139 research outputs found
Robots, computer algebra and eight connected components
Answering connectivity queries in semi-algebraic sets is a long-standing and
challenging computational issue with applications in robotics, in particular
for the analysis of kinematic singularities. One task there is to compute the
number of connected components of the complementary of the singularities of the
kinematic map. Another task is to design a continuous path joining two given
points lying in the same connected component of such a set. In this paper, we
push forward the current capabilities of computer algebra to obtain
computer-aided proofs of the analysis of the kinematic singularities of various
robots used in industry. We first show how to combine mathematical reasoning
with easy symbolic computations to study the kinematic singularities of an
infinite family (depending on paramaters) modelled by the UR-series produced by
the company ``Universal Robots''. Next, we compute roadmaps (which are curves
used to answer connectivity queries) for this family of robots. We design an
algorithm for ``solving'' positive dimensional polynomial system depending on
parameters. The meaning of solving here means partitioning the parameter's
space into semi-algebraic components over which the number of connected
components of the semi-algebraic set defined by the input system is invariant.
Practical experiments confirm our computer-aided proof and show that such an
algorithm can already be used to analyze the kinematic singularities of the
UR-series family. The number of connected components of the complementary of
the kinematic singularities of generic robots in this family is
Proposal for new experimental schemes to realize the Avogadro constant
We propose two experimental schemes to determine and so to realize the
Avogadro constant at the level of 10 or better with a watt
balance experiment and a cold atom experiment measuring (where is
the Planck constant and the mass of the atom ). We give some
prospects about achievable uncertainties and we discuss the opportunity to test
the existence of possible unknown correction factors for the Josephson effect
and quantum Hall effect
Amenability of groups and -sets
This text surveys classical and recent results in the field of amenability of
groups, from a combinatorial standpoint. It has served as the support of
courses at the University of G\"ottingen and the \'Ecole Normale Sup\'erieure.
The goals of the text are (1) to be as self-contained as possible, so as to
serve as a good introduction for newcomers to the field; (2) to stress the use
of combinatorial tools, in collaboration with functional analysis, probability
etc., with discrete groups in focus; (3) to consider from the beginning the
more general notion of amenable actions; (4) to describe recent classes of
examples, and in particular groups acting on Cantor sets and topological full
groups
Background Light in Potential Sites for the ANTARES Undersea Neutrino Telescope
The ANTARES collaboration has performed a series of {\em in situ}
measurements to study the background light for a planned undersea neutrino
telescope. Such background can be caused by K decays or by biological
activity. We report on measurements at two sites in the Mediterranean Sea at
depths of 2400~m and 2700~m, respectively. Three photomultiplier tubes were
used to measure single counting rates and coincidence rates for pairs of tubes
at various distances. The background rate is seen to consist of three
components: a constant rate due to K decays, a continuum rate that
varies on a time scale of several hours simultaneously over distances up to at
least 40~m, and random bursts a few seconds long that are only correlated in
time over distances of the order of a meter. A trigger requiring coincidences
between nearby photomultiplier tubes should reduce the trigger rate for a
neutrino telescope to a manageable level with only a small loss in efficiency.Comment: 18 pages, 8 figures, accepted for publication in Astroparticle
Physic
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Locative Media and Sociability:Using Location-Based Social Networks to Coordinate Everyday Life
Foursquare was a mobile social networking application that enabled people to share location with friends in the form of âcheck-ins.â The visualization of surrounding known social connections as well as unknown others has the potential to impact how people coordinate social encounters and forge new social ties. While many studies have explored mobile phones and sociability, there is a lack of empirical research examining location-based social networkâs (LSBNs) from a sociability perspective. Drawing on a dataset of original qualitative research with a range of Foursquare users, the paper examines the application in the context of social coordination and sociability in three ways. First, the paper explores if Foursquare is used to organize certain social encounters, and if so, why. Second, the paper examines the visualization of surrounding social connections and whether this leads to âserendipitous encounters.â Lastly, the paper examines whether the use of Foursquare
can produce new social relationships
A baby steps/giant steps Monte Carlo algorithm for computing roadmaps in smooth compact real hypersurfaces
International audienceWe consider the problem of constructing roadmaps of real algebraic sets. The problem was introduced by Canny to answer connectivity questions and solve motion planning problems. Given polynomial equations with rational coefficients, of degree in variables, Canny's algorithm has a Monte Carlo cost of operations in ; a deterministic version runs in time . The next improvement was due to Basu, Pollack and Roy, with an algorithm of deterministic cost for the more general problem of computing roadmaps of semi-algebraic sets ( is the dimension of an associated object). We give a Monte Carlo algorithm of complexity for the problem of computing a roadmap of a compact hypersurface of degree in variables; we also have to assume that has a finite number of singular points. Even under these extra assumptions, no previous algorithm featured a cost better than
Sedimentation and Fouling of Optical Surfaces at the ANTARES Site
ANTARES is a project leading towards the construction and deployment of a
neutrino telescope in the deep Mediterranean Sea. The telescope will use an
array of photomultiplier tubes to detect the Cherenkov light emitted by muons
resulting from the interaction with matter of high energy neutrinos. In the
vicinity of the deployment site the ANTARES collaboration has performed a
series of in-situ measurements to study the change in light transmission
through glass surfaces during immersions of several months. The average loss of
light transmission is estimated to be only ~2% at the equator of a glass sphere
one year after deployment. It decreases with increasing zenith angle, and tends
to saturate with time. The transmission loss, therefore, is expected to remain
small for the several year lifetime of the ANTARES detector whose optical
modules are oriented downwards. The measurements were complemented by the
analysis of the ^{210}Pb activity profile in sediment cores and the study of
biofouling on glass plates. Despite a significant sedimentation rate at the
site, in the 0.02 - 0.05 cm.yr^{-1} range, the sediments adhere loosely to the
glass surfaces and can be washed off by water currents. Further, fouling by
deposits of light-absorbing particulates is only significant for surfaces
facing upwards.Comment: 18 pages, 14 figures (pdf), submitted to Astroparticle Physic
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