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...

We take advantage of different generalizations of the tangent manifold to the context of graded manifolds, together with the notion of super section along a morphism of graded manifolds, to obtain intrinsic definitions of the main objects in supermechanics such as, the vertical endomorphism, the canonical and the Cartan’s graded forms, the total time derivative operator and the super–Legendre t...

in this current study a generalized super-efficiency model is first proposed for ranking extreme efficient decision making units (dmus) in stochastic data envelopment analysis (dea) and then, a deterministic (crisp) equivalent form of the stochastic generalized super-efficiency model is presented. it is shown that this deterministic model can be converted to a quadratic programming model. so fa...

We discuss infinite-dimensional hidden symmetry algebras (and hence an infinite number of conserved nonlocal charges) of the N -extented self-dual super Yang-Mills equations for general N ≤ 4 by using the supertwistor correspondence. Furthermore, by enhancing the supertwistor space, we construct the N -extended self-dual super Yang-Mills hierarchies, which describe infinite sets of graded Abeli...

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...

Near infrared spectroscopy (NIRS) is a non-invasive method to measure brain activity via changes in the degree of hemoglobin oxygenation through the intact skull. As optically measured hemoglobin signals strongly correlate with BOLD signals, simultaneous measurement using NIRS and fMRI promises a significant mutual enhancement of temporal and spatial resolutions. Although there exists a powerfu...

In this paper we introduce the concept of (ε)-almost paracontact manifolds, and in particular, of (ε)-para Sasakian manifolds. Several examples are presented. Some typical identities for curvature tensor and Ricci tensor of (ε)-para Sasakian manifolds are obtained. We prove that if a semi-Riemannian manifold is one of flat, proper recurrent or proper Ricci-recurrent, then it can not admit an (ε...

Full understanding of synchronous behavior in coupled dynamical systems beyond the identical case requires an explicit construction of the generalized synchronization manifold, whether we wish to compare the systems or to understand their stability. Nonetheless, while synchronization has become an extremely popular topic, the bulk of the research in this area has been focused on the identical c...

Based on Colombeau’s theory of algebras of generalized functions we introduce the concepts of generalized functions taking values in differentiable manifolds as well as of generalized vector bundle homomorphisms. We study their basic properties, in particular with respect to some new point value concepts for generalized functions and indicate applications of the resulting theory in general rela...