This article develops tools to quantify the importance of agent interactions and its impact on global performance metrics for networks with scalar states modeled as linear time-invariant systems. We consider Gramian-based propose a novel notion edge centrality that encodes first-order variation in metric respect modification corresponding weight, including those edges not present network. The p...

A common approach in model reduction is balanced truncation, which is based on Gramian matrices classifying certain attributes of states or parameters of a given dynamic system. Initially restricted to linear systems, the empirical Gramians not only extended this concept to nonlinear systems but also provided a uniform computational method. This work introduces a unified software framework supp...

Objective functions for sensor selection are investigated in linear time-invariant systems with a large number of candidates. This study compared the performance sets obtained using three types D-optimality-based indices as objective based on greedy method. The computed snapshot-to-snapshot Fisher information matrix, observability Gramian and Kalman filter-based matrix. Both random eigenmodes c...

The berization of a ne systems via dual Gramian techniques, that was developed in previous papers of the authors, is applied here for the study of a ne frames which have an a ne dual system. Gramian techniques are also used to verify whether a dual pair of a ne frames is a also a pair of bi-orthogonal Riesz bases. A general method for a painless derivation of a dual pair of a ne frames from an ...

In the linear control theory, the observability Popov-Belevitch-Hautus (PBH) test plays an important role in studying observability along with the observability rank condition and observability Gramian. The observability rank condition and observability Gramian have been extended to nonlinear systems and have found applications in the analysis of nonlinear systems. On the other hand, there is n...

The problem we are interested in is the best approximation of a given matrix by a positive semi–definite symmetric Toeplitz matrix. Toeplitz matrices appear naturally in a variety of problems in engineering. Since positive semi–definite Toeplitz matrices can be viewed as shift invariant autocorrelation matrices, considerable attention has been paid to them, especially in the areas of stochastic...

Let X be a graph with vertex set V and let A be its adjacency matrix. If E is the matrix representing orthogonal projection onto an eigenspace of A with dimension m, then E is positive semi-deenite. Hence it is the Gram matrix of a set of jV j vectors in R m. We call the convex hull of a such a set of vectors an eigenpolytope of X. The connection between the properties of this polytope and the ...

A popular series of style transfer methods apply a style to a content image by controlling mean and covariance of values in early layers of a feature stack. This is insufficient for transferring styles that have strong structure across spatial scales like, e.g., textures where dots lie on long curves. This paper demonstrates that controlling inter-layer correlations yields visible improvements ...

Following our paper [Linear Algebra Appl. 433(2010), 699–717], we present a framework and computational tools for the Coxeter spectral classification of finite posets J ≡ (J, ⪯). One of themainmotivations for the study is an application ofmatrix representations of posets in representation theory explained by Drozd [Funct. Anal. Appl. 8(1974), 219–225]. We are mainly interested in a Coxeter spec...