Results 1  10
of
387
Models of Random Regular Graphs
 In Surveys in combinatorics
, 1999
"... In a previous paper we showed that a random 4regular graph asymptotically almost surely (a.a.s.) has chromatic number 3. Here we extend the method to show that a random 6regular graph asymptotically almost surely (a.a.s.) has chromatic number 4 and that the chromatic number of a random dregular g ..."
Abstract

Cited by 225 (33 self)
 Add to MetaCart
In a previous paper we showed that a random 4regular graph asymptotically almost surely (a.a.s.) has chromatic number 3. Here we extend the method to show that a random 6regular graph asymptotically almost surely (a.a.s.) has chromatic number 4 and that the chromatic number of a random dregular graph for other d between 5 and 10 inclusive is a.a.s. restricted to a range of two integer values: {3, 4} for d = 5, {4, 5} for d = 7, 8, 9, and {5, 6} for d = 10. The proof uses efficient algorithms which a.a.s. colour these random graphs using the number of colours specified by the upper bound. These algorithms are analysed using the differential equation method, including an analysis of certain systems of differential equations with discontinuous right hand sides. 1
Software Watermarking: Models and Dynamic Embeddings
, 1999
"... Watermarking embeds a secret message into a cover message. In media watermarking the secret is usually a copyright notice and the cover a digital image. Watermarking an object discourages intellectual property theft, or when such theft has occurred, allows us to prove ownership. The Software Waterma ..."
Abstract

Cited by 161 (21 self)
 Add to MetaCart
Watermarking embeds a secret message into a cover message. In media watermarking the secret is usually a copyright notice and the cover a digital image. Watermarking an object discourages intellectual property theft, or when such theft has occurred, allows us to prove ownership. The Software Watermarking problem can be described as follows. Embed a structure W into a program P such that: W can be reliably located and extracted from P even after P has been subjected to code transformations such as translation, optimization and obfuscation; W is stealthy; W has a high data rate; embedding W into P does not adversely affect the performance of P ; and W has a mathematical property that allows us to argue that its presence in P is the result of deliberate actions. In the first part of the paper we construct an informal taxonomy of software watermarking techniques. In the second part we formalize these results. Finally, we propose a new software watermarking technique in which a dynamic gr...
Motifs in brain networks
 PLOS BIOL
, 2004
"... Complex brains have evolved a highly efficient network architecture whose structural connectivity is capable of generating a large repertoire of functional states. We detect characteristic network building blocks (structural and functional motifs) in neuroanatomical data sets and identify a small se ..."
Abstract

Cited by 110 (7 self)
 Add to MetaCart
Complex brains have evolved a highly efficient network architecture whose structural connectivity is capable of generating a large repertoire of functional states. We detect characteristic network building blocks (structural and functional motifs) in neuroanatomical data sets and identify a small set of structural motifs that occur in significantly increased numbers. Our analysis suggests the hypothesis that brain networks maximize both the number and the diversity of functional motifs, while the repertoire of structural motifs remains small. Using functional motif number as a cost function in an optimization algorithm, we obtain network topologies that resemble real brain networks across a broad spectrum of structural measures, including smallworld attributes. These results are consistent with the hypothesis that highly evolved neural architectures are organized to maximize functional repertoires and to support highly efficient integration of information.
Boltzmann Samplers For The Random Generation Of Combinatorial Structures
 Combinatorics, Probability and Computing
, 2004
"... This article proposes a surprisingly simple framework for the random generation of combinatorial configurations based on what we call Boltzmann models. The idea is to perform random generation of possibly complex structured objects by placing an appropriate measure spread over the whole of a combina ..."
Abstract

Cited by 108 (3 self)
 Add to MetaCart
(Show Context)
This article proposes a surprisingly simple framework for the random generation of combinatorial configurations based on what we call Boltzmann models. The idea is to perform random generation of possibly complex structured objects by placing an appropriate measure spread over the whole of a combinatorial class  an object receives a probability essentially proportional to an exponential of its size. As demonstrated here, the resulting algorithms based on realarithmetic operations often operate in linear time. They can be implemented easily, be analysed mathematically with great precision, and, when suitably tuned, tend to be very efficient in practice.
Evaluating efficiency of selfreconfiguration in a class of modular robots
 Journal of Robotic Systems
, 1996
"... In this article we examine the problem of dynamic selfreconfiguration of a class of modular robotic systems referred to as metumorpkic systems. A metamorphic robotic system is a collection of mechatronic modules, each of which has the ability to connect, disconnect, and climb over adjacent modules. ..."
Abstract

Cited by 81 (7 self)
 Add to MetaCart
In this article we examine the problem of dynamic selfreconfiguration of a class of modular robotic systems referred to as metumorpkic systems. A metamorphic robotic system is a collection of mechatronic modules, each of which has the ability to connect, disconnect, and climb over adjacent modules. A change in the macroscopic morphology results from the locomotion of each module over its neighbors. Metamorphic systems can therefore be viewed as a large swarm of physically connected robotic modules that collectively act as a single entity. What distinguishes metamorphic systems from other reconfigurable robots is that they possess all of the following properties: (1) a large number of homogeneous modules; (2) a geometry such that modules fit within a regular lattice; (3) selfreconfigurability without outside help; (4) physical constraints which ensure contact between modules. In this article, the kinematic constraints governing metamorphic robot selfreconfiguration are addressed, and lower and upper bounds are established for the minimal number of moves needed to change such systems from any initial to any final specified configuration. These bounds are functions of initial and final configuration geometry and can be computed very quickly, while it appears that solving for the precise number of minimal moves cannot be done in polynomial time. It is then shown how the bounds developed here are useful in evaluating the performance of heuristic motion planning/reconfiguration algorithms for metamorphic systems. 0 2996 Iohn Wiky 6 Sons, rnc. *To whom all correspondence should be addressed
On the fixed parameter complexity of graph enumeration problems definable in monadic secondorder logic
, 2001
"... ..."
Asymptotics of the partition function for random matrices via RiemannHilbert techniques, and applications to graphical enumeration
 Internat. Math. Research Notices
, 2003
"... Abstract. We study the partition function from random matrix theory using a well known connection to orthogonal polynomials, and a recently developed RiemannHilbert approach to the computation of detailed asymptotics for these orthogonal polynomials. We obtain the first proof of a complete large N ..."
Abstract

Cited by 73 (9 self)
 Add to MetaCart
(Show Context)
Abstract. We study the partition function from random matrix theory using a well known connection to orthogonal polynomials, and a recently developed RiemannHilbert approach to the computation of detailed asymptotics for these orthogonal polynomials. We obtain the first proof of a complete large N expansion for the partition function, for a general class of probability measures on matrices, originally conjectured by Bessis, Itzykson, and Zuber. We prove that the coefficients in the asymptotic expansion are analytic functions of parameters in the original probability measure, and that they are generating functions for the enumeration of labelled maps according to genus and valence. Central to the analysis is a large N expansion for the mean density of eigenvalues, uniformly valid on the entire real axis.