Power-Law Distributions in Empirical Data
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Black Swans, Dragons-Kings and Prediction
Black Swans, Dragons-Kings and Prediction Professor of Entrepreneurial Risks Didier SORNETTE Professor of Geophysics associated with the ETH Zurich Department of Earth Sciences (D-ERWD), ETH Zurich Professor of Physics associated with the Department of Physics (D-PHYS), ETH Zurich Professor of Finance at the Swiss Finance Institute Director of the Financial Crisis Observatory co-founder of the Competence Center for Coping with Crises in Socio-Economic Systems, ETH Zurich (http://www.ccss.ethz.ch/) Black Swan (Cygnus atratus) www.er.ethz.ch EXTREME EVENTS in Natural SYSTEMS •Earthquakes •Volcanic eruptions •Hurricanes and tornadoes •Landslides, mountain collapses •Avalanches, glacier collapses •Lightning strikes •Meteorites, asteroid impacts •Catastrophic events of environmental degradations EXTREME EVENTS in SOCIO-ECONOMIC SYSTEMS •Failure of engineering structures •Crashes in the stock markets •Social unrests leading to large scale strikes and upheavals •Economic recessions on regional and global scales •Power blackouts •Traffic gridlocks •Social epidemics •Block-busters •Discoveries-innovations •Social groups, cities, firms... •Nations •Religions... Extreme events are epoch changing in the physical structure and in the mental spaces • Droughts and the collapse of the Mayas (760-930 CE)... and many others... • French revolution (1789) and the formation of Nation states • Great depression and Glass-Steagall act • Crash of 19 Oct. 1987 and volatility smile (crash risk) • Enron and Worldcom accounting scandals and Sarbanes-Oxley (2002) • Great Recession 2007-2009: consequences to be4 seen... The Paradox of the 2007-20XX Crisis (trillions of US$) 2008 FINANCIAL CRISIS 6 Jean-Pierre Danthine: Swiss monetary policy and Target2-Securities Introductory remarks by Mr Jean-Pierre Danthine, Member of the Governing Board of the Swiss National Bank, at the end-of-year media news conference, Zurich, 16 December 2010. -
Aaron Clauset
Aaron Clauset Contact Department of Computer Science voice: 303{492{6643 Information University of Colorado at Boulder fax: 303{492{2844 430 UCB email: [email protected] Boulder CO, 80309-0430 USA web: www.santafe.edu/∼aaronc Research Network science (methods, theories, applications); Data science, statistical inference, machine learn- Interests ing; Models and simulations; Collective dynamics and complex systems; Rare events, power laws and forecasting; Computational social science; Computational biology and biological computation. Education Ph.D. Computer Science, University of New Mexico (with distinction) 2002 { 2006 B.S. Physics, Haverford College (with honors and concentration in Computer Science) 1997 { 2001 Academic Associate Professor, Computer Science Dept., University of Colorado, Boulder 2018 { present Positions Core Faculty, BioFrontiers Institute, University of Colorado, Boulder 2010 { present External Faculty, Santa Fe Institute 2012 { present Affiliated Faculty, Ecology & Evo. Biology Dept., University of Colorado, Boulder 2011 { present Affiliated Faculty, Applied Mathematics Dept., University of Colorado, Boulder 2012 { present Affiliated Faculty, Information Dept., University of Colorado, Boulder 2015 { present Assistant Professor, Computer Science Dept., University of Colorado, Boulder 2010 { 2018 Omidyar Fellow, Santa Fe Institute 2006 { 2010 Editorial Deputy Editor, Science Advances, AAAS 2017 { present Positions Associate Editor, Science Advances, AAAS 2014 { 2017 Associate Editor, Journal of Complex Networks, Oxford University Press 2012 { 2017 Honors & Top 20 Teachers, College of Engineering, U. Colorado, Boulder 2016 Awards Erd}os-R´enyi Prize in Network Science 2016 (Selected) NSF CAREER Award 2015 { 2020 Kavli Fellow 2014 Santa Fe Institute Public Lecture Series (http://bit.ly/I6t9gf) 2010 Graduation Speaker, U. New Mexico School of Engineering Convocation 2006 Outstanding Graduate Student Award, U. -
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, -
Time-Varying Volatility and the Power Law Distribution of Stock Returns
Finance and Economics Discussion Series Divisions of Research & Statistics and Monetary Affairs Federal Reserve Board, Washington, D.C. Time-varying Volatility and the Power Law Distribution of Stock Returns Missaka Warusawitharana 2016-022 Please cite this paper as: Warusawitharana, Missaka (2016). “Time-varying Volatility and the Power Law Distribution of Stock Returns,” Finance and Economics Discussion Se- ries 2016-022. Washington: Board of Governors of the Federal Reserve System, http://dx.doi.org/10.17016/FEDS.2016.022. NOTE: Staff working papers in the Finance and Economics Discussion Series (FEDS) are preliminary materials circulated to stimulate discussion and critical comment. The analysis and conclusions set forth are those of the authors and do not indicate concurrence by other members of the research staff or the Board of Governors. References in publications to the Finance and Economics Discussion Series (other than acknowledgement) should be cleared with the author(s) to protect the tentative character of these papers. Time-varying Volatility and the Power Law Distribution of Stock Returns Missaka Warusawitharana∗ Board of Governors of the Federal Reserve System March 18, 2016 JEL Classifications: C58, D30, G12 Keywords: Tail distributions, high frequency returns, power laws, time-varying volatility ∗I thank Yacine A¨ıt-Sahalia, Dobislav Dobrev, Joshua Gallin, Tugkan Tuzun, Toni Whited, Jonathan Wright, Yesol Yeh and seminar participants at the Federal Reserve Board for helpful comments on the paper. Contact: Division of Research and Statistics, Board of Governors of the Federal Reserve System, Mail Stop 97, 20th and C Street NW, Washington, D.C. 20551. [email protected], (202)452-3461. -