No Escape

The initial idea for the film came from an inspiring performance of Chaplin's Easy Street (1917) accompanied by Donald MacKenzie, resident organist at the Odeon Leicester Square, which led me into researches of early cinema (c1895-1907), a period described by Tom Gunning as the ‘cinema of attractions’. James Lastra points out that during this time competition between cinemas was based on the success of various sound strategies all emphasising the ‘liveness’ of the film experience and films were made to motivate particular types of sound accompaniment. Particularly intriguing was the use of live sound effects performed by a skilled troupe from behind the film screen to produce ‘realistic’ sound effects. This is translated in No Escape into the manipulation of on-screen diegetic sound, also inspired by Pierre Schaeffer's musique concrète and his notions of the sound object and reduced listening. The interaction between the live piano and the onscreen sound is crucial to No Escape as is that of the piano and images, which exist alone together for long stretches. The visual content and structure of the film draws on the city symphonies of Walter Ruttman and especially Dziga Vertov whose formal experimentation, startling juxtaposition of images and very rapid editing is important to No Escape’s non-narrative and at times complex montage of British rural and urban vistas. Vertov’s Man with a Movie Camera (1929) is by and partially about the man with the camera as is No Escape, the title of which refers to the idea that though we may travel to get away from something, there is no escape from the inner life. This is represented by the piano music, which varies but within fairly restricted limits. It does respond or drive image choice and editing but the overall sense should be that one cannot escape and these responses are temporary and fleeting Extrapolating from Tom Gunning's cinema of attractions, James Beattie's concept of ‘documentary display’ - a poetic, sensual and subjective approach which encourages listening and looking rather than cognitive understanding - underpins the aesthetic of No Escape, as is a belief in the supremacy of sound and of film as a performative event

Introduction to Vassiliev Knot Invariants

This book is a detailed introduction to the theory of finite type (Vassiliev) knot invariants, with a stress on its combinatorial aspects. It is intended to serve both as a textbook for readers with no or little background in this area, and as a guide to some of the more advanced material. Our aim is to lead the reader to understanding by means of pictures and calculations, and for this reason we often prefer to convey the idea of the proof on an instructive example rather than give a complete argument. While we have made an effort to make the text reasonably self-contained, an advanced reader is sometimes referred to the original papers for the technical details of the proofs. Version 3: some typos and inaccuracies are corrected.Comment: 512 pages, thousands picture

Ribbon Graph Minors and Low-Genus Partial Duals

We give an excluded minor characterisation of the class of ribbon graphs that admit partial duals of Euler genus at most one

Bipartite partial duals and circuits in medial graphs

It is well known that a plane graph is Eulerian if and only if its geometric dual is bipartite. We extend this result to partial duals of plane graphs. We then characterize all bipartite partial duals of a plane graph in terms of oriented circuits in its medial graph.Comment: v2: minor changes. To appear in Combinatoric

Generalization of the Bollob\'as-Riordan polynomial for tensor graphs

Tensor models are used nowadays for implementing a fundamental theory of quantum gravity. We define here a polynomial $\mathcal T$ encoding the supplementary topological information. This polynomial is a natural generalization of the Bollob\'as-Riordan polynomial (used to characterize matrix graphs) and is different of the Gur\uau polynomial, (R. Gur\uau, "Topological Graph Polynomials in Colored Group Field Theory", Annales Henri Poincare {\bf 11}, 565-584 (2010)) defined for a particular class of tensor graphs, the colorable ones. The polynomial $\mathcal T$ is defined for both colorable and non-colorable graphs and it is proved to satisfy the contraction/deletion relation. A non-trivial example of a non-colorable graphs is analyzed.Comment: 22 pages, 20 figure

Explicit computation of Drinfeld associator in the case of the fundamental representation of gl(N)

We solve the regularized Knizhnik-Zamolodchikov equation and find an explicit expression for the Drinfeld associator. We restrict to the case of the fundamental representation of $gl(N)$. Several tests of the results are presented. It can be explicitly seen that components of this solution for the associator coincide with certain components of WZW conformal block for primary fields. We introduce the symmetrized version of the Drinfeld associator by dropping the odd terms. The symmetrized associator gives the same knot invariants, but has a simpler structure and is fully characterized by one symmetric function which we call the Drinfeld prepotential.Comment: 14 pages, 2 figures; several flaws indicated by referees correcte

Resolving brane collapse with 1/N corrections in non-Abelian DBI

A collapsing spherical D2-brane carrying magnetic flux can be described in the region of small radius in a dual zero-brane picture using Tseytlin's proposal for a non-Abelian Dirac-Born-Infeld action for N D0-branes. A standard large N approximation of the D0-brane action, familiar from the brane dielectric effect, gives a time evolution which agrees with the Abelian D2-brane Born-Infeld equations which describe a D2-brane collapsing to zero size. The first 1/N correction from the symmetrised trace prescription in the zero-brane action leads to a class of classical solutions where the minimum radius of a collapsing D2-brane is lifted away from zero. We discuss the validity of this approximation to the zero-brane action in the region of the minimum, and explore higher order 1/N corrections as well as an exact finite N example. The 1/N corrected Lagrangians and the finite N example have an effective mass squared which becomes negative in some regions of phase space. We discuss the physics of this tachyonic behaviour.Comment: 51 pages, 5 figures, LaTeX2e. Version 4: Formulae in Section 8 simplifie

Periodic orbits in the restricted three-body problem and Arnold's J+J^+-invariant

We apply Arnold's theory of generic smooth plane curves to Stark-Zeeman systems. This is a class of Hamiltonian dynamical systems that describes the dynamics of an electron in an external electric and magnetic field, and includes many systems from celestial mechanics. Based on Arnold's $J^+$-invariant, we introduce invariants of periodic orbits in planar Stark-Zeeman systems and study their behaviour.Comment: 36 Pages, 16 Figure