**Courses in Network Science at Yale**

**AFST 348: Islamic Social Movements**

Wyrtzen, Jonathan

Social movement and network theory used to analyze the emergence and evolution of Islamic movements from the early twentieth century to the present. Organization, mobilization, and framing of political, nonpolitical, militant, and nonmilitant movements; transnational dimensions of Islamic activism. Case studies include the Muslim Brotherhood, Hamas, Hizbollah, Al-Qaeda, Al-Adl wa-Ihsann, and Tablighi Jama’at.

**AFST 356: Collective Action and Social Movements**

Wood, Elisabeth

The emergence and evolution of collective mobilizations for social change, among them demonstrations, land occupations, strikes, abortion clinic blockades, revolutions, and genocide. Case studies are drawn from environmental justice, living wage, and South African labor movements, as well as from religious mobilization, social movements in Central America, and the Rwandan genocide. Theoretical approaches to political opportunity, social networks, and social preferences.

**AMTH 160: The Structure of Networks**

Coifman, Ronald

Network structures and network dynamics described through examples and applications ranging from marketing to epidemics and the world climate. Study of social and biological networks as well as networks in the humanities. Mathematical graphs provide a simple common language to describe the variety of networks and their properties.

**AMTH 364: Information Theory**

Barron, Andrew

Foundations of information theory in communications, statistical inference, statistical mechanics, probability, and algorithmic complexity. Quantities of information and their properties: entropy, conditional entropy, divergence, redundancy, mutual information, channel capacity. Basic theorems of data compression, data summarization, and channel coding. Applications in statistics and finance.

**AMTH 462: Graphs and Networks**

Spielman, Daniel

A mathematical examination of graphs and their applications in the sciences. Families of graphs include social networks, small-world graphs, Internet graphs, planar graphs, well-shaped meshes, power-law graphs, and classic random graphs. Phenomena include connectivity, clustering, communication, ranking, and iterative processes.

**AMTH 561: Spectral Graph Theory**

Spielman, Daniel

An applied approach to spectral graph theory. The combinatorial meaning of the eigenvalues and eigenvectors of matrices associated with graphs. Applications to optimization, numerical linear algebra, error-correcting codes, computational biology, and the discovery of graph structure.

**ARCH 341: Globalization Space**

Easterling, Keller

Infrastructure space as a primary medium of change in global polity. Networks of trade, energy, communication, transportation, spatial products, finance, management, and labor, as well as new strains of political opportunity that reside within their spatial disposition. Case studies include free zones and automated ports around the world, satellite urbanism in South Asia, high-speed rail in Japan and the Middle East, agripoles in southern Spain, fiber optic submarine cable in East Africa, spatial products of tourism in North Korea, and management platforms of the International Organization for Standardization.

**CB&B 752/MCDB452/MB&B752/MCDB752/CPSC752/MB&B452****: Bioinformatics: Practical Application of Data Mining & Simulation**

Gerstein, Mark

Bioinformatics encompasses the analysis of gene sequences, macromolecular structures, and functional genomics data on a large scale. It represents a major practical application for modern techniques in data mining and simulation. Specific topics to be covered include sequence alignment, large-scale processing, next-generation sequencing data, comparative genomics, phylogenetics, biological database design, geometric analysis of protein structure, molecular-dynamics simulation, biological networks, normalization of microarray data, mining of functional genomics data sets, and machine-learning approaches to data integration.

**CPSC 365: Design and Analysis of Algorithms**

Spielman, Daniel

Paradigms for problem solving: divide and conquer, recursion, greedy algorithms, dynamic programming, randomized and probabilistic algorithms. Techniques for analyzing the efficiency of algorithms and designing efficient algorithms and data structures. Algorithms for graph theoretic problems, network flows, and numerical linear algebra. Provides algorithmic background essential to further study of computer science.

**CPSC 433: Computer Networks**

Yang, Yang

An introduction to the design, implementation, analysis, and evaluation of computer networks and their protocols. Topics include layered network architectures, applications, transport, congestion, routing, data link protocols, local area networks, performance analysis, multimedia networking, network security, and network management. Emphasis on protocols used in the Internet.

