A positive map between Euclidean Jordan algebras is a (symmetric cone) order preserving linear map. We show that the norm of such a map is attained at the unit element, thus obtaining an analog of the operator/matrix theoretic Russo-Dye theorem. A doubly stochastic map between Euclidean Jordan algebras is a positive, unital, and trace preserving map. We relate such maps to Jordan algebra automo...

We have recently reported the phenomenon of doubly stochastic resonance [Phys. Rev. Lett. 85, 227 (2000)], a synthesis of noise-induced transition and stochastic resonance. The essential feature of this phenomenon is that multiplicative noise induces a bimodality and additive noise causes stochastic resonance behavior in the induced structure. In the present paper we outline possible applicatio...

In this paper, we develop a regularization framework for image deblurring based on a new definition of the normalized graph Laplacian. We apply a fast scaling algorithm to the kernel similarity matrix to derive the symmetric, doubly stochastic filtering matrix from which the normalized Laplacian matrix is built. We use this new definition of the Laplacian to construct a cost function consisting...

Two graphs with adjacency matrices A and B are isomorphic if there exists a permutation matrix P for which the identity PAP = B holds. Multiplying through by P and relaxing the permutation matrix to a doubly stochastic matrix leads to the notion of fractional isomorphism. We show that the levels of the Sherali-Adams hierarchy of linear programming relaxations applied to fractional isomorphism i...

It is becoming to be well-known that an internally stabilizable transfer matrix does not necessarily admit doubly coprime factorizations. The equivalence between these two concepts is still open for important classes of plants. Hence, we may wonder whether or not it is possible to parametrize all stabilizing controllers of an internally stabilizable plant which does not necessarily admit doubly...