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

This paper provides a theoretical framework for analysis of consensus algorithms for multi-agent networked systems with an emphasis on the role of directed information flow, robustness to changes in network topology due to link/node failures, time-delays, and performance guarantees. An overview of basic concepts of information consensus in networks and methods of convergence and performance analysis for the algorithms are provided. Our analysis framework is based on tools from matrix theory, algebraic graph theory, and control theory. We discuss the connections between consensus problems in networked dynamic systems and diverse applications including synchronization of coupled oscillators, flocking, formation control, fast consensus in small-world networks, Markov processes and gossip-based algorithms, load balancing in networks, rendezvous in space, distributed sensor fusion in sensor networks, and belief propagation. We establish direct connections between spectral and structural properties of complex networks and the speed of information diffusion of consensus algorithms. A brief introduction is provided on networked systems with nonlocal information flow that are considerably faster than distributed systems with lattice-type nearest neighbor interactions. Simulation results are presented that demonstrate the role of small-world effects on the speed of consensus algorithms and cooperative control of multivehicle formations

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Consensus and Cooperation in Networked Multi-Agent Systems

In recent years, spectral clustering has become one of the most popular modern clustering algorithms. It is simple to implement, can be solved efficiently by standard linear algebra software, and very often outperforms traditional clustering algorithms such as the k-means algorithm. On the first glance spectral clustering appears slightly mysterious, and it is not obvious to see why it works at all and what it really does. The goal of this tutorial is to give some intuition on those questions. We describe different graph Laplacians and their basic properties, present the most common spectral clustering algorithms, and derive those algorithms from scratch by several different approaches. Advantages and disadvantages of the different spectral clustering algorithms are discussed.

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A tutorial on spectral clustering

The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices of the same cluster and comparatively few edges joining vertices of different clusters. Such clusters, or communities, can be considered as fairly independent compartments of a graph, playing a similar role like, e. g., the tissues or the organs in the human body. Detecting communities is of great importance in sociology, biology and computer science, disciplines where systems are often represented as graphs. This problem is very hard and not yet satisfactorily solved, despite the huge effort of a large interdisciplinary community of scientists working on it over the past few years. We will attempt a thorough exposition of the topic, from the definition of the main elements of the problem, to the presentation of most methods developed, with a special focus on techniques designed by statistical physicists, from the discussion of crucial issues like the significance of clustering and how methods should be tested and compared against each other, to the description of applications to real networks.

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Community detection in graphs

Power-law distributions occur in many situations of scientific interest and have significant consequences for our understanding of natural and man-made phenomena. Unfortunately, the detection and characterization of power laws is complicated by the large fluctuations that occur in the tail of the distribution—the part of the distribution representing large but rare events—and by the difficulty of identifying the range over which power-law behavior holds. Commonly used methods for analyzing power-law data, such as least-squares fitting, can produce substantially inaccurate estimates of parameters for power-law distributions, and even in cases where such methods return accurate answers they are still unsatisfactory because they give no indication of whether the data obey a power law at all. Here we present a principled statistical framework for discerning and quantifying power-law behavior in empirical data. Our approach combines maximum-likelihood fitting methods with goodness-of-fit tests based on the Kolmogorov-Smirnov (KS) statistic and likelihood ratios. We evaluate the effectiveness of the approach with tests on synthetic data and give critical comparisons to previous approaches. We also apply the proposed methods to twenty-four real-world data sets from a range of different disciplines, each of which has been conjectured to follow a power-law distribution. In some cases we find these conjectures to be consistent with the data, while in others the power law is ruled out.

