Bernard Brooks Bio

Research Endeavours

  Mathematical modeling of rumour

  Easter Island and Mathematical Archeology

  Dynamical Systems

  Evolutionary Game Theory

  Conferences Organized

Research Centres

  Center for Applied and Computational Mathematics (CACM)

  Consortium for Mathematical Methods in Counterterrorism (CMMC)

 

Mathematical modeling of rumour

Our interdisciplinary team, lead by psychologist Dr. N. DiFonzo, answered the question: What are the mechanisms involved in rumour propagation over time and across social spaces? Mathematical models of rumour propagation have traditionally used a rumour as epidemic approach that oversimplifies the spatial and demographic distribution of the people infected with the rumour. Instead, our model involves a population connected together in a social network. How does the architecture of the network itself affect propagation? How does the distribution of social subgroups on the network affect rumour propagation?

  Selected Publications

o   Brooks, B.P., DiFonzo, N., Ross, D., GBN-Dialogue Model of Outgroup-Negative Rumor Transmission: Group Membership, Belief, and Novelty, Accepted by Nonlinear Dynamics, Psychology and Life Sciences. April Vol. 17

o   DiFonzo, N., Bourgeois, M. J., Suls, J. M., Homan, C., Stupak, N., Brooks, B., Ross, D. S., & Bordia, P. (2013). Rumor Clustering, Consensus, and Polarization: Dynamic Social Impact and Self-Organization of Hearsay. Journal of Experimental Social Psychology, 49(3), 378-399.

o   Brooks, B.P. Rumour Propagation on Social Networks as a Function of Diversity, Advanced Dynamic Modeling of Economic and Social Systems: Studies in Computational Intelligence, (2013), Volume 448/2013, 49-60.

o   Long, M.E., Morabito, P.N., Brooks, B.P., Schneider, J.L., Modelling Communication Network Effect on Emergency Evacuation Times: Public vs. Personal, International Journal of Business Continuity and Risk Management special issue on Emergency Information Systems, (2012) Volume 3, No. 4, 306-26.

o   Repeated Hearing Increases Belief in Rumor, Moderated Slightly by Skepticism, Poster by DiFonzo, N., Beckstead, J., Stupak, N., Walders, K., Brooks, B. P., Ross, D. S., presented at the Annual Conference of the Society for Personality and Social Psychology, Tampa, Florida, February 7, 2009.

o   Morabito, P.N., Long, M.E., Brooks, B.P., Schneider, J.L., Impact of Personal Communication Networks on Emergency Evacuation Times, Journal of Emergency Management, (2011) 9(6):75 80.

o   Dynamic Social Impact Mechanisms in Rumor Propagation, Poster by DiFonzo, N., Bourgeois, M. J., Homan, C., Suls, J. M., Brooks, B. P., Ross, D. S., Bordia, P., Stupak, N., Frazee, M., Brougher, S., Schwab, N., & McKinlay, M. presented to the Group Processes and Intergroup Relations Meeting at the 2008 Annual Conference of the Society for Personality and Social Psychology, February 7, Albuquerque, NM.

o   Rumor Propagation: Modeling & Testing Dynamic Social Influence Mechanisms, Poster by N. DiFonzo, P Bordia, M. Bourgeois, B. P. Brooks, D. Ross, C. Homan, J Suls & J. Beckstead presented at the Human and Social Dynamics 2006 Principal Investigators Meeting, Washington, DC, October 1-2, 2007.

o   Basener, W.F., Brooks, B.P., Ross, D., Brouwer Fixed Point Theorem Applied to Rumour Transmission, Applied Mathematics Letters (2006) 19(8), 841-842.

o   Empirically-based Mathematical Modeling of Rumor Transmission within Social Networks, Poster by Bernard P. Brooks, N. DiFonzo & D. Ross presented at the Human and Social Dynamics 2006 Principal Investigators Meeting, Washington, DC, September 13-15, 2006.

