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A tutorial on EMPA: A theory of concurrent processes with nondeterminism, priorities, probabilities and time
 Theoretical Computer Science
, 1998
"... In this tutorial we give an overview of the process algebra EMPA, a calculus devised in order to model and analyze features of realworld concurrent systems such as nondeterminism, priorities, probabilities and time, with a particular emphasis on performance evaluation. The purpose of this tutorial ..."
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Cited by 95 (9 self)
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In this tutorial we give an overview of the process algebra EMPA, a calculus devised in order to model and analyze features of realworld concurrent systems such as nondeterminism, priorities, probabilities and time, with a particular emphasis on performance evaluation. The purpose of this tutorial is to explain the design choices behind the development of EMPA and how the four features above interact, and to show that a reasonable trade off between the expressive power of the calculus and the complexity of its underlying theory has been achieved.
An Efficient Approach to Removing Geometric Degeneracies (Extended Abstract)
, 1992
"... Our aim is to perturb the input so that an algorithm designed under the hypothesis of input nondegeneracy can execute on arbitrary instances. The deterministic scheme of [EmCa] was the first efficient method and was applied to two important predicates. Here it is extended in a consistent manner to ..."
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Cited by 35 (4 self)
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Our aim is to perturb the input so that an algorithm designed under the hypothesis of input nondegeneracy can execute on arbitrary instances. The deterministic scheme of [EmCa] was the first efficient method and was applied to two important predicates. Here it is extended in a consistent manner to another two common predicates, thus making it valid for most algorithms in computational geometry. It is shown that this scheme incurs no extra algebraic complexity over the original algorithm while it increases the bit complexity by a factor roughly proportional to the dimension of the geometric space. The second contribution of this paper is a variant scheme for a restricted class of algorithms that is asymptotically optimal with respect to the algebraic as well as the bit complexity. Both methods are simple to implement and require no symbolic computation. They also conform to certain criteria ensuring that the solution to the original input can be restored from the output on the perturbed input. This is immediate when the input to solution mapping obeys a continuity property and requires some casespecific work otherwise. Finally we discuss extensions and limitations to our approach.
The smallest enclosing ball of balls: combinatorial structure and algorithms
 International Journal of Computational Geometry & Application
, 2004
"... We develop algorithms for computing the smallest enclosing ball of a set of n balls in ddimensional space. Unlike previous methods, we explicitly address small cases (n ≤ d +1), derive the necessary primitive operations and show that they can efficiently be realized with rational arithmetic. An exa ..."
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Cited by 24 (3 self)
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We develop algorithms for computing the smallest enclosing ball of a set of n balls in ddimensional space. Unlike previous methods, we explicitly address small cases (n ≤ d +1), derive the necessary primitive operations and show that they can efficiently be realized with rational arithmetic. An exact implementation (along with a fast 1 and robust floatingpoint version) is available as part of the CGAL library. 2 Our algorithms are based on novel insights into the combinatorial structure of the problem. As it turns out, results for smallest enclosing balls of points do not extend as one might expect. For example, we show that Welzl’s randomized lineartime algorithm for computing the ball spanned by a set of points fails to work for balls. Consequently, David White’s adaptation of the method to the ball case—as the only available implementation so far it is mentioned in many link collections—is incorrect and may crash or, in the better case, produce wrong balls. In solving the small cases we may assume that the ball centers are affinely independent; in this case, the problem is surprisingly wellbehaved: via a geometric transformation and suitable generalization, it fits into the combinatorial model of unique sink orientations whose rich structure has recently received considerable attention. One consequence is that Welzl’s algorithm does work for small instances; moreover, there is a wide variety of pivoting methods for unique sink orientations which have the potential of being fast in practice even for high dimensions. Partly supported by the IST Programme of the EU and
Neighborly cubical polytopes
 Discrete & Computational Geometry
, 2000
"... Neighborly cubical polytopes exist: for any n ≥ d ≥ 2r + 2, there is a cubical whose rskeleton is combinatorially equivalent to that of the convex dpolytope Cn d ndimensional cube. This solves a problem of Babson, Billera & Chan. Kalai conjectured that the boundary ∂Cn d of a neighborly cubical p ..."
