Aaron Clauset
Total Page:16
File Type:pdf, Size:1020Kb
Load more
Recommended publications
-
Power-Law Distributions in Empirical Data
Power-law distributions in empirical data Aaron Clauset,1, 2 Cosma Rohilla Shalizi,3 and M. E. J. Newman1, 4 1Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, NM 87501, USA 2Department of Computer Science, University of New Mexico, Albuquerque, NM 87131, USA 3Department of Statistics, Carnegie Mellon University, Pittsburgh, PA 15213, USA 4Department of Physics and Center for the Study of Complex Systems, University of Michigan, Ann Arbor, MI 48109, USA Power-law distributions occur in many situations of scientific interest and have significant conse- quences for our understanding of natural and man-made phenomena. Unfortunately, the empirical detection and characterization of power laws is made difficult by the large fluctuations that occur in the tail of the distribution. In particular, standard methods such as least-squares fitting are known to produce systematically biased estimates of parameters for power-law distributions and should not be used in most circumstances. Here we review statistical techniques for making ac- curate parameter estimates for power-law data, based on maximum likelihood methods and the Kolmogorov-Smirnov statistic. We also show how to tell whether the data follow a power-law dis- tribution at all, defining quantitative measures that indicate when the power law is a reasonable fit to the data and when it is not. We demonstrate these methods by applying them to twenty- four real-world data sets from a range of different disciplines. Each of the data sets has been conjectured previously 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. -
On Biological and Non-Biological Networks Biyolojik Ve Biyolojik Olmayan Ağlar Üzerine
Gursakal, N., Ugurlu, E., Goncer Demiral, D. / Journal of Yasar University, 2021, 16/61, 330-347 On Biological And Non-Biological Networks Biyolojik ve Biyolojik Olmayan Ağlar Üzerine Necmi GURSAKAL, Fenerbahçe University, Turkey, [email protected] Orcid No: 0000-0002-7909-3734 Erginbay UGURLU, İstanbul Aydın University, Turkey, [email protected] Orcid No: 0000-0002-1297-1993 Dilek GONCER DEMIRAL, Recep Tayyip Erdoğan University, Turkey, [email protected] Orcid No: 0000-0001-7400-1899 Abstract: With a general classification, there are two types of networks in the world: Biological and non-biological networks. We are unable to change the structure of biological networks. However, for networks such as social networks, technological networks and transportation networks, the architectures of non-biological networks are designed and can be changed by people. Networks can be classified as random networks, small-world networks and scale-free networks. However, we have problems with small-world networks and scale free networks. As some authors ask, “how small is a small-world network and how does it compare to other models?” Even the issue of scale-free networks are whether abundant or rare is still debated. Our main goal in this study is to investigate whether biological and non-biological networks have basic defining features. Especially if we can determine the properties of biological networks in a detailed way, then we may have the chance to design more robust and efficient non-biological networks. However, this research results shows that discussions on the properties of biological networks are not yet complete. Keywords: Biological Networks, Non-Biological Networks, Scale-Free Networks, Small-World Networks, Network Models JEL Classification: D85, O31, C10 Öz: Genel bir sınıflandırmayla, dünyada iki tür ağ vardır: Biyolojik ve biyolojik olmayan ağlar. -
Arxiv:0706.1062V2 [Physics.Data-An] 2 Feb 2009
POWER-LAW DISTRIBUTIONS IN EMPIRICAL DATA AARON CLAUSET∗, COSMA ROHILLA SHALIZI† , AND M. E. J. NEWMAN‡ Abstract. 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 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 beconsistentwiththedatawhilein others the power law is ruled out. Key words. Power-law distributions; Pareto; Zipf; maximum likelihood; heavy-tailed distribu- tions; likelihood ratio test; model selection AMS subject classifications. -
Cristopher Moore
