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...

A study was conducted to determine differences in performance, carcass characteristics , and profitability of a calf-feeding and a yearling production system. Year-lings had higher daily gains compared to calf-feds; however, calf-feds were more efficient than yearlings. Yearlings produced more weight than calf-feds leading to an improvement in profitability for yearlings compared to calf-feds. ...

Let E/Q be an elliptic curve defined by the equation y 2 = x 3 + ax + b. For a prime p, p ∤ ∆ = −16(4a 3 + 27b 2) = 0, define N p = p + 1 − a p = |E(F p)|. As a precursor to their celebrated conjecture, Birch and Swinnerton-Dyer originally conjectured that for some constant c, p≤x,p∤∆ N p p ∼ c(log x) r , x → ∞. Let α p and β p be the eigenvalues of the Frobenius at p. Define ˜ c n =    α k ...