Mathematical genealogy and department prestige

Myers, Sean A.; Mucha, Peter J.; Porter, Mason A.

doi:10.1063/1.3668043

Cited by 22 publications

(23 citation statements)

References 4 publications

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“…PageRank has also been used to rank professional tennis players [282], and PageRank and other RW-based ranking methods have been used for ranking teams in U.S. college football [283,284] and ranking players in Major League Baseball [285]. PageRank and other eigenvector-based centrality measures have also been used to rank universities [286], mathematics research programs [273,287], baby names [288], and many other things.…”

Section: Pagerankmentioning

confidence: 99%

Random walks and diffusion on networks

2017

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Random walks are ubiquitous in the sciences, and they are interesting from both theoretical and practical perspectives. They are one of the most fundamental types of stochastic processes; can be used to model numerous phenomena, including diffusion, interactions, and opinions among humans and animals; and can be used to extract information about important entities or dense groups of entities in a network. Random walks have been studied for many decades on both regular lattices and (especially in the last couple of decades) on networks with a variety of structures. In the present article, we survey the theory and applications of random walks on networks, restricting ourselves to simple cases of single and non-adaptive random walkers. We distinguish three main types of random walks: discrete-time random walks, node-centric continuous-time random walks, and edge-centric continuous-time random walks. We first briefly survey random walks on a line, and then we consider random walks on various types of networks. We extensively discuss applications of random walks, including ranking of nodes (e.g., PageRank), community detection, respondent-driven sampling, and opinion models such as voter models.Comment: 12 figures, 2 table

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Section: Pagerankmentioning

confidence: 99%

Random walks and diffusion on networks

2017

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“…Most of our calculations for these examples use a temporal generalization of hub and authority scores [73], which are particularly appropriate for directed networks (such as our three examples). We also note that hub and authority scores have been used previously to examine time-independent faculty-hiring networks [39,93] and Supreme Court decisions [39,41]. To illustrate a comparison with another choice of centrality, we also study a temporal generalization of PageRank for the MGP network.…”

Section: Case Studies With Empirical Network Datamentioning

confidence: 99%

“…For each mathematical scientist, the information includes graduation year, his/her official academic advisor(s), the degree-granting university, and a list of his/her students who have also obtained doctoral degrees. A subset of the present authors previously utilized this data to approximate the flow of doctorates between universities-that is, a person graduates from one university and is then hired at a second university-and quantified the resulting hub and authority scores for the total flow during a specified time period as a candidate measure of these universities' relative mathematical prestige [93]. Moreover, hub and authority scores have been used previously to study Ph.D. exchange networks in other disciplines [39].…”

Section: Doctoral Degree Exchange In the Mathematics Genealogy Projecmentioning

confidence: 99%

Eigenvector-Based Centrality Measures for Temporal Networks

Taylor¹,

Myers²,

Clauset³

et al. 2017

Multiscale Model. Simul.

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169

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Numerous centrality measures have been developed to quantify the importances of nodes in time-independent networks, and many of them can be expressed as the leading eigenvector of some matrix. With the increasing availability of network data that changes in time, it is important to extend such eigenvector-based centrality measures to time-dependent networks. In this paper, we introduce a principled generalization of network centrality measures that is valid for any eigenvector-based centrality. We consider a temporal network with N nodes as a sequence of T layers that describe the network during different time windows, and we couple centrality matrices for the layers into a supra-centrality matrix of size NT × NT whose dominant eigenvector gives the centrality of each node i at each time t. We refer to this eigenvector and its components as a joint centrality, as it reflects the importances of both the node i and the time layer t. We also introduce the concepts of marginal and conditional centralities, which facilitate the study of centrality trajectories over time. We find that the strength of coupling between layers is important for determining multiscale properties of centrality, such as localization phenomena and the time scale of centrality changes. In the strong-coupling regime, we derive expressions for time-averaged centralities, which are given by the zeroth-order terms of a singular perturbation expansion. We also study first-order terms to obtain first-order-mover scores, which concisely describe the magnitude of nodes’ centrality changes over time. As examples, we apply our method to three empirical temporal networks: the United States Ph.D. exchange in mathematics, costarring relationships among top-billed actors during the Golden Age of Hollywood, and citations of decisions from the United States Supreme Court.

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“…A number of studies have employed faculty hiring data to investigate disciplinary characteristics, such as those on sociology (Hanneman 2001), political science (Fowler et al 2007), economics (Amir and Knauff 2008), communication (Barnett et al 2010), law (Katz et al 2011), and mathematics (Myers et al 2011).…”

Section: Introductionmentioning

confidence: 99%

Understanding the evolving academic landscape of library and information science through faculty hiring data

2016

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Using a 40-year (from 1975 to 2015) hiring dataset of 642 library and Information science (LIS) faculty members from 44 US universities, this research reveals the disciplinary characteristics of LIS through several key aspects including gender, rank, country, university, major, and research area. Results show that genders and ranks among LIS faculty members are evenly distributed; geographically, more than 90 % of LIS faculty members received doctoral degrees in the US; meanwhile, 60 % of LIS faculty received Ph.D. in LIS, followed by Computer Science and Education; in regards to research interests, Human-Computer interaction, Digital Librarianship, Knowledge Organization and Management, and Information Behavior are the most popular research areas among LIS faculty members. Through a series of dynamic analyses, this study shows that the educational background of LIS faculty members is becoming increasingly diverse; in addition, research areas such as Human-Computer interaction, Social Network Analysis, Services for Children and Youth, Information Literacy, Information Ethics and Policy, and Data and Text Mining, Natural Language Processing, Machine Learning have received an increasing popularity. Predictive analyses are performed to discover trends on majors and research areas. Results show that the growth rate of LIS faculty members is linearly distributed. In addition, among faculty member's Ph.D. majors, the share of LIS is decreasing while that the share of Computer Science is growing; among faculty members' research areas, the share of Human-Computer interaction is on the rise.

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Mathematical genealogy and department prestige

Cited by 22 publications

References 4 publications

Random walks and diffusion on networks

Random walks and diffusion on networks

Eigenvector-Based Centrality Measures for Temporal Networks

Understanding the evolving academic landscape of library and information science through faculty hiring data

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