The article presents a method for both the unsupervised partitioning of a sample of data and the estimation of the possible number of inherent clusters which generate the data. This work exploits the notion that performing a nonlinear data transformation into some high dimensional feature space increases the probability of the linear separability of the patterns within the transformed space and...

Several popular graph embedding techniques for representation learning and dimensionality reduction rely on performing computationally expensive eigendecompositions to derive a nonlinear transformation of the input data space. The resulting eigenvectors encode the embedding coordinates for the training samples only, preventing the transformation of novel data samples without recomputation. In t...

This paper suggests an optimization-based design methodology for improving the strength and overall stability of framed structures, the capacities of which are governed by inelastic limit-load behavior. The optimization objective function, comprising the dominant linearized buckling eigenvalue of the structure weighted by a frequency-dependent penalty function, is motivated by a simple model of...

We consider time-dependent Schrödinger equations in one dimension with doublewell potential and an external nonlinear perturbation. If the initial state belongs to the eigenspace spanned by the eigenvectors associated to the two lowest eigenvalues, then, in the semiclassical limit, we show that the reduction of the time-dependent equation to a 2-mode equation gives the dominant term of the solu...

In this paper, we show that the eigenvectors associated with the zero eigenvalues of the Laplacian and signless Lapacian tensors of a k-uniform hypergraph are closely related to some configured components of that hypergraph. We show that the components of an eigenvector associated with the zero eigenvalue of the Laplacian or signless Lapacian tensor have the same modulus. Moreover, under a cano...

We consider the dynamics of a classical charge in flat spacetime six dimensions. The mass shell relation free admits nonlinear oscillations. Having analyzed problem on eigenvalues and eigenvectors Faraday tensor, we establish algebraic structure electromagnetic field 6D. elaborate classification scheme based three field's invariants. Using basic properties tensor analyze motion constant field. ...

many natural and real-world applications, the measured signals are controlled by underlying processes or drivers. As a result, these signals exhibit highly redundant representations and their temporal evolution can be compactly described by a dynamical process on a low-dimensional manifold. In this paper, we propose a graph-based method for revealing the low-dimensional manifold and inferring t...

Algorithms for nonlinear eigenvalue problems (EP), often require solving selfconsistently a large number of EP. Convergence di culties may occur if the solution is not sought in a right neighborhood; if global constraints have to be satis ed; and if close or equal eigenvalues are present. Multigrid (MG) algorithms for nonlinear problems and for EP obtained from discretizations of partial di ere...

be an orthonormal basis of H consisting of eigenvectors of A where {ek : k ∈ N} is a set of eigenvectors of A corresponding to nonzero eigenvalues of A and {fm : m ∈ I} is a set of eigenvectors of A corresponding to the zero eigenvalue (we know that we may assume that I is a countable set by exercise 6.10). We make the assumption that the elements of {ek : k ∈ N} are ordered so that the first e...