes or when observing curves. We
demonstrate that even such difficult problems can be solved robustly using a
suitable homotopy continuation technique and we provide an implementation
optimized for minimal problems that can be integrated into engineering
applications. Our simulated and real experiments demonstrate our solvers in the
camera geometry computation task in structure from motion. We show that new
solvers allow for reconstructing challenging scenes where the standard two-view
initialization of structure from motion fails.Comment: This material is based upon work supported by the National Science
Foundation under Grant No. DMS-1439786 while most authors were in residence
at Brown University's Institute for Computational and Experimental Research
in Mathematics -- ICERM, in Providence, R
Boolean delay equations on networks: An application to economic damage propagation
We introduce economic models based on Boolean Delay Equations: this formalism
makes easier to take into account the complexity of the interactions between
firms and is particularly appropriate for studying the propagation of an
initial damage due to a catastrophe. Here we concentrate on simple cases, which
allow to understand the effects of multiple concurrent production paths as well
as the presence of stochasticity in the path time lengths or in the network
structure.
In absence of flexibility, the shortening of production of a single firm in
an isolated network with multiple connections usually ends up by attaining a
finite fraction of the firms or the whole economy, whereas the interactions
with the outside allow a partial recovering of the activity, giving rise to
periodic solutions with waves of damage which propagate across the structure.
The damage propagation speed is strongly dependent upon the topology. The
existence of multiple concurrent production paths does not necessarily imply a
slowing down of the propagation, which can be as fast as the shortest path.Comment: Latex, 52 pages with 22 eps figure
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