In this tutorial we give an overview of the process algebra EMPA, a calculus devised in order to model and analyze features of real-world 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.

Our aim is to perturb the input so that an algorithm designed under the hypothesis of input non-degeneracy 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 case-specific work otherwise. Finally we discuss extensions and limitations to our approach.

Neighborly cubical polytopes exist: for any n ≥ d ≥ 2r + 2, there is a cubical whose r-skeleton is combinatorially equivalent to that of the convex d-polytope Cn d n-dimensional 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 f-vector 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 counter-example for d = 4 and n = 6. Further, the existence of neighborly cubical polytopes shows that the graph of the n-dimensional cube, where n ≥ 5, is “dimensionally ambiguous ” in the sense of Grünbaum. We also show that the graph of the 5-cube is “strongly 4-ambiguous”. In the special case d = 4, neighborly cubical polytopes have f3 = f0 4 log2 f0 4 vertices, so the facet-vertex ratio f3/f0 is not bounded; this solves a problem of Kalai, Perles and Stanley studied by Jockusch.

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 t-structure 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.

The red-black tree model for implementing balanced search trees, introduced by Guibas and Sedgewick thirty years ago, is now found throughout our computational infrastructure. Red-black trees are described in standard textbooks and are the underlying data structure for symbol-table 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 one-fourth as much code as in implementations in common use. All red-black trees are based on implementing 2-3 or 2-3-4 trees within a binary tree, using red links to bind together internal nodes into 3-nodes or 4-nodes. The new code is based on combining three ideas: • Use a recursive implementation. • Require that all 3-nodes lean left.

The emittance growth in HERA at luminosity is about 1#mmmrad /hr. Intra-beam scattering and the beam-beam 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 non-linear 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...

We show how to compute terms in an expansion of the world-volume superpotential for fairly general D-branes on the quintic Calabi-Yau using linear sigma model techniques, and show in examples that this superpotential captures the geometry and obstruction theory of bundles and sheaves on this Calabi-Yau.

We show how to compute terms in an expansion of the world-volume superpotential for fairly general D-branes on the quintic Calabi-Yau using linear sigma model techniques, and show in examples that this superpotential captures the geometry and obstruction theory of bundles and sheaves on this Calabi-Yau.