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Cited by 10 (1 self)
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Neighborly cubical polytopes exist: for any n ≥ d ≥ 2r + 2, there is a cubical whose rskeleton is combinatorially equivalent to that of the convex dpolytope Cn d ndimensional cube. This solves a problem of Babson, Billera & Chan. Kalai conjectured that the boundary ∂Cn d of a neighborly cubical polytope Cn d maximizes the fvector among all cubical (d − 1)spheres with 2n vertices. While we show that this is true for polytopal spheres if n ≤ d+1, we also give a counterexample for d = 4 and n = 6. Further, the existence of neighborly cubical polytopes shows that the graph of the ndimensional cube, where n ≥ 5, is “dimensionally ambiguous ” in the sense of Grünbaum. We also show that the graph of the 5cube is “strongly 4ambiguous”. In the special case d = 4, neighborly cubical polytopes have f3 = f0 4 log2 f0 4 vertices, so the facetvertex ratio f3/f0 is not bounded; this solves a problem of Kalai, Perles and Stanley studied by Jockusch.
Affine tangles and irreducible exotic sheaves
, 802
"... Abstract. We construct a weak representation of the category of framed affine tangles on a disjoint union of triangulated categories D2n. The categories we use are that of coherent sheaves on Springer fibers over a nilpotent element of sl2n with two equal Jordan blocks. This representation allows us ..."
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Cited by 1 (0 self)
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Abstract. We construct a weak representation of the category of framed affine tangles on a disjoint union of triangulated categories D2n. The categories we use are that of coherent sheaves on Springer fibers over a nilpotent element of sl2n with two equal Jordan blocks. This representation allows us to enumerate the irreducible objects in the heart of the exotic tstructure on D2n by crossingless matchings of 2n points on a circle. We also describe the algebra of endomorphisms of the direct sum of the irreducible objects. 1.
Leftleaning RedBlack Trees
"... The redblack tree model for implementing balanced search trees, introduced by Guibas and Sedgewick thirty years ago, is now found throughout our computational infrastructure. Redblack trees are described in standard textbooks and are the underlying data structure for symboltable implementations w ..."
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The redblack tree model for implementing balanced search trees, introduced by Guibas and Sedgewick thirty years ago, is now found throughout our computational infrastructure. Redblack trees are described in standard textbooks and are the underlying data structure for symboltable implementations within C++, Java, Python, BSD Unix, and many other modern systems. However, many of these implementations have sacrificed some of the original design goals (primarily in order to develop an effective implementation of the delete operation, which was incompletely specified in the original paper), so a new look is worthwhile. In this paper, we describe a new variant of redblack trees that meets many of the original design goals and leads to substantially simpler code for insert/delete, less than onefourth as much code as in implementations in common use. All redblack trees are based on implementing 23 or 234 trees within a binary tree, using red links to bind together internal nodes into 3nodes or 4nodes. The new code is based on combining three ideas: • Use a recursive implementation. • Require that all 3nodes lean left.
Effect Of Quadrupole Noise On The Emittance Growthof Protons In Hera
"... The emittance growth in HERA at luminosity is about 1#mmmrad /hr. Intrabeam scattering and the beambeam interaction coupled with tune modulation account for only part of the growth. Here we discuss the contribution of random tune fluctuations in the presence of nonlinear fields to the emittance g ..."
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The emittance growth in HERA at luminosity is about 1#mmmrad /hr. Intrabeam scattering and the beambeam interaction coupled with tune modulation account for only part of the growth. Here we discuss the contribution of random tune fluctuations in the presence of nonlinear fields to the emittance growth of protons. At injection energy, a recent experiment with noise deliberately injected into a chain of correction quadrupoles showed no significant effect on the emittance growth and loss rates except at high noise voltages. The results of this experiment are compared with a tracking study. We also present the results of a study done of the emittance growth due to the beambeam interaction in the presence of tune noise. A future experiment to determine the effects of tune noise on the proton emittance growth rate with colliding beams is planned. I. DYNAMIC APERTURE AND DIFFUSION AT INJECTION ENERGY Particles are tracked through the model of the HERA lattice in SIXTRACK with multipolar...
unknown title
, 2003
"... A new general purpose event horizon finder for 3D numerical spacetimes ..."