Diffusion of innovations in social networks

While social networks do affect diffusion of innovations, the exact nature of these effects are far from clear, and, in many cases, there exist conflicting hypotheses among researchers. In this paper, we focus on the linear threshold model where each individual requires exposure to (potentially) multiple sources of adoption in her neighborhood before adopting the innovation herself. In contrast with the conclusions in the literature, our bounds suggest that innovations might spread further across networks with a smaller degree of clustering. We provide both analytical evidence and simulations for our claims. Finally, we propose an extension for the linear threshold model to better capture the notion of path dependence, i.e., a few minor shocks along the way could alter the course of diffusion significantly.Charles Stark Draper Laboratory. Independent Research and Development. University Research & DevelopmentNational Science Foundation (U.S.). (Grant number SES-0729361)United States. Air Force Office of Scientific Research (Grant number FA9550-09-1-0420)United States. Air Force Office of Scientific Research. (Grant number W911NF-09-1-0556

A primer on noise-induced transitions in applied dynamical systems

Noise plays a fundamental role in a wide variety of physical and biological dynamical systems. It can arise from an external forcing or due to random dynamics internal to the system. It is well established that even weak noise can result in large behavioral changes such as transitions between or escapes from quasi-stable states. These transitions can correspond to critical events such as failures or extinctions that make them essential phenomena to understand and quantify, despite the fact that their occurrence is rare. This article will provide an overview of the theory underlying the dynamics of rare events for stochastic models along with some example applications

Automating agent-based modeling : data-driven generation and application of innovation diffusion models

Simulation modeling is useful to understand the mechanisms of the diffusion of innovations, which can be used for forecasting the future of innovations. This study aims to make the identification of such mechanisms less costly in time and labor. We present an approach that automates the generation of diffusion models by: (1) preprocessing of empirical data on the diffusion of a specific innovation, taken out by the user; (2) testing variations of agent-based models for their capability of explaining the data; (3) assessing interventions for their potential to influence the spreading of the innovation. We present a working software implementation of this procedure and apply it to the diffusion of water-saving showerheads. The presented procedure successfully generated simulation models that explained diffusion data. This progresses agent-based modeling methodologically by enabling detailed modeling at relative simplicity for users. This widens the circle of persons that can use simulation to shape innovation