Cristopher Moore Santa Fe Institute Santa Fe, NM 87501 [email protected] August 23, 2021 1 Education Born March 12, 1968 in New Brunswick, New Jersey. Northwestern University, B.A. in Physics, Mathematics, and the Integrated Science Program, with departmental honors in all three departments, 1986. Cornell University, Ph.D. in Physics, 1991. Philip Holmes, advisor. Thesis: “Undecidability and Unpredictability in Dynamical Systems.” 2 Employment Professor, Santa Fe Institute 2012–present Professor, Computer Science Department with a joint appointment in the Department of Physics and Astronomy, University of New Mexico, Albuquerque 2008–2012 Associate Professor, University of New Mexico 2005–2008 Assistant Professor, University of New Mexico 2000–2005 Research Professor, Santa Fe Institute 1998–1999 City Councilor, District 2, Santa Fe 1994–2002 Postdoctoral Fellow, Santa Fe Institute 1992–1998 Lecturer, Cornell University Spring 1991 Graduate Intern, Niels Bohr Institute/NORDITA, Copenhagen Summers 1988 and 1989 Teaching Assistant, Cornell University Physics Department Fall 1986–Spring 1990 Computer programmer, Bio-Imaging Research, Lincolnshire, Illinois Summers 1984–1986 3 Other Appointments Visiting Researcher, Microsoft Research New England Fall 2019 Visiting Professor, Ecole´ Normale Sup´erieure October–November 2016 Visiting Professor, Northeastern University October–November 2015 Visiting Professor, University of Michigan, Ann Arbor September–October 2005 Visiting Professor, Ecole´ Normale Sup´erieure de Lyon June 2004 Visiting Professor, -
So, You Think You Have a Power Law, Do You? Well Isn't That Special?
So, You Think You Have a Power Law, Do You? Well Isn't That Special? Cosma Shalizi Statistics Department, Carnegie Mellon University Santa Fe Institute 18 October 2010, NY Machine Learning Meetup 1 Everything good in the talk I owe to my co-authors, Aaron Clauset and Mark Newman 2 Power laws, p(x) / x−α, are cool, but not that cool 3 Most of the studies claiming to nd them use unreliable 19th century methods, and have no value as evidence either way 4 Reliable methods exist, and need only very straightforward mid-20th century statistics 5 Using reliable methods, lots of the claimed power laws disappear, or are at best not proven You are now free to tune me out and turn on social media Power Laws: What? So What? Bad Practices Better Practices No Really, So What? References Summary Cosma Shalizi So, You Think You Have a Power Law? 2 Power laws, p(x) / x−α, are cool, but not that cool 3 Most of the studies claiming to nd them use unreliable 19th century methods, and have no value as evidence either way 4 Reliable methods exist, and need only very straightforward mid-20th century statistics 5 Using reliable methods, lots of the claimed power laws disappear, or are at best not proven You are now free to tune me out and turn on social media Power Laws: What? So What? Bad Practices Better Practices No Really, So What? References Summary 1 Everything good in the talk I owe to my co-authors, Aaron Clauset and Mark Newman Cosma Shalizi So, You Think You Have a Power Law? 3 Most of the studies claiming to nd them use unreliable 19th century methods, -
Curriculum Vitae of Danny Dorling
January 2021 1993 to 1996: British Academy Fellow, Department of Geography, Newcastle University 1991 to 1993: Joseph Rowntree Foundation Curriculum Vitae Fellow, Many Departments, Newcastle University 1987 to 1991: Part-Time Researcher/Teacher, Danny Dorling Geography Department, Newcastle University Telephone: +44(0)1865 275986 Other Posts [email protected] skype: danny.dorling 2020-2023 Advisory Board Member: ‘The political economies of school exclusion and their consequences’ (ESRC project ES/S015744/1). Current appointment: Halford Mackinder 2020-Assited with the ‘Time to Care’ Oxfam report. Professor of Geography, School of 2020- Judge for data visualisation competition Geography and the Environment, The Nuffield Trust, the British Medical Journal, the University of Oxford, South Parks Road, British Medical Association and NHS Digital. Oxford, OX1 3QY 2019- Judge for the annual Royal Geographical th school 6 form essay competition. 2019 – UNDP (United Nations Development Other Appointments Programme) Human Development Report reviewer. 2019 – Advisory Broad member: Sheffield Visiting Professor, Department of Sociology, University Nuffield project on an Atlas of Inequality. Goldsmiths, University of London, 2013-2016. 2019 – Advisory board member - Glasgow Centre for Population Health project on US mortality. Visiting Professor, School of Social and 2019- Editorial Board Member – Bristol University Community Medicine, University of Bristol, UK Press, Studies in Social Harm Book Series. 2018 – Member of the Bolton Station Community Adjunct Professor in the Department of Development Partnership. Geography, University of Canterbury, NZ 2018-2022 Director of the Graduate School, School of Geography and the Environment, Oxford. 2018 – Member of the USS review working group of the Council of the University of Oxford. -
A Preferential Attachment Paradox: How Preferential Attachment Combines with Growth to Produce Networks with Log-Normal In-Degree Distributions
