Classroom Examples of Robustness Problems in Geometric Computations

International audienceThe algorithms of computational geometry are designed for a machine model with exact real arithmetic. Substituting floating point arithmetic for the assumed real arithmetic may cause implementations to fail. Although this is well known, there is no comprehensive documentation of what can go wrong and why. In this extended abstract, we study a simple incremental algorithm for planar convex hulls and give examples which make the algorithm fail in all possible ways. We also show how to construct failure-examples semi-systematically and discuss the geometry of the floating point implementation of the orientation predicate. We hope that our work will be useful for teaching computational geometry. The full paper is available at http://hal.inria.fr/inria-00344310/. It contains further examples, more theory, and color pictures. We strongly recommend to read the full paper instead of this extended abstract

Network Farthest-Point Diagrams

Consider the continuum of points along the edges of a network, i.e., an undirected graph with positive edge weights. We measure distance between these points in terms of the shortest path distance along the network, known as the network distance. Within this metric space, we study farthest points. We introduce network farthest-point diagrams, which capture how the farthest points---and the distance to them---change as we traverse the network. We preprocess a network G such that, when given a query point q on G, we can quickly determine the farthest point(s) from q in G as well as the farthest distance from q in G. Furthermore, we introduce a data structure supporting queries for the parts of the network that are farther away from q than some threshold R > 0, where R is part of the query. We also introduce the minimum eccentricity feed-link problem defined as follows. Given a network G with geometric edge weights and a point p that is not on G, connect p to a point q on G with a straight line segment pq, called a feed-link, such that the largest network distance from p to any point in the resulting network is minimized. We solve the minimum eccentricity feed-link problem using eccentricity diagrams. In addition, we provide a data structure for the query version, where the network G is fixed and a query consists of the point p.Comment: A preliminary version of this work was presented at the 24th Canadian Conference on Computational Geometr

Presentation of a new magnetic field therapy system for the treatment of human solid tumors with magnetic fluid hyperthermia

Magnetic fluid hyperthermia (MFH) selectively heats up tissue by coupling alternating current (AC) magnetic fields to targeted magnetic fluids, so that boundaries of different conductive tissues do not interfere with power absorption. In this paper, a new AC magnetic field therapy system for clinical application of MFH is described. With optimized magnetic nanoparticle preparations it will be used for target-specific glioblastoma and prostate carcinoma therapy

Crossroads between contrastive linguistics, translation studies and machine translation: TC3-II

Contrastive Linguistics (CL), Translation Studies (TS) and Machine Translation (MT) have common grounds: They all work at the crossroad where two or more languages meet. Despite their inherent relatedness, methodological exchange between the three disciplines is rare. This special issue touches upon areas where the three fields converge. It results directly from a workshop at the 2011 German Association for Language Technology and Computational Linguistics (GSCL) conference in Hamburg where researchers from the three fields presented and discussed their interdisciplinary work. While the studies contained in this volume draw from a wide variety of objectives and methods, and various areas of overlaps between CL, TS and MT are addressed, the volume is by no means exhaustive with regard to this topic. Further cross-fertilisation is not only desirable, but almost mandatory in order to tackle future tasks and endeavours, and this volume is committed to bringing these three fields even closer together

Crossroads between contrastive linguistics, translation studies and machine translation: TC3-II

Contrastive Linguistics (CL), Translation Studies (TS) and Machine Translation (MT) have common grounds: They all work at the crossroad where two or more languages meet. Despite their inherent relatedness, methodological exchange between the three disciplines is rare. This special issue touches upon areas where the three fields converge. It results directly from a workshop at the 2011 German Association for Language Technology and Computational Linguistics (GSCL) conference in Hamburg where researchers from the three fields presented and discussed their interdisciplinary work. While the studies contained in this volume draw from a wide variety of objectives and methods, and various areas of overlaps between CL, TS and MT are addressed, the volume is by no means exhaustive with regard to this topic. Further cross-fertilisation is not only desirable, but almost mandatory in order to tackle future tasks and endeavours, and this volume is committed to bringing these three fields even closer together

Crossroads between contrastive linguistics, translation studies and machine translation: TC3-II

