The emergence of order in natural systems is a constant source of inspiration for both physical and biological sciences. While the spatial order characterizing for example the crystals has been the basis of many advances in contemporary physics, most complex systems in nature do not offer such high degree of order. Many of these systems form complex networks whose nodes are the elements of the system and edges represent the interactions between them. 
Traditionally complex networks have been described by the random graph theory founded in 1959 by Paul Erdohs and Alfred Renyi. One of the defining features of random graphs is that they are statistically homogeneous, and their degree distribution (characterizing the spread in the number of edges starting from a node) is a Poisson distribution. In contrast, recent empirical studies, including the work of our group, indicate that the topology of real networks is much richer than that of random graphs. In particular, the degree distribution of real networks is a power-law, indicating a heterogeneous topology in which the majority of the nodes have a small degree, but there is a significant fraction of highly connected nodes that play an important role in the connectivity of the network. 
The scale-free topology of real networks has very important consequences on their functioning. For example, we have discovered that scale-free networks are extremely resilient to the random disruption of their nodes. On the other hand, the selective removal of the nodes with highest degree induces a rapid breakdown of the network to isolated subparts that cannot communicate with each other. 
The non-trivial scaling of the degree distribution of real networks is also an indication of their assembly and evolution. Indeed, our modeling studies have shown us that there are general principles governing the evolution of networks. Most networks start from a small seed and grow by the addition of new nodes which attach to the nodes already in the system. This process obeys preferential attachment: the new nodes are more likely to connect to nodes with already high degree. We have proposed a simple model based on these two principles wich was able to reproduce the power-law degree distribution of real networks. Perhaps even more importantly, this model paved the way to a new paradigm of network modeling, trying to capture the evolution of networks, not just their static topology.

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Statistical mechanics of complex networks

Inspired by empirical studies of networked systems such as the Internet, social networks, and biological networks, researchers have in recent years developed a variety of techniques and models to help us understand or predict the behavior of these systems. Here we review developments in this field, including such concepts as the small-world effect, degree distributions, clustering, network correlations, random graph models, models of network growth and preferential attachment, and dynamical processes taking place on networks.

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The Structure and Function of Complex Networks

A number of recent studies have focused on the statistical properties of networked systems such as social networks and the Worldwide Web. Researchers have concentrated particularly on a few properties that seem to be common to many networks: the small-world property, power-law degree distributions, and network transitivity. In this article, we highlight another property that is found in many networks, the property of community structure, in which network nodes are joined together in tightly knit groups, between which there are only looser connections. We propose a method for detecting such communities, built around the idea of using centrality indices to find community boundaries. We test our method on computer-generated and real-world graphs whose community structure is already known and find that the method detects this known structure with high sensitivity and reliability. We also apply the method to two networks whose community structure is not well known—a collaboration network and a food web—and find that it detects significant and informative community divisions in both cases.

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Community structure in social and biological networks

We propose and study a set of algorithms for discovering community structure in networks-natural divisions of network nodes into densely connected subgroups. Our algorithms all share two definitive features: first, they involve iterative removal of edges from the network to split it into communities, the edges removed being identified using any one of a number of possible "betweenness" measures, and second, these measures are, crucially, recalculated after each removal. We also propose a measure for the strength of the community structure found by our algorithms, which gives us an objective metric for choosing the number of communities into which a network should be divided. We demonstrate that our algorithms are highly effective at discovering community structure in both computer-generated and real-world network data, and show how they can be used to shed light on the sometimes dauntingly complex structure of networked systems.

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Finding and evaluating community structure in networks.

Deposits of clastic carbonate-dominated (calciclastic) sedimentary slope systems in the rock record have been identified mostly as linearly-consistent carbonate apron deposits, even though most ancient clastic carbonate slope deposits fit the submarine fan systems better. Calciclastic submarine fans are consequently rarely described and are poorly understood. Subsequently, very little is known especially in mud-dominated calciclastic submarine fan systems. Presented in this study are a sedimentological core and petrographic characterisation of samples from eleven boreholes from the Lower Carboniferous of Bowland Basin (Northwest England) that reveals a >250 m thick calciturbidite complex deposited in a calciclastic submarine fan setting. Seven facies are recognised from core and thin section characterisation and are grouped into three carbonate turbidite sequences. They include: 1) Calciturbidites, comprising mostly of highto low-density, wavy-laminated bioclast-rich facies; 2) low-density densite mudstones which are characterised by planar laminated and unlaminated muddominated facies; and 3) Calcidebrites which are muddy or hyper-concentrated debrisflow deposits occurring as poorly-sorted, chaotic, mud-supported floatstones. These

