827 research outputs found
About the Algebraic Solutions of Smallest Enclosing Cylinders Problems
Given n points in Euclidean space E^d, we propose an algebraic algorithm to
compute the best fitting (d-1)-cylinder. This algorithm computes the unknown
direction of the axis of the cylinder. The location of the axis and the radius
of the cylinder are deduced analytically from this direction. Special attention
is paid to the case d=3 when n=4 and n=5. For the former, the minimal radius
enclosing cylinder is computed algebrically from constrained minimization of a
quartic form of the unknown direction of the axis. For the latter, an
analytical condition of existence of the circumscribed cylinder is given, and
the algorithm reduces to find the zeroes of an one unknown polynomial of degree
at most 6. In both cases, the other parameters of the cylinder are deduced
analytically. The minimal radius enclosing cylinder is computed analytically
for the regular tetrahedron and for a trigonal bipyramids family with a
symmetry axis of order 3.Comment: 13 pages, 0 figure; revised version submitted to publication
(previous version is a copy of the original one of 2010
Improved Implementation of Point Location in General Two-Dimensional Subdivisions
We present a major revamp of the point-location data structure for general
two-dimensional subdivisions via randomized incremental construction,
implemented in CGAL, the Computational Geometry Algorithms Library. We can now
guarantee that the constructed directed acyclic graph G is of linear size and
provides logarithmic query time. Via the construction of the Voronoi diagram
for a given point set S of size n, this also enables nearest-neighbor queries
in guaranteed O(log n) time. Another major innovation is the support of general
unbounded subdivisions as well as subdivisions of two-dimensional parametric
surfaces such as spheres, tori, cylinders. The implementation is exact,
complete, and general, i.e., it can also handle non-linear subdivisions. Like
the previous version, the data structure supports modifications of the
subdivision, such as insertions and deletions of edges, after the initial
preprocessing. A major challenge is to retain the expected O(n log n)
preprocessing time while providing the above (deterministic) space and
query-time guarantees. We describe an efficient preprocessing algorithm, which
explicitly verifies the length L of the longest query path in O(n log n) time.
However, instead of using L, our implementation is based on the depth D of G.
Although we prove that the worst case ratio of D and L is Theta(n/log n), we
conjecture, based on our experimental results, that this solution achieves
expected O(n log n) preprocessing time.Comment: 21 page
Exchange bias in GeMn nanocolumns: the role of surface oxidation
We report on the exchange biasing of self-assembled ferromagnetic GeMn
nanocolumns by GeMn-oxide caps. The x-ray absorption spectroscopy analysis of
this surface oxide shows a multiplet fine structure that is typical of the Mn2+
valence state in MnO. A magnetization hysteresis shift |HE|~100 Oe and a
coercivity enhancement of about 70 Oe have been obtained upon cooling (300-5 K)
in a magnetic field as low as 0.25 T. This exchange bias is attributed to the
interface coupling between the ferromagnetic nanocolumns and the
antiferromagnetic MnO-like caps. The effect enhancement is achieved by
depositing a MnO layer on the GeMn nanocolumns.Comment: 7 pages, 5 figure
Reinventing residual reserves in the sea: Are we favouring ease of establishment over need for protection?
© 2014 The Authors. As systems of marine protected areas (MPAs) expand globally, there is a risk that new MPAs will be biased toward places that are remote or unpromising for extractive activities, and hence follow the trend of terrestrial protected areas in being 'residual' to commercial uses. Such locations typically provide little protection to the species and ecosystems that are most exposed to threatening processes. There are strong political motivations to establish residual reserves that minimize costs and conflicts with users of natural resources. These motivations will likely remain in place as long as success continues to be measured in terms of area (km2) protected. The global pattern of MPAs was reviewed and appears to be residual, supported by a rapid growth of large, remote MPAs. The extent to which MPAs in Australia are residual nationally and also regionally within the Great Barrier Reef (GBR) Marine Park was also examined. Nationally, the recently announced Australian Commonwealth marine reserves were found to be strongly residual, making almost no difference to 'business as usual' for most ocean uses. Underlying this result was the imperative to minimize costs, but without the spatial constraints of explicit quantitative objectives for representing bioregions or the range of ecological features in highly protected zones. In contrast, the 2004 rezoning of the GBR was exemplary, and the potential for residual protection was limited by applying a systematic set of planning principles, such as representing a minimum percentage of finely subdivided bioregions. Nonetheless, even at this scale, protection was uneven between bioregions. Within-bioregion heterogeneity might have led to no-take zones being established in areas unsuitable for trawling with a risk that species assemblages differ between areas protected and areas left available for trawling. A simple four-step framework of questions for planners and policy makers is proposed to help reverse the emerging residual tendency of MPAs and maximize their effectiveness for conservation. This involves checks on the least-cost approach to establishing MPAs in order to avoid perverse outcomes
Presentations: from Kac-Moody groups to profinite and back
We go back and forth between, on the one hand, presentations of arithmetic
and Kac-Moody groups and, on the other hand, presentations of profinite groups,
deducing along the way new results on both
Simultaneous Petri Net Synthesis
Petri net synthesis deals with the problem whether, given a labelled transition system TS, one can find a Petri net N with an initial marking M0 such that the reachability graph of (N. M0) is isomorphic to TS. This may be preceded by a pre-synthesis phase that will quickly reject ill-formed transition systems (and give structural reasons for the failure) and otherwise build data structures needed by the proper synthesis. The last phase proceeds by solving systems of linear inequalities, and may still fail but for less transparent reasons. In this paper, we consider an extended problem. A finite set of transition systems {TS1, ...,TSm} shall be called simultaneously Petri net solvable if there is a single Petri net N with several initial markings {M01,...,M0m}, such that for every i = 1,...,m, the reachability graph of (N, M0i) is isomorphic to TSi. The focus will be on choice-free nets, that is, nets without structural choices, and we explore how previously published efficient algorithms for the pre-synthesis and proper synthesis of bounded and choice-free Petri nets can be generalised for the simultaneous pre-synthesis and synthesis of such multi-marked nets. At the same time, the choice-free pre-synthesis of a single transition system shall be strengthened by introducing new structural checks
Hiérarchisation des insecticides potentiellement utilisables en lutte anti-vectorielle (LAV)
P19-02. High protection of female macaques from repeated intravaginal challenges with SHIV-162P3 upon mucosal vaccination with Gp41 subunits-virosomes
- …