Results

**11 - 17**of**17**### A Questionable Distance-Regular Graph

"... Abstract In this paper, we introduce distance-regular graphs and develop the intersection algebra for these graphs which is based upon its intersection numbers. We discuss results following from the definition of the intersection algebra. We investigate two examples of distance-regular graphs and sh ..."

Abstract
- Add to MetaCart

Abstract In this paper, we introduce distance-regular graphs and develop the intersection algebra for these graphs which is based upon its intersection numbers. We discuss results following from the definition of the intersection algebra. We investigate two examples of distance-regular graphs and show how these results apply. Finally, we introduce parameters that determine intersection numbers. We investigate if these intersection numbers are nonnegative and feasible. 1.

### www.elsevier.com/locate/physa Symmetry-based structure entropy of complex networks

, 2008

"... Precisely quantifying the heterogeneity or disorder of network systems is important and desired in studies of behaviors and functions of network systems. Although various degree-based entropies have been available to measure the heterogeneity of real networks, heterogeneity implicated in the structu ..."

Abstract
- Add to MetaCart

(Show Context)
Precisely quantifying the heterogeneity or disorder of network systems is important and desired in studies of behaviors and functions of network systems. Although various degree-based entropies have been available to measure the heterogeneity of real networks, heterogeneity implicated in the structures of networks can not be precisely quantified yet. Hence, we propose a new structure entropy based on automorphism partition. Analysis of extreme cases shows that entropy based on automorphism partition can quantify the structural heterogeneity of networks more precisely than degree-based entropies. We also summarized symmetry and heterogeneity statistics of many real networks, finding that real networks are more heterogeneous in the view of automorphism partition than what have been depicted under the measurement of degree-based entropies; and that structural heterogeneity is strongly negatively correlated to symmetry of real networks. c © 2008 Elsevier B.V. All rights reserved.

### XiStrat Manual

, 2010

"... License". Furthermore we dual-licence this documentation under the GNU Lesser General Public License, Ver-sion 3. All modified versions of this document must prominently state that they do not necessarily represent the opinions of the original author. XiStrat is distributed under the GNU Lesser ..."

Abstract
- Add to MetaCart

License". Furthermore we dual-licence this documentation under the GNU Lesser General Public License, Ver-sion 3. All modified versions of this document must prominently state that they do not necessarily represent the opinions of the original author. XiStrat is distributed under the GNU Lesser General Public License, Version 3; without any warranty, to the extent not prohibited by applicable state law. We distribute XiStrat as is without warranty of any kind, either expressed or implied, including, but not limited to, the implied warranties of mer-chantability and fitness for a particular purpose. In no case unless required by applicable law will we, and/or any other party who may modify and redistribute XiStrat as permitted above, be liable to you for damages, including lost profits, lost monies or other special, incidental or consequential damages arising out of the use or inability to use XiStrat. Many of the designations used by manufacturers and sellers to distinguish their products are claimed as trademarks. Where those designations appear in this book, and we were aware of a trademark claim, the designations have been printed in caps or initial caps. While every precaution has been taken in the preparation of this manual, the publisher assumes no re-

### A BRIEF INTRODUCTION TO RAMSEY THEORY OF GRAPHS

"... Abstract. This paper provides proof of Ramsey's Theorem as it applies to (undirected) graphs, along with a short discussion of the thereom and the ..."

Abstract
- Add to MetaCart

(Show Context)
Abstract. This paper provides proof of Ramsey's Theorem as it applies to (undirected) graphs, along with a short discussion of the thereom and the

### On the Stability of Swarm Consensus Under Noisy Control

"... Abstract — Representation of a swarm of independent robotic agents under graph-theoretic constructs allows for more formal analysis of convergence properties. We consider the local and global convergence behavior of an N-member swarm of agents in a modified consensus problem wherein the connectivity ..."

Abstract
- Add to MetaCart

Abstract — Representation of a swarm of independent robotic agents under graph-theoretic constructs allows for more formal analysis of convergence properties. We consider the local and global convergence behavior of an N-member swarm of agents in a modified consensus problem wherein the connectivity of agents is governed by probabilistic functions. The addition of a random walk control ensures Lyapunov stability of the swarm consensus. Simulation results are given and planned experiments are described. I.

### AN ALGEBRAIC MODEL OF COMPUTATION FOR SYSTEMS WITH DYNAMIC STRUCTURE

"... We introduce the Structure Model- a formalism for modelling and controlling networked systems with dynamic structure. The pervasiveness of networked computing devices is raising attention on models of computation which entail the network structure as a first-class concept. Modelling how the network ..."

Abstract
- Add to MetaCart

(Show Context)
We introduce the Structure Model- a formalism for modelling and controlling networked systems with dynamic structure. The pervasiveness of networked computing devices is raising attention on models of computation which entail the network structure as a first-class concept. Modelling how the network evolves and how entities interact is now paramount for a correct understanding of the overall system and for the design and synthesis of effective controllers. We address this problem by introducing a formalism for modelling and controlling systems with dynamic structures. The Structure Model (SM) consists of a set of entities, and a set of unary relations and a binary relation over the set of entities. The unary relations are used to model state properties of the entities while the binary relation is used to model interaction between entities such as communication. The SM can be manipulated using a set of algebraic operators. The dynamics of the structure are modelled using a transition system. The SM is designed to compose with an underlying model that describes the entities behaviour. We present how the structure can be abstracted from an underlying model and how the changes at the structure level can be propagated back to the system. This provides means controlling the system from a structure perspective. The structure model aims at being agnostic to the underlying model of computation. In this work we compose the structure model with Nancy Lynch’s Synchronous Network Model and present a case study using a version of the “agree and pursue ” communication and control law.

### Analysis of High-Throughput Biological Data

"... examined the final electronic copy of this dissertation for form and content and recommend ..."

Abstract
- Add to MetaCart

(Show Context)
examined the final electronic copy of this dissertation for form and content and recommend