The Novikov equation is an integrable analogue of the CamassaHolm equation with a cubic (rather than quadratic) nonlinear term. Both these equations support a special family of weak solutions called multipeakon solutions. In this paper, an approach involving Pfaffians is applied to study multipeakons of the Novikov equation. First, we show that the Novikov peakon ODEs describe an isospectral flow on the manifold cut out by certain Pfaffian identities. Then, a link between the Novikov peakons and the finite Toda lattice of BKP type (B-Toda lattice) is established based on the use of Pfaffians. Finally, certain generalizations of the Novikov equation and the finite B-Toda lattice are proposed together with special solutions. To our knowledge, it is the first time that the peakon problem is interpreted in terms of Pfaffians.

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We present an automatic reconstruction pipeline for large scale urban scenes from aerial images captured by a camera mounted on an unmanned aerial vehicle. Using state-of-the-art Structure from Motion and Multi-View Stereo algorithms, we first generate a dense point cloud from the aerial images. Based on the statistical analysis of the footprint grid of the buildings, the point cloud is classified into different categories (i.e., buildings, ground, trees, and others). Roof structures are extracted for each individual building using Markov random field optimization. Then, a contour refinement algorithm based on pivot point detection is utilized to refine the contour of patches. Finally, polygonal mesh models are extracted from the refined contours. Experiments on various scenes as well as comparisons with state-of-the-art reconstruction methods demonstrate the effectiveness and robustness of the proposed method.

The Hidden Field Equations (HFE) Cryptosystem as proposed by Patarin is one of the best known and most studied multivariate schemes. While the security of the basic scheme appeared to be very weak, the HFEv- variant seems to be a good candidate for digital signature schemes on the basis of multivariate polynomials. However, the currently existing scheme of this type, the QUARTZ signature scheme, is hardly used in practice because of its poor efficiency. In this paper we analyze recent results from Ding and Yang about the degree of regularity of HFEv- systems and derive from them design principles for signature schemes of the HFEv- type. Based on these results we propose the new HFEv- based signature scheme Gui, which is more than 100 times faster than QUARTZ and therefore highly comparable with classical signature schemes such as RSA and ECDSA.

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