531 research outputs found
A review of Monte Carlo simulations of polymers with PERM
In this review, we describe applications of the pruned-enriched Rosenbluth
method (PERM), a sequential Monte Carlo algorithm with resampling, to various
problems in polymer physics. PERM produces samples according to any given
prescribed weight distribution, by growing configurations step by step with
controlled bias, and correcting "bad" configurations by "population control".
The latter is implemented, in contrast to other population based algorithms
like e.g. genetic algorithms, by depth-first recursion which avoids storing all
members of the population at the same time in computer memory. The problems we
discuss all concern single polymers (with one exception), but under various
conditions: Homopolymers in good solvents and at the point, semi-stiff
polymers, polymers in confining geometries, stretched polymers undergoing a
forced globule-linear transition, star polymers, bottle brushes, lattice
animals as a model for randomly branched polymers, DNA melting, and finally --
as the only system at low temperatures, lattice heteropolymers as simple models
for protein folding. PERM is for some of these problems the method of choice,
but it can also fail. We discuss how to recognize when a result is reliable,
and we discuss also some types of bias that can be crucial in guiding the
growth into the right directions.Comment: 29 pages, 26 figures, to be published in J. Stat. Phys. (2011
A graph-spectral approach to shape-from-shading
In this paper, we explore how graph-spectral methods can be used to develop a new shape-from-shading algorithm. We characterize the field of surface normals using a weight matrix whose elements are computed from the sectional curvature between different image locations and penalize large changes in surface normal direction. Modeling the blocks of the weight matrix as distinct surface patches, we use a graph seriation method to find a surface integration path that maximizes the sum of curvature-dependent weights and that can be used for the purposes of height reconstruction. To smooth the reconstructed surface, we fit quadrics to the height data for each patch. The smoothed surface normal directions are updated ensuring compliance with Lambert's law. The processes of height recovery and surface normal adjustment are interleaved and iterated until a stable surface is obtained. We provide results on synthetic and real-world imagery
Search-based 3D Planning and Trajectory Optimization for Safe Micro Aerial Vehicle Flight Under Sensor Visibility Constraints
Safe navigation of Micro Aerial Vehicles (MAVs) requires not only
obstacle-free flight paths according to a static environment map, but also the
perception of and reaction to previously unknown and dynamic objects. This
implies that the onboard sensors cover the current flight direction. Due to the
limited payload of MAVs, full sensor coverage of the environment has to be
traded off with flight time. Thus, often only a part of the environment is
covered.
We present a combined allocentric complete planning and trajectory
optimization approach taking these sensor visibility constraints into account.
The optimized trajectories yield flight paths within the apex angle of a
Velodyne Puck Lite 3D laser scanner enabling low-level collision avoidance to
perceive obstacles in the flight direction. Furthermore, the optimized
trajectories take the flight dynamics into account and contain the velocities
and accelerations along the path.
We evaluate our approach with a DJI Matrice 600 MAV and in simulation
employing hardware-in-the-loop.Comment: In Proceedings of IEEE International Conference on Robotics and
Automation (ICRA), Montreal, Canada, May 201
On the Approximability of the Traveling Salesman Problem with Line Neighborhoods
We study the variant of the Euclidean Traveling Salesman problem where
instead of a set of points, we are given a set of lines as input, and the goal
is to find the shortest tour that visits each line. The best known upper and
lower bounds for the problem in , with , are
-hardness and an -approximation algorithm which is
based on a reduction to the group Steiner tree problem.
We show that TSP with lines in is APX-hard for any .
