1,411 research outputs found
Nonpositively curved 2-complexes with isolated flats
We introduce the class of nonpositively curved 2-complexes with the Isolated
Flats Property. These 2-complexes are, in a sense, hyperbolic relative to their
flats. More precisely, we show that several important properties of
Gromov-hyperbolic spaces hold `relative to flats' in nonpositively curved
2-complexes with the Isolated Flats Property.
We introduce the Relatively Thin Triangle Property, which states roughly that
the fat part of a geodesic triangle lies near a single flat. We also introduce
the Relative Fellow Traveller Property, which states that pairs of
quasigeodesics with common endpoints fellow travel relative to flats, in a
suitable sense. The main result of this paper states that in the setting of
CAT(0) 2-complexes, the Isolated Flats Property is equivalent to the Relatively
Thin Triangle Property and is also equivalent to the Relative Fellow Traveller
Property.Comment: Published by Geometry and Topology at
http://www.maths.warwick.ac.uk/gt/GTVol8/paper5.abs.htm
AFLOW-CHULL: Cloud-Oriented Platform for Autonomous Phase Stability Analysis
A priori prediction of phase stability of materials is a challenging practice, requiring knowledge of all energetically-competing structures at formation conditions. Large materials repositories - housing properties of both experimental and hypothetical compounds - offer a path to prediction through the construction of informatics-based, ab-initio phase diagrams. However, limited access to relevant data and software infrastructure has rendered thermodynamic characterizations largely peripheral, despite their continued success in dictating synthesizability. Herein, a new module is presented for autonomous thermodynamic stability analysis implemented within the open-source, ab-initio framework AFLOW. Powered by the AFLUX Search-API, AFLOW-CHULL leverages data of more than 1.8 million compounds currently characterized in the AFLOW.org repository and can be employed locally from any UNIX-like computer. The module integrates a range of functionality: the identification of stable phases and equivalent structures, phase coexistence, measures for robust stability, and determination of decomposition reactions. As a proof-of-concept, thorough thermodynamic characterizations have been performed for more than 1,300 binary and ternary systems, enabling the identification of several candidate phases for synthesis based on their relative stability criterion - including 18 promising C15b-type structures and two half-Heuslers. In addition to a full report included herein, an interactive, online web application has been developed showcasing the results of the analysis, and is located at aflow.org/aflow-chull
Topomap: Topological Mapping and Navigation Based on Visual SLAM Maps
Visual robot navigation within large-scale, semi-structured environments
deals with various challenges such as computation intensive path planning
algorithms or insufficient knowledge about traversable spaces. Moreover, many
state-of-the-art navigation approaches only operate locally instead of gaining
a more conceptual understanding of the planning objective. This limits the
complexity of tasks a robot can accomplish and makes it harder to deal with
uncertainties that are present in the context of real-time robotics
applications. In this work, we present Topomap, a framework which simplifies
the navigation task by providing a map to the robot which is tailored for path
planning use. This novel approach transforms a sparse feature-based map from a
visual Simultaneous Localization And Mapping (SLAM) system into a
three-dimensional topological map. This is done in two steps. First, we extract
occupancy information directly from the noisy sparse point cloud. Then, we
create a set of convex free-space clusters, which are the vertices of the
topological map. We show that this representation improves the efficiency of
global planning, and we provide a complete derivation of our algorithm.
Planning experiments on real world datasets demonstrate that we achieve similar
performance as RRT* with significantly lower computation times and storage
requirements. Finally, we test our algorithm on a mobile robotic platform to
prove its advantages.Comment: 8 page
Cluster Expansion by Transfer Learning from Empirical Potentials
Cluster expansions provide effective representations of the potential energy
landscape of multicomponent crystalline solids. Notwithstanding major advances
in cluster expansion implementations, it remains computationally demanding to
construct these expansions for systems of low dimension or with a large number
of components, such as clusters, interfaces, and multimetallic alloys. We
address these challenges by employing transfer learning to accelerate the
computationally demanding step of generating configurational data from first
principles. The proposed approach exploits Bayesian inference to incorporate
prior knowledge from physics-based or machine-learning empirical potentials,
enabling one to identify the most informative configurations within a dataset.
The efficacy of the method is tested on face-centered cubic Pt:Ni binaries,
yielding a two- to three-fold reduction in the number of first-principles
calculations, while ensuring robust convergence of the energies with low
statistical fluctuations
Computational Approaches to Lattice Packing and Covering Problems
We describe algorithms which address two classical problems in lattice
geometry: the lattice covering and the simultaneous lattice packing-covering
problem. Theoretically our algorithms solve the two problems in any fixed
dimension d in the sense that they approximate optimal covering lattices and
optimal packing-covering lattices within any desired accuracy. Both algorithms
involve semidefinite programming and are based on Voronoi's reduction theory
for positive definite quadratic forms, which describes all possible Delone
triangulations of Z^d.
In practice, our implementations reproduce known results in dimensions d <= 5
and in particular solve the two problems in these dimensions. For d = 6 our
computations produce new best known covering as well as packing-covering
lattices, which are closely related to the lattice (E6)*. For d = 7, 8 our
approach leads to new best known covering lattices. Although we use numerical
methods, we made some effort to transform numerical evidences into rigorous
proofs. We provide rigorous error bounds and prove that some of the new
lattices are locally optimal.Comment: (v3) 40 pages, 5 figures, 6 tables, some corrections, accepted in
Discrete and Computational Geometry, see also
http://fma2.math.uni-magdeburg.de/~latgeo
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