Classical Predicative Logic-Enriched Type Theories

A logic-enriched type theory (LTT) is a type theory extended with a primitive mechanism for forming and proving propositions. We construct two LTTs, named LTTO and LTTO*, which we claim correspond closely to the classical predicative systems of second order arithmetic ACAO and ACA. We justify this claim by translating each second-order system into the corresponding LTT, and proving that these translations are conservative. This is part of an ongoing research project to investigate how LTTs may be used to formalise different approaches to the foundations of mathematics. The two LTTs we construct are subsystems of the logic-enriched type theory LTTW, which is intended to formalise the classical predicative foundation presented by Herman Weyl in his monograph Das Kontinuum. The system ACAO has also been claimed to correspond to Weyl's foundation. By casting ACAO and ACA as LTTs, we are able to compare them with LTTW. It is a consequence of the work in this paper that LTTW is strictly stronger than ACAO. The conservativity proof makes use of a novel technique for proving one LTT conservative over another, involving defining an interpretation of the stronger system out of the expressions of the weaker. This technique should be applicable in a wide variety of different cases outside the present work.Comment: 49 pages. Accepted for publication in special edition of Annals of Pure and Applied Logic on Computation in Classical Logic. v2: Minor mistakes correcte

QPEL: Quantum Program and Effect Language

We present the syntax and rules of deduction of QPEL (Quantum Program and Effect Language), a language for describing both quantum programs, and properties of quantum programs - effects on the appropriate Hilbert space. We show how semantics may be given in terms of state-and-effect triangles, a categorical setting that allows semantics in terms of Hilbert spaces, C*-algebras, and other categories. We prove soundness and completeness results that show the derivable judgements are exactly those provable in all state-and-effect triangles.Comment: In Proceedings QPL 2014, arXiv:1412.810

A homotopy-theoretic view of Bott-Taubes integrals and knot spaces

We construct cohomology classes in the space of knots by considering a bundle over this space and "integrating along the fiber" classes coming from the cohomology of configuration spaces using a Pontrjagin-Thom construction. The bundle we consider is essentially the one considered by Bott and Taubes, who integrated differential forms along the fiber to get knot invariants. By doing this "integration" homotopy-theoretically, we are able to produce integral cohomology classes. We then show how this integration is compatible with the homology operations on the space of long knots, as studied by Budney and Cohen. In particular we derive a product formula for evaluations of cohomology classes on homology classes, with respect to connect-sum of knots.Comment: 32 page

Market Power in Outputs and Inputs: An Empirical Application to Banking

This paper provides evidence on the empirical separability of input and output market imperfections. We specify a model of banking competition and simultaneously estimate bank conduct in output (loan) and input (deposit) markets. Our results suggest that firms display some degree of noncompetitive behavior in both the loan and the deposit markets. Moreover, we find that the input side and the output side are empirically separable, that is the measurement of market power on one side of the market is not affected by assuming that the other side of the market is perfectly competitive. Our results suggest that empirical studies of market power that concentrate on either the input side or the output side, are not subject to significant misspecification error. ZUSAMMENFASSUNG - (Marktmacht auf Input- und Outputmärkten: Eine Empirische Anwendung auf den Bankensektor) Der Aufsatz untersucht den Zusammenhang von Unvollkommenheiten auf Input- und auf Outputmärkten. Im Rahmen eines Wettbewerbsmodells für den Bankensektor wird die Wechselwirkung zwischen Outputmarkt, d.h. bei der Kreditvergabe, und Inputmarkt (Geldanlage) empirisch untersucht. Die Ergebnisse zeigen, dass Banken auf beiden Seiten des Marktes eine gewisse Marktmacht ausüben können. Allerdings ist die Wechselwirkung begrenzt, sodass eine separate Betrachtungsweise von Input- und Outputmärkten möglich ist. Dies bedeutet wiederum, dass empirische Untersuchungen, die jeweils nur eine Seite des Marktes analysieren, keinen signifikanten Verzerrungen unterliegen.Measuring Market Power, Banking

Measuring Market Power in Input and Output Markets: An Empirical Application to Banking

This paper develops and estimates a model of market conduct in the US banking industry during the 1990s. Competition in both output and factor markets is measured in a static Cournot model in the spirit of Bresnahan (1989), Shaffer (1991,1994a), Neven and Roeller (1997), and others. Banks can exert market power in loans as well as in deposit markets. Previous studies on banking competition center on the structure conduct hypothesis, where reduced form models with market concentration measures are used to estimate the degree of competition. We consider a disaggregated structural model of bank loan markets, where bank's competitive behavior is measured in input and output markets. Our results indicate that the standard model which measures only output market behavior is potentially biased.

Echoes in a concrete canyon : Graham, Cummings, and Apollinaire

This study explores the poetry of Jorie Graham, E.E. Cummings, and Guillaume Apollinaire, focusing particularly on the rich tradition of concrete and visual poetry and the concept of rule breaking in writing. The connection between Cummings, taking elements of visual poetry and free verse to experimental new heights with typographic techniques, and Apollinaire, whose poetry explores similar aesthetic challenges, is obvious. Graham may seem to be the one who doesn\u27t belong, but part of my emphasis is to demonstrate how she does fit into this study. Her poetry, as is Cummings\u27 and Apollinaire\u27s, is as visual as it is audible. All three of these poets went beyond the constraints of poetry trapped in traditional form Additionally, I am including my own work of poetry, The Manipulation of Echoes in a Shallow Canyon in this study. I am a poet and a breaker of rules. Part of my desire to begin this study in the first place is to exonerate my poetry and myself, and to be taken seriously as a writer