Multidimensional minimax single facility location problems with Chebyshev distance are examined within the framework of idempotent algebra. A new algebraic solution based on an extremal property of the eigenvalues of irreducible matrices is given. The solution reduces both unconstrained and constrained location problems to evaluation of the eigenvalue and eigenvectors of an appropriate matrix. ...

Due to the significant increment of the volume of interactions among the population, probabilistic process on complex network can be often utilized to analyse diffusion phenomena in the society, then a number of researchers have studied especially from the perspectives of social network analysis, computer virus spread study, and epidemics study. So far, it has been believed that the largest eig...

In this paper we present a novel technique for wavelet-based corner detection using singular value decomposition (SVD). Here SVD facilitates the selection of global natural scale in discrete wavelet transform. We define natural scale as the level associated with most prominent (dominant) eigenvalue. Eigenvector corresponding to dominant eigenvalue is considered as the natural scale. The corners...

Pile buckling is infrequent, but sometimes it can occur in slender piles (i.e., micropiles) driven into soils with soft layers and/or voids. Buckling analysis of becomes more complex if the pile surrounded by multi-layered soil. In this case, well-known Timoshenko’s solution for no use because refers to single-layered soils. A variational approach herein proposed. The proposed method allows est...

In this paper we present a novel technique for wavelet-based corner detection using singular value decomposition (SVD). Here SVD facilitates the selection of global natural scale in discrete wavelet transform. We de®ne natural scale as the level associated with most prominent (dominant) eigenvalue. Eigenvector corresponding to dominant eigenvalue is considered as the optimal scale. The corners ...

We provide a review of different approaches to linking model structure to observed behavior with a particular view towards using models for theory building. We identify four such approaches, namely the " classical " approach, the " pathway participation " approach, the " eigenvalue elasticity " approach, and the " eigenvector " approach, respectively. We outline our assessment of the strengths ...

The largest eigenvalue λ1 of the adjacency matrix powerfully characterizes dynamic processes on networks, such as virus spread and synchronization. The minimization of the spectral radius by removing a set of links (or nodes) has been shown to be an NP-complete problem. So far, the best heuristic strategy is to remove links/nodes based on the principal eigenvector corresponding to the largest e...

This paper introduces activity recognition based on our proposed array sensor. The array sensor consists of an antenna array on the receiver side and decomposes received signals into eigenvectors and eigenvalues. It exploits these components depending on its applications, such as activity recognition. When an event occurs, the propagation environment changes, and thus the eigenvector and eigenv...

We are now going to begin our study of the other eigenvalues and eigenvectors of the Laplacian. I will begin the lecture by showing how much of the theory we established can be preserved. We will then determine the eigenvalues of the hypercube, and begin to see why λ 2 is so important. Recall that we showed that the kth eigenvector of a path graph crosses the origin at most k − 1 times. For exa...