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Okamoto H, Yoshimoto I, Kato S, Ahsan B, Shinohara S. Testing the power-law hypothesis of the interconflict interval. Sci Rep 2023; 13:22686. [PMID: 38114563 PMCID: PMC10730599 DOI: 10.1038/s41598-023-50002-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/11/2023] [Accepted: 12/14/2023] [Indexed: 12/21/2023] Open
Abstract
War is an extreme form of collective human behaviour characterized by coordinated violence. We show that this nature of war is substantiated in the temporal patterns of conflict occurrence that obey power law. The focal metric is the interconflict interval (ICI), the interval between the end of a conflict in a dyad (i.e. a pair of states) and the start of the subsequent conflict in the same dyad. Using elaborate statistical tests, we confirmed that ICI samples compiled from the history of interstate conflicts from 1816 to 2014 followed a power-law distribution. We then demonstrate that the power-law properties of ICIs can be explained by a hypothetical model assuming an information-theoretic formulation of the Clausewitz thesis on war: the use of force is a means of interstate communication. Our findings help us to understand the nature of wars between regular states, the significance of which has increased since the Russian invasion of Ukraine in 2022.
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Affiliation(s)
- Hiroshi Okamoto
- Department of Bioengineering, School of Engineering, The University of Tokyo, Tokyo, Japan.
| | - Iku Yoshimoto
- Department of Advanced Social and International Studies, Graduate School of Arts and Sciences, The University of Tokyo, Tokyo, Japan
| | - Sota Kato
- The Tokyo Foundation for Policy Research, Tokyo, Japan
| | - Budrul Ahsan
- The Tokyo Foundation for Policy Research, Tokyo, Japan
| | - Shuji Shinohara
- School of Science and Engineering, Tokyo Denki University, Saitama, Japan
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2
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Kushwaha N, Lee ED. Discovering the mesoscale for chains of conflict. PNAS NEXUS 2023; 2:pgad228. [PMID: 37533894 PMCID: PMC10392960 DOI: 10.1093/pnasnexus/pgad228] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 02/16/2023] [Revised: 06/09/2023] [Accepted: 06/20/2023] [Indexed: 08/04/2023]
Abstract
Conflicts, like many social processes, are related events that span multiple scales in time, from the instantaneous to multi-year development, and in space, from one neighborhood to continents. Yet, there is little systematic work on connecting the multiple scales, formal treatment of causality between events, and measures of uncertainty for how events are related to one another. We develop a method for extracting causally related chains of events that addresses these limitations with armed conflict. Our method explicitly accounts for an adjustable spatial and temporal scale of interaction for clustering individual events from a detailed data set, the Armed Conflict Event & Location Data Project. With it, we discover a mesoscale ranging from a week to a few months and tens to hundreds of kilometers, where long-range correlations and nontrivial dynamics relating conflict events emerge. Importantly, clusters in the mesoscale, while extracted from conflict statistics, are identifiable with mechanism cited in field studies. We leverage our technique to identify zones of causal interaction around conflict hotspots that naturally incorporate uncertainties. Thus, we show how a systematic, data-driven, and scalable procedure extracts social objects for study, providing a scope for scrutinizing and predicting conflict and other processes.
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Affiliation(s)
| | - Edward D Lee
- To whom correspondence should be addressed. Emails: ;
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3
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Lee ED, Daniels BC, Myers CR, Krakauer DC, Flack JC. Scaling theory of armed-conflict avalanches. Phys Rev E 2020; 102:042312. [PMID: 33212735 DOI: 10.1103/physreve.102.042312] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/04/2020] [Accepted: 10/01/2020] [Indexed: 11/07/2022]
Abstract
Armed conflict data display features consistent with scaling and universal dynamics in both social and physical properties like fatalities and geographic extent. We propose a randomly branching armed conflict model to relate the multiple properties to one another. The model incorporates a fractal lattice on which conflict spreads, uniform dynamics driving conflict growth, and regional virulence that modulates local conflict intensity. The quantitative constraints on scaling and universal dynamics we use to develop our minimal model serve more generally as a set of constraints for other models for armed conflict dynamics. We show how this approach akin to thermodynamics imparts mechanistic intuition and unifies multiple conflict properties, giving insight into causation, prediction, and intervention timing.
