1,840 research outputs found
Nonlinear cross Gramians and gradient systems
We study the notion of cross Gramians for non-linear gradient systems, using the characterization in terms of prolongation and gradient extension associated to the system. The cross Gramian is given for the variational system associated to the original nonlinear gradient system. We obtain linearization results that precisely correspond to the notion of a cross Gramian for symmetric linear systems. Furthermore, first steps towards relations with the singular value functions of the nonlinear Hankel operator are studied and yield promising results.
Unsupervised Domain Adaptation for 3D Keypoint Estimation via View Consistency
In this paper, we introduce a novel unsupervised domain adaptation technique
for the task of 3D keypoint prediction from a single depth scan or image. Our
key idea is to utilize the fact that predictions from different views of the
same or similar objects should be consistent with each other. Such view
consistency can provide effective regularization for keypoint prediction on
unlabeled instances. In addition, we introduce a geometric alignment term to
regularize predictions in the target domain. The resulting loss function can be
effectively optimized via alternating minimization. We demonstrate the
effectiveness of our approach on real datasets and present experimental results
showing that our approach is superior to state-of-the-art general-purpose
domain adaptation techniques.Comment: ECCV 201
Integral Human Pose Regression
State-of-the-art human pose estimation methods are based on heat map
representation. In spite of the good performance, the representation has a few
issues in nature, such as not differentiable and quantization error. This work
shows that a simple integral operation relates and unifies the heat map
representation and joint regression, thus avoiding the above issues. It is
differentiable, efficient, and compatible with any heat map based methods. Its
effectiveness is convincingly validated via comprehensive ablation experiments
under various settings, specifically on 3D pose estimation, for the first time
Inflectional loci of scrolls
Let be a scroll over a smooth curve and let
\L=\mathcal O_{\mathbb P^N}(1)|_X denote the hyperplane bundle. The special
geometry of implies that some sheaves related to the principal part bundles
of \L are locally free. The inflectional loci of can be expressed in
terms of these sheaves, leading to explicit formulas for the cohomology classes
of the loci. The formulas imply that the only uninflected scrolls are the
balanced rational normal scrolls.Comment: 9 pages, improved version. Accepted in Mathematische Zeitschrif
Birkhoff Normal form for Gravity Water Waves
We consider the gravity water waves system with a one-dimensional periodic interface in infinite depth, and present the proof of the rigorous reduction of these equations to their cubic Birkhoff normal form (Berti et al. in Birkhoff normal form and long-time existence for periodic gravity Water Waves. arXiv:1810.11549, 2018). This confirms a conjecture of Zakharov\u2013Dyachenko (Phys Lett A 190:144\u2013148, 1994) based on the formal Birkhoff integrability of the water waves Hamiltonian truncated at degree four. As a consequence, we also obtain a long-time stability result: periodic perturbations of a flat interface that are of size \u3b5 in a sufficiently smooth Sobolev space lead to solutions that remain regular and small up to times of order \u3b5 123
Graph complexes in deformation quantization
Kontsevich's formality theorem and the consequent star-product formula rely
on the construction of an -morphism between the DGLA of polyvector
fields and the DGLA of polydifferential operators. This construction uses a
version of graphical calculus. In this article we present the details of this
graphical calculus with emphasis on its algebraic features. It is a morphism of
differential graded Lie algebras between the Kontsevich DGLA of admissible
graphs and the Chevalley-Eilenberg DGLA of linear homomorphisms between
polyvector fields and polydifferential operators. Kontsevich's proof of the
formality morphism is reexamined in this light and an algebraic framework for
discussing the tree-level reduction of Kontsevich's star-product is described.Comment: 39 pages; 3 eps figures; uses Xy-pic. Final version. Details added,
mainly concerning the tree-level approximation. Typos corrected. An abridged
version will appear in Lett. Math. Phy
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