Diffusion of Innovation in Small-world Networks with Social Interactions

학위논문 (박사)-- 서울대학교 대학원 : 협동과정 기술경영·경제·정책전공, 2015. 2. 이종수.인터넷과 무선통신, 사회연결망서비스 등의 등장으로 사회 네트워크가 발전하면서, 예전보다 소비자들은 서로 더 자주, 신속하게 정보를 교환하고 서로의 제품 구매에 영향을 미치고 있다. 그러나, 기존에 널리 이용되어 온 배스 모형을 비롯한 여러 확산 예측 모형들은 이론적 기반이 취약할 뿐만 아니라, 시장 수준에서의 분석만을 행하고 있기 때문에 이러한 소비자간 상호작용의 효과를 통합적이고 한정적으로 반영하고 있어 최근의 사회 현상을 제대로 설명하지 못하는 한계가 있다. 그 대안으로 등장한 행위자 기반 모형들은 개인 단위 분석을 가능하게 한 장점은 있으나, 여전히 이론적 기반이 취약하고 총 시장 수준 자료를 통한 분석은 요원한 실정이다. 이 연구에서는 소비자들이 서로의 선택으로부터 영향을 받는 사회적 효용함수가 있다고 가정하고, 이와 같은 사회적 상호작용으로부터 오는 효용을 개개인의 효용구조에 직접적으로 반영시켜 이것이 확산 곡선에 어떤 영향을 미치는 지를 상호작용 기반 확산 모형이라 명명된 새로운 모형을 통해 보고자 한다. 또한 기존의 대표적인 확산 모형과의 비교를 통해 실제로 본 모형이 최근의 사회 현상을 설명하는 데 적합한 지 살펴보고자 한다. 더불어, 혁신 확산을 잘 설명하기 위해서는 위해서는 기존에 널리 사용되었던 세포자동자 격자구조보다는 작은 세상 연결망 사회구조가 더 적합함을 밝힌다. 이 연구를 통해, 개인의 효용과 상호작용에 기반한 경제학적 확산 모형을 얻을 수 있었을 뿐만 아니라, 기존 확산 모형과 달리 상호작용의 이질성까지 반영할 수 있는 확산 모형을 구축할 수 있었다. 또한 본 연구는 개인 단위의 모형이 시장 전체 수준의 수요 예측에 활용될 수 있는 새로운 접근방식을 제안하고 있으며, 실제 자료의 분석에 대해서도 모형이 충분히 활용가능 할 수 있음을 보였다. 이 연구에서 제시하는 모형은 경제학적 이론에 기반을 두었기 때문에 연구 대상에 따른 확장이 용이하다는 장점이 있으며, 이러한 일반적인 모형 구축은 향후 확산 과정에 대한 이해를 더욱 확장시켜 줄 수 있을 것으로 기대한다.The advent of the Internet, mobile communications, and social network services has stimulated social interactions among consumers, allowing people to affect one anothers innovation adoptions by exchanging information more frequently and more quickly. Previous diffusion models, such as the Bass model, however, face limitations in reflecting such recent phenomena in society. These models are weak in their ability to model interactions between agentsthey model aggregated-level behaviors only. The agent-based model, which is an alternative to the aggregate model, is good for individual modeling, but it is still not based on an economic perspective of social interactions so far. This study assumes the presence of social utility from other consumers in the adoption of innovation and investigates the effect of individual interactions on innovation diffusion by developing a new model called the interaction-based diffusion model. By comparing this model with previous diffusion models, the study also examines how the proposed model explains innovation diffusion from the perspective of economics. In addition, the study recommends the use of a small-world network topology instead of cellular automata to describe innovation diffusion. This study develops a model based on individual preference and heterogeneous social interactions using utility specification, which is expandable and, thus, able to encompass various issues in diffusion research, such as reservation price. Furthermore, the study proposes a new framework to forecast aggregated-level market demand from individual-level modeling. The model also exhibits a good fit to real market data. It is expected that the study will contribute to our understanding of the innovation diffusion process through its microeconomic theoretical approach.Abstract iii Contents v List of Tables vii List of Figures viii Chapter 1. Introduction 1 1.1 Research Background 1 1.2 Objective of the Study 3 1.3 Outline of the Study 4 Chapter 2. Literature Review 7 2.1 Overview of the Diffusion of Innovation 7 2.2 Diffusion Models 12 2.2.1 Aggregate Models 13 2.2.2 Agent-Based Models 20 2.2.3 Diffusion models based on individual behavior 26 2.3 Interaction-Based Model 31 2.4 Research Motivation 36 Chapter 3. Interaction-Based Diffusion Model 41 3.1 Utility Model 41 3.2 Structure of Social Network 52 3.3 Diffusion Process 61 Chapter 4. Interpretation of the Interaction-Based Diffusion Model 65 4.1 Specification of Simulation 65 4.2 Simulation Results 74 4.2.1 Effect of Price Coefficients 78 4.2.2 Effect of Social Interactions 87 4.3 Summary 92 Chapter 5. Empirical Availability of the Interaction-Based Diffusion Model 99 5.1 Adjustment of the Model for Fitting 99 5.2 Analysis of Real Market Data 111 5.2.1 Fitting Procedure 111 5.2.2 Analysis Results 114 5.3 Summary 119 Chapter 6. Conclusion 121 6.1 Concluding Remarks 121 6.2 Contributions and Limitations 122 6.3 Future Research Topics 125 Bibliography 127 Appendix I: Raw data of mobile communication subscriptions in three countries. 143 Abstract (Korean) 145Docto

Stochastic Algorithms in Riemannian Manifolds and Adaptive Networks

The combination of adaptive network algorithms and stochastic geometric dynamics has the potential to make a large impact in distributed control and signal processing applications. However, both literatures contain fundamental unsolved problems. The thesis is thus in two main parts. In part I, we consider stochastic differential equations (SDEs) evolving in a matrix Lie group. To undertake any kind of statistical signal processing or control task in this setting requires the simulation of such geometric SDEs. This foundational issue has barely been addressed previously. Chapter 1 contains background and motivation. Chapter 2 develops numerical schemes for simulating SDEs that evolve in SO(n) and SE(n). We propose novel, reliable, efficient schemes based on diagonal Padé approximants, where each trajectory lies in the respective manifold. We prove first order convergence in mean uniform squared error using a new proof technique. Simulations for SDEs in SO(50) are provided. In part II, we study adaptive networks. These are collections of individual agents (nodes) that cooperate to solve estimation, detection, learning and adaptation problems in real time from streaming data, without a fusion center. We study general diffusion LMS algorithms - including real time consensus - for distributed MMSE parameter estimation. This choice is motivated by two major flaws in the literature. First, all analyses assume the regressors are white noise, whereas in practice serial correlation is pervasive. Dealing with it however is much harder than the white noise case. Secondly, since the algorithms operate in real time, we must consider realization-wise behavior. There are no such results. To remedy these flaws, we uncover the mixed time scale structure of the algorithms. We then perform a novel mixed time scale stochastic averaging analysis. Chapter 3 contains background and motivation. Realization-wise stability (chapter 4) and performance including network MSD, EMSE and realization-wise fluctuations (chapter 5) are then studied. We develop results in the difficult but realistic case of serial correlation. We observe that the popular ATC, CTA and real time consensus algorithms are remarkably similar in terms of stability and performance for small constant step sizes. Parts III and IV contain conclusions and future work