Lecture Notes on Network Information Theory

These lecture notes have been converted to a book titled Network Information Theory published recently by Cambridge University Press. This book provides a significantly expanded exposition of the material in the lecture notes as well as problems and bibliographic notes at the end of each chapter. The authors are currently preparing a set of slides based on the book that will be posted in the second half of 2012. More information about the book can be found at http://www.cambridge.org/9781107008731/. The previous (and obsolete) version of the lecture notes can be found at http://arxiv.org/abs/1001.3404v4/

Essays on Applied Network Theory.

Network economics is a fast growing area of study, with a lot of potential for addressing a wide variety of socio-economic phenomena. Networks literally permeate our social and economic lives. The unemployed find jobs using the information and assistance of their friends and relatives. Consumers benefit from the research of friends and family into new products. In medicine and other technical fields, professional networks shape research patterns. In all these settings, the well-being of participants depends on social, geographic, or trading relationships. The countless ways in which network structures affect our well-being make it critical to understand: (i) how network structures impact behavior, (ii) what can be done, in the way of design by policymakers, to improve systemic outcomes. This area of study, broadly called network economics, is at the heart of my research interests. In my dissertation I focus on three specific applications of network theory. The first application concerns networks in trade, where network structure represents the organization of trade agreements between countries. The second application deals with networks in financial market, and the network is used to model the structure of interbank exposures. Lastly, for the third application, I consider networks in labor markets and migration. In this context, the network represents the structure of social relations between people. Each of these applications of network analysis is addressed by one of three chapters in the thesis.Network analysis (Planning); Social networks -- Mathematical models; Social sciences -- Network analysis; Economics, Mathematical;

Comment on "microscopic theory of network glasses"

Calorimetric experiments on network glasses provide information on the ergodicity (landscape) temperature of supercooled liquids and can be compared with a recent theory developed by Hall and Wolynes [PRL90, 085505 (2003)]Comment: 2 pages, 2 EPS figures RevTEX. to appear in Physical review Letter

Signed Network Modeling Based on Structural Balance Theory

The modeling of networks, specifically generative models, have been shown to provide a plethora of information about the underlying network structures, as well as many other benefits behind their construction. Recently there has been a considerable increase in interest for the better understanding and modeling of networks, but the vast majority of this work has been for unsigned networks. However, many networks can have positive and negative links(or signed networks), especially in online social media, and they inherently have properties not found in unsigned networks due to the added complexity. Specifically, the positive to negative link ratio and the distribution of signed triangles in the networks are properties that are unique to signed networks and would need to be explicitly modeled. This is because their underlying dynamics are not random, but controlled by social theories, such as Structural Balance Theory, which loosely states that users in social networks will prefer triadic relations that involve less tension. Therefore, we propose a model based on Structural Balance Theory and the unsigned Transitive Chung-Lu model for the modeling of signed networks. Our model introduces two parameters that are able to help maintain the positive link ratio and proportion of balanced triangles. Empirical experiments on three real-world signed networks demonstrate the importance of designing models specific to signed networks based on social theories to obtain better performance in maintaining signed network properties while generating synthetic networks.Comment: CIKM 2018: https://dl.acm.org/citation.cfm?id=327174

MPA network design based on graph network theory and emergent properties of larval dispersal

Despite the recognised effectiveness of networks of Marine Protected Areas (MPAs) as a biodiversity conservation instrument, nowadays MPA network design frequently disregards the importance of connectivity patterns. In the case of sedentary marine populations, connectivity stems not only from the stochastic nature of the physical environment that affects early-life stages dispersal, but also from the spawning stock attributes that affect the reproductive output (e.g., passive eggs and larvae) and its survivorship. Early-life stages are virtually impossible to track in the ocean. Therefore, numerical ocean current simulations coupled to egg and larval Lagrangian transport models remain the most common approach for the assessment of marine larval connectivity. Inferred larval connectivity may be different depending on the type of connectivity considered; consequently, the prioritisation of sites for marine populations' conservation might also differ. Here, we introduce a framework for evaluating and designing MPA networks based on the identification of connectivity hotspots using graph theoretic analysis. We use as a case of study a network of open-access areas and MPAs, off Mallorca Island (Spain), and test its effectiveness for the protection of the painted comber Serranus scriba. Outputs from network analysis are used to: (1) identify critical areas for improving overall larval connectivity; (2) assess the impact of species' biological parameters in network connectivity; and (3) explore alternative MPA configurations to improve average network connectivity. Results demonstrate the potential of graph theory to identify non-trivial egg/larval dispersal patterns and emerging collective properties of the MPA network which are relevant for increasing protection efficiency.Comment: 8 figures, 3 tables, 1 Supplementary material (including 4 table; 3 figures and supplementary methods

A General Framework for Complex Network Applications

Complex network theory has been applied to solving practical problems from different domains. In this paper, we present a general framework for complex network applications. The keys of a successful application are a thorough understanding of the real system and a correct mapping of complex network theory to practical problems in the system. Despite of certain limitations discussed in this paper, complex network theory provides a foundation on which to develop powerful tools in analyzing and optimizing large interconnected systems.Comment: 8 page

Network Identification for Diffusively-Coupled Systems with Minimal Time Complexity

The theory of network identification, namely identifying the (weighted) interaction topology among a known number of agents, has been widely developed for linear agents. However, the theory for nonlinear agents using probing inputs is less developed and relies on dynamics linearization. We use global convergence properties of the network, which can be assured using passivity theory, to present a network identification method for nonlinear agents. We do so by linearizing the steady-state equations rather than the dynamics, achieving a sub-cubic time algorithm for network identification. We also study the problem of network identification from a complexity theory standpoint, showing that the presented algorithms are optimal in terms of time complexity. We also demonstrate the presented algorithm in two case studies.Comment: 12 pages, 3 figure

Gauge Theory for the Rate Equations: Electrodynamics on a Network

Systems of coupled rate equations are ubiquitous in many areas of science, for example in the description of electronic transport through quantum dots and molecules. They can be understood as a continuity equation expressing the conservation of probability. It is shown that this conservation law can be implemented by constructing a gauge theory akin to classical electrodynamics on the network of possible states described by the rate equations. The properties of this gauge theory are analyzed. It turns out that the network is maximally connected with respect to the electromagnetic fields even if the allowed transitions form a sparse network. It is found that the numbers of degrees of freedom of the electric and magnetic fields are equal. The results shed light on the structure of classical abelian gauge theory beyond the particular motivation in terms of rate equations.Comment: 4 pages, 2 figures included, v2: minor revision, as publishe