Numerical Algorithm for the Topology of Singular Plane Curves

International audienceWe are interested in computing the topology of plane singular curves. For this, the singular points must be isolated. Numerical methods for isolating singular points are efficient but not certified in general. We are interested in developing certified numerical algorithms for isolating the singularities. In order to do so, we restrict our attention to the special case of plane curves that are projections of smooth curves in higher dimensions. In this setting, we show that the singularities can be encoded by a regular square system whose isolation can be certified by numerical methods. This type of curves appears naturally in robotics applications and scientific visualization

Certified numerical algorithm for isolating the singularities of the plane projection of generic smooth space curves

International audienceIsolating the singularities of a plane curve is the first step towards computing its topology. For this, numerical methods are efficient but not certified in general. We are interested in developing certified numerical algorithms for isolating the singularities. In order to do so, we restrict our attention to the special case of plane curves that are projections of smooth curves in higher dimensions. This type of curve appears naturally in robotics applications and scientific visualization. In this setting, we show that the singularities can be encoded by a regular square system whose solutions can be isolated with certified numerical methods. Our analysis is conditioned by assumptions that we prove to be generic using transversality theory. We also provide a semi-algorithm to check their validity. Finally, we present experiments, some of which are not reachable by other methods, and discuss the efficiency of our method

Isolating the singularities of the plane projection of a generic space curve

Isolating the singularities of a plane curve is the first step towards computing its topology. For this, numerical methods are efficient but not certified in general. We are interested in developing certified numerical algorithms for isolating the singularities. In order to do so, we restrict our attention to the special case of plane curves that are projections of smooth curves in higher dimensions. This type of curves appears naturally in robotics applications and scientific visualization. In this setting, we show that the singularities can be encoded by a regular square system whose solutions can be isolated with certified numerical methods. Our analysis is conditioned by assumptions that we prove to be generic using transversality theory, we also provide a semi-algorithm to check their validity

Numerical Algorithm for the Topology of Singular Plane Curves

International audienceWe are interested in computing the topology of plane singular curves. For this, the singular points must be isolated. Numerical methods for isolating singular points are efficient but not certified in general. We are interested in developing certified numerical algorithms for isolating the singularities. In order to do so, we restrict our attention to the special case of plane curves that are projections of smooth curves in higher dimensions. In this setting, we show that the singularities can be encoded by a regular square system whose isolation can be certified by numerical methods. This type of curves appears naturally in robotics applications and scientific visualization

Ballistic spin-polarized transport and Rashba spin precession in semiconductor nanowires

We present numerical calculations of the ballistic spin-transport properties of quasi-one-dimensional wires in the presence of the spin-orbit (Rashba) interaction. A tight-binding analog of the Rashba Hamiltonian which models the Rashba effect is used. By varying the robustness of the Rashba coupling and the width of the wire, weak and strong coupling regimes are identified. Perfect electron spin-modulation is found for the former regime, regardless of the incident Fermi energy and mode number. In the latter however, the spin-conductance has a strong energy dependence due to a nontrivial subband intermixing induced by the strong Rashba coupling. This would imply a strong suppression of the spin-modulation at higher temperatures and source-drain voltages. The results may be of relevance for the implementation of quasi-one-dimensional spin transistor devices.Comment: 19 pages (incl. 9 figures). To be published in PR

The Mehweb language: Essays on phonology, morphology and syntax

This book is an investigation into the grammar of Mehweb (Dargwa, East Caucasian also known as Nakh-Daghestanian) based on several years of team fieldwork. Mehweb is spoken in one village community in Daghestan, Russia, with a population of some 800 people, In many ways, Mehweb is a typical East Caucasian language: it has a rich inventory of consonants; an extensive system of spatial forms in nouns and converbs and volitional forms in verbs; pervasive gender-number agreement; and ergative alignment in case marking and in gender agreement. It is also a typical language of the Dargwa branch, with symmetrical verb inflection in the imperfective and perfective paradigm and extensive use of spatial encoding for experiencers. Although Mehweb is clearly close to the northern varieties of Dargwa, it has been long isolated from the main body of Dargwa varieties by speakers of Avar and Lak. As a result of both independent internal evolution and contact with its neighbours, Mehweb developed some deviant properties, including accusatively aligned egophoric agreement, a split in the feminine class, and the typologically rare grammatical categories of verificative and apprehensive. But most importantly, Mehweb is where our friends live

