Resilient architecture (preliminary version)

The main objectives of WP2 are to define a resilient architecture and to develop a range of middleware solutions (i.e. algorithms, protocols, services) for resilience to be applied in the design of highly available, reliable and trustworthy networking solutions. This is the first deliverable within this work package, a preliminary version of the resilient architecture. The deliverable builds on previous results from WP1, the definition of a set of applications and use cases, and provides a perspective of the middleware services that are considered fundamental to address the dependability requirements of those applications. Then it also describes the architectural organisation of these services, according to a number of factors like their purpose, their function within the communication stack or their criticality/specificity for resilience. WP2 proposes an architecture that differentiates between two classes of services, a class including timeliness and trustworthiness oracles, and a class of so called complex services. The resulting architecture is referred to as a "hybrid architecture". The hybrid architecture is motivated and discussed in this document. The services considered within each of the service classes of the hybrid architecture are described. This sets the background for the work to be carried on in the scope of tasks 2.2 and 2.3 of the work package. Finally, the deliverable also considers high-level interfacing aspects, by providing a discussion about the possibility of using existing Service Availability Forum standard interfaces within HIDENETS, in particular discussing possibly necessary extensions to those interfaces in order to accommodate specific HIDENETS services suited for ad-hoc domain

Revised reference model

This document contains an update of the HIDENETS Reference Model, whose preliminary version was introduced in D1.1. The Reference Model contains the overall approach to development and assessment of end-to-end resilience solutions. As such, it presents a framework, which due to its abstraction level is not only restricted to the HIDENETS car-to-car and car-to-infrastructure applications and use-cases. Starting from a condensed summary of the used dependability terminology, the network architecture containing the ad hoc and infrastructure domain and the definition of the main networking elements together with the software architecture of the mobile nodes is presented. The concept of architectural hybridization and its inclusion in HIDENETS-like dependability solutions is described subsequently. A set of communication and middleware level services following the architecture hybridization concept and motivated by the dependability and resilience challenges raised by HIDENETS-like scenarios is then described. Besides architecture solutions, the reference model addresses the assessment of dependability solutions in HIDENETS-like scenarios using quantitative evaluations, realized by a combination of top-down and bottom-up modelling, as well as verification via test scenarios. In order to allow for fault prevention in the software development phase of HIDENETS-like applications, generic UML-based modelling approaches with focus on dependability related aspects are described. The HIDENETS reference model provides the framework in which the detailed solution in the HIDENETS project are being developed, while at the same time facilitating the same task for non-vehicular scenarios and application

www.elsevier.com/locate/cagd Computing real inflection points of cubic algebraic curves

Shape modeling using planar cubic algebraic curves calls for computing the real inflection points of these curves since inflection points represents important shape feature. A real inflection point is also required for transforming projectively a planar cubic algebraic curve to the normal form, in order to facilitate further analysis of the curve. However, the naive method for computing the inflection points of a planar cubic algebraic curve f = 0 by directly intersecting f = 0 and its Hessian curve H(f) = 0 requires solving a degree nine univariate polynomial equation, and thus is relatively inefficient. In this paper we present an algorithm for computing the real inflection points of a real planar cubic algebraic curve. The algorithm follows Hilbert’s solution for computing the inflection points of a cubic algebraic curve in the complex projective plane. Hilbert’s solution is based on invariant theory and requires solving only a quartic polynomial equation and several cubic polynomial equations. Through a detailed study with emphasis on the distinction between real and imaginary inflection points, we adapt Hilbert’s solution to efficiently compute only the real inflection points of a cubic algebraic curve f = 0, without exhaustive but unnecessary search and root testing. To compute the real inflection points of f = 0, only two cubic polynomial equations need to be solved in our algorithm and it is unnecessary to solve numerically the quartic equation prescribed in Hilbert’s solution. In addition, the invariants of f = 0 are used to analyze the singularity of a singular curve, since the number of the real inflection points of f = 0 depends on its singularity type

Geometric Modelling, Interoperability and New Challenges (Dagstuhl Seminar 17221)

This report documents the program and the outcomes of Dagstuhl Seminar 17221 "Geometric Modelling, Interoperability and New Challenges". While previous Dagstuhl seminars on geometric modeling were focused on basic research, this seminar was focused on applications of geometric modeling to four topic areas: big data and cloud computing, multi-material additive manufacturing, isogeometric analysis, and design optimization. For this purpose we brought together participants from industry urgently in need of better solutions, researchers in the above application areas, and researchers in the geometric modeling community

The l-basis of a planar rational curve—properties and

computatio

www.elsevier.com/locate/jsc Computing singular points of plane rational curves

We compute the singular points of a plane rational curve, parametrically given, using the implicitization matrix derived from the μ-basis of the curve. It is shown that singularity factors, which are defined and uniquely determined by the elementary divisors of the implicitization matrix, contain all the information about the singular points, such as the parameter values of the singular points and their multiplicities. Based on this observation, an efficient and numerically stable algorithm for computing the singular points is devised, and inversion formulae for the singular points are derived. In particular, high order singular points can be detected and computed effectively. This approach based on singularity factors can also determine whether a rational curve has any non-ordinary singular points that contain singular points in its infinitely near neighborhood. Furthermore, a method is proposed to determine whether a singular point is ordinary or not. Finally, a conjecture in [Chionh, E.-W., Sederberg, T.W., 2001. On the minors of the implicitization bézout matrix for a rational plane curve. Computer Aided Geometric Design 18, 21–36] regarding the multiplicity of the singular points of a plane rational curve is proved