Contrastive Linguistics (CL), Translation Studies (TS) and Machine Translation (MT) have common grounds: They all work at the crossroad where two or more languages meet. Despite their inherent relatedness, methodological exchange between the three disciplines is rare. This special issue touches upon areas where the three fields converge. It results directly from a workshop at the 2011 German Association for Language Technology and Computational Linguistics (GSCL) conference in Hamburg where researchers from the three fields presented and discussed their interdisciplinary work. While the studies contained in this volume draw from a wide variety of objectives and methods, and various areas of overlaps between CL, TS and MT are addressed, the volume is by no means exhaustive with regard to this topic. Further cross-fertilisation is not only desirable, but almost mandatory in order to tackle future tasks and endeavours, and this volume is committed to bringing these three fields even closer together

Crossroads between contrastive linguistics, translation studies and machine translation: TC3-II

Contrastive Linguistics (CL), Translation Studies (TS) and Machine Translation (MT) have common grounds: They all work at the crossroad where two or more languages meet. Despite their inherent relatedness, methodological exchange between the three disciplines is rare. This special issue touches upon areas where the three fields converge. It results directly from a workshop at the 2011 German Association for Language Technology and Computational Linguistics (GSCL) conference in Hamburg where researchers from the three fields presented and discussed their interdisciplinary work. While the studies contained in this volume draw from a wide variety of objectives and methods, and various areas of overlaps between CL, TS and MT are addressed, the volume is by no means exhaustive with regard to this topic. Further cross-fertilisation is not only desirable, but almost mandatory in order to tackle future tasks and endeavours, and this volume is committed to bringing these three fields even closer together

Crossroads between contrastive linguistics, translation studies and machine translation: TC3-II

Contrastive Linguistics (CL), Translation Studies (TS) and Machine Translation (MT) have common grounds: They all work at the crossroad where two or more languages meet. Despite their inherent relatedness, methodological exchange between the three disciplines is rare. This special issue touches upon areas where the three fields converge. It results directly from a workshop at the 2011 German Association for Language Technology and Computational Linguistics (GSCL) conference in Hamburg where researchers from the three fields presented and discussed their interdisciplinary work. While the studies contained in this volume draw from a wide variety of objectives and methods, and various areas of overlaps between CL, TS and MT are addressed, the volume is by no means exhaustive with regard to this topic. Further cross-fertilisation is not only desirable, but almost mandatory in order to tackle future tasks and endeavours, and this volume is committed to bringing these three fields even closer together

Crossroads between contrastive linguistics, translation studies and machine translation: TC3-II

Contrastive Linguistics (CL), Translation Studies (TS) and Machine Translation (MT) have common grounds: They all work at the crossroad where two or more languages meet. Despite their inherent relatedness, methodological exchange between the three disciplines is rare. This special issue touches upon areas where the three fields converge. It results directly from a workshop at the 2011 German Association for Language Technology and Computational Linguistics (GSCL) conference in Hamburg where researchers from the three fields presented and discussed their interdisciplinary work. While the studies contained in this volume draw from a wide variety of objectives and methods, and various areas of overlaps between CL, TS and MT are addressed, the volume is by no means exhaustive with regard to this topic. Further cross-fertilisation is not only desirable, but almost mandatory in order to tackle future tasks and endeavours, and this volume is committed to bringing these three fields even closer together

Crossroads between contrastive linguistics, translation studies and machine translation: TC3-II

Contrastive Linguistics (CL), Translation Studies (TS) and Machine Translation (MT) have common grounds: They all work at the crossroad where two or more languages meet. Despite their inherent relatedness, methodological exchange between the three disciplines is rare. This special issue touches upon areas where the three fields converge. It results directly from a workshop at the 2011 German Association for Language Technology and Computational Linguistics (GSCL) conference in Hamburg where researchers from the three fields presented and discussed their interdisciplinary work. While the studies contained in this volume draw from a wide variety of objectives and methods, and various areas of overlaps between CL, TS and MT are addressed, the volume is by no means exhaustive with regard to this topic. Further cross-fertilisation is not only desirable, but almost mandatory in order to tackle future tasks and endeavours, and this volume is committed to bringing these three fields even closer together