research-article

Free access

Natural algorithms and influence systems

Author:

Bernard ChazelleAuthors Info & Claims

Communications of the ACM, Volume 55, Issue 12

Pages 101 - 110

https://doi.org/10.1145/2380656.2380679

Published: 01 December 2012 Publication History

All formats PDF

Abstract

Algorithms offer a rich, expressive language for modelers of biological and social systems. They lay the grounds for numerical simulations and, crucially, provide a powerful framework for their analysis. The new area of natural algorithms may reprise in the life sciences the role differential equations have long played in the physical sciences. For this to happen, however, an "algorithmic calculus" is needed. We discuss what this program entails in the context of influence systems, a broad family of multiagent models arising in social dynamics.

References

[1]

Afek, Y., Alon, N., Barad, O., Hornstein, E., Barkai, N., Bar-Joseph, Z. A biological solution to a fundamental distributed computing problem. Science 331 (2011), 183--185.

[2]

Bonifaci, V., Mehlhorn, K., Varma, G. Physarum can compute shortest paths. In Proceedings of 23rd Annual ACM-SIAM Symposium on Discrete Algorithms (2012), 233--240.

Digital Library

[3]

Camazine, S., Deneubourg, J.L., Franks, N., Sneyd, J., Bonabeau, E., Theraulaz, G. Self-Organization in Biological Systems, Princeton University Press, 2001.

Digital Library

[4]

Chazelle, B. The convergence of bird flocking, arXiv:0905.4241vl, 2009. Prelim, version in Proceedings of SIAM SODA 2009, with improvements in Proceedings of ACM SoCG 2010.

[5]

Chazelle, B. The total s-energy of a multiagent system, SIAM J. Control Optim. 49 (2011), 1680--1706.

[6]

Chazelle, B. The dynamics of influence systems, arXiv:1204.3946v2, 2012. Prelim, version in Proceedings of 53rd FOCS, 2012.

Digital Library

[7]

Collins, G. E. Quantifier elimination for real closed fields by cylindrical algebraic decomposition. In Proceedings of 2nd GI Conference on Automata Theory and Formal Languages (1975), Springer-Verlag, New York, 134--183.

Digital Library

[8]

Cucker, F., Smale, S. Emergent behavior in flocks. IEEE Trans. Automatic Control 52 (2007), 852--862.

[9]

Fisher, J., Harel, D., Henzinger, T.A. Biology as reactivity. Commun. ACM 54 (2011), 72--82.

Digital Library

[10]

Hegselmann, R., Krause, U. Opinion dynamics and bounded confidence models, analysis, and simulation. J. Artif. Soc. Soc. Simulat. 5 (2002), 3.

[11]

Hegselmann R, Krause U. Truth and cognitive division of labor: first steps towards a computer aided social epistemology. J. Artif. Soc. Soc. Simulat. 9 (2006).

[12]

Hendrickx, J.M., Blondel, V.D. Convergence of different linear and non-linear Vicsek models. In Proceedings of 17th International Symposium on Mathematical Theory of Networks and Systems (MTNS2006) (July 2006, Kyoto, Japan), 1229--1240.

[13]

Jadbabaie, A., Lin, J., Morse, A.S. Coordination of groups of mobile autonomous agents using nearest neighbor rules. IEEE Trans. Automatic Control 48 (2003), 988--1001.

[14]

Lorenz, J. A stabilization theorem for dynamics of continuous opinions. Phys. Stat. Mech. Appl. 355 (2005), 217--223.

[15]

Lynch, N.A. Distributed Algorithms, Morgan Kaufmann Publishers Inc., San Francisco, CA, 1996.

Digital Library

[16]

Moreau, L. Stability of multiagent systems with time-dependent communication links. IEEE Trans. Automatic Control 50 (2005), 169--182.

[17]

Navlakha, S., Bar-Joseph, Z. Algorithms in nature: the convergence of systems biology and computational thinking. Mol. Syst. Biol. 7 (2011), 546.

[18]

Okubo, A., Levin, S.A. Diffusion and Ecological Problems, 2nd edn, Springer, 2002.

[19]

Parrish, J.K., Hamner, W.M. Animal Groups in Three Dimensions, Cambridge University Press, 1997.

[20]

Prusinkiewicz, P., Lindenmayer, A., Hanan, J.S., Fracchia, F.D. The Algorithmic Beauty of Plants, Springer-Verlag, 1996.

Digital Library

[21]

Reynolds, C.W. Flocks, herds, and schools: a distributed behavioral model. Comput. Graph. 21 (1987), 25--34.

Digital Library

[22]

Seneta, E. Non-Negative Matrices and Markov Chains, 2nd edn, Springer, 2006.

[23]

Strogatz, S.H. From Kuramoto to Crawford: exploring the onset of synchronization in populations of coupled oscillators. Physica D 143 (2000), 1--20.

Digital Library

[24]

Vicsek, T., Czirók, A., Ben-Jacob, E., Cohen, I., Shochet, O. Novel type of phase transition in a system, of self-driven particles. Phys. Rev. Lett. 75 (1995), 1226--1229.

[25]

Winfree, A.T. Biological rhythms and the behavior of populations of coupled oscillators. J. Theoret. Biol. 16, 1 (1967), 15--42.

