6,385 research outputs found
Betti number signatures of homogeneous Poisson point processes
The Betti numbers are fundamental topological quantities that describe the
k-dimensional connectivity of an object: B_0 is the number of connected
components and B_k effectively counts the number of k-dimensional holes.
Although they are appealing natural descriptors of shape, the higher-order
Betti numbers are more difficult to compute than other measures and so have not
previously been studied per se in the context of stochastic geometry or
statistical physics.
As a mathematically tractable model, we consider the expected Betti numbers
per unit volume of Poisson-centred spheres with radius alpha. We present
results from simulations and derive analytic expressions for the low intensity,
small radius limits of Betti numbers in one, two, and three dimensions. The
algorithms and analysis depend on alpha-shapes, a construction from
computational geometry that deserves to be more widely known in the physics
community.Comment: Submitted to PRE. 11 pages, 10 figure
Actual Confusion in Trademark Infringement Litigation: Restraining Subjectivity Through A Factor-Based Approach to Valuing Evidence
Movement of Franklin\u27s Ground Squirrel Into Northeastern Minnesota
Specimens of Franklin\u27s ground squirrel have been obtained in several localities in St. Louis County, Minnesota. The movement of this prairie-dwelling rodent into the montane coniferous forest region of northeastern Minnesota may be related to recent man-made changes in the habitat
Tactile Interactions with a Humanoid Robot : Novel Play Scenario Implementations with Children with Autism
Acknowledgments: This work has been partially supported by the European Commission under contract number FP7-231500-ROBOSKIN. Open Access: This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.The work presented in this paper was part of our investigation in the ROBOSKIN project. The project has developed new robot capabilities based on the tactile feedback provided by novel robotic skin, with the aim to provide cognitive mechanisms to improve human-robot interaction capabilities. This article presents two novel tactile play scenarios developed for robot-assisted play for children with autism. The play scenarios were developed against specific educational and therapeutic objectives that were discussed with teachers and therapists. These objectives were classified with reference to the ICF-CY, the International Classification of Functioning â version for Children and Youth. The article presents a detailed description of the play scenarios, and case study examples of their implementation in HRI studies with children with autism and the humanoid robot KASPAR.Peer reviewedFinal Published versio
Remote Detection of Saline Intrusion in a Coastal Aquifer Using Borehole Measurements of Self-Potential
Funded by NERC CASE studentship . Grant Number: NE/I018417/1Peer reviewedPublisher PD
Pulsed pumping of a Bose-Einstein condensate
In this work, we examine a system for coherent transfer of atoms into a
Bose-Einstein condensate. We utilize two spatially separate Bose-Einstein
condensates in different hyperfine ground states held in the same dc magnetic
trap. By means of a pulsed transfer of atoms, we are able to show a clear
resonance in the timing of the transfer, both in temperature and number, from
which we draw conclusions about the underlying physical process. The results
are discussed in the context of the recently demonstrated pumped atom laser.Comment: 5 pages, 5 figures, published in Physical Review
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