An optimal algorithm for the boundary of a cell in a union of rays

In this paper we study a cell of the subdivision induced by a union ofn half-lines (or rays) in the plane. We present two results. The first one is a novel proof of theO(n) bound on the number of edges of the boundary of such a cell, which is essentially of methodological interest. The second is an algorithm for constructing the boundary of any cell, which runs in optimal (n logn) time. A by-product of our results are the notions of skeleton and of skeletal order, which may be of interest in their own right.This work was partly supported by CEE ESPRIT Project P-940, by the Ecole Normale Supérieure, Paris, and by NSF Grant ECS-84-10902.This work was done in part while this author was visiting the Ecole Normale Supérieure, Paris, France.     

Oxidation of proteins: Basic principles and perspectives for blood proteomics

Protein oxidation mechanisms result in a wide array of modifications, from backbone cleavage or protein crosslinking to more subtle modifications such as side chain oxidations. Protein oxidation occurs as part of normal regulatory processes, as a defence mechanism against oxidative stress, or as a deleterious processes when antioxidant defences are overcome. Because blood is continually exposed to reactive oxygen and nitrogen species, blood proteomics should inherently adopt redox proteomic strategies. In this review, we recall the biochemical basis of protein oxidation, review the proteomic methodologies applied to analyse redox modifications, and highlight some physiological and in vitro responses to oxidative stress of various blood components.     

NodeTrix: a hybrid visualization of social networks

The need to visualize large social networks is growing as hardware capabilities make analyzing large networks feasible and many new data sets become available. Unfortunately, the visualizations in existing systems do not satisfactorily resolve the basic dilemma of being readable both for the global structure of the network and also for detailed analysis of local communities. To address this problem, we present NodeTrix, a hybrid representation for networks that combines the advantages of two traditional representations: node-link diagrams are used to show the global structure of a network, while arbitrary portions of the network can be shown as adjacency matrices to better support the analysis of communities. A key contribution is a set of interaction techniques. These allow analysts to create a NodeTrix visualization by dragging selections to and from node-link and matrix forms, and to flexibly manipulate the NodeTrix representation to explore the dataset and create meaningful summary visualizations of their findings. Finally, we present a case study applying NodeTrix to the analysis of the InfoVis 2004 coauthorship dataset to illustrate the capabilities of NodeTrix as both an exploration tool and an effective means of communicating results.     

The Simplex Tree: An Efficient Data Structure for General Simplicial Complexes

This paper introduces a new data structure, called simplex tree, to represent abstract simplicial complexes of any dimension. All faces of the simplicial complex are explicitly stored in a trie whose nodes are in bijection with the faces of the complex. This data structure allows to efficiently implement a large range of basic operations on simplicial complexes. We provide theoretical complexity analysis as well as detailed experimental results. We more specifically study Rips and witness complexes.     

Rational Interpolation from Stochastic Data: A New Froissart's Phenomenon

The analytic structure of Rational Interpolants (R.I.) f (z) built from randomly perturbed data is explored; the interpolation nodes x _j , j = 1,...,M, are real points where the function f reaches these prescribed data . It is assumed that the data are randomly perturbed values of a rational function _(n) ^(m) (m / n is the degree of the numerator/denominator). Much attention is paid to the R.I. familyf _(n+1) ^(m–1), in the small stochasticity régime. The main result is that the additional zero and pole are located nearby the root of the same random polynomial, called the Froissart Polynomial (F.P.). With gaussian hypothesis on the noise, the random real root of F.P. is distributed according to a Cauchy-Lorentz law, with parameters such that the integrated probability over the interpolation interval x ₁, x _M is always larger than 1/2; in two cases studied in detail, it reaches 2/3 in one case and almost 3/4 in the other. For the families f _(n+k) ^(m+k), numerical explorations point to similar phenomena; inspection shows that, in the mean, the localization occurs in the complex and/or real vicinity of the interpolation interval.     

Biexciton emission and crystalline quality of ZnO nano-objects

The design of cost-effective standards for the quality of nano-objects is currently a key issue toward their massive use for optoelectronic applications. The observation by photoluminescence of narrow excitonic and biexcitonic emission lines in semiconductor nanowires is usually accepted as evidence for high structural quality. Here, we perform time-resolved cathodoluminescence experiments on isolated ZnO nanobelts grown by chemical vapor deposition. We observe narrow emission lines at low temperature, together with a clear biexciton line. Still, drastic alterations in both the CL intensity and lifetime are observed locally along the nano-object. We attribute these to non-radiative recombinations at edge dislocations, closing basal plane stacking faults, inhomogeneously distributed along the NB length. This leads us to the conclusion that the observation of narrow excitonic and biexcitonic emission lines is far from sufficient to grade the quality of a nano-object.     