**CPSC434: Mobile Computing and Wireless Networking**

Yang, Yang

Introduction to the principles of mobile computing and its enabling technologies. Topics include wireless systems; information management; location-independent and location-dependent computing models; disconnected and weakly-connected operation models; human-computer interactions; mobile applications and services; security; power management; and sensor networks.

**CPSC477: Neural Networks for Computing**

Miranker, Willard

Artificial neural networks as a computational paradigm studied with application to problems in associative memory, learning, pattern recognition, perception, robotics, and other areas. Development of models for the dynamics of neurons and methods such as learning for designing neural networks. Concepts, designs, and methods compared and tested in software simulation. Brain and consciousness studies are optional topics.

**ECON460: Social Networks**

Laclau, Marie

Introduction to the study of social networks. Methods draw heavily on game theory, but also incorporate approaches from other disciplines, including sociology, mathematics, and computer science. Applications include risk sharing and microfinance; job searching; the spread of information, fads, and diseases; supply chains; collusion; and local public goods.

**ECON471: Cooperative Game Theory**

Dubey, Pradeep

The theory and applications of cooperative games. Topics include matching, bargaining, cost allocation, market games, voting games, and games on networks.

**EENG 202: Communication, Computation, and Control**

Tatikonda, Sekhar

Introduction to systems that sense, process, control, and communicate. Topics include communication systems (compression, channel coding); network systems (network architecture and routing, wireless networks, network security); estimation and learning (classification, regression); and signals and systems (linear systems, Fourier techniques, bandlimited sampling, modulation). MATLAB programming and laboratory experiments illustrate concepts.

**EENG 310: Signals and Systems**

Narendra, Kumpati

Concepts for the analysis of continuous and discrete-time signals including time series. Techniques for modeling continuous and discrete-time linear dynamical systems including linear recursions, difference equations, and shift sequences. Topics include continuous and discrete Fourier analysis, Laplace and Z transforms, convolution, sampling, data smoothing, and filtering.

**EENG 436: Systems and Control**

Narendra, Kumpati

Design of feedback control systems with applications to engineering, biological, and economic systems. Topics include state-space representation, stability, controllability, and observability of discrete-time systems; system identification; optimal control of systems with multiple outputs.

**EENG 437: Optimization Techniques**

Tatikonda, Sekhar

Fundamental theory and algorithms of optimization, emphasizing convex optimization. The geometry of convex sets, basic convex analysis, the principle of optimality, duality. Numerical algorithms: steepest descent, Newton’s method, interior point methods, dynamic programming, unimodal search. Applications from engineering and the sciences.

**EENG 438: Neural Networks for Pattern Recognition**

Narendra, Kumpati

Design of artificial neural networks (ANN) for approximation, pattern recognition, identification, and control. Introduction to the theory of artificial neural networks and linear adaptive control; adaptive identification and control problems in nonlinear dynamical systems. Applications in engineering and biology.

**EENG 442/**E&AS 902/AMTH 342**: Linear Systems**

Morse, A. Stephen

Introduction to finite-dimensional, continuous, and discrete-time linear dynamical systems. Exploration of the basic properties and mathematical structure of the linear systems used for modeling dynamical processes in robotics, signal and image processing, economics, statistics, environmental and biomedical engineering, and control theory.

**EENG 444/ENAS 944: Digital Communication Systems**

Hu, Wenjun

Introduction to the fundamental theory underlying modern digital communication. Quantitative measures of information and data compression: the Huffman and Lempel-Ziv algorithms, scalar and vector quantization. Representations of signal waveforms: sampling, orthonormal expansions, waveforms as vectors in signal space. Transmission of signals through noisy channels; pulse amplitude and quadrature amplitude modulation, orthogonal signaling, signal design, noise processes, optimal detection, and error probability analysis. Applications to practical systems such as CD players, telephone modems, and wireless networks.

