748 research outputs found
Further Results on Arithmetic Filters for Geometric Predicates
An efficient technique to solve precision problems consists in using exact
computations. For geometric predicates, using systematically expensive exact
computations can be avoided by the use of filters. The predicate is first
evaluated using rounding computations, and an error estimation gives a
certificate of the validity of the result. In this note, we studies the
statistical efficiency of filters for cosphericity predicate with an assumption
of regular distribution of the points. We prove that the expected value of the
polynomial corresponding to the in sphere test is greater than epsilon with
probability O(epsilon log 1/epsilon) improving the results of a previous paper
by the same authors.Comment: 7 pages 2 figures presented at the 15th European Workshop Comput.
Geom., 113--116, 1999 improve previous results (in other paper
A Probabilistic Analysis of the Power of Arithmetic Filters
The assumption of real-number arithmetic, which is at the basis of
conventional geometric algorithms, has been seriously challenged in recent
years, since digital computers do not exhibit such capability.
A geometric predicate usually consists of evaluating the sign of some
algebraic expression. In most cases, rounded computations yield a reliable
result, but sometimes rounded arithmetic introduces errors which may invalidate
the algorithms. The rounded arithmetic may produce an incorrect result only if
the exact absolute value of the algebraic expression is smaller than some
(small) varepsilon, which represents the largest error that may arise in the
evaluation of the expression. The threshold varepsilon depends on the structure
of the expression and on the adopted computer arithmetic, assuming that the
input operands are error-free.
A pair (arithmetic engine,threshold) is an "arithmetic filter". In this paper
we develop a general technique for assessing the efficacy of an arithmetic
filter. The analysis consists of evaluating both the threshold and the
probability of failure of the filter.
To exemplify the approach, under the assumption that the input points be
chosen randomly in a unit ball or unit cube with uniform density, we analyze
the two important predicates "which-side" and "insphere". We show that the
probability that the absolute values of the corresponding determinants be no
larger than some positive value V, with emphasis on small V, is Theta(V) for
the which-side predicate, while for the insphere predicate it is Theta(V^(2/3))
in dimension 1, O(sqrt(V)) in dimension 2, and O(sqrt(V) ln(1/V)) in higher
dimensions. Constants are small, and are given in the paper.Comment: 22 pages 7 figures Results for in sphere test inproved in
cs.CG/990702
Strain and correlation of self-organized Ge_(1-x)Mn_x nanocolumns embedded in Ge (001)
We report on the structural properties of Ge_(1-x)Mn_x layers grown by
molecular beam epitaxy. In these layers, nanocolumns with a high Mn content are
embedded in an almost-pure Ge matrix. We have used grazing-incidence X-ray
scattering, atomic force and transmission electron microscopy to study the
structural properties of the columns. We demonstrate how the elastic
deformation of the matrix (as calculated using atomistic simulations) around
the columns, as well as the average inter-column distance can account for the
shape of the diffusion around Bragg peaks.Comment: 9 pages, 7 figure
Structure and magnetism of self-organized Ge(1-x)Mn(x) nano-columns
We report on the structural and magnetic properties of thin Ge(1-x)Mn(x)films
grown by molecular beam epitaxy (MBE) on Ge(001) substrates at temperatures
(Tg) ranging from 80deg C to 200deg C, with average Mn contents between 1 % and
11 %. Their crystalline structure, morphology and composition have been
investigated by transmission electron microscopy (TEM), electron energy loss
spectroscopy and x-ray diffraction. In the whole range of growth temperatures
and Mn concentrations, we observed the formation of manganese rich
nanostructures embedded in a nearly pure germanium matrix. Growth temperature
mostly determines the structural properties of Mn-rich nanostructures. For low
growth temperatures (below 120deg C), we evidenced a two-dimensional spinodal
decomposition resulting in the formation of vertical one-dimensional
nanostructures (nanocolumns). Moreover we show in this paper the influence of
growth parameters (Tg and Mn content) on this decomposition i.e. on nanocolumns
size and density. For temperatures higher than 180deg C, we observed the
formation of Ge3Mn5 clusters. For intermediate growth temperatures nanocolumns
and nanoclusters coexist. Combining high resolution TEM and superconducting
quantum interference device magnetometry, we could evidence at least four
different magnetic phases in Ge(1-x)Mn(x) films: (i) paramagnetic diluted Mn
atoms in the germanium matrix, (ii) superparamagnetic and ferromagnetic low-Tc
nanocolumns (120 K 400 K) and
(iv) Ge3Mn5 clusters.Comment: 10 pages 2 colonnes revTex formatte
Evaluating Signs of Determinants Using Single-Precision Arithmetic
We propose a method of evaluating signs of 2×2 and 3×3 determinants with b-bit integer entries using only b and (b + 1)-bit arithmetic, respectively. This algorithm has numerous applications in geometric computation and provides a general and practical approach to robustness. The algorithm has been implemented and compared with other exact computation methods
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
Load-Balancing for Parallel Delaunay Triangulations
Computing the Delaunay triangulation (DT) of a given point set in
is one of the fundamental operations in computational geometry.
Recently, Funke and Sanders (2017) presented a divide-and-conquer DT algorithm
that merges two partial triangulations by re-triangulating a small subset of
their vertices - the border vertices - and combining the three triangulations
efficiently via parallel hash table lookups. The input point division should
therefore yield roughly equal-sized partitions for good load-balancing and also
result in a small number of border vertices for fast merging. In this paper, we
present a novel divide-step based on partitioning the triangulation of a small
sample of the input points. In experiments on synthetic and real-world data
sets, we achieve nearly perfectly balanced partitions and small border
triangulations. This almost cuts running time in half compared to
non-data-sensitive division schemes on inputs exhibiting an exploitable
underlying structure.Comment: Short version submitted to EuroPar 201
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