A Preferential Attachment Paradox: How Preferential Attachment Combines with Growth to Produce Networks with Log-normal In-degree Distributions Paul Sheridan1,* and Taku Onodera2 1Hirosaki University, Department of Active Life Promotion Science, Hirosaki, 036-8562, Japan 2The University of Tokyo, Institute of Medical Science, Human Genome Center, Tokyo, 108-8639, Japan *[email protected] ABSTRACT Every network scientist knows that preferential attachment combines with growth to produce networks with power-law in-degree distributions. How, then, is it possible for the network of American Physical Society journal collection citations to enjoy a log-normal citation distribution when it was found to have grown in accordance with preferential attachment? This anomalous result, which we exalt as the preferential attachment paradox, has remained unexplained since the physicist Sidney Redner first made light of it over a decade ago. Here we propose a resolution. The chief source of the mischief, we contend, lies in Redner having relied on a measurement procedure bereft of the accuracy required to distinguish preferential attachment from another form of attachment that is consistent with a log-normal in-degree distribution. There was a high-accuracy measurement procedure in use at the time, but it would have have been difficult to use it to shed light on the paradox, due to the presence of a systematic error inducing design flaw. In recent years the design flaw had been recognised and corrected. We show that the bringing of the newly corrected measurement procedure to bear on the data leads to a resolution of the paradox. Introduction The physicist Sidney Redner reported a rather curious anomaly in a decade-old study on the citation statistics of the American Physical Society (APS) journal collection1. -
Network Modularity Controls the Speed of Information Diffusion
Network Modularity Controls the Speed of Information Diffusion 1 2 1 3, Hao Peng, Azadeh Nematzadeh, Daniel M. Romero, and Emilio Ferrara ∗ 1School of Information, University of Michigan 2S&P Global 3Information Sciences Institute, University of Southern California (Dated: July 31, 2020) The rapid diffusion of information and the adoption of social behaviors are of critical importance in situations as diverse as collective actions, pandemic prevention, or advertising and marketing. Although the dynamics of large cascades have been extensively studied in various contexts, few have systematically examined the impact of network topology on the efficiency of information diffusion. Here, by employing the linear threshold model on networks with communities, we demonstrate that a prominent network feature—the modular structure—strongly affects the speed of information diffusion in complex contagion. Our simulations show that there always exists an optimal network modularity for the most efficient spreading process. Beyond this critical value, either a stronger or a weaker modular structure actually hinders the diffusion speed. These results are confirmed by an analytical approximation. We further demonstrate that the optimal modularity varies with both the seed size and the target cascade size, and is ultimately dependent on the network under investigation. We underscore the importance of our findings in applications from marketing to epidemiology, from neuroscience to engineering, where the understanding of the structural design of complex systems focuses on the efficiency of information propagation. I. INTRODUCTION and viral marketing [13, 22]. However, some studies re- vealed that the threshold model is more applicable to the The spread of information in complex networks con- spread of risky or contentious social behaviors for which trols or modulates fundamental processes that can have each additional exposure increases the likelihood of adop- local effects on individual actors and groups thereof, and tion [1, 5, 25, 31, 37]. -
Hierarchical Structure and the Prediction of Missing Links in Networks
Hierarchical structure and the prediction of missing links in networks Aaron Clauset,1,3 Cristopher Moore,1,2,3 M. E. J. Newman3,4∗ 1Department of Computer Science and 2Department of Physics and Astronomy, University of New Mexico, Albuquerque, NM 87131, USA 3Santa Fe Institute, 1399 Hyde Park Rd., Santa Fe, NM 87501, USA 4Department of Physics and Center for the Study of Complex Systems, University of Michigan, Ann Arbor, MI 48109, USA ∗To whom correspondence should be addressed. E-mail: [email protected]. Networks have in recent years emerged as an invaluable tool for describing and quan- tifying complex systems in many branches of science (1–3). Recent studies suggest that networks often exhibit hierarchical organization, where vertices divide into groups that further subdivide into groups of groups, and so forth over multiple scales. In many cases these groups are found to correspond to known functional units, such as ecological niches in food webs, modules in