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Algebraic Graph Theory
, 2011
"... Algebraic graph theory comprises both the study of algebraic objects arising in connection with graphs, for example, automorphism groups of graphs along with the use of algebraic tools to establish interesting properties of combinatorial objects. One of the oldest themes in the area is the investiga ..."
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Cited by 892 (13 self)
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Algebraic graph theory comprises both the study of algebraic objects arising in connection with graphs, for example, automorphism groups of graphs along with the use of algebraic tools to establish interesting properties of combinatorial objects. One of the oldest themes in the area
Constructing Free Energy Approximations and Generalized Belief Propagation Algorithms
 IEEE Transactions on Information Theory
, 2005
"... Important inference problems in statistical physics, computer vision, errorcorrecting coding theory, and artificial intelligence can all be reformulated as the computation of marginal probabilities on factor graphs. The belief propagation (BP) algorithm is an efficient way to solve these problems t ..."
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Cited by 585 (13 self)
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Important inference problems in statistical physics, computer vision, errorcorrecting coding theory, and artificial intelligence can all be reformulated as the computation of marginal probabilities on factor graphs. The belief propagation (BP) algorithm is an efficient way to solve these problems
Consensus Problems in Networks of Agents with Switching Topology and TimeDelays
, 2003
"... In this paper, we discuss consensus problems for a network of dynamic agents with fixed and switching topologies. We analyze three cases: i) networks with switching topology and no timedelays, ii) networks with fixed topology and communication timedelays, and iii) maxconsensus problems (or leader ..."
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Cited by 1112 (21 self)
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in convergence analysis of consensus protocols. A distinctive feature of this work is to address consensus problems for networks with directed information flow. We provide analytical tools that rely on algebraic graph theory, matrix theory, and control theory. Simulations are provided that demonstrate
Consensus and cooperation in networked multiagent systems
 Proceedings of the IEEE
, 2007
"... Summary. 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 ove ..."
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Cited by 807 (4 self)
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. 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
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 506 (2 self)
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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
GromovWitten classes, quantum cohomology, and enumerative geometry
 Commun. Math. Phys
, 1994
"... The paper is devoted to the mathematical aspects of topological quantum field theory and its applications to enumerative problems of algebraic geometry. In particular, it contains an axiomatic treatment of Gromov–Witten classes, and a discussion of their properties for Fano varieties. Cohomological ..."
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Cited by 474 (3 self)
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The paper is devoted to the mathematical aspects of topological quantum field theory and its applications to enumerative problems of algebraic geometry. In particular, it contains an axiomatic treatment of Gromov–Witten classes, and a discussion of their properties for Fano varieties. Cohomological
EXERCISES IN THE BIRATIONAL GEOMETRY OF ALGEBRAIC VARIETIES
, 2008
"... The book [KM98] gave an introduction to the birational geometry of algebraic varieties, as the subject stood in 1998. The developments of the last decade made the more advanced parts of Chapters 6 and 7 less important and the detailed treatment of surface singularities in Chapter 4 less necessary. H ..."
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Cited by 322 (1 self)
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applications. 1. Birational classification of algebraic surfaces For more detail, see [BPVdV84]. The theory of algebraic surfaces rests on the following three theorems. Theorem 1. Any birational morphism between smooth projective surfaces is a composite of blowdowns to points. Any birational map between
The monadic secondorder logic of graphs I. Recognizable sets of Finite Graphs
 Information and Computation
, 1990
"... The notion of a recognizable sef offinite graphs is introduced. Every set of finite graphs, that is definable in monadic secondorder logic is recognizable, but not vice versa. The monadic secondorder theory of a contextfree set of graphs is decidable. 0 19W Academic Press. Inc. This paper begins ..."
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Cited by 301 (17 self)
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an investigation of the monadic secondorder logic of graphs and of sets of graphs, using techniques from universal algebra, and the theory of formal languages. (By a graph, we mean a finite directed hyperedgelabelled hypergraph, equipped with a sequence of distinguished vertices.) A survey of this research can
Nested Linear/Lattice Codes for Structured Multiterminal Binning
, 2002
"... Network information theory promises high gains over simple pointtopoint communication techniques, at the cost of higher complexity. However, lack of structured coding schemes limited the practical application of these concepts so far. One of the basic elements of a network code is the binning sch ..."
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Cited by 345 (14 self)
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Network information theory promises high gains over simple pointtopoint communication techniques, at the cost of higher complexity. However, lack of structured coding schemes limited the practical application of these concepts so far. One of the basic elements of a network code is the binning
Results 1  10
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