 

  Selected rumour modeling presentations by Dr. Brooks

o   How Popular are You on Facebook?, Presented at the U.S. Department of Energys National Science Bowl, Washington, DC, April 30, 2011.

o   Rumour Propagation on Social Networks as a Function of Diversity, Presented at the Fifth International Workshop on Dynamics of Social and Economical Systems, University of Sannio, Benevento, Italy, September 23, 2010.

o   The BIG-Dialogue Model of Rumor Transmission, Presented at the S.N.Bose National Centre For Basic Sciences, Calcutta, India, March 9, 2009.

o   Can Math help me stop that awful Rumour on Facebook?,

Presented at Nipissing University, North Bay, Ontario, October 24, 2008.

o   Dialogue Model of Rumor Transmission, Presented at the 41st Annual Society for Mathematical Psychology Conference in Washington DC, July 28, 2008.

o   Spreading Rumours on Facebook, Presented at Science on Saturday Lecture Series, Princeton Plasma Physics Laboratory, Princeton, New Jersey, March 8, 2008.

o   Mathematical Models of Rumour Propagation, Presented at The Mathematics of Public Security 2, Institute for Advanced Studies, Vienna, November 19, 2007.

o   NPR Science Friday: Using Math to Track Terrorists, September 14, 2008.

o   The Dialogue Dynamic of Rumour Transmission on Various Network Topologies, Presented at the Workshop on Dynamical Systems and Applications, Banff International Research Station, Banff, June, 2007.

o   Mathematical Modeling of Rumor Transmission during a Dialogue, Presented at the Joint Mathematics Meetings, New Orleans, January 7, 2007.

o   The Effect of Network Structure on a Rumour Propagation Dynamic, Presented at the 4th Annual Workshop Topology and Related Areas, Nipissing University, May 9, 2006.

o   Rumour Propagation on a Small World Network, Presented at the MAA Seaway Sections Spring Meeting, Ithaca College, April 29, 2006.

o   Mathematical Models of the Propagation of Disaster Rumours, Presented at the 2nd Conference on Mathematical Methods in Counterterrorism, Benedict College, November 3, 2005.

o   Mathematical Models of Rumour Propagation, Presented at the Department of Mathematics and Statistics, University of Guelph, November 2, 2004.

o   Rumour Propagation Modeled as a Dynamical System on a Network, Presented at the Canadian Mathematical Society 2004 summer meeting at Dalhousie University in Halifax, June 13th 2004

  Links

o   www.ritrumormill.org

o   www.rumorexpert.com

o   www.snopes.com

o   CACM Rumour Group

o   Ask Prof Nick

 

Easter Island and Mathematical Archaeology

The Easter Island Research Group of Bill Basener, Bernard Brooks, Mike Radin, and Tamas Wiandt create mathematical models of ancient populations. Mathematical modeling of ancient civilizations involves the construction of models, based on accurate archeological evidence and anthropological understanding of the civilization, together with the analysis of such models for testing the plausibility of anthropological theories.

The Easter Island Research Group of the Center for Applied and Computational Mathematics (CACM) of RIT has published mathematical models establishing the credibility of some of the recent archeological theories concerning the collapse of the population of Easter Island. The mathematical models are based on differential equations, difference equations, dynamical systems, stochastic processes and game theory. The goal is often to develop assumptions on underlying ecological, economic and social factors into models and predictions of dynamic behavior that can be compared to archeological evidence.

  Publications

o   Basener, W.F., Brooks, B.P., Radin, M., Wiandt, T., Spatial Effects and Turing Instabilities in the Invasive Species Model, Nonlinear Dynamics, Psychology and Life Sciences. (2011) 15(4):455-64.

o   Basener, W.F., Brooks, B.P., Radin, M., Wiandt, T., Rat Instigated Human Population Collapse on Easter Island, Nonlinear Dynamics, Psychology and Life Sciences, (2008) Vol. 12, No. 3, pp. 227-240.

o   Basener, W.F., Brooks, B.P., Radin, M., Wiandt, T., Dynamics of a Population Model for Extinction and Sustainability in Ancient Civilizations, Nonlinear Dynamics, Psychology and Life Sciences, (2008) 12(1), 29-53.