**EENG 451: Wireless Communications: WiFi, LTE, and Other Everyday Technologies**

Hu, Wenjun

This course aims to weave together fundamental theory of wireless communications, its application, and the design and implementation of wireless network architectures. The concepts are illustrated using examples such as WiFi and LTE. Particular emphasis is placed on the interplay between concepts and their implementation in real systems. Students can expect to learn background knowledge of some everyday wireless technologies and how to design systems based on the fundamental communications concepts.

**EENG 452/ENAS 952: Internet Engineering**

Tassiulas, Leandros

The aim of the course is to introduce the basic Internet protocols and architectures. The topics to be covered include packet-switch and multi-access networks, routing, flow control, congestion control, Internet protocols (IP, TCP, BGP), the client-server model, naming and DNS, wireless access networks (WIFI), mobile communications. The basic architectural concepts of packet switching networks will be studied extensively, including important operating algorithms. Extensive experimentation in networking testbeds will be used as a vehicle to illustrate the concepts.

**ENAS 496: Probability and Stochastic Processes**

Karbasi, Amin

A study of stochastic processes and estimation, including fundamentals of detection and estimation. Vector space representation of random variables, Bayesian and Neyman-Pearson hypothesis testing, Bayesian and nonrandom parameter estimation, minimum-variance unbiased estimators, and the Cramer-Rao bound. Stochastic processes. Linear prediction and Kalman filtering. Poison counting process and renewal processes, Markov chains, branching processes, birth-death processes, and semi-Markov processes. Applications from communications, networking, and stochastic control.

### ENAS 900b: Distributed Computation and Decision Making

Morse, A. Stephen

Within the field of network science there has long been interest in distributed modeling, distributed computation and distributed decision making problems of many types. Among these are flocking problems, consensus problems with and without antagonistic interactions, the multi-robot rendezvous problem, distributed averaging, localization of sensors in a multi-sensor network, opinion dynamics, and the distributed management of robotic formations. The aim of this course is to explain what these problems are and to discuss their solutions. Related concepts from spectral graph theory, rigid graph theory, nonhomogeneous Markov chain theory, stability theory, and linear system theory will be covered. Although most of the mathematics need will be covered in the lectures, students taking this course should have a working understanding of basic linear algebra.

**ENAS 962: Theoretical Challenges in Network Science**

Karbasi, Amin

This is an interdisciplinary course with a focus on the emerging science of complex networks and their mathematical models. Students learn about the recent research on the structure and analysis of such networks, and on models that abstract their basic properties. Topics include random graphs and their properties, probabilistic techniques for link analysis, centralized and decentralized search algorithms, random walks, diffusion and epidemic processes, and spectral methods.

**ENAS 963: Network Algorithms and Stochastic Optimization**

Tassiulas, Leandros

This course focuses on resource allocation models as well as associated algorithms and design and optimization methodologies that capture the intricacies of complex networking systems in communications computing as well as transportation, manufacturing and energy systems. Max-weight scheduling, back-pressure routing, wireless opportunistic scheduling, time-varying topology network control, energy efficient management are sample topics to be considered in addition to Lyapunov stability and optimization, stochastic ordering and notions of fairness in network resource consumption.

**HSAR 321: Global Contemporary Art**

Joselit, David

Global and transregional developments in visual arts from the mid-twentieth century to the present. Attention to differences masked by stylistic similarities. The effects of cultural revolution in the USSR and China, decolonization in Africa, and countercultural movements in Europe and America. The emergence of international networks and the possibility of an international style that closely follows worldwide liberalization of economic markets.

**MATH 244: Discrete Math**

Kaplan, Nathan

Basic concepts and results in discrete mathematics: graphs, trees, connectivity, Ramsey theorem, enumeration, binomial coefficients, Stirling numbers. Properties of finite set systems.

**MB&B 723: Macromolecular Interactions**

Regan, Lynne

The course examines the nature of the intricate networks of macromolecular interactions that underlie the functioning of every cell and the modern biophysical methods available for their study across multiple length, time, and energy scales. Counts as 0.5 credit toward MB&B graduate course requirements.

