The Bounded Height Conjecture for Semiabelian Varieties

The Bounded Height Conjecture of Bombieri, Masser, and Zannier states that for any sufficiently generic algebraic subvariety of a semiabelian $\overline{\mathbb{Q}}$-variety $G$ there is an upper bound on the Weil height of the points contained in its intersection with the union of all algebraic subgroups having (at most) complementary dimension in $G$. This conjecture has been shown by Habegger in the case where $G$ is either a multiplicative torus or an abelian variety. However, there are new obstructions to his approach if $G$ is a general semiabelian variety. In particular, the lack of Poincar\'e reducibility means that quotients of a given semiabelian variety are intricate to describe. To overcome this, we study directly certain families of line bundles on $G$. This allows us to demonstrate the conjecture for general semiabelian varieties.Comment: revised, 46 page

The Relative Bogomolov Conjecture for Fibered Products of Elliptic Surfaces

We deduce an analogue of the Bogomolov conjecture for non-degenerate subvarieties in fibered products of elliptic families from the author's recent theorem on equidistribution in families of abelian varieties. This generalizes results of DeMarco and Mavraki and improves certain results of Manin-Mumford type proven by Masser and Zannier to results of Bogomolov type, yielding the first results of this type for subvarieties of relative dimension $>1$ in families of abelian varieties with trivial trace.Comment: 26 page

Effective estimates for the degrees of maximal special subvarieties

Let Z be an algebraic subvariety of a Shimura variety. We extend results of the first author to prove an effective upper bound for the degree of a non-facteur maximal special subvariety of Z

A parallel algorithm for computing the flow complex: theory and applications

Wir präsentieren einen parallelen Algorithmus zur Berechnung des Hasse-Diagramms des Flow-Komplexes einer Punktwolke im euklidischen Raum. Bekannte Algorithmen in zwei und drei Dimensionen berechnen zunächst dessen geometrische Realisierung und müssen vorher die Delaunay-Triangulierung berechnen. Unser Algorithmus berechnet nur das Hasse-Diagramm des Flow-Komplexes, welches, mit ausreichend geometrischen Informationen versehen, die selbe topologische Multiskalenanalyse ermöglicht wie die Alpha-Shape Filtration. Wir zeigen mit experimentelle Ergebnissen für mittlere Dimensionen, dass unser Algorithmus gut mit der Anzahl der verfügbaren Kerne auf einer Mehrkern-Architektur skaliert. Wir wenden unseren Algorithmus an, um den Träger eines wahrscheinlichkeitsmaßes auf Basis von Punkten zu skizzieren, welche aus dem euklidischen Raum gezogen wurden. Des Weiteren wenden wir unseren Algorithmus auf Streudiagramme an, welche zur Korrelationsanalyse verwendet werden, aber auch ein nützliches Werkzeug sind, um die Verteilung hochdimensionaler Punktwolken zu verstehen

Unlikely Intersections of Curves with Algebraic Subgroups in Semiabelian Varieties

Let $G$ be a semiabelian variety and $C$ a curve in $G$ that is not contained in a proper algebraic subgroup of $G$. In this situation, conjectures of Pink and Zilber imply that there are at most finitely many points contained in the so-called unlikely intersections of $C$ with subgroups of codimension at least $2$. In this note, we establish this assertion for general semiabelian varieties over $\bar{\mathbb{Q}}$. This extends results of Maurin and Bombieri, Habegger, Masser, and Zannier in the toric case as well as Habegger and Pila in the abelian case.Comment: Comments are welcom

Revision der Gattung Nanna Birket-Smith, 1965 (Lepidoptera, Arctiidae, Lithosiinae).

