Abstract. Manifold learning has been successfully used for finding dominant factors (low-dimensional manifold) in a high-dimensional data set. However, most existing manifold learning algorithms only consider one manifold based on one dissimilarity matrix. For utilizing multiple manifolds, a key question is how different pieces of information can be integrated when multiple measurements are ava...

Abstract This article is a natural continuation of the paper Tiwari, D., Giordano, P., Hyperseries in non-Archimedean ring Colombeau generalized numbers this journal. We study one variable hyper-power series by analyzing notion radius convergence and proving classical results such as algebraic operations, composition reciprocal series. then define real analytic functions, considering their deri...

We find the conditions under which a Riemannian manifold equipped with a closed threeform and a vector field define an on–shell N = (2, 2) supersymmetric gauged sigma model. The conditions are that the manifold admits a twisted generalized Kähler structure, that the vector field preserves this structure, and that a so–called generalized moment map exists for it. By a theorem in generalized comp...

We investigate the existence of a true invariant manifold given an approximately invariant manifold for an infinite-dimensional dynamical system. We prove that if the given manifold is approximately invariant and approximately normally hyperbolic, then the dynamical system has a true invariant manifold nearby. We apply this result to reveal the global dynamics of boundary spike states for the g...

Maximum flow problem on hypergraphs (hyper-networks) is an extension of maximum flow problem on normal graphs. In this paper, we consider a generalized fuzzy version of maximum flow problem in hyper-networks setting. Our algorithm is a class of genetic algorithms and based on genetic tricks. The crisp equivalents of fuzzy chance constraints in hyper-networks setting are defined, and the executi...

This work proposes a model-reduction approach for the material point method on nonlinear manifolds. Our technique approximates kinematics by approximating deformation map using an implicit neural representation that restricts trajectories to reside low-dimensional manifold. By explicitly map, its spatiotemporal gradients—in particular gradient and velocity—can be computed via analytical differe...