Rigid realizations of modular forms in Calabi--Yau threefolds

We construct examples of modular rigid Calabi--Yau threefolds, which give a realization of some new weight 4 cusp forms

Catherine Raisin, a role-model professional geologist

This is a PDF version of an article published in Geology Today© 2003. The definitive version is available at www.blackwell-synergy.com. The illustrations have been removed.This article discusses the life and career of British geologist Catherine Raisin (1855-1945), especially her time teaching at Bedford College (where she was Head of Geography, Head of Botany, and Head of Geology, and became the first woman appointed as Vice-Principal of a college in 1898)

Emily Dix, palaeobotanist - a promising career cut short

This is a PDF version of an article published in Geology today© 2005. The definitive version is available at www.blackwell-synergy.com. The illustrations have been removed.This article discusses the life and career of British palaeobotanist Emily Dix (1904-1972)

A new upper bound for numbers with the Lehmer property and its application to repunit numbers

A composite positive integer $n$ has the Lehmer property if $\phi(n)$ divides $n-1,$ where $\phi$ is an Euler totient function. In this note we shall prove that if $n$ has the Lehmer property, then $n\leq 2^{2^{K}}-2^{2^{K-1}}$, where $K$ is the number of prime divisors of $n$. We apply this bound to repunit numbers and prove that there are at most finitely many numbers with the Lehmer property in the set $$\left\{\frac{g^{n}-1}{g-1}\ \bigg|\ n,g\in\mathbb{N},\ \nu_{2}(g)+\nu_{2}(g+1)\leq L\ \right\},$$ where $\nu_{2}(g)$ denotes the highest power of $2$ that divides $g$, and $L\geq 1$ is a fixed real number.Comment: 4 page

Equitable Labelings of Caterpillar Graphs

The Graceful Tree Conjecture in graph theory has been open for almost half a century. The conjecture states that the vertices of any tree can be labeled with distinct integers between 0 and the number of edges of the tree in a way that the edges can be uniquely identified by the absolute value of the difference between their vertex labels. One possible approach to prove the conjecture is to prove the more general k-equitable tree conjecture. In a k-equitable labeling we assign integers from the set {0,1,2,…,k-1} to the vertices. Each edge will receive a label that is the absolute value of the difference of its vertex labels. We want to distribute the labels as equally as possible both for the edges and for the vertices. The conjecture states that this kind of labeling is possible for every tree and every k. This conjecture is equivalent to the graceful tree conjecture when k is the number of vertices of the tree. It has already been proven that every tree is 2-equitable and 3-equitable. We attempt to show a part of the k-equitable tree conjecture by choosing a large collection of trees called caterpillars, and examining different values of k

Positioning for conceptual development using latent semantic analysis

With increasing opportunities to learn online, the problem of positioning learners in an educational network of content offers new possibilities for the utilisation of geometry-based natural language processing techniques. In this article, the adoption of latent semantic analysis (LSA) for guiding learners in their conceptual development is investigated. We propose five new algorithmic derivations of LSA and test their validity for positioning in an experiment in order to draw back conclusions on the suitability of machine learning from previously accredited evidence. Special attention is thereby directed towards the role of distractors and the calculation of thresholds when using similarities as a proxy for assessing conceptual closeness. Results indicate that learning improves positioning. Distractors are of low value and seem to be replaceable by generic noise to improve threshold calculation. Furthermore, new ways to flexibly calculate thresholds could be identified

A pattern-based approach to a cell tracking ontology

Time-lapse microscopy has thoroughly transformed our understanding of biological motion and developmental dynamics from single cells to entire organisms. The increasing amount of cell tracking data demands the creation of tools to make extracted data searchable and interoperable between experiment and data types. In order to address that problem, the current paper reports on the progress in building the Cell Tracking Ontology (CTO): An ontology framework for describing, querying and integrating data from complementary experimental techniques in the domain of cell tracking experiments. CTO is based on a basic knowledge structure: the cellular genealogy serving as a backbone model to integrate specific biological ontologies into tracking data. As a first step we integrate the Phenotype and Trait Ontology (PATO) as one of the most relevant ontologies to annotate cell tracking experiments. The CTO requires both the integration of data on various levels of generality as well as the proper structuring of collected information. Therefore, in order to provide a sound foundation of the ontology, we have built on the rich body of work on top-level ontologies and established three generic ontology design patterns addressing three modeling challenges for properly representing cellular genealogies, i.e. representing entities existing in time, undergoing changes over time and their organization into more complex structures such as situations