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Quadratic pencils arising from applications are often inherently structured. Factors contributing to the structure include the connectivity of elements within the underlying physical system and the mandatory nonnegativity of physical parameters. For physical feasibility, structural constraints must be respected. Consequently, they impose additional… (More)

We investigated the phenomenon of activity cycles in ants, taking into account the spatial structure of colonies. In our study species, Leptothorax acervorum, there are two spatially segregated groups in the nest. We developed a model that considers the two groups as coupled oscillators which can produce synchronized activity. By investigating the e¡ects of… (More)

In various applications, data in multi-dimensional space are normalized to unit length. This paper considers the problem of best fitting given points on the m-dimensional unit sphere S m−1 by k-dimensional great circles with k much less than m. The task is cast as an algebraically constrained low-rank matrix approximation problem. Using the fidelity of the… (More)

Nonnegative matrix factorization (NMF) is a widely-used method for multivariate analysis of nonnegative data to obtain a reduced representation of data matrix only using a basis matrix and a encoding variable matrix having non-negative elements. A NMF of a data matrix can be obtained by finding a solution of a nonlinear optimization problem over a specified… (More)

Quadratic pencils, λ 2 M + λC + K, where M , C, and K are n × n real matrices with or without some additional properties such as symmetry, connectivity, bandedness, or positive definiteness, arise in many important applications. Recently an existence theory has been established, showing that almost all n-degree-of-freedom second order systems can be reduced… (More)

We study the problem of detecting and localizing objects in still, gray-scale images making use of the part-based representation provided by non-negative matrix factorizations. Non-negative matrix factoriza-tion represents an emerging example of subspace methods which is able to extract interpretable parts from a set of template image objects and then to… (More)