Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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Sensitivity to noise variance in a social network dynamics model


Authors: H. T. Banks, A. F. Karr, H. K. Nguyen and J. R. Samuels Jr.
Journal: Quart. Appl. Math. 66 (2008), 233-247
MSC (2000): Primary 91D30, 34F05, 60H10, 60H35, 90B15
Published electronically: March 27, 2008
MathSciNet review: 2416772
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Abstract | References | Similar Articles | Additional Information

Abstract: The dynamics of social networks are modeled with a system of continuous Stochastic Ordinary Differential Equations (SODE). With the proper amount of noise input, the SODE model captures dynamic features that are lacking in the corresponding deterministic ODE model. Therefore, sensitivity to noise levels is investigated by considering four different regimes: essentially deterministic, noise-enriched, noise-enlarged, and noise-dominated. Each regime is defined based on the behavior of solutions of the SODE, and geometry of the regimes are categorized with stochastic simulations.


References [Enhancements On Off] (What's this?)

  • 1. Kenneth A. Bollen, Structural equations with latent variables, Wiley Series in Probability and Mathematical Statistics: Applied Probability and Statistics, John Wiley & Sons, Inc., New York, 1989. A Wiley-Interscience Publication. MR 996025
  • 2. B. W. Bush, The TRAMSIMS simulation framework, 2001; Presented at the Agent-Based Modeling Seminar, Los Alamos National Laboratory. Available on-line at www.lanl.gov/tools/media/realmetafiles/tsa/bbtransims.ram.
  • 3. K. Carley, Computational organizational science and organizational engineering, Simulation Modeling Practice and Theory 10:253-269, 2003.
  • 4. P. J. Carrington, J. Scott, and S. Wasserman, Models and Methods in Social Network Analysis, Cambridge University Press, New York, 2005.
  • 5. A. Chaturvedi, D. Dolk, and H. J. Sebastian, Agent-based simulation and model integration, 2004; Presented at the IFIP WG7.6 Workshop on Virtual Environment for Advanced Modeling (VEAM). Available on-line at web.nps.navy.mil/drdolk/ABS-Model-Integration.ppt.
  • 6. M. Dombroski, P. Fischbeck, and K. Carley, Estimating the shape of covert networks, in Proceedings of the 8th International Command and Control Research and Technology Symposium, National Defense War College, Washington, 2003.
  • 7. L. Festinger, The analysis of sociograms using matrix algebra, Human Relations 2:153-158, 1949.
  • 8. L. Festinger, A theory of social comparison processes, Human Relations 7:117-140, 1954.
  • 9. Ove Frank and David Strauss, Markov graphs, J. Amer. Statist. Assoc. 81 (1986), no. 395, 832–842. MR 860518
  • 10. Thomas C. Gard, Introduction to stochastic differential equations, Monographs and Textbooks in Pure and Applied Mathematics, vol. 114, Marcel Dekker, Inc., New York, 1988. MR 917064
  • 11. G. R. Grimmett and D. R. Stirzaker, Probability and random processes, 2nd ed., The Clarendon Press, Oxford University Press, New York, 1992. MR 1199812
  • 12. M. Handcock, Progress in statistical modeling of drug user and sexual networks, Technical report, University of Washington, 2000.
  • 13. Peter D. Hoff, Adrian E. Raftery, and Mark S. Handcock, Latent space approaches to social network analysis, J. Amer. Statist. Assoc. 97 (2002), no. 460, 1090–1098. MR 1951262, 10.1198/016214502388618906
  • 14. John H. Holland, Adaptation in natural and artificial systems, University of Michigan Press, Ann Arbor, Mich., 1975. An introductory analysis with applications to biology, control, and artificial intelligence. MR 0441393
  • 15. L. Katz, On the matrix analysis of sociometric data, Sociometry 10:233-241, 1947.
  • 16. L. Katz, Measurement of the tendency towards reciprocation of choice, Sociometry and the Science of Man 18:659-665, 1955.
  • 17. Peter E. Kloeden, Eckhard Platen, and Henri Schurz, Numerical solution of SDE through computer experiments, Universitext, Springer-Verlag, Berlin, 1994. With 1 IBM-PC floppy disk (3.5 inch; HD). MR 1260431
  • 18. J. L. Moreno, Who Shall Survive? Nervous and Mental Disease Publishing, Washington, 1934.
  • 19. Krzysztof Nowicki and Tom A. B. Snijders, Estimation and prediction for stochastic blockstructures, J. Amer. Statist. Assoc. 96 (2001), no. 455, 1077–1087. MR 1947255, 10.1198/016214501753208735
  • 20. T. Snijders, The SIENA Homepage, Available on-line at stat.gamma.rug.nl/snijders/index.html.
  • 21. T. Snijders, The statistical evaluation of social network dynamics, in Sociological Methodology, M. E. Sobel and M. P. Becker, eds., Basil Blackwell, Boston & London, 2001, pp. 361-395.
  • 22. J. Von Neumann, Theory of Self-Reproducing Automata, University of Illinois Press, Urbana, IL, 1966.
  • 23. Yuchung J. Wang and George Y. Wong, Stochastic blockmodels for directed graphs, J. Amer. Statist. Assoc. 82 (1987), no. 397, 8–19. MR 883333
  • 24. S. Wasserman and K. Faust, Social Network Analysis: Methods and Applications, Cambridge University Press, New York, 1994.
  • 25. S. Wasserman and J. Galaskiewicz, Advances in Social Network Analysis: Research in the Social and Behavioral Sciences, Sage Publications, Thousands Oaks, CA, 1994.
  • 26. Stanley Wasserman and Philippa Pattison, Logit models and logistic regressions for social networks. I. An introduction to Markov graphs and 𝑝, Psychometrika 61 (1996), no. 3, 401–425. MR 1424909, 10.1007/BF02294547

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Additional Information

H. T. Banks
Affiliation: Center for Research in Scientific Computation, Box 8205, North Carolina State University, Raleigh, North Carolina 27695–8205
Email: htbanks@ncsu.edu

A. F. Karr
Affiliation: National Institute of Statistical Sciences, P.O. Box 14006, Research Triangle Park, North Carolina 27709–4006
Email: karr@niss.org

H. K. Nguyen
Affiliation: Center for Research in Scientific Computation, Box 8205, North Carolina State University, Raleigh, North Carolina 27695–8205
Email: hknguyen@ncsu.edu

J. R. Samuels Jr.
Affiliation: Center for Research in Scientific Computation, Box 8205, North Carolina State University, Raleigh, North Carolina 27695–8205
Email: jrsamue2@ncsu.edu

DOI: https://doi.org/10.1090/S0033-569X-08-01124-0
Received by editor(s): November 18, 2005
Published electronically: March 27, 2008
Article copyright: © Copyright 2008 Brown University


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