Stationary waves on nonlinear quantum graphs: General framework and canonical perturbation theory

In this paper we present a general framework for solving the stationary nonlinear Schr\"odinger equation (NLSE) on a network of one-dimensional wires modelled by a metric graph with suitable matching conditions at the vertices. A formal solution is given that expresses the wave function and its derivative at one end of an edge (wire) nonlinearly in terms of the values at the other end. For the cubic NLSE this nonlinear transfer operation can be expressed explicitly in terms of Jacobi elliptic functions. Its application reduces the problem of solving the corresponding set of coupled ordinary nonlinear differential equations to a finite set of nonlinear algebraic equations. For sufficiently small amplitudes we use canonical perturbation theory which makes it possible to extract the leading nonlinear corrections over large distances.Comment: 26 page

Indoor Activity Detection and Recognition for Sport Games Analysis

Activity recognition in sport is an attractive field for computer vision research. Game, player and team analysis are of great interest and research topics within this field emerge with the goal of automated analysis. The very specific underlying rules of sports can be used as prior knowledge for the recognition task and present a constrained environment for evaluation. This paper describes recognition of single player activities in sport with special emphasis on volleyball. Starting from a per-frame player-centered activity recognition, we incorporate geometry and contextual information via an activity context descriptor that collects information about all player's activities over a certain timespan relative to the investigated player. The benefit of this context information on single player activity recognition is evaluated on our new real-life dataset presenting a total amount of almost 36k annotated frames containing 7 activity classes within 6 videos of professional volleyball games. Our incorporation of the contextual information improves the average player-centered classification performance of 77.56% by up to 18.35% on specific classes, proving that spatio-temporal context is an important clue for activity recognition.Comment: Part of the OAGM 2014 proceedings (arXiv:1404.3538

Quantum Corrections to Fidelity Decay in Chaotic Systems

By considering correlations between classical orbits we derive semiclassical expressions for the decay of the quantum fidelity amplitude for classically chaotic quantum systems, as well as for its squared modulus, the fidelity or Loschmidt echo. Our semiclassical results for the fidelity amplitude agree with random matrix theory (RMT) and supersymmetry predictions in the universal Fermi golden rule regime. The calculated quantum corrections can be viewed as arising from a static random perturbation acting on nearly self-retracing interfering paths, and hence will be suppressed for time-varying perturbations. Moreover, using trajectory-based methods we show a relation, recently obtained in RMT, between the fidelity amplitude and the cross-form factor for parametric level correlations. Beyond RMT, we compute Ehrenfest-time effects on the fidelity amplitude. Furthermore our semiclassical approach allows for a unified treatment of the fidelity, both in the Fermi golden rule and Lyapunov regimes, demonstrating that quantum corrections are suppressed in the latter.Comment: 14 pages, 4 figure

A sub-determinant approach for pseudo-orbit expansions of spectral determinants in quantum maps and quantum graphs

We study implications of unitarity for pseudo-orbit expansions of the spectral determinants of quantum maps and quantum graphs. In particular, we advocate to group pseudo-orbits into sub-determinants. We show explicitly that the cancellation of long orbits is elegantly described on this level and that unitarity can be built in using a simple sub-determinant identity which has a non-trivial interpretation in terms of pseudo-orbits. This identity yields much more detailed relations between pseudo orbits of different length than known previously. We reformulate Newton identities and the spectral density in terms of sub-determinant expansions and point out the implications of the sub-determinant identity for these expressions. We analyse furthermore the effect of the identity on spectral correlation functions such as the auto-correlation and parametric cross correlation functions of the spectral determinant and the spectral form factor.Comment: 25 pages, one figur

Getting an Heir: Adoption and the Construction of Kinship in Late Imperial China

Humanities Open Book Program, a joint initiative of the National Endowment for the Humanities and the Andrew W. Mellon FoundationThe need for heirs in any traditional society is a compelling one. In traditional China, where inheritance and notions of filiality depended on the production of progeny, the need was nearly absolute. As Ann Waltner makes clear in this broadly researched study of adoption in the late Ming and early Ch'ing periods, the getting of an heir was a complex, even paradoxical undertaking. Although adoption involving persons of the same surname was the only arrangement ritually and legally sanctioned in Chinese society, adoption of persons of a different surname was a relatively common practice. Using medical and ritual texts, legal codes, local gazetteers, biography, and fiction, Waltner examines the multiple dimensions of the practice of adoption and identifies not only the dominant ideology prohibiting adoption across surname lines, but also a parallel discourse justifying the practice