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Power-Law Distributions in Empirical Data

Models for the processes by which ideas and influence propagate through a social network have been studied in a number of domains, including the diffusion of medical and technological innovations, the sudden and widespread adoption of various strategies in game-theoretic settings, and the effects of "word of mouth" in the promotion of new products. Recently, motivated by the design of viral marketing strategies, Domingos and Richardson posed a fundamental algorithmic problem for such social network processes: if we can try to convince a subset of individuals to adopt a new product or innovation, and the goal is to trigger a large cascade of further adoptions, which set of individuals should we target?We consider this problem in several of the most widely studied models in social network analysis. The optimization problem of selecting the most influential nodes is NP-hard here, and we provide the first provable approximation guarantees for efficient algorithms. Using an analysis framework based on submodular functions, we show that a natural greedy strategy obtains a solution that is provably within 63% of optimal for several classes of models; our framework suggests a general approach for reasoning about the performance guarantees of algorithms for these types of influence problems in social networks.We also provide computational experiments on large collaboration networks, showing that in addition to their provable guarantees, our approximation algorithms significantly out-perform node-selection heuristics based on the well-studied notions of degree centrality and distance centrality from the field of social networks.

/pdf/maximizing-the-spread-of-influence-through-a-social-network-3nnj0jic76.pdf

Maximizing the spread of influence through a social network

/pdf/maximizing-the-spread-of-influence-through-a-social-network-47y1ehuvwi.pdf

Maximizing the Spread of Influence through a Social Network

Over the last decade, we have seen a revolution in connectivity between computers, and a resulting paradigm shift from centralized to highly distributed systems. With massive scale also comes massive instability, as node and link failures become the norm rather than the exception. For such highly volatile systems, decentralized gossip-based protocols are emerging as an approach to maintaining simplicity and scalability while achieving fault-tolerant information dissemination. In this paper, we study the problem of computing aggregates with gossip-style protocols. Our first contribution is an analysis of simple gossip-based protocols for the computation of sums, averages, random samples, quantiles, and other aggregate functions, and we show that our protocols converge exponentially fast to the true answer when using uniform gossip. Our second contribution is the definition of a precise notion of the speed with which a node's data diffuses through the network. We show that this diffusion speed is at the heart of the approximation guarantees for all of the above problems. We analyze the diffusion speed of uniform gossip in the presence of node and link failures, as well as for flooding-based mechanisms. The latter expose interesting connections to random walks on graphs.

/pdf/gossip-based-computation-of-aggregate-information-4dn4z6oqnd.pdf

Gossip-based computation of aggregate information

We study the problem of maximizing the expected spread of an innovation or behavior within a social network, in the presence of “word-of-mouth” referral. Our work builds on the observation that individuals’ decisions to purchase a product or adopt an innovation are strongly influenced by recommendations from their friends and acquaintances. Understanding and leveraging this influence may thus lead to a much larger spread of the innovation than the traditional view of marketing to individuals in isolation.

In this paper, we define a natural and general model of influence propagation that we term the decreasing cascade model, generalizing models used in the sociology and economics communities. In this model, as in related ones, a behavior spreads in a cascading fashion according to a probabilistic rule, beginning with a set of initially “active” nodes. We study the target set selection problem: we wish to choose a set of individuals to target for initial activation, such that the cascade beginning with this active set is as large as possible in expectation. We show that in the decreasing cascade model, a natural greedy algorithm is a 1-1/ e-e approximation for selecting a target set of size k.

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Influential nodes in a diffusion model for social networks

Social networks often serve as a medium for the diffusion of ideas or innovations An individual's decision whether to adopt a product or innovation will be highly dependent on the choices made by the individual's peers or neighbors in the social network In this work, we study the game of innovation diffusion with multiple competing innovations such as when multiple companies market competing products using viral marketing Our first contribution is a natural and mathematically tractable model for the diffusion of multiple innovations in a network We give a (1-1/e) approximation algorithm for computing the best response to an opponent's strategy, and prove that the "price of competition" of this game is at most 2 We also discuss "first mover" strategies which try to maximize the expected diffusion against perfect competition Finally, we give an FPTAS for the problem of maximizing the influence of a single player when the underlying graph is a tree

David Kempe

Papers

Maximizing the spread of influence through a social network

Maximizing the Spread of Influence through a Social Network

Gossip-based computation of aggregate information

Influential nodes in a diffusion model for social networks

Competitive influence maximization in social networks