I want to thank my supervisor, Martin Grohe, for his patience, many illuminative discussions and for encouraging me to develop questions of my own. I would like to thank Dzifa Ametowobla for supporting me throughout this work especially by reading several parts of it and helping me greatly with the design. Furthermore, I am indebted to Bettina Hepp and Kay Thurley for helpful comments on earlie...

Later on in [2], Grekos refined the previous results, in some cases, by introducing the infimum of the radii of curvature r(Γ ) of the curve. He succeeded in showing an upper bound of the shape N(Γ ) l(Γ )r(Γ )−1/3 and conversely constructed a family of curves Γ0 with N(Γ0) l(Γ0)r(Γ0)−1/3. Naturally, Grekos’ results suppose that the curve has at least C2-regularity. In fact, this is the maximal...

We answer a question of Golumbic, Monma and Trotter by constructing proper tolerance graphs that are not unit tolerance graphs. An infinite family of graphs that are minimal in this respect is specified.

This edition of “Ask the Author” features a discussion with Andrew Martin, who is a professor of law and chair of the political science department at Washington University in St. Louis. Andrew has done some very influential work on the Supreme Court, including co-authoring a paper on ideological drift of Supreme Court Justices, see [1] here, that will appear in issue four of the Northwestern Un...

A graph G = (V,E) is a threshold tolerance graph if each vertex v ∈ V can be assigned a weight wv and a tolerance tv such that two vertices x, y ∈ V are adjacent if wx +wy ≥ min(tx, ty). Currently, the most efficient recognition algorithm for threshold tolerance graphs is the algorithm of Monma, Reed, and Trotter which has an O(n) runtime. We give an O(n) algorithm for recognizing threshold tol...

In [8], Swinnerton-Dyer considered the proportion of twists of an elliptic curve with full 2-torsion that have 2-Selmer group of a particular dimension. Swinnerton-Dyer obtained asymptotic results on the number of such twists using an unusual notion of asymptotic density. We build on this work to obtain similar results on the density of twists with particular rank of 2-Selmer group using the na...

Martin KAY has shown that parsing and generation could be done using Functional Grammars. APPELT lAPP85] and McKEOWN [McK82], among others, have used Functional Grammars for generation. Usually the grammar formalism is more suited to parsing than to generation. The way a grammar is processed for parsing is rather clear, while the generating process needs strong assumptions on the interpreter to...

The composition graph of a family of n+1 disjoint graphs {Hi : 0 ≤ i ≤ n} is the graph H obtained by substituting the n vertices of H0 respectively by the graphs H1, H2, ..., Hn. If H has some hereditary property P , then necessarily all its factors enjoy the same property. For some sort of graphs it is sufficient that all factors {Hi : 0 ≤ i ≤ n} have a certain common P to endow H with this P ...

In this paper, I give the English progressive a semantic analysis as an intensional operator within the framework of modal semantics proposed by Kratzer. This treatment allows a combination of the central idea of Dowty’s influential analysis, that the progressive’s meaning has a major modal component, with the insights of other scholars (Parsons, Vlach, and Landman). My claim is that using a mo...

A graph G = (V,E) is a threshold tolerance graph if each vertex v ∈ V can be assigned a weight wv and a tolerance tv such that two vertices x, y ∈ V are adjacent if wx +wy ≥ min(tx, ty). Currently, the most efficient recognition algorithm for threshold tolerance graphs is the algorithm of Monma, Reed, and Trotter which has an O(n) runtime. We give an O(n) algorithm for recognizing threshold tol...