More generally, this implies that TSP with -dimensional flats does not admit
a PTAS for any unless , which gives a
complete classification of the approximability of these problems, as there are
known PTASes for (i.e., points) and (hyperplanes). We are able to
give a stronger inapproximability factor for by showing that TSP
with lines does not admit a -approximation in dimensions
under the unique games conjecture. On the positive side, we leverage recent
results on restricted variants of the group Steiner tree problem in order to
give an -approximation algorithm for the problem, albeit with a
running time of
On the Approximability of the Traveling Salesman Problem with Line Neighborhoods
We study the variant of the Euclidean Traveling Salesman problem where instead of a set of points, we are given a set of lines as input, and the goal is to find the shortest tour that visits each line. The best known upper and lower bounds for the problem in , with , are -hardness and an -approximation algorithm which is based on a reduction to the group Steiner tree problem. We show that TSP with lines in is APX-hard for any . More generally, this implies that TSP with -dimensional flats does not admit a PTAS for any unless , which gives a complete classification of the approximability of these problems, as there are known PTASes for (i.e., points) and (hyperplanes). We are able to give a stronger inapproximability factor for by showing that TSP with lines does not admit a -approximation in dimensions under the unique games conjecture. On the positive side, we leverage recent results on restricted variants of the group Steiner tree problem in order to give an -approximation algorithm for the problem, albeit with a running time of
Second-order cone programming formulations for a class of problems in structural optimization
This paper provides efficient and easy to
implement formulations for two problems in structural
optimization as second-order cone programming
(SOCP) problems based on the minimum compliance
method and derived using the principle of complementary
energy. In truss optimization both single and
multiple loads (where we optimize the worst-case compliance)
are considered. By using a heuristic which is
based on the SOCP duality we can consider a simple
ground structure and add only the members which
improve the compliance of the structure. It is also
shown that thickness optimization is a problem similar
to truss optimization. Examples are given to illustrate
the method developed in this pape
3D Trajectory Design for UAV-Assisted Oblique Image Acquisition
In this correspondence, we consider a new unmanned aerial vehicle
(UAV)-assisted oblique image acquisition system where a UAV is dispatched to
take images of multiple ground targets (GTs). To study the three-dimensional
(3D) UAV trajectory design for image acquisition, we first propose a novel
UAV-assisted oblique photography model, which characterizes the image
resolution with respect to the UAV's 3D image-taking location. Then, we
formulate a 3D UAV trajectory optimization problem to minimize the UAV's
traveling distance subject to the image resolution constraints. The formulated
problem is shown to be equivalent to a modified 3D traveling salesman problem
with neighbourhoods, which is NP-hard in general. To tackle this difficult
problem, we propose an iterative algorithm to obtain a high-quality suboptimal
solution efficiently, by alternately optimizing the UAV's 3D image-taking
waypoints and its visiting order for the GTs. Numerical results show that the
proposed algorithm significantly reduces the UAV's traveling distance as
compared to various benchmark schemes, while meeting the image resolution
requirement
Creating large-scale city models from 3D-point clouds: a robust approach with hybrid representation
International audienceWe present a novel and robust method for modeling cities from 3D-point data. Our algorithm pro- vides a more complete description than existing ap- proaches by reconstructing simultaneously buildings, trees and topologically complex grounds. A major con- tribution of our work is the original way of model- ing buildings which guarantees a high generalization level while having semantized and compact represen- tations. Geometric 3D-primitives such as planes, cylin- ders, spheres or cones describe regular roof sections, and are combined with mesh-patches that represent irregu- lar roof components. The various urban components in- teract through a non-convex energy minimization prob- lem in which they are propagated under arrangement constraints over a planimetric map. Our approach is ex- perimentally validated on complex buildings and large urban scenes of millions of points, and is compared to state-of-the-art methods
Search for the lepton-family-number nonconserving decay \mu -> e + \gamma
The MEGA experiment, which searched for the muon- and electron-number
violating decay \mu -> e + \gamma, is described. The spectrometer system, the
calibrations, the data taking procedures, the data analysis, and the
sensitivity of the experiment are discussed. The most stringent upper limit on
the branching ratio of \mu -> e + \gamma) < 1.2 x 10^{-11} was obtained
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