33,537 research outputs found
Applying spatial reasoning to topographical data with a grounded geographical ontology
Grounding an ontology upon geographical data has been pro-
posed as a method of handling the vagueness in the domain more effectively. In order to do this, we require methods of reasoning about the spatial relations between the regions within the data. This stage can be computationally expensive, as we require information on the location of
points in relation to each other. This paper illustrates how using knowledge about regions allows us to reduce the computation required in an efficient and easy to understand manner. Further, we show how this system can be implemented in co-ordination with segmented data to reason abou
Dihedral symmetries of multiple logarithms
This paper finds relationships between multiple logarithms with a dihedral
group action on the arguments. I generalize the combinatorics developed in
Gangl, Goncharov and Levin's R-deco polygon representation of multiple
logarithms to find these relations. By writing multiple logarithms as iterated
integrals, my arguments are valid for iterated integrals as over an arbitrary
field
Engineering Art Galleries
The Art Gallery Problem is one of the most well-known problems in
Computational Geometry, with a rich history in the study of algorithms,
complexity, and variants. Recently there has been a surge in experimental work
on the problem. In this survey, we describe this work, show the chronology of
developments, and compare current algorithms, including two unpublished
versions, in an exhaustive experiment. Furthermore, we show what core
algorithmic ingredients have led to recent successes
Identification of rolling resistance as a shape parameter in sheared granular media
Using contact dynamics simulations, we compare the effect of rolling
resistance at the contacts in granular systems composed of disks with the
effect of angularity in granular systems composed of regular polygonal
particles. In simple shear conditions, we consider four aspects of the
mechanical behavior of these systems in the steady state: shear strength, solid
fraction, force and fabric anisotropies, and probability distribution of
contact forces. Our main finding is that, based on the energy dissipation
associated with relative rotation between two particles in contact, the effect
of rolling resistance can explicitly be identified with that of the number of
sides in a regular polygonal particle. This finding supports the use of rolling
resistance as a shape parameter accounting for particle angularity and shows
unambiguously that one of the main influencing factors behind the mechanical
behavior of granular systems composed of noncircular particles is the partial
hindrance of rotations as a result of angular particle shape.Comment: Soumis a Physical Review E; Statistical, Nonlinear, and Soft Matter
Physics http://link.aps.org/doi/10.1103/PhysRevE.84.01130
- …