A Feynman integral via higher normal functions

We study the Feynman integral for the three-banana graph defined as the scalar two-point self-energy at three-loop order. The Feynman integral is evaluated for all identical internal masses in two space-time dimensions. Two calculations are given for the Feynman integral; one based on an interpretation of the integral as an inhomogeneous solution of a classical Picard-Fuchs differential equation, and the other using arithmetic algebraic geometry, motivic cohomology, and Eisenstein series. Both methods use the rather special fact that the Feynman integral is a family of regulator periods associated to a family of K3 surfaces. We show that the integral is given by a sum of elliptic trilogarithms evaluated at sixth roots of unity. This elliptic trilogarithm value is related to the regulator of a class in the motivic cohomology of the K3 family. We prove a conjecture by David Broadhurst that at a special kinematical point the Feynman integral is given by a critical value of the Hasse-Weil L-function of the K3 surface. This result is shown to be a particular case of Deligne's conjectures relating values of L-functions inside the critical strip to periods.Comment: Latex. 70 pages. 3 figures. v3: minor changes and clarifications. Version to appear in Compositio Mathematic

General Rotating Charged Kaluza-Klein AdS Black Holes in Higher Dimensions

I construct exact solutions for general nonextremal rotating, charged Kaluza-Klein black holes with a cosmological constant and with arbitrary angular momenta in all higher dimensions. I then investigate their thermodynamics and find their generalizations with the NUT charges. The metrics are given in both Boyer-Lindquist coordinates and a form very similar to the famous Kerr-Schild ansatz, which highlights its potential application to include multiple electric charges into solutions yet to be found in gauged supergravity. It is also observed that the metric ansatz in $D = 4$ dimensions is similar to those previously suggested by Yilmaz and later by Bekenstein.Comment: 5 pages, revtex4.cl

Authorship, autobiography and the archive: Marilyn on Marilyn, television and documentary theory

In 2004, documentary theorist Michael Renov described ‘the recent turn to filmic autobiography’ as ‘the defining trend of “post-verite” documentary practice...’ In 2008 Renov went further still, suggesting that ‘the very idea of autobiography challenges/reinvents the VERY IDEA of documentary.’ Archive based autobiographical filmmaking, meanwhile, is even more problematic for documentary theory. Indeed, a number of recent documentaries, because of their status somewhere in the spectrum between biography and autobiography, have prompted the construction of an entirely new conceptual category, deploying archival film, often in the form of home movies, to document the lives of their human subjects in Renov’s formulation ‘shared textual authority’. In this article I examine one of ‘my’ own archive based documentaries, ‘Marilyn on Marilyn’ (BBC2 2001), as a way of asking questions not just about biographical and autobiographical documentary but also - and perhaps more urgently - about attributions of authorship in archive-based documentary

The magnificent seven Mirisch companies: competitive strategy and corporate authorship

The Mirisch Company (and its six corporate siblings) was the most commercially and critically successful independent production company in Hollywood in the late 1950s and 1960s – winning Best Picture Oscar three times between 1960 and 1967 and supplying United Artists with five of its ten most profitable films between 1957 and 1969. However, there is still no academic study of the company. In this chapter, I ask whether understanding how the Mirisch companies operated as suppliers for UA (1957 to 1974) helps explain why so many memorable late fifties, sixties and early seventies films including Some Like it Hot, The Magnificent Seven, The Apartment, West Side Story, The Great Escape, The Pink Panther, In the Heat of the Night, The Thomas Crown Affair and Fiddler on the Roof were all made by the Mirisches? Would expanding our knowledge, not just of the individuals working there, but also of their corporate working practices, their business structures and strategies, enable us to understand the characteristics such films may have in common – and why - and distinguish them from other contemporaneous Hollywood productions and production companies? To answer those questions, I rely on Michael E Porter’s book, Competitive Strategy and on the concept of corporate authorship

Rational-spline approximation with automatic tension adjustment

An algorithm for weighted least-squares approximation with rational splines is presented. A rational spline is a cubic function containing a distinct tension parameter for each interval defined by two consecutive knots. For zero tension, the rational spline is identical to a cubic spline; for very large tension, the rational spline is a linear function. The approximation algorithm incorporates an algorithm which automatically adjusts the tension on each interval to fulfill a user-specified criterion. Finally, an example is presented comparing results of the rational spline with those of the cubic spline

A user oriented computer program for the analysis of microwave mixers, and a study of the effects of the series inductance and diode capacitance on the performance of some simple mixers

A user oriented computer program for analyzing microwave and millimeter wave mixers with a single Schottky barrier diode of known I-V and C-V characteristics is described. The program first performs a nonlinear analysis to determine the diode conductance and capacitance waveforms produced by the local oscillator. A small signal linear analysis is then used to find the conversion loss, port impedances, and input noise temperature of the mixer. Thermal noise from the series resistance of the diode and shot noise from the periodically pumped current in the diode conductance are considered. The effects of the series inductance and diode capacitance on the performance of some simple mixer circuits using a conventional Schottky diode, a Schottky diode in which there is no capacitance variation, and a Mott diode are studied. It is shown that the parametric effects of the voltage dependent capacitance of a conventional Schottky diode may be either detrimental or beneficial depending on the diode and circuit parameters