Romantic Partnerships and the Dispersion of Social Ties: A Network Analysis of Relationship Status on Facebook

A crucial task in the analysis of on-line social-networking systems is to identify important people --- those linked by strong social ties --- within an individual's network neighborhood. Here we investigate this question for a particular category of strong ties, those involving spouses or romantic partners. We organize our analysis around a basic question: given all the connections among a person's friends, can you recognize his or her romantic partner from the network structure alone? Using data from a large sample of Facebook users, we find that this task can be accomplished with high accuracy, but doing so requires the development of a new measure of tie strength that we term `dispersion' --- the extent to which two people's mutual friends are not themselves well-connected. The results offer methods for identifying types of structurally significant people in on-line applications, and suggest a potential expansion of existing theories of tie strength.Comment: Proc. 17th ACM Conference on Computer Supported Cooperative Work and Social Computing (CSCW), 201

Representations of p-brane topological charge algebras

The known extended algebras associated with p-branes are shown to be generated as topological charge algebras of the standard p-brane actions. A representation of the charges in terms of superspace forms is constructed. The charges are shown to be the same in standard/extended superspace formulations of the action.Comment: 22 pages. Typos fixed, refs added. Minor additions to comments sectio

Remarks on Legendrian Self-Linking

The Thurston-Bennequin invariant provides one notion of self-linking for any homologically-trivial Legendrian curve in a contact three-manifold. Here we discuss related analytic notions of self-linking for Legendrian knots in Euclidean space. Our definition is based upon a reformulation of the elementary Gauss linking integral and is motivated by ideas from supersymmetric gauge theory. We recover the Thurston-Bennequin invariant as a special case.Comment: 42 pages, many figures; v2: minor revisions, published versio

The Non-Trapping Degree of Scattering

We consider classical potential scattering. If no orbit is trapped at energy E, the Hamiltonian dynamics defines an integer-valued topological degree. This can be calculated explicitly and be used for symbolic dynamics of multi-obstacle scattering. If the potential is bounded, then in the non-trapping case the boundary of Hill's Region is empty or homeomorphic to a sphere. We consider classical potential scattering. If at energy E no orbit is trapped, the Hamiltonian dynamics defines an integer-valued topological degree deg(E) < 2. This is calculated explicitly for all potentials, and exactly the integers < 2 are shown to occur for suitable potentials. The non-trapping condition is restrictive in the sense that for a bounded potential it is shown to imply that the boundary of Hill's Region in configuration space is either empty or homeomorphic to a sphere. However, in many situations one can decompose a potential into a sum of non-trapping potentials with non-trivial degree and embed symbolic dynamics of multi-obstacle scattering. This comprises a large number of earlier results, obtained by different authors on multi-obstacle scattering.Comment: 25 pages, 1 figure Revised and enlarged version, containing more detailed proofs and remark

Pattern equivariant functions and cohomology

The cohomology of a tiling or a point pattern has originally been defined via the construction of the hull or the groupoid associated with the tiling or the pattern. Here we present a construction which is more direct and therefore easier accessible. It is based on generalizing the notion of equivariance from lattices to point patterns of finite local complexity.Comment: 8 pages including 2 figure

Putting String/Fivebrane Duality to the Test

According to string/fivebrane duality, the Green-Schwarz factorization of the $D=10$ spacetime anomaly polynomial $I_{12}$ into $X_4\, X_8$ means that just as $X_4$ is the anomaly polynomial of the $d=2$ string worldsheet so $X_8$ should be the anomaly polynomial of the $d=6$ fivebrane worldvolume. To test this idea we perform a fivebrane calculation of $X_8$ and find perfect agreement with the string one--loop result.Comment: 14 pages, CERN TH-6614/92, CTP-TAMU 60/9

Representation theory of finite W algebras

In this paper we study the finitely generated algebras underlying $W$ algebras. These so called 'finite $W$ algebras' are constructed as Poisson reductions of Kirillov Poisson structures on simple Lie algebras. The inequivalent reductions are labeled by the inequivalent embeddings of $sl_2$ into the simple Lie algebra in question. For arbitrary embeddings a coordinate free formula for the reduced Poisson structure is derived. We also prove that any finite $W$ algebra can be embedded into the Kirillov Poisson algebra of a (semi)simple Lie algebra (generalized Miura map). Furthermore it is shown that generalized finite Toda systems are reductions of a system describing a free particle moving on a group manifold and that they have finite $W$ symmetry. In the second part we BRST quantize the finite $W$ algebras. The BRST cohomology is calculated using a spectral sequence (which is different from the one used by Feigin and Frenkel). This allows us to quantize all finite $W$ algebras in one stroke. Explicit results for $sl_3$ and $sl_4$ are given. In the last part of the paper we study the representation theory of finite $W$ algebras. It is shown, using a quantum version of the generalized Miura transformation, that the representations of finite $W$ algebras can be constructed from the representations of a certain Lie subalgebra of the original simple Lie algebra. As a byproduct of this we are able to construct the Fock realizations of arbitrary finite $W$ algebras.Comment: 62 pages, THU-92/32, ITFA-28-9

Liouville integrability of a class of integrable spin Calogero-Moser systems and exponents of simple Lie algebras

In previous work, we introduced a class of integrable spin Calogero-Moser systems associated with the classical dynamical r-matrices with spectral parameter, as classified by Etingof and Varchenko for simple Lie algebras. Here the main purpose is to establish the Liouville integrability of these systems by a uniform method

Coherent Backscattering of light in a magnetic field

This paper describes how coherent backscattering is altered by an external magnetic field. In the theory presented, magneto-optical effects occur inside Mie scatterers embedded in a non-magnetic medium. Unlike previous theories based on point-like scatterers, the decrease of coherent backscattering is obtained in leading order of the magnetic field using rigorous Mie theory. This decrease is strongly enhanced in the proximity of resonances, which cause the path length of the wave inside a scatterer to be increased. Also presented is a novel analysis of the shape of the backscattering cone in a magnetic field.Comment: 27 pages, 5 figures, Revtex, to appear in Phys. Rev.

Mapping between dissipative and Hamiltonian systems

Theoretical studies of nonequilibrium systems are complicated by the lack of a general framework. In this work we first show that a transformation introduced by Ao recently (J. Phys. A {\bf 37}, L25 (2004)) is related to previous works of Graham (Z. Physik B {\bf 26}, 397 (1977)) and Eyink {\it et al.} (J. Stat. Phys. {\bf 83}, 385 (1996)), which can also be viewed as the generalized application of the Helmholtz theorem in vector calculus. We then show that systems described by ordinary stochastic differential equations with white noise can be mapped to thermostated Hamiltonian systems. A steady-state of a dissipative system corresponds to the equilibrium state of the corresponding Hamiltonian system. These results provides a solid theoretical ground for corresponding studies on nonequilibrium dynamics, especially on nonequilibrium steady state. The mapping permits the application of established techniques and results for Hamiltonian systems to dissipative non-Hamiltonian systems, those for thermodynamic equilibrium states to nonequilibrium steady states. We discuss several implications of the present work.Comment: 18 pages, no figure. final version for publication on J. Phys. A: Math & Theo