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Affiliation(s)
- Edward D Lee
- Santa Fe Institute, Santa Fe, New Mexico 87501, USA.,Department of Physics, Cornell University, Ithaca, New York 14853, USA
| | - Bryan C Daniels
- ASU-SFI Center for Biosocial Complex Systems, Arizona State University, Tempe, Arizona 85287, USA
| | - Christopher R Myers
- Department of Physics, Cornell University, Ithaca, New York 14853, USA.,Center for Advanced Computing, Cornell University, Ithaca, New York 14853, USA
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Guo W. Common statistical patterns in urban terrorism. ROYAL SOCIETY OPEN SCIENCE 2019; 6:190645. [PMID: 31598299 PMCID: PMC6774967 DOI: 10.1098/rsos.190645] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 04/06/2019] [Accepted: 08/16/2019] [Indexed: 06/10/2023]
Abstract
The underlying reasons behind modern terrorism are seemingly complex and intangible. Despite diverse causal mechanisms, research has shown that there exists general statistical patterns at the global scale that can shed light on human confrontation behaviour. While many policing and counter-terrorism operations are conducted at a city level, there has been a lack of research in building city-level resolution prediction engines based on statistical patterns. For the first time, the paper shows that there exist general commonalities between global cities under frequent terrorist attacks. By examining over 30 000 geo-tagged terrorism acts over 7000 cities worldwide from 2002 to today, the results show the following. All cities experience attacks A that are uncorrelated to the population and separated by a time interval t that is negative exponentially distributed with a death-toll per attack that follows a power-law distribution. The prediction parameters yield a high confidence of explaining up to 87% of the variations in frequency and 89% in the death-toll data. These findings show that the aggregate statistical behaviour of terror attacks are seemingly random and memoryless for all global cities. They enabled the author to develop a data-driven city-specific prediction system, and we quantify its information-theoretic uncertainty and information loss. Further analysis shows that there appears to be an increase in the uncertainty over the predictability of attacks, challenging our ability to develop effective counter-terrorism capabilities.
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Affiliation(s)
- Weisi Guo
- The Alan Turing Institute, London, UK
- Warwick Institute for Science of Cities, University of Warwick, Coventry, UK
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Guo F, Yang D, Yang Z, Zhao ZD, Zhou T. Bounds of memory strength for power-law series. Phys Rev E 2017; 95:052314. [PMID: 28618564 DOI: 10.1103/physreve.95.052314] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/07/2016] [Indexed: 06/07/2023]
Abstract
Many time series produced by complex systems are empirically found to follow power-law distributions with different exponents α. By permuting the independently drawn samples from a power-law distribution, we present nontrivial bounds on the memory strength (first-order autocorrelation) as a function of α, which are markedly different from the ordinary ±1 bounds for Gaussian or uniform distributions. When 1<α≤3, as α grows bigger, the upper bound increases from 0 to +1 while the lower bound remains 0; when α>3, the upper bound remains +1 while the lower bound descends below 0. Theoretical bounds agree well with numerical simulations. Based on the posts on Twitter, ratings of MovieLens, calling records of the mobile operator Orange, and the browsing behavior of Taobao, we find that empirical power-law-distributed data produced by human activities obey such constraints. The present findings explain some observed constraints in bursty time series and scale-free networks and challenge the validity of measures such as autocorrelation and assortativity coefficient in heterogeneous systems.