Die afrotropische Gattung Nanna Birket-Smith, 1965 wird revidiert. Sieben Arten und zwei Unterarten werden neu beschrieben: broetheri sp. nov., hoppei sp. nov., distyi sp. nov., eningae albifrons ssp. nov., eningae subflava ssp. nov., tanzaniae sp. nov., luteolata sp. nov. griseoides sp. nov. und falcata sp. nov. Der Status von pia (Strand, 1912) wird revidiert (stat. rev.) und ein Lectotypus designiert und das Taxon magna Birket-Smith, 1965 als Synonym (syn. nov.) von pia Strand gewertet.StichwörterLepidoptera, Arctiidae, Lithosiinae, genus Nanna, revision, taxonomy, Africa.Nomenklatorische Handlungenbroetheri Kühne, 2014 (Nanna), spec. n.distyi Kühne, 2014 (Nanna), spec. n.falcata Kühne, 2014 (Nanna), spec. n.griseoides Kühne, 2014 (Nanna), spec. n.hoppei Kühne, 2014 (Nanna), spec. n.luteolata Kühne, 2014 (Nanna), spec. n.magna Birkett-Smith, 1965 (Nanna), syn. n. of Nanna pia (Strand, 1912)pia (Strand, 1912) (Nanna), stat. n. described as Eilema eningae, var. pia Strand, 1912tanzaniae Kühne, 2014 (Nanna), spec. n.albifrons Kühne, 2014 (Nanna eningae), subspec. n.subflava Kühne, 2014 (Nanna eningae), subspec. n.The Afrotropical genus Nanna Birket-Smith, 1965 is revised. Seven new species and two new subspecies are described: broetheri sp. nov., hoppei sp. nov., distyi sp. nov., eningae albifrons ssp. nov., eningae subflava ssp. nov., tanzaniae sp. nov., luteolata sp. nov. griseoides sp. nov. and falcata sp. nov. The status of pia (Strand, 1912) is revised (stat. rev.) and a lectotype is signed. The taxon magna Birket-Smith, 1965 is a synonym (syn. nov.) of pia Strand.KeywordsLepidoptera, Arctiidae, Lithosiinae, genus Nanna, revision, taxonomy, Africa.Nomenclatural Actsbroetheri Kühne, 2014 (Nanna), spec. n.distyi Kühne, 2014 (Nanna), spec. n.falcata Kühne, 2014 (Nanna), spec. n.griseoides Kühne, 2014 (Nanna), spec. n.hoppei Kühne, 2014 (Nanna), spec. n.luteolata Kühne, 2014 (Nanna), spec. n.magna Birkett-Smith, 1965 (Nanna), syn. n. of Nanna pia (Strand, 1912)pia (Strand, 1912) (Nanna), stat. n. described as Eilema eningae, var. pia Strand, 1912tanzaniae Kühne, 2014 (Nanna), spec. n.albifrons Kühne, 2014 (Nanna eningae), subspec. n.subflava Kühne, 2014 (Nanna eningae), subspec. n

Fast and Robust Vectorized In-Place Sorting of Primitive Types

Modern CPUs provide single instruction-multiple data (SIMD) instructions. SIMD instructions process several elements of a primitive data type simultaneously in fixed-size vectors. Classical sorting algorithms are not directly expressible in SIMD instructions. Accelerating sorting algorithms with SIMD instruction is therefore a creative endeavor. A promising approach for sorting with SIMD instructions is to use sorting networks for small arrays and Quicksort for large arrays. In this paper we improve vectorization techniques for sorting networks and Quicksort. In particular, we show how to use the full capacity of vector registers in sorting networks and how to make vectorized Quicksort robust with respect to different key distributions. To demonstrate the performance of our techniques we implement an in-place hybrid sorting algorithm for the data type int with AVX2 intrinsics. Our implementation is at least 30% faster than state-of-the-art high-performance sorting alternatives

Implementation of a vectorized Quicksort using AVX-512 intrinsics

Jahrzehntelang wurden Verbesserungen der Rechengeschwindigkeit erreicht, indem die Taktfrequenz der CPU erhöht wurde. Im Laufe der letzten Jahre wurde dieser Mechanismus durch physikalische Einflüsse gebremst. Daher müssen moderne Single-Thread-Anwendungen stärker CPU-Funktionen ausnutzen, um von den Fortschritten neuer Prozessorgenerationen zu profitieren. Eine dieser Funktionen ist die Vektorverarbeitung, um mehrere Datenelemente gleichzeitig zu verarbeiten. Diese Arbeit untersucht die Verwendung von AVX-512-Befehlen zur Sortierung von primitiven Typen der Länge 32 bit. Die Nutzung von Vektorinstruktionen für die Sortierung ist eine Herausforderung, da Sortieralgorithmen erst vektorisierungsfreundlich umgestaltet werden müssen. Glücklicherweise hat Mark Blacher einen effizienten vektorisierten Sortieralgorithmus auf Basis von Sortiernetzwerken und einem nichtquadratischen Quicksort entwickelt. In dieser Arbeit wird Blachers AVX2-basierte vektorisierte Implementierung auf den moderneren AVX-512-Befehlssatz portiert. Im Geschwindigkeitsvergleich schlägt Blachers AVX2-Version die in dieser Arbeit entwickelte AVX-512-Implementierung. Diese ist jedoch in der Lage, den bisherigen AVX-512-Sortieralgorithmus von Bramas zu übertreffen

APPLICATION OF STEEL FIBRES IN ALKALI-ACTIVATED MORTARS

Alkali-activated materials are ideal for the repair of concrete structures in harsh environmental conditions due to their high durability in chemically aggressive environments. However, slag-based mortars, in particular, are prone to shrinkage and associated cracks. In this respect, the application of steel fibres is one solution to reduce the formation of shrinkage induced cracks and to improve post cracking behaviour of these mortars. This study investigated the influence of two different types of steel fibres on the tensile properties of two alkali-activated mortars. Direct tensile tests and single fibre pull-outs were performed to analyse the determining failure modes both on macro and micro scale. Mechanical testing was accompanied by non-destructive testing methods such as digital image correlation and acoustic emission for a detailed analysis of the fracture process