A combinatorial field WG is a multi-field underlying a graph G, established on a smoothly combinatorial manifold. This paper first presents a quick glance to its mathematical basis with motivation, such as those of why the WORLD is combinatorial? and what is a topological or differentiable combinatorial manifold? After then, we explain how to construct principal fiber bundles on combinatorial m...

In this paper, we will study compatible triples on Lie algebroids. Using a suitable decomposition for a Lie algebroid, we construct an integrable generalized distribution on the base manifold. As a result, the symplectic form on the Lie algebroid induces a symplectic form on each integral submanifold of the distribution. The induced Poisson structure on the base manifold can be represented by m...

A distance measure, along with a shape feature, is the most critical components in a shape-based 3D model retrieval system. While various distance measures have been proposed, a single distance measure can’t handle variations per database. We have previously reported that a non-linear manifold learning algorithm that trained unsupervised by a set of 3D models database could significantly improv...

For a compact manifold with boundary X we introduce the n-fold scattering stretched product Xn sc which is a compact manifold with corners for each n, coinciding with the previously known cases for n = 2, 3. It is constructed by iterated blow up of boundary faces and boundary faces of multi-diagonals in Xn. The resulting space is shown to map smoothly, by a b-fibration, covering the usual proje...

Many complex and high dimensional real-world classification problems require a carefully chosen set of features, algorithms and hyperparameters to achieve the desired generalization performance. The choice of a suitable feature representation has a great effect on the prediction performance. Manifold learning techniques – like PCA, Isomap, Local Linear Embedding (LLE) or Autoencoders – are able...

We study multi-pulse solutions in excitable media. Under the assumption that a single pulse is asymptotically stable, we show that there is a well-defined ”shooting manifold”, consisting of two pulses traveling towards each other. In the phase space, the two-dimensional manifold is a graph over the manifold of linear superpositions of two pulses located at x1 and x2, with x1 − x2 1. It is local...

‎The object of the present paper is to introduce and study a type of non-flat semi-Riemannian manifolds‎, ‎called‎, ‎super generalized recurrent manifolds which generalizes both the notion of hyper generalized recurrent manifolds [‎A.A‎. ‎Shaikh and A‎. ‎Patra‎, On a generalized class of recurrent manifolds‎, Arch‎. ‎Math‎. ‎(Brno) 46 (2010) 71--78‎.] and weakly generalized recurrent manifolds ...

The problem of multi-view/view-invariant recognition remains one of the most fundamental challenges to the progress of the computer vision. In this paper we consider the problem of modeling the combined object-viewpoint manifold. The shape and appearance of an object in a given image is a function of its category, style within category, viewpoint, and several other factors. The visual manifold ...

For a compact manifold with boundary X we introduce the n-fold scattering stretched product Xn sc which is a compact manifold with corners for each n; coinciding with the previously known cases for n = 2; 3: It is constructed by iterated blow up of boundary faces and boundary faces of multi-diagonals in Xn: The resulting space is shown to map smoothly, by a bbration, covering the usual projecti...