Cited By

Függer MNowak TRybicki JKuznetsov PGelles ROlivetti D(2024)Majority Consensus Thresholds in Competitive Lotka-Volterra PopulationsProceedings of the 43rd ACM Symposium on Principles of Distributed Computing10.1145/3662158.3662823(76-86)Online publication date: 17-Jun-2024
https://dl.acm.org/doi/10.1145/3662158.3662823
Berenbrink PCooper CGava CMarzagão DMallmann-Trenn FRadzik TRivera NOshman RNolin AHalldorsson MBalliu A(2023)Distributed Averaging in Opinion DynamicsProceedings of the 2023 ACM Symposium on Principles of Distributed Computing10.1145/3583668.3594593(211-221)Online publication date: 19-Jun-2023
https://dl.acm.org/doi/10.1145/3583668.3594593
Garg SShiragur KGordon DCharikar M(2023)Distributed algorithms from arboreal ants for the shortest path problemProceedings of the National Academy of Sciences10.1073/pnas.2207959120120:6Online publication date: 30-Jan-2023
https://doi.org/10.1073/pnas.2207959120
Show More Cited By

Index Terms

Natural algorithms and influence systems
1. Computing methodologies
  1. Symbolic and algebraic manipulation
    1. Symbolic and algebraic algorithms

Recommendations

Models and algorithms for social influence analysis
WSDM '13: Proceedings of the sixth ACM international conference on Web search and data mining

Social influence is the behavioral change of a person because of the perceived relationship with other people, organizations and society in general. Social influence has been a widely accepted phenomenon in social networks for decades. Many applications ...
Peirce's rule in natural deduction

In stark contrast to Natural Deduction for Intuitionistic Logic, Natural Deduction for Classical Logic suffers from some well-known limitations: although normalisation can be proved, the standard proof of Prawitz (Natural deduction. A proof Theoretical ...
Unification Algorithms for Eliminating and Introducing Quantifiers in Natural Deduction Automated Theorem Proving

A natural deduction system was adapted from Gentzen system. It enables valid wffs to be deduced in a very ‘natural’ way. One need not transform a formula into other normal forms. Robinson’s unification algorithm is used to handle clausal formulas. ...

Comments

Information & Contributors

Information

Published In

cover image Communications of the ACM

Communications of the ACM Volume 55, Issue 12

December 2012

102 pages

ISSN:0001-0782

EISSN:1557-7317

DOI:10.1145/2380656

Issue’s Table of Contents

Copyright © 2012 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 December 2012

Published in CACM Volume 55, Issue 12

Permissions

Request permissions for this article.

Request Permissions

Check for updates

Qualifiers

Research-article
Popular
Refereed

Funding Sources

Division of Computing and Communication Foundations

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

53
Total Citations
View Citations
6,722
Total Downloads

Downloads (Last 12 months)323
Downloads (Last 6 weeks)28

Reflects downloads up to 10 Nov 2024

Other Metrics

View Author Metrics

Citations

Cited By

Függer MNowak TRybicki JKuznetsov PGelles ROlivetti D(2024)Majority Consensus Thresholds in Competitive Lotka-Volterra PopulationsProceedings of the 43rd ACM Symposium on Principles of Distributed Computing10.1145/3662158.3662823(76-86)Online publication date: 17-Jun-2024
https://dl.acm.org/doi/10.1145/3662158.3662823
Berenbrink PCooper CGava CMarzagão DMallmann-Trenn FRadzik TRivera NOshman RNolin AHalldorsson MBalliu A(2023)Distributed Averaging in Opinion DynamicsProceedings of the 2023 ACM Symposium on Principles of Distributed Computing10.1145/3583668.3594593(211-221)Online publication date: 19-Jun-2023
https://dl.acm.org/doi/10.1145/3583668.3594593
Garg SShiragur KGordon DCharikar M(2023)Distributed algorithms from arboreal ants for the shortest path problemProceedings of the National Academy of Sciences10.1073/pnas.2207959120120:6Online publication date: 30-Jan-2023
https://doi.org/10.1073/pnas.2207959120
Amir MAgmon NBruckstein A(2022)A Locust-Inspired Model of Collective Marching on RingsEntropy10.3390/e2407091824:7(918)Online publication date: 30-Jun-2022
https://doi.org/10.3390/e24070918
Straszak DVishnoi N(2022)Iteratively reweighted least squares and slime mold dynamics: connection and convergenceMathematical Programming: Series A and B10.1007/s10107-021-01644-z194:1-2(685-717)Online publication date: 1-Jul-2022
https://dl.acm.org/doi/10.1007/s10107-021-01644-z
Caragiannis IKanellopoulos PVoudouris A(2022)Bounding the Inefficiency of Compromise in Opinion FormationAlgorithmica10.1007/s00453-021-00892-x84:1(234-271)Online publication date: 1-Jan-2022
https://dl.acm.org/doi/10.1007/s00453-021-00892-x
Amir MAgmon NBruckstein A(2022)A Discrete Model of Collective Marching on RingsDistributed Autonomous Robotic Systems10.1007/978-3-030-92790-5_25(320-334)Online publication date: 3-Jan-2022
https://doi.org/10.1007/978-3-030-92790-5_25
Krafft PShmueli EGriffiths TTenenbaum JPentland A(2021)Bayesian collective learning emerges from heuristic social learningCognition10.1016/j.cognition.2020.104469212(104469)Online publication date: Jul-2021
https://doi.org/10.1016/j.cognition.2020.104469
Jadbabaie A(2021)Flocking in Networked SystemsEncyclopedia of Systems and Control10.1007/978-3-030-44184-5_215(822-827)Online publication date: 4-Aug-2021
https://doi.org/10.1007/978-3-030-44184-5_215
Becchetti LClementi ANatale E(2020)Consensus DynamicsACM SIGACT News10.1145/3388392.338840351:1(58-104)Online publication date: 12-Mar-2020
https://dl.acm.org/doi/10.1145/3388392.3388403
Show More Cited By

View Options

View options

PDF

View or Download as a PDF file.

eReader

View online with eReader.

Digital Edition

View this article in digital edition.

Digital Edition

Magazine Site

View this article on the magazine site (external)

Get Access

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Full Access

Get this Article

Media

Figures

Other

Tables

View Issue’s Table of Contents