ar X iv : s ub m it / 07 37 83 1 [ cs . S Y ] 1 3 Ju n 20 13 The Deformed Consensus Protocol Extended
نویسنده
چکیده
This paper studies a generalization of the standard continuous-time consensus protocol, obtained by replacing the Laplacian matrix of the communication graph with the so-called deformed Laplacian. The deformed Laplacian is a second-degree matrix polynomial in the real variable s which reduces to the standard Laplacian for s equal to unity. The stability properties of the ensuing deformed consensus protocol are studied in terms of parameter s for some special families of undirected and directed graphs, and for arbitrary graph topologies by leveraging the spectral theory of quadratic eigenvalue problems. Examples and simulation results are provided to illustrate our theoretical findings.
منابع مشابه
ar X iv : n uc l - th / 9 40 60 13 v 1 1 0 Ju n 19 94 Shape Coexistence Around 4416 S 28 : The Deformed N = 28 Region
Masses, deformations, radii, and single-particle properties of the very neutron-rich Sulfur isotopes are investigated in the framework of the self-consistent mean-field theory. The stability of the N=28 magic gap around 44 S is discussed.
متن کاملar X iv : m at h / 06 06 28 9 v 1 [ m at h . A G ] 1 2 Ju n 20 06 On correspondences of a K 3 surface with itself . IV
Let X be a K3 surface with a polarization H of the degree H 2 = 2rs, r, s ≥ 1, and the isotropic Mukai vector v = (r, H, s) is primitive. The moduli space of sheaves over X with the isotropic Mukai vector (r, H, s) is again a K3 surface, Y. In [11] the second author gave necessary and sufficient conditions in terms of Picard lattice N (X) of X when Y is isomorphic to X (some important particula...
متن کاملar X iv : m at h / 02 01 07 7 v 3 [ m at h . G N ] 1 6 Ja n 20 03 A family of pseudo metrics on B 3 and its application
We define a family of pseudo metrics on B and study elementary properties of the associated metric spaces. As an application we prove that, for any a > 0 and for any countable-to-one function f from (S, dE) to [0, a], the set NMnf = {x ∈ S 2 | ∃y ∈ S such that f(x)− f(y) > ndE(x, y)} is uncountable for all n ∈ N, where dE is the standard Euclidean metric on S = { (x, y, z) ∈ R | x + y + z = 1 }
متن کاملar X iv : m at h / 06 06 28 9 v 2 [ m at h . A G ] 1 9 Ju n 20 06 On correspondences of a K 3 surface with itself . IV
Let X be a K3 surface with a polarization H of the degree H 2 = 2rs, r, s ≥ 1, and the isotropic Mukai vector v = (r, H, s) is primitive. Moduli space of sheaves over X with the isotropic Mukai vector (r, H, s) is again a K3 surface, Y. In [12] second author gave necessary and sufficient conditions in terms of Picard lattice N (X) of X when Y is isomorphic to X (important particular cases were ...
متن کاملar X iv : m at h / 03 03 37 7 v 2 [ m at h . G T ] 1 3 Ju n 20 03 ALMOST NORMAL HEEGAARD SURFACES
We present a new and shorter proof of Stocking's result that any strongly irreducible Heegaard surface of a closed orientable triangulated 3– manifold is isotopic to an almost normal surface. To make our paper essentially self-contained, we reprove a result of Jaco and Rubinstein on normal spheres, Scharlemann's " no nesting " lemma, and the fact that S 3 has no strongly irre-ducible Heegaard s...
متن کامل