 

  Selected Presentations

o   A two-population competition model for a finite natural resource, Presented at Canadian Mathematical Society Winter Meeting, Montreal, December 8, 2012.

o   The Polynesian Rats of Easter Island and the Invasive Species Model, Poster by Basener, W.F., Brooks, B.P., Radin, M., Wiandt, T, presented at the New York Conference on Applied Mathematics, Rochester, NY, October 17, 2009.

o   Introducing Easter Island as a Mathematical Model, Presented at a Mathematics Seminar for the Department of Mathematics and Statistics, RIT, February 15, 2005.

o   Discrete Population Dynamic of Easter Island, Presented at the Canadian Mathematical Society's winter 2004 Meeting at McGill University in Montreal, December 12, 2004.

o   Discrete Population Dynamics of Easter Island, Presented at a Curiosity Seminar for the Department of Mathematics and Statistics, RIT, October 6, 2004.

 

Applied Dynamical Systems

In my mathematical modeling I have developed a few tools that are useful in obtaining analytical stability results in dynamical systems that produce Jacobians with elements that are a complicated jumble of parameters.

  Selected Publications

o   Brooks, B.P., Linear Stability Conditions for a First Order 4-Dimensional Discrete Dynamic, In press.

o   Brooks, B.P., The Coefficients of the Characteristic Polynomial in terms of the Eigenvalues and the Elements of an nn Matrix, Applied Mathematics Letters, (2006) 19(6), 511-515.

o   Brooks, B.P., Linear Stability Conditions for a First Order 3-Dimensional Discrete Dynamic, Applied Mathematics Letters, (2004) 17(4), 463-466.

 

  Selected Presentations

o   First order 4-dimensional discrete dynamic linear stability conditions, AMS Fall Eastern Sectional Meeting, University Park, PA, October 24, 2009.

o   Linear Stability Conditions in Discrete Dynamical Systems, Department of Mathematics and Statistics, RIT, February 3, 2004.

o   Searching for Linear Stability Conditions of a First-Order 4-Dimensional Discrete Dynamic, Presented at the Canadian Mathematical Society 2003 summer meeting at the University of Alberta in Edmonton, June 14th 2003.

o   Linear Stability Conditions for a First Order 3-Dimensional Discrete Dynamic, Department of Mathematics and Statistics, RIT, November 6, 2001.

 

Evolutionary Game Theory

A Turing instability is a spatial instability caused by diffusion. The appearance of Turing instabilities in multi-allele diploid and haploid organisms using the replicator dynamic is investigated.

  Publications

o   Toa Yi, Cressman R, Brooks, B. Nonlinear frequency-dependent selection at a single locus with two alleles and two phenotypes. J. Math. Biol. (1999) 39: 283-308.

  Presentations

o   Two Interpretations of Discrete Diffusion and Their Consequences on Turing Instabilities presented at the MAA Seaway Sections fall meeting at SUNY Potsdam November 2, 2002.

o   A Frequency and Density Dependent Multi-allele Haploid Dynamic presented at the Canadian Mathematical Society 2002 summer meeting at the University of Laval in Quebec City, June 16th 2002.

 

Conferences Organized

  1st New York Conference on Applied Mathematics, October 17, 2009, at the Center for Applied and Computational Mathematics, Rochester Institute of Technology.

  4th Conference on Mathematical Methods in Counterterrorism, September 20-22, 2007, at Rochester Institute of Technology.

 

  3rd Conference on Mathematical Methods in Counterterrorism, September 28-30, 2006, at the Institute of World Politics, Washington, DC.

 

  Nineteenth Midwest Conference on Combinatorics, Cryptography and Computing, October 7-9, 2005, at Rochester Institute of Technology

 

  Eighteenth Midwest Conference on Combinatorics, Cryptography and Computing, October 28-30, 2004, at Rochester Institute of Technology

 

  MAA Seaway Section's fall meeting, November 7 & 8, 2003, at Rochester Institute of Technology.

 

  Dynamic Evolutionary Game Theory in Biology and Economics, Wilfrid Laurier University, 1995.