The Mehweb language: Essays on phonology, morphology and syntax

This book is an investigation into the grammar of Mehweb (Dargwa, East Caucasian also known as Nakh-Daghestanian) based on several years of team fieldwork. Mehweb is spoken in one village community in Daghestan, Russia, with a population of some 800 people, In many ways, Mehweb is a typical East Caucasian language: it has a rich inventory of consonants; an extensive system of spatial forms in nouns and converbs and volitional forms in verbs; pervasive gender-number agreement; and ergative alignment in case marking and in gender agreement. It is also a typical language of the Dargwa branch, with symmetrical verb inflection in the imperfective and perfective paradigm and extensive use of spatial encoding for experiencers. Although Mehweb is clearly close to the northern varieties of Dargwa, it has been long isolated from the main body of Dargwa varieties by speakers of Avar and Lak. As a result of both independent internal evolution and contact with its neighbours, Mehweb developed some deviant properties, including accusatively aligned egophoric agreement, a split in the feminine class, and the typologically rare grammatical categories of verificative and apprehensive. But most importantly, Mehweb is where our friends live

The Mehweb language: Essays on phonology, morphology and syntax

This book is an investigation into the grammar of Mehweb (Dargwa, East Caucasian also known as Nakh-Daghestanian) based on several years of team fieldwork. Mehweb is spoken in one village community in Daghestan, Russia, with a population of some 800 people, In many ways, Mehweb is a typical East Caucasian language: it has a rich inventory of consonants; an extensive system of spatial forms in nouns and converbs and volitional forms in verbs; pervasive gender-number agreement; and ergative alignment in case marking and in gender agreement. It is also a typical language of the Dargwa branch, with symmetrical verb inflection in the imperfective and perfective paradigm and extensive use of spatial encoding for experiencers. Although Mehweb is clearly close to the northern varieties of Dargwa, it has been long isolated from the main body of Dargwa varieties by speakers of Avar and Lak. As a result of both independent internal evolution and contact with its neighbours, Mehweb developed some deviant properties, including accusatively aligned egophoric agreement, a split in the feminine class, and the typologically rare grammatical categories of verificative and apprehensive. But most importantly, Mehweb is where our friends live

The Mehweb language: Essays on phonology, morphology and syntax

This book is an investigation into the grammar of Mehweb (Dargwa, East Caucasian also known as Nakh-Daghestanian) based on several years of team fieldwork. Mehweb is spoken in one village community in Daghestan, Russia, with a population of some 800 people, In many ways, Mehweb is a typical East Caucasian language: it has a rich inventory of consonants; an extensive system of spatial forms in nouns and converbs and volitional forms in verbs; pervasive gender-number agreement; and ergative alignment in case marking and in gender agreement. It is also a typical language of the Dargwa branch, with symmetrical verb inflection in the imperfective and perfective paradigm and extensive use of spatial encoding for experiencers. Although Mehweb is clearly close to the northern varieties of Dargwa, it has been long isolated from the main body of Dargwa varieties by speakers of Avar and Lak. As a result of both independent internal evolution and contact with its neighbours, Mehweb developed some deviant properties, including accusatively aligned egophoric agreement, a split in the feminine class, and the typologically rare grammatical categories of verificative and apprehensive. But most importantly, Mehweb is where our friends live

The Mehweb language: Essays on phonology, morphology and syntax

This book is an investigation into the grammar of Mehweb (Dargwa, East Caucasian also known as Nakh-Daghestanian) based on several years of team fieldwork. Mehweb is spoken in one village community in Daghestan, Russia, with a population of some 800 people, In many ways, Mehweb is a typical East Caucasian language: it has a rich inventory of consonants; an extensive system of spatial forms in nouns and converbs and volitional forms in verbs; pervasive gender-number agreement; and ergative alignment in case marking and in gender agreement. It is also a typical language of the Dargwa branch, with symmetrical verb inflection in the imperfective and perfective paradigm and extensive use of spatial encoding for experiencers. Although Mehweb is clearly close to the northern varieties of Dargwa, it has been long isolated from the main body of Dargwa varieties by speakers of Avar and Lak. As a result of both independent internal evolution and contact with its neighbours, Mehweb developed some deviant properties, including accusatively aligned egophoric agreement, a split in the feminine class, and the typologically rare grammatical categories of verificative and apprehensive. But most importantly, Mehweb is where our friends live