Shortest paths of bounded curvature in the plane

Given two oriented points in the plane, we determine and compute the shortest paths of bounded curvature joining them. This problem has been solved recently by Dubins in the no-cusp case, and by Reeds and Shepp otherwise. We propose a new solution based on the minimum principle of Pontryagin. Our approach simplifies the proofs and makes clear the global or local nature of the results.     

Exploiting Multi-Beam Antennas for End-to-End Delay Reduction in Ad Hoc Networks

A Multi-Beam Antenna (MBA) can be defined as a set of directional radio transceivers. These transceivers are facing different directions to prevent signal interference with each other. MBA nodes have two main characteristics: the Multi-Packet Transmission (MPT) capability and the Multi-Packet Reception (MPR) capability whereby a node can transmit/receive multiple packets at the same time. In this paper, we provide an analysis of how this MPT/MPR capability can be used to reduce the end-to-end delay for delivered packets in ad hoc networks. Taking beam considerations (determination of the beam in which neighbors are located) into account, we formulate the delay reduction issue as an optimization problem that we solve. Our results show that to maximally exploit the full potential of MBAs for delay reduction, the scheduling of links has to promote the formation of star nodes and keep the formation of bridges to a minimum; all of which leads to the selection of routes that very often are not the shortest. In fact, using only the shortest routes has a negative impact on the delay. However, the optimal link scheduling comes at the expense of a higher overhead in terms of the total number of packet transmissions. Furthermore, the beamwidth has a direct and significant impact on the end-to-end delay and the computation time.     

Comparison of several formulations and integration methods for the resolution of DAEs formulations in event-driven simulation of nonsmooth frictionless multibody dynamics

This article is devoted to the comparison of numerical integration methods for nonsmooth multibody dynamics with joints, unilateral contacts and impacts in an industrial context. With an event-driven strategy, the smooth dynamics, which is integrated between two events, can be equivalently formulated as a Differential Algebraic Equation (DAE) of index 1, 2 or 3. It is well known that these reformulations are no longer equivalent when a numerical time-integration technique is used. The drift-off effect and the stability of the numerical scheme strongly depend on the index of the formulation. But, besides the standard properties of accuracy and stability of the DAE solvers, the event-driven context imposes some further requirements that are crucial for a robust and efficient event-driven strategy. In this article, several state-of-the-art numerical time integration methods for each formulation are compared: the generalized-\(\alpha\) scheme for index-3 formulation and stabilized index-2 formulation, (Partitioned) Runge–Kutta Half-Explicit Method of order 5 (HEM5 and PHEM56) for index-2 DAEs with projection techniques, and Runge–Kutta explicit scheme of order 5, the Dormand–Prince scheme (DOPRI5), for index-1 DAEs with projection techniques (MDOP5). We compare these schemes in terms of efficiency, violation of the constraints and the way they handle stiff dynamics on numerous industrial benchmarks, where a CAD software is in this loop. One of the major conclusions is that the index-2 DAEs solvers prove to be better than other schemes to maintain low violations at position and acceleration levels. The best compromise allows us to design efficient event-driven solvers. When the dynamics is stiff, implicit schemes outperform explicit and half-explicit methods which are sometimes unable to compute the dynamics when the system’s frequency range is wide. Furthermore, in industrial context, some solvers fail to reproduce the properties that they enjoy in theory. This is particularly true for half-explicit schemes when the Jacobian of the constraints has not full rank.     

基于ANSYS的概率有限元分析

受激烈的竞争所驱使,工业制造商们处于一个持续增长的压力当中,即在产品日趋复杂化的今天,他们还需要保持技术和利益的最优化。此外,产品的随机性和不确定性也是一个挑战。因此,需要概率工具来为这些挑战寻找一个平衡。ANSYS公司开发了两个工具,分别是ANSYS概率设计系统和ANSYS Design Xplorer。本文介绍了这些软件的运算法则和方法原理,并特别对软件中提供的变分法提出讨论和解释。变分法是一种非常有效的方法,可以基于单个有限元分析,提供准确、高阶的反应面。本文还讨论了此法的功能和优缺点以及通过并行计算减少程序运行时间的可能性。强调了评估结果准确性和有效性的各种方法、程序对结果进行后处理的多种功能、对多种或可能冲突的目标进行优化的方法和功能。最后,运用各种工程实例说明了软件的应用过程。