
A mathematical framework for graph signal processing of timevarying signals
We propose a general framework from which to understand the design of fi...
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Characterizing total negativity and testing their interval hulls
A matrix is called totally negative (totally nonpositive) of order k, i...
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Copulas and Preserver Problems
Preserver problems concern the characterization of operators on general ...
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Identification of linear timeinvariant systems with Dynamic Mode Decomposition
Dynamic mode decomposition (DMD) is a popular datadriven framework to e...
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Sign nonreversal property for totally positive matrices and testing total positivity on their interval hull
We establish a novel characterization of totally positive matrices via a...
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Addition Machines, Automatic Functions and Open Problems of Floyd and Knuth
Floyd and Knuth investigated in 1990 register machines which can add, su...
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Toward an Algebraic Theory of Systems
We propose the concept of a system algebra with a parallel composition o...
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Variation diminishing linear timeinvariant systems
This paper studies the variation diminishing property of kpositive systems, which map inputs with k1 sign changes to outputs with at most the same variation. We characterize this property for the Toeplitz and Hankel operators of finitedimensional linear time invariant systems. Our main result is that these operators have a dominant approximation in the form of series or parallel interconnections of k first order positive systems. This is shown by expressing the kpositivity of a LTI system as the external positivity (that is, 1positivity) of k compound LTI systems. Our characterization generalizes well known properties of externally positive systems (k=1) and totally positive systems (k=∞).
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