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Affiliation(s)
- Fangjian Guo
- CompleX Lab, Web Sciences Center, University of Electronic Science and Technology of China, Chengdu 611731, People's Republic of China
- Department of Computer Science, Duke University, Durham, North Carolina 27708, USA
| | - Dan Yang
- CompleX Lab, Web Sciences Center, University of Electronic Science and Technology of China, Chengdu 611731, People's Republic of China
- Big Data Research Center, University of Electronic Science and Technology of China, Chengdu 611731, People's Republic of China
| | - Zimo Yang
- CompleX Lab, Web Sciences Center, University of Electronic Science and Technology of China, Chengdu 611731, People's Republic of China
| | - Zhi-Dan Zhao
- CompleX Lab, Web Sciences Center, University of Electronic Science and Technology of China, Chengdu 611731, People's Republic of China
| | - Tao Zhou
- CompleX Lab, Web Sciences Center, University of Electronic Science and Technology of China, Chengdu 611731, People's Republic of China
- Big Data Research Center, University of Electronic Science and Technology of China, Chengdu 611731, People's Republic of China
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Perc M, Szolnoki A. A double-edged sword: Benefits and pitfalls of heterogeneous punishment in evolutionary inspection games. Sci Rep 2015; 5:11027. [PMID: 26046673 PMCID: PMC4457152 DOI: 10.1038/srep11027] [Citation(s) in RCA: 61] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/27/2015] [Accepted: 05/14/2015] [Indexed: 11/09/2022] Open
Abstract
As a simple model for criminal behavior, the traditional two-strategy inspection game yields counterintuitive results that fail to describe empirical data. The latter shows that crime is often recurrent, and that crime rates do not respond linearly to mitigation attempts. A more apt model entails ordinary people who neither commit nor sanction crime as the third strategy besides the criminals and punishers. Since ordinary people free-ride on the sanctioning efforts of punishers, they may introduce cyclic dominance that enables the coexistence of all three competing strategies. In this setup ordinary individuals become the biggest impediment to crime abatement. We therefore also consider heterogeneous punisher strategies, which seek to reduce their investment into fighting crime in order to attain a more competitive payoff. We show that this diversity of punishment leads to an explosion of complexity in the system, where the benefits and pitfalls of criminal behavior are revealed in the most unexpected ways. Due to the raise and fall of different alliances no less than six consecutive phase transitions occur in dependence on solely the temptation to succumb to criminal behavior, leading the population from ordinary people-dominated across punisher-dominated to crime-dominated phases, yet always failing to abolish crime completely.
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Affiliation(s)
- Matjaž Perc
- Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška cesta 160, SI-2000 Maribor, Slovenia
- Department of Physics, Faculty of Sciences, King Abdulaziz University, Jeddah, Saudi Arabia
- CAMTP – Center for Applied Mathematics and Theoretical Physics, University of Maribor, Krekova 2, SI-2000 Maribor, Slovenia
| | - Attila Szolnoki
- Institute of Technical Physics and Materials Science, Research Centre for Natural Sciences, Hungarian Academy of Sciences, P.O. Box 49, H-1525 Budapest, Hungary
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D'Orsogna MR, Perc M. Statistical physics of crime: a review. Phys Life Rev 2014; 12:1-21. [PMID: 25468514 DOI: 10.1016/j.plrev.2014.11.001] [Citation(s) in RCA: 193] [Impact Index Per Article: 19.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/05/2014] [Revised: 10/20/2014] [Accepted: 11/03/2014] [Indexed: 11/28/2022]
Abstract
Containing the spread of crime in urban societies remains a major challenge. Empirical evidence suggests that, if left unchecked, crimes may be recurrent and proliferate. On the other hand, eradicating a culture of crime may be difficult, especially under extreme social circumstances that impair the creation of a shared sense of social responsibility. Although our understanding of the mechanisms that drive the emergence and diffusion of crime is still incomplete, recent research highlights applied mathematics and methods of statistical physics as valuable theoretical resources that may help us better understand criminal activity. We review different approaches aimed at modeling and improving our understanding of crime, focusing on the nucleation of crime hotspots using partial differential equations, self-exciting point process and agent-based modeling, adversarial evolutionary games, and the network science behind the formation of gangs and large-scale organized crime. We emphasize that statistical physics of crime can relevantly inform the design of successful crime prevention strategies, as well as improve the accuracy of expectations about how different policing interventions should impact malicious human activity that deviates from social norms. We also outline possible directions for future research, related to the effects of social and coevolving networks and to the hierarchical growth of criminal structures due to self-organization.
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Affiliation(s)
- Maria R D'Orsogna
- Department of Mathematics, California State University at Northridge, Los Angeles, CA 91330, USA; Department of Biomathematics, UCLA, Los Angeles, CA 90095, USA.
| | - Matjaž Perc
- Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška cesta 160, SI-2000 Maribor, Slovenia; Department of Physics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia; CAMTP - Center for Applied Mathematics and Theoretical Physics, University of Maribor, Krekova 2, SI-2000 Maribor, Slovenia.
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