Stronger ILPs for the Graph Genus Problem

The minimum genus of a graph is an important question in graph theory and a key ingredient in several graph algorithms. However, its computation is NP-hard and turns out to be hard even in practice. Only recently, the first non-trivial approach - based on SAT and ILP (integer linear programming) models - has been presented, but it is unable to successfully tackle graphs of genus larger than 1 in practice. Herein, we show how to improve the ILP formulation. The crucial ingredients are two-fold. First, we show that instead of modeling rotation schemes explicitly, it suffices to optimize over partitions of the (bidirected) arc set A of the graph. Second, we exploit the cycle structure of the graph, explicitly mapping short closed walks on A to faces in the embedding. Besides the theoretical advantages of our models, we show their practical strength by a thorough experimental evaluation. Contrary to the previous approach, we are able to quickly solve many instances of genus > 1

An Itzykson-Zuber-like Integral and Diffusion for Complex Ordinary and Supermatrices

We compute an analogue of the Itzykson-Zuber integral for the case of arbitrary complex matrices. The calculation is done for both ordinary and supermatrices by transferring the Itzykson-Zuber diffusion equation method to the space of arbitrary complex matrices. The integral is of interest for applications in Quantum Chromodynamics and the theory of two-dimensional Quantum Gravity.Comment: 20 pages, RevTeX, no figures, agrees with published version, including "Note added in proof" with an additional result for rectangular supermatrice

Automated Visual Fin Identification of Individual Great White Sharks

This paper discusses the automated visual identification of individual great white sharks from dorsal fin imagery. We propose a computer vision photo ID system and report recognition results over a database of thousands of unconstrained fin images. To the best of our knowledge this line of work establishes the first fully automated contour-based visual ID system in the field of animal biometrics. The approach put forward appreciates shark fins as textureless, flexible and partially occluded objects with an individually characteristic shape. In order to recover animal identities from an image we first introduce an open contour stroke model, which extends multi-scale region segmentation to achieve robust fin detection. Secondly, we show that combinatorial, scale-space selective fingerprinting can successfully encode fin individuality. We then measure the species-specific distribution of visual individuality along the fin contour via an embedding into a global `fin space'. Exploiting this domain, we finally propose a non-linear model for individual animal recognition and combine all approaches into a fine-grained multi-instance framework. We provide a system evaluation, compare results to prior work, and report performance and properties in detail.Comment: 17 pages, 16 figures. To be published in IJCV. Article replaced to update first author contact details and to correct a Figure reference on page

Bosonic color-flavor transformation for the special unitary group

We extend Zirnbauer's color-flavor transformation in the bosonic sector to the color group SU(N_c). Because the flavor group U(N_b, N_b) is non-compact, the algebraic method by which the original color-flavor transformation was derived leads to a useful result only for 2N_b \le N_c. Using the character expansion method, we obtain a different form of the transformation in the extended range N_b \le N_c. This result can also be used for the color group U(N_c). The integrals to which the transformation can be applied are of relevance for the recently proposed boson-induced lattice gauge theory.Comment: 34 pages, 2 figure