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We determine the bounded cohomology of the group of homeomorphisms of certain low-dimensional manifolds. In particular, for the group of orientation-preserving homeomorphisms of the circle and of the closed 2-disc, it is isomorphic to the polynomial ring g ...
In this work, we focus on the Dynamical Low Rank (DLR) approximation of PDEs equations with random parameters. This can be interpreted as a reduced basis method, where the approximate solution is expanded in separable form over a set of few deterministic b ...
In this paper, the differential geometry of the novel hierarchical Tucker format for tensors is derived. The set HT,k of tensors with fixed tree T and hierarchical rank k is shown to be a smooth quotient manifold, namely the set of orbits of a Lie group ac ...
State-of-the-art 2D image compression schemes rely on the power of convolutional neural networks (CNNs). Although CNNs offer promising perspectives for 2D image compression, extending such models to omnidirectional images is not straightforward. First, omn ...
In this paper, we generalize the famous Hasimoto's transformation by showing that the dynamics of a closed unidimensional vortex filament embedded in a three-dimensional manifold M of constant curvature, gives rise under Hasimoto's transformation to the no ...
This paper describes a two-sweep control design method to stabilize the acrobot, an input-affine under-actuated system, at the upper equilibrium point. In the forward sweep, the system is successively reduced, one dimension at a time, until a two-dimensiona ...
Glacier retreat as a consequence of climate change influences freshwater ecosystems in manifold ways, yet the physical and chemical bases of these effects are poorly studied. Here, we characterize how water temperature differs between alpine lakes with and ...
Manifold models provide low-dimensional representations that are useful for processing and analyzing data in a transformation-invariant way. In this paper, we study the problem of learning smooth pattern transformation manifolds from image sets that are ob ...
Institute of Electrical and Electronics Engineers2013
An algorithmic method is proposed to design stabilizing control laws for a class of nonlinear systems that comprises single-input feedback-linearizable systems and a particular set of single-input non feedback-linearizable systems. The method proceeds iter ...
IEEE Service Center, 445 Hoes Lane, Po Box 1331, Piscataway, Nj 08855-1331 Usa2011
A numerical manifold method (NMM) for plane micropolar elasticity is proposed in this paper to consider the microstructure influence of materials. First, the basic formulations of plane micropolar elasticity are briefly introduced. Then, the equations of s ...
