We quantify the dynamical implications of the small-world phenomenon by considering the generic synchronization of oscillator networks of arbitrary topology. The linear stability of the synchronous state is linked to an algebraic condition of the Laplacian matrix of the network. Through numerics and analysis, we show how the addition of random shortcuts translates into improved network synchronizability. Applied to networks of low redundancy, the small-world route produces synchronizability more efficiently than standard deterministic graphs, purely random graphs, and ideal constructive schemes. However, the small-world property does not guarantee synchronizability: the synchronization threshold lies within the boundaries, but linked to the end of the small-world region.

/pdf/synchronization-in-small-world-systems-32o70f3kuj.pdf

Synchronization in small-world systems.

Cayley graphs as classifiers for data mining: The influence of asymmetries

This in-depth coverage of important areas of graph theory maintains a focus on symmetry properties of graphs. Standard topics on graph automorphisms are presented early on, while in later chapters more specialised topics are tackled, such as graphical regular representations and pseudosimilarity. The final four chapters are devoted to the reconstruction problem, and here special emphasis is given to those results that involve the symmetry of graphs, many of which are not to be found in other books. This second edition expands on several of the topics found in the first edition and includes both an enriched bibliography and a wide collection of exercises. Clearer proofs are provided, as are new examples of graphs with interesting symmetry properties. Any student who masters the contents of this book will be well prepared for current research in many aspects of the theory of graph automorphisms and the reconstruction problem.

Topics in Graph Automorphisms and Reconstruction

Part I: Data Storage and Access An RDF Query and Transformation Language RDF and Traditional Query Architectures Query Processing in RDF/S-based Peer-to-Peer Database Systems- Part II: Querying the Network Cayley DHTs A Group-Theoretic Framework for Analyzing DHTs Based on Cayley Graphs Semantic Query Routing in Unstructured Networks Using Social Metaphors Expertise-Based Peer Selection Personalized Information Access in a Bibliographic Peer-to-Peer System Designing Semantic Publish/Subscribe Networks Using Super-Peers- Part III: Semantic Integration Semantic Coordination of Heterogeneous Classification Schemas Semantic Mapping by Approximation Satisficing Ontology Mapping Scalable, Peer-Based Mediation across XML Schemas and Ontologies Semantic Gossiping: Fostering Semantic Interoperability in Peer Data Management Systems- Part IV: Methodology and Systems A Methodology for Distributed Knowledge Management using Ontologies and Peer-to-Peer Distributed Engineering of Ontologies A Peer-to-Peer Solution for Distributed Knowledge Management Xarop - A Semantic Peer-to-Peer System for a Virtual Organization Bibster - A Semantics-Based Bibliographic Peer-to-Peer System

Semantic Web and Peer-to-Peer: Decentralized Management and Exchange of Knowledge and Information

The theory of fitness landscapes has been developed to provide a suitable mathematical framework for studying the evolvability of a variety of complex systems In evolutionary computation the notion of evolvability refers to the efficiency of evolutionary search It has been shown that the structure of a fitness landscape affects the ability of evolutionary algorithms to search Three characteristics specify the structure of landscapes These are the landscape smoothness, ruggedness and neutrality The interplay of these characteristics plays a vital role in evolutionary search This has motivated the appearance of a variety of techniques for studying the structure of fitness landscapes An important feature of these techniques is that they characterize the landscapes by their smoothness and ruggedness, ignoring the existence of neutrality Perhaps, the reason for this is that the role of neutrality in evolutionary search is still poorly understoodIn this chapter some recent results on the spectral properties of the algebraic structures of fitness landscapes are summarized to provide a basis for studying the landscape structure This approach is further employed to introduce an information analysis that characterizes the structure of fitness landscapes in terms of their smoothness, ruggedness and neutrality The findings are finally applied in a study of the fitness landscapes generated by evolving digital circuits using an idealized model of a field-programmable gate array The landscapes of this engineering problem are quite different from many recently studied landscapes that tend to be defined over simplified combinatorial and optimization problems The difference originates from the genotype representation that is a configuration defined over two completely different alphabets This makes the study of the corresponding landscapes much more involved It is shown that the circuit evolution landscapes are products of subspaces with different characteristics They are landscapes with vast neutrality and sharply differentiated plateau

Smoothness, ruggedness and neutrality of fitness landscapes: from theory to application

Preface. Isomorphism and Cayley Graphs on Abelian Groups B. Alspach. Oligomorphic Groups and Homogeneous Graphs P.J. Cameron. Symmetry and Eigenvectors A. Chan, C.D. Godsil. Graph Homomorphisms: Structure and Symmetry G. Hahn, C. Tardif. Cayley Graphs and Interconnection Networks B. Mohar. Finite Transitive Permutation Groups and Finite Vertex-Transitive Graphs C.E. Praeger. Vertex-Transitive Graphs and Digraphs R. Scapellato. Ends and Automorphisms of Infinite Graphs M.E. Watkins. Index.

Graph symmetry : algebraic methods and applications

Linkability in Countable-Like Webs.- Decomposition into Cycles I: Hamilton Decompositions.- An Order- and Graph- Theoretical Characterisation of Weakly Compact Cardinals.- Small Cycle Double Covers of Graphs.- ?-Transformations, Local Complementations and Switching.- Two Extremal Problems in Infinite Ordered Sets and Graphs: Infinite Versions of Menger and Gallai-Milgram Theorems for Ordered Sets and Graphs.- Chvatal-Erd?s Theorem for Digraphs.- Long Cycles and the Codiameter of a Graph II.- Compatible Euler Tours in Eulerian Digraphs.- A.J.W. Hilton, C.A. Rodger, Edge-Colouring Graphs and Embedding Partial Triple Systems of Even Index.- On the Rank of Fixed Point Sets of Automorphisms of Free Groups.- On Transition Polynomials of 4-Regular Graphs.- On Infinite n-Connected Graphs.- Ordered Graphs Without Infinite Paths.- Ends of Infinite Graphs, Potential Theory and Electrical Networks.- Topological Aspects of Infinite Graphs.- Dendroids, End-Separators, and Almost Circuit-Connected Trees.- Partition Theorems for Graphs Respecting the Chromatic Number.- Vertex-Transitive Graphs That Are Not Cayley Graphs.

Cycles and rays

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Graph symmetry : algebraic methods and applications

Cycles and rays