Permutation Complexity and the Letter Doubling Map

Given a countable set X (usually taken to be N or Z), an infinite permutation $\pi$ of X is a linear ordering $<_\pi$ of X. This paper investigates the combinatorial complexity of infinite permutations on N associated with the image of uniformly recurrent aperiodic binary words under the letter doubling map. An upper bound for the complexity is found for general words, and a formula for the complexity is established for the Sturmian words and the Thue-Morse word

Wordsworth's Aeneid and the influence of its eighteenth-century predecessors

William Wordsworth's attempt at translating Virgil's Aeneid reached as far as Book 4, and mostly survives in manuscript drafts. The literary influences behind it can be illuminated through the poet's correspondence, and analysed more fully by tracing verbal echoes and other resonances in his translation. Despite the hostility he expressed towards Dryden and Pope, the foremost translators of the previous age, Wordsworth followed them in using heroic couplets, and, as has previously been argued, his translation draws increasingly on Dryden's Aeneis the further he advanced with his project. But Wordsworth owes an equally large debt, hitherto unrecognized, to the eighteenth-century blank verse renderings by Joseph Trapp and others, who anticipated many of his supposed stylistic innovations

Quasi-alternating Montesinos links

The aim of this article is to detect new classes of quasi-alternating links. Quasi-alternating links are a natural generalization of alternating links. Their knot Floer and Khovanov homology are particularly easy to compute. Since knot Floer homology detects the genus of a knot as well as whether a knot is fibered, as provided bounds on unknotting number and slice genus, characterization of quasi-alternating links becomes an interesting open problem. We show that there exist classes of non-alternating Montesinos links, which are quasi-alternating.Comment: 11 pages, 7 figure

Permutation Complexity Related to the Letter Doubling Map

Given a countable set X (usually taken to be the natural numbers or integers), an infinite permutation, \pi, of X is a linear ordering of X. This paper investigates the combinatorial complexity of infinite permutations on the natural numbers associated with the image of uniformly recurrent aperiodic binary words under the letter doubling map. An upper bound for the complexity is found for general words, and a formula for the complexity is established for the Sturmian words and the Thue-Morse word.Comment: In Proceedings WORDS 2011, arXiv:1108.341

Counting points of fixed degree and bounded height

We consider the set of points in projective $n$-space that generate an extension of degree $e$ over given number field $k$, and deduce an asymptotic formula for the number of such points of absolute height at most $X$, as $X$ tends to infinity. We deduce a similar such formula with instead of the absolute height, a so-called adelic-Lipschitz height

Schizophrenie in lacanianischer Perspektive

Im folgenden werde ich versuchen, etwas von dem darzustellen, was mich in den letzten Jahren in zunehmendem Maße beschäftigt hat, nämlich das Studium der Schizophrenie. Man kann ohne jegliche Übertreibung sagen, dass die Schizophrenie ein Stiefkind der Psychoanalyse geblieben ist, ja, nicht nur das, darüber hinaus ist sie seit jeher ein ungeliebtes Stiefkind. Dies im Gegensatz zur Paranoia. Freud wie auch Lacan haben zur Para­noia ungleich mehr beigetragen als zur Schizophrenie; das zeigt sich mit aller Deutlichkeit am Paradebeispiel des Senatspräsidenten Schreber, des­sen Buch Denkwürdigkeiten eines Nervenkranken Gegenstand einer um­fangreichen Untersuchung Freuds geworden ist, was wiederum Lacan dazu veranlasste, einen Grossteil seines Seminars über die Psychosen wie auch seiner Arbeit .D. une question préliminaire d. un traitement possible de la psychose. / .Von einer Frage, die jeder möglichen Behandlung der Psy­chose vorausgeht. Freud und Schreber zu widmen.1 \ud In der Psychiatrie ist es dagegen eher umgekehrt; ein so renommierter Psychiater wie Eugen Bleuler hat der Schizophrenie auf dem Feld der Psychosen einen vorrangigen Platz eingeräumt und sogar die Paranoia seinem Konzept der Schizophrenie subsumiert2. Die Untersuchungen über Schizophrenie sind auch in der zeitgenössischen Psychiatrie zahlreich geblieben. \ud Wie kommt es, dass sich die Psychoanalyse seit jeher kaum für die Schi­zophrenie interessiert? Ich glaube, dass dies etwas mit der Bedeutung des Vaters zu tun hat, dessen Funktionen für Neurosen wie auch für Paranoi

Integral points of fixed degree and bounded height

By Northcott's Theorem there are only finitely many algebraic points in affine $n$-space of fixed degree over a given number field and of height at most $X$. For large $X$ the asymptotics of these cardinalities have been investigated by Schanuel, Schmidt, Gao, Masser and Vaaler, and the author. In this paper we study the case where the coordinates of the points are restricted to algebraic integers, and we derive the analogues of Schanuel's, Schmidt's, Gao's and the author's results.Comment: to appear in Int. Math. Res. Notice