**MGT 535: Managing Strategic Networks**

King, Marissa

Each week will focus on one set of network concepts applied in different organizational settings. The first third of the course examines the way in which patterns of social interaction influence an individual’s ability to achieve their goals (e.g., get a job or get promoted). The middle of the course focuses on how networks can affect the ability of organizations to implement change and realize competitive advantage. Finally, we will examine how increasing connectedness in the broader social world is transforming the way business is done.

**PLSC 250: Infrastructure: Politics and Design**

Rubin, Elihu

Infrastructures—the physical frameworks for human settlement, urbanization, and social life, including networks for transportation, water, energy, and communication. Current debates on infrastructure spending in the context of historical investments in the modern American city.

**SOCY 126: Health of the Public**

Christakis, Nicholas A.

Biological and social factors that jointly determine the health of individuals and populations. The influence of medical care, social networks, and socioeconomic inequality on illness, recovery, and death.

**SOCY 133: Computers, Networks, and Society**

Boorman, Scott

Comparison of major algorithm-centered approaches to the analysis of complex social network and organizational data. Fundamental principles for developing a disciplined and coherent perspective on the effects of modern information technology on societies worldwide. Software warfare and algorithm sabotage; blockmodeling and privacy; legal, ethical, and policy issues.

**SOCY 167: Social Networks and Society**

Erikson, Emily

Introduction to the theory and practice of social network analysis. The role of social networks in contemporary society; basic properties of network measures, matrices, and statistics. Theoretical concepts such as centrality and power, cohesion and community, structural holes, duality of persons and groups, small worlds, and diffusion and contagion. Use of social structural, dynamic, and statistical approaches, as well as network analysis software.

**SOCY 625: Analysis of Social Structure**

Boorman, Scott

Emphasizing analytically integrated viewpoints, the course develops a variety of major contemporary approaches to the study of social structure and social organization. Building in part on research viewpoints articulated by Kenneth J. Arrow in The Limits of Organization (1974), by János Kornai in an address at the Hungarian Academy of Sciences published in 1984, and by Harrison C. White in Identity and Control (2nd ed., 2008), four major species of social organization are identified as focal: (1) social networks, (2) competitive markets, (3) hierarchies/bureaucracy, and (4) collective choice. This lecture course uses mathematical and computational models—and comparisons of their scientific styles and contributions—as analytical vehicles in coordinated development of the four species.

**SOCY 632: Social Network Analysis**

Erikson, Emily

Social Network Analysis (SNA) refers to both a theoretical perspective and a set of methodological techniques. As a theoretical perspective, SNA stresses the interdependence among social actors. This approach views the social world as patterns or regularities in relationships among interacting units and focuses on how such patterns affect the behavior of network units or actors. A “structure” emerges as a persistent pattern of interaction that can influence a multitude of behaviors, such as getting a job, income attainment, political decision making, social revolutions, organizational merges, global finance and trade markets, delinquent youth behaviors, the spread of infectious diseases, and so on. As a methodological approach, SNA refers to a catalog of techniques steeped in mathematical graph theory and now extending to statistical simulation and algebraic models. This course surveys the growing field of SNA, emphasizing the merger of theory and method, while gaining hands-on experience with network data and software.

**SOCY 511: Social Interaction: Modeling the Emergence of Social Structure**

Breen, Richard

Approaches to developing explanatory theories aimed at addressing specific empirical questions in contemporary sociology. Rational choice, game theory, and social (or endogenous) interaction models. The use of agent-based models and other simulation techniques in building models of social phenomena. Testing of explanatory models against empirical data.

**THST 292: Gossip and 18th Century English Performance**

Fawcett, Julia

Major works of eighteenth-century British comedy introduced through the theme of gossip and social networks. Performance practices, literary style, and social norms of the period. Gossip as a kind of performance criticism that dissects the actor in a social drama. The ability of gossip to empower or disempower the spectator/gossiper and the subject of gossip. Attention to contemporary performance and media theory.