Phd by thesis

The study of the web as a graph is not only fascinating in its own right, but also yields valuable insight into web algorithms for crawling, searching and community discovery, and the sociological phenomena which characterize its evolution. We report on experiments on local and global properties of the web graph using two Altavista crawls each with over 200 million pages and 1.5 billion links. Our study indicates that the macroscopic structure of the web is considerably more intricate than suggested by earlier experiments on a smaller scale.

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Graph structure in the Web

Software development and maintenance are costly endeavors. The cost can be reduced if more software defects are detected earlier in the development cycle. This paper introduces the Extended Static Checker for Java (ESC/Java), an experimental compile-time program checker that finds common programming errors. The checker is powered by verification-condition generation and automatic theorem-proving techniques. It provides programmers with a simple annotation language with which programmer design decisions can be expressed formally. ESC/Java examines the annotated software and warns of inconsistencies between the design decisions recorded in the annotations and the actual code, and also warns of potential runtime errors in the code. This paper gives an overview of the checker architecture and annotation language and describes our experience applying the checker to tens of thousands of lines of Java programs.

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Extended static checking for Java

Java is typically compiled into an intermediate language, JVML, that is interpreted by the Java Virtual Machine. Because mobile JVML code is not always trusted, a bytecode verifier enforces static constraints that prevent various dynamic errors. Given the importance of the bytecode verifier for security, its current descriptions are inadequate. This article proposes using typing rules to describe the bytecode verifier because they are more precise than prose, clearer than code, and easier to reason about than either. JVML has a subroutine construct which is used for the compilation of Java's try-finally statement. Subroutines are a major source of complexity for the bytecode verifier because they are not obviously last-in/first-out and because they require a kind of polymorphism. Focusing on subroutines, we isolate an interesting, small subset of JVML. We give typing rules for this subset and prove their correctness. Our type system constitutes a sound basis for bytecode verification and a rational reconstruction of a delicate part of Sun's bytecode verifier.

/pdf/a-type-system-for-java-bytecode-subroutines-1sjiuvpa6k.pdf

A type system for Java bytecode subroutines

Java is typically compiled into an intermediate language, JVML, that is interpreted by the Java Virtual Machine. Because mobile JVML code is not always trusted, a bytecode verifier enforces static constraints that prevent various dynamic errors. Given the importance of the bytecode verifier for security, its current descriptions are inadequate. This paper proposes using typing rules to describe the bytecode verifier because they are more precise than prose, clearer than code, and easier to reason about than either.JVML has a subroutine construct used for the compilation of Java's try-finally statement. Subroutines are a major source of complexity for the bytecode verifier because they are not obviously last-in/first-out and because they require a kind of polymorphism. Focusing on subroutines, we isolate an interesting, small subset of JVML. We give typing rules for this subset and prove their correctness. Our type system constitutes a sound basis for bytecode verification and a rational reconstruction of a delicate part of Sun's bytecode verifier.

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This paper defines a simple guarded-command–like language and its semantics. The language is used as an intermediate language in generating verification conditions for Java. The paper discusses why it is a good idea to generate verification conditions via an intermediate language, rather than directly. Publication history. This paper appears in Formal Techniques for Java Programs, workshop proceedings. Bart Jacobs, Gary T. Leavens, Peter Muller, and Arnd PoetzschHeffter, editors. Technical Report 251, Fernuniversitat Hagen, 1999. Available from www.informatik.fernuni-hagen.de/pi5/publications.html. Checking Java programs via guarded commands K. Rustan M. Leino, James B. Saxe, and Raymie Stata Compaq Systems Research Center {rustan,saxe,stata}@pa.dec.com

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Raymie Stata

Papers

Graph structure in the Web

Extended static checking for Java

A type system for Java bytecode subroutines

A type system for Java bytecode subroutines

Checking Java Programs via Guarded Commands