biochemical networks (protein interaction networks, metabolic networks, or genetic regulatory networks), or communities in social networks (4–7). Here we present a general technique for inferring hierarchical structure from network data and demonstrate that the existence of hierarchy can simultaneously explain and quanti- tatively reproduce many commonly observed topological properties of networks, such as right-skewed degree distributions, high clustering coefficients, and short path lengths. We further show that knowledge of hierarchical structure can be used to predict missing con- nections in partially known networks with high accuracy, and for more general network 1 structures than competing techniques (8). Taken together, our results suggest that hierar- chy is a central organizing principle of complex networks, capable of offering insight into many network phenomena. -
Eigenvector-Based Centrality Measures for Temporal Networks∗
MULTISCALE MODEL.SIMUL. c 2017 Society for Industrial and Applied Mathematics Vol. 15, No. 1, pp. 537{574 EIGENVECTOR-BASED CENTRALITY MEASURES FOR TEMPORAL NETWORKS∗ DANE TAYLORy , SEAN A. MYERSz , AARON CLAUSETx , MASON A. PORTER{, AND PETER J. MUCHAk Abstract. 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 supracentrality 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. -
Small-World File-Sharing Communities
Small-World File-Sharing Communities Adriana Iamnitchi, Matei Ripeanu, Ian Foster Department of Computer Science The University of Chicago Chicago, IL 60637 {anda, matei, foster}@cs.uchicago.edu Abstract— Web caches, content distribution networks, ration for designing efficient mechanisms for large-scale, peer-to-peer file sharing networks, distributed file systems, dynamic, self-organizing resource-sharing communities. and data grids all have in common that they involve a We look at these communities in a novel way: we community of users who generate requests for shared study the relationships that form among users based on data. In each case, overall system performance can be the data in which they are interested. We capture and improved significantly if we can first identify and then quantify these relationships by modeling the community exploit interesting structure within a community’s access patterns. To this end, we propose a novel perspective on file as a data-sharing graph. To this end, we propose a sharing based on the study of the relationships that form new structure that captures common user interests in among users based on the files in which they are interested. data (Section III) and justify its utility with studies We propose a new structure that captures common user on three data-distribution systems (Section IV): a high- interests in data—the data-sharing graph— and justify its energy physics collaboration, the Web, and the Kazaa utility with studies on three data-distribution systems: a peer-to-peer network. We find small-world patterns in the high-energy physics collaboration, the Web, and the Kazaa data-sharing graphs of all three communities (SectionV). -
Annual Report 2010-11
Institute for the Study of the Americas Annual Report 2010-2011 Mission and Aims Institute for the Study of the Americas Annual Report 2010-2011 Table of Contents Governance 2 Te Institute was founded in August 2004 through a merger of the Institute of Latin American Studies (ILAS) with Staf List 3 the Institute of United States Studies (IUSS), both of which had been founded in 1965 at 31 Tavistock Square. Like its predecessors, the new Institute forms part of the University of London’s School of Advanced Study. Director’s Report 4 ISA occupies a unique position at the core of academic study of the region in the UK. Internationally recognised as a centre of excellence for research and research facilitation, ISA also provides resources to the wider academic Academic Staf Profles 8 community, serving and strengthening national networks of North Americanist, Latin Americanist and Caribbeanist Fellowships 20 scholars. Te Institute actively maintains and builds ties with cultural, diplomatic and business organisations with interests in the Americas and, as part of the School of Advanced Study within the University of London, benefts from Events 25 academic opportunities, facilities and stimulation across and between a wide range of subject felds in the humanities and social sciences. Postgraduate Programmes 36 Te Council of the University of London approved the establishment of ISA on the understanding that it would be dedicated to teaching and research, not just on the USA and Latin America, but to the Americas as a whole, with Publications 40 proper attention to Canada and the Caribbean. ISA will uphold the dedication to area studies and multi-disciplinarity that animated its predecessors.