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

Machine Learning is the study of methods for programming computers to learn. Computers are applied to a wide range of tasks, and for most of these it is relatively easy for programmers to design and implement the necessary software. However, there are many tasks for which this is difficult or impossible. These can be divided into four general categories. First, there are problems for which there exist no human experts. For example, in modern automated manufacturing facilities, there is a need to predict machine failures before they occur by analyzing sensor readings. Because the machines are new, there are no human experts who can be interviewed by a programmer to provide the knowledge necessary to build a computer system. A machine learning system can study recorded data and subsequent machine failures and learn prediction rules. Second, there are problems where human experts exist, but where they are unable to explain their expertise. This is the case in many perceptual tasks, such as speech recognition, hand-writing recognition, and natural language understanding. Virtually all humans exhibit expert-level abilities on these tasks, but none of them can describe the detailed steps that they follow as they perform them. Fortunately, humans can provide machines with examples of the inputs and correct outputs for these tasks, so machine learning algorithms can learn to map the inputs to the outputs. Third, there are problems where phenomena are changing rapidly. In finance, for example, people would like to predict the future behavior of the stock market, of consumer purchases, or of exchange rates. These behaviors change frequently, so that even if a programmer could construct a good predictive computer program, it would need to be rewritten frequently. A learning program can relieve the programmer of this burden by constantly modifying and tuning a set of learned prediction rules. Fourth, there are applications that need to be customized for each computer user separately. Consider, for example, a program to filter unwanted electronic mail messages. Different users will need different filters. It is unreasonable to expect each user to program his or her own rules, and it is infeasible to provide every user with a software engineer to keep the rules up-to-date. A machine learning system can learn which mail messages the user rejects and maintain the filtering rules automatically. Machine learning addresses many of the same research questions as the fields of statistics, data mining, and psychology, but with differences of emphasis. Statistics focuses on understanding the phenomena that have generated the data, often with the goal of testing different hypotheses about those phenomena. Data mining seeks to find patterns in the data that are understandable by people. Psychological studies of human learning aspire to understand the mechanisms underlying the various learning behaviors exhibited by people (concept learning, skill acquisition, strategy change, etc.).

Machine learning

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.

We consider efficient parallel algorithms for the evaluat ion of game trees. We prove an inherent limit at ion on the speedup achievable, and give an algorithm that achieves its best performance bounds on trees of the sort that are likely to arise in game-playing programs.

On the parallel complexity of evaluating game trees

In the past decade, Web search engines have evolved from a first generation based on classic Information Retrieval (IR) algorithms scaled to web size and thus supporting only informational queries, to a second generation supporting navigational queries using web specific information (primarily link analysis), to a third generation enabling transactional and other "semantic" queries based on a variety of technologies aimed to directly satisfy the unexpressed "user intent."

What is coming next? In this talk, we argue for the trend towards context driven Information Supply (IS), that is, the goal of Web IR will widen to include the supply of relevant information from multiple sources without requiring the user to make an explicit query. The information supply concept greatly precedes information retrieval. What is new in the web framework is the ability to supply relevant information specific to a given activity and a given user, while the activity is being performed. A prime example is the matching of ads to content being read, however the information supply paradigm is starting to appear in other contexts such as social networks, e-commerce, browsers, e-mail, and others.

The future of web search: from information retrieval to information supply

1. I n t r o d u c t i o n The subject of this paper is a protocol ~0r distributed lottery agreement (DLA), that is defined as agreement on an unbiased random bit in a network of n processors, out of which up to t might be faulty and malicious. The interest in this problem was sparked by the work of Rabin ([Rabin83]) who showed that in such an environment it is possible to achieve agreement on a sender's value (Byzantine agreement 1) in constant expected time, provided that at each round all processors have access to a common random bit, S e e n e x t s e c t i o n f o r d e f i n i t i o n s . Permission to copy without fee all or part of this material is granted provided that the copies are not made or distributed for direct commercial advantage, the ACM copyright notice and the title of the publication and its date appear, and notice is given that copying is by permission of the Association for Computing Machinery. To copy otherwise, or to republish, requires a fee and/or specific permission. ©1985 ACM 0-89791-167-9/1985/0800-0136 $00.75

A provably secure polynomial approximation scheme for the distributed lottery problem (extended abstract)

Systems and methods for estimating an amount of traffic associated with a digital ad are disclosed. Generally, a forecasting module identifies a set of candidate webpages on which a digital ad may be displayed and estimates a click through rate associated with the digital ad and a webpage of the set of candidate webpages. The forecasting module determines a ranking score associated with the digital ad based on the determined click through rate and a bid price associated with the digital ad. The forecasting module then examines historical data, such as search logs, to determine an estimate of traffic associated with the digital ad with respect to the webpage in response to determining the ranking score of the digital ad exceeds a ranking score associated with another digital ad that was previously displayed on the webpage.

System and Method for Estimating an Amount of Traffic Associated with a Digital Advertisement

A cornerstone concept in classical Information Retrieval is the vector space model, whereby both documents and queries are viewed as vectors in a multidimensional space. Relevance of a given document to a given query is determined by evaluating the similarity between these vectors, using a measure like the cosine measure of similarity, for instance. The vector space model has been highly successful for dealing with plain text collections, in both theoretical and practical terms. In prior work, we extended this classic approach to the search of XML collections by requiring queries to be presented as XML Fragments, which allows for a very simple extension of the cosine similarity measure to the XML framework.

In this paper, we formalize this approach by presenting the full syntax and semantics of XML Fragments as implemented in a practical system. Furthermore, we show how small additions to the pure model improve the expressiveness of queries and enable us to deal with a wide range of users' needs. These additions introduce certain novel constructs that are not syntactically correct XML but implement essential operators. We evaluate the expressiveness of our model, both from a formal viewpoint, by comparing it to the XPath language, and from a practical viewpoint by running experiments on the INEX (Initiative for XML Retrieval) collection. Our conclusion is that the coupling of the classic vector space approach with a carefully chosen small set of relational operators allows us to express XML informational searches as enhanced XML fragments in a natural and powerful way.

Andrei Z. Broder

Papers

On the parallel complexity of evaluating game trees

The future of web search: from information retrieval to information supply

A provably secure polynomial approximation scheme for the distributed lottery problem (extended abstract)

System and Method for Estimating an Amount of Traffic Associated with a Digital Advertisement

Using XML to query XML: from theory to practice