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Algebraic Graph Theory
Chris Godsil,Gordon F. Royle +1 more
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The Laplacian of a Graph and Cuts and Flows are compared to the Rank Polynomial.Abstract:
Graphs.- Groups.- Transitive Graphs.- Arc-Transitive Graphs.- Generalized Polygons and Moore Graphs.- Homomorphisms.- Kneser Graphs.- Matrix Theory.- Interlacing.- Strongly Regular Graphs.- Two-Graphs.- Line Graphs and Eigenvalues.- The Laplacian of a Graph.- Cuts and Flows.- The Rank Polynomial.- Knots.- Knots and Eulerian Cycles.- Glossary of Symbols.- Index.read more
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Journal Article
Visualizing Data using t-SNE
TL;DR: A new technique called t-SNE that visualizes high-dimensional data by giving each datapoint a location in a two or three-dimensional map, a variation of Stochastic Neighbor Embedding that is much easier to optimize, and produces significantly better visualizations by reducing the tendency to crowd points together in the center of the map.
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Consensus problems in networks of agents with switching topology and time-delays
TL;DR: A distinctive feature of this work is to address consensus problems for networks with directed information flow by establishing a direct connection between the algebraic connectivity of the network and the performance of a linear consensus protocol.
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Consensus and Cooperation in Networked Multi-Agent Systems
TL;DR: A theoretical framework for analysis of consensus algorithms for multi-agent networked systems with an emphasis on the role of directed information flow, robustness to changes in network topology due to link/node failures, time-delays, and performance guarantees is provided.
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Complex networks: Structure and dynamics
TL;DR: The major concepts and results recently achieved in the study of the structure and dynamics of complex networks are reviewed, and the relevant applications of these ideas in many different disciplines are summarized, ranging from nonlinear science to biology, from statistical mechanics to medicine and engineering.
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Coordination of groups of mobile autonomous agents using nearest neighbor rules
Ali Jadbabaie,Jie Lin,A.S. Morse +2 more
TL;DR: A theoretical explanation for the observed behavior of the Vicsek model, which proves to be a graphic example of a switched linear system which is stable, but for which there does not exist a common quadratic Lyapunov function.
References
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Intersection theorems for systems of finite sets
Paul Erdös,Chao Ko,Richard Rado +2 more
TL;DR: In this article, the obliteration operator is used to remove from any system of elements the element above which it is placed, and the set of all systems (ao,av...,dn) such that avc[0,m); \av\ 1 (v < »),
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Optimal state-determination by mutually unbiased measurements
TL;DR: It is shown that if one can find N + 1 mutually unbiased bases for a complex vector space of N dimensions, then the measurements corresponding to these bases provide an optimal means of determining the density matrix of an ensemble of systems having N orthogonal states.
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The exact bound in the Erdös-Ko-Rado theorem
TL;DR: The bound (t+1)(k-t-1) represents the best possible strengthening of the original 1961 theorem of Erdös, Ko, and Rado which reaches the same conclusion under the hypothesisn≧t+(k−t) .
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New code upper bounds from the Terwilliger algebra and semidefinite programming
TL;DR: A new upper bound on the maximum size A(n,d) of a binary code of word length n and minimum distance at least d is given, based on block-diagonalizing the Terwilliger algebra of the Hamming cube.
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The Erdo¨s-Ko-Rado theorem for vector spaces
Peter Frankl,Richard M. Wilson +1 more
TL;DR: It is shown that m q (n,k,t), the maximum possible number of subspaces in a t-intersecting family F of k-dimensional subspaced of V, holds for all F, F′ ϵ F .
Related Papers (5)
Consensus problems in networks of agents with switching topology and time-delays
Coordination of groups of mobile autonomous agents using nearest neighbor rules
Ali Jadbabaie,Jie Lin,A.S. Morse +2 more