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Automorphism Groups and Isomorphisms of Cayley Digraphs of Abelian Groups*
"... Let S be a minimal generating subset of the finite abelian group G. We prove that if the Sylow 2subgroup of G is cyclic, then Sand S U Sl are CIsubsets and the corresponding Cayley digraph and graph are normal. Let G be a finite group and let S be a subset of G not containing the identity element ..."
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Let S be a minimal generating subset of the finite abelian group G. We prove that if the Sylow 2subgroup of G is cyclic, then Sand S U Sl are CIsubsets and the corresponding Cayley digraph and graph are normal. Let G be a finite group and let S be a subset of G not containing the identity
CAYLEY DIGRAPHS OF FINITE ABELIAN GROUPS AND MONOMIAL IDEALS∗
"... Abstract. In the study of doubleloop computer networks, the diagrams known as Lshapes arise as a graphical representation of an optimal routing for every graph’s node. The description of these diagrams provides an efficient method for computing the diameter and the average minimum distance of the ..."
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of the corresponding graphs. We extend these diagrams to multiloop computer networks. For each Cayley digraph with a finite abelian group as vertex set, we define a monomial ideal and consider its representations via its minimal system of generators or its irredundant irreducible decomposition. From this last piece
CAYLEY DIGRAPHS OF FINITE ABELIAN GROUPS AND MONOMIAL IDEALS
, 2007
"... In the study of doubleloop computer networks, the diagrams known as Lshapes arise as a graphical representation of an optimal routing for every graph’s node. The description of these diagrams provides an efficient method for computing the diameter and the average minimum distance of the correspon ..."
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of the corresponding graphs. We extend these diagrams to multiloop computer networks. For each Cayley digraph with a finite abelian group as vertex set, we define a monomial ideal and consider its representations via its minimal system of generators or its irredundant irreducible decomposition. From this last piece
Recognizing Abelian Cayley Colored Digraphs
, 2000
"... Given a class S of Cayley digraphs, and given a properly colored digraph G of order n and size m, we are interested in the problem of checking whether there exists an isomorphism preserving the colors such that G is isomorphic by to a digraph in S colored by the elements of its generating set. ..."
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is colorisomorphic to an abelian Cayley digraph (i.e., on a commutative group) where k is the in and outdegree of G. More precisely, we give an O(mr)time algorithm to check whether G is colorisomorphic to a Cayley digraph on an abelian group of rank r. If the answer is armative, then each of our
The irreducibility of the space of curves of given genus
 Publ. Math. IHES
, 1969
"... Fix an algebraically closed field k. Let Mg be the moduli space of curves of genus g over k. The main result of this note is that Mg is irreducible for every k. Of course, whether or not M s is irreducible depends only on the characteristic of k. When the characteristic s o, we can assume that k ~ ..."
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Cited by 512 (2 self)
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; for abelian varieties. This result was first proved independently in char. o by Grothendieck, using methods of etale cohomology (private correspondence with J. Tate), and by Mumford, applying the easy half of Theorem (2.5), to go from curves to abelian varieties (cf. [M2]). Grothendieck has recently
String theory and noncommutative geometry
 JHEP
, 1999
"... We extend earlier ideas about the appearance of noncommutative geometry in string theory with a nonzero Bfield. We identify a limit in which the entire string dynamics is described by a minimally coupled (supersymmetric) gauge theory on a noncommutative space, and discuss the corrections away from ..."
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Cited by 801 (8 self)
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We extend earlier ideas about the appearance of noncommutative geometry in string theory with a nonzero Bfield. We identify a limit in which the entire string dynamics is described by a minimally coupled (supersymmetric) gauge theory on a noncommutative space, and discuss the corrections away from
Consensus and cooperation in networked multiagent systems
 PROCEEDINGS OF THE IEEE
"... This paper provides a theoretical framework for analysis of consensus algorithms for multiagent networked systems with an emphasis on the role of directed information flow, robustness to changes in network topology due to link/node failures, timedelays, and performance guarantees. An overview of ..."
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Cited by 772 (2 self)
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This paper provides a theoretical framework for analysis of consensus algorithms for multiagent networked systems with an emphasis on the role of directed information flow, robustness to changes in network topology due to link/node failures, timedelays, and performance guarantees. An overview of basic concepts of information consensus in networks and methods of convergence and performance analysis for the algorithms are provided. Our analysis framework is based on tools from matrix theory, algebraic graph theory, and control theory. We discuss the connections between consensus problems in networked dynamic systems and diverse applications including synchronization of coupled oscillators, flocking, formation control, fast consensus in smallworld networks, Markov processes and gossipbased algorithms, load balancing in networks, rendezvous in space, distributed sensor fusion in sensor networks, and belief propagation. We establish direct connections between spectral and structural properties of complex networks and the speed of information diffusion of consensus algorithms. A brief introduction is provided on networked systems with nonlocal information flow that are considerably faster than distributed systems with latticetype nearest neighbor interactions. Simulation results are presented that demonstrate the role of smallworld effects on the speed of consensus algorithms and cooperative control of multivehicle formations.
Results 1  10
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46,754