**Research ****Endeavours**

Ø Mathematical
modeling of rumour

Ø Easter Island and Mathematical Archeology

**Research Centres**

Ø Center for Applied and Computational
Mathematics (CACM)

Ø Consortium for Mathematical Methods in Counterterrorism (CMMC)

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?

Ø 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.

Ø Selected rumour modeling
presentations by Dr. Brooks

o
*How
Popular are You on Facebook?,* Presented at the U.S. Department of Energy’s
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 Section’s
Spring Meeting,

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

Ø Links

o www.ritrumormill.org

o www.rumorexpert.com

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.

Ø 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.

Ø 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

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

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.

Ø 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 n×n 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.

Ø 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

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

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.

Ø 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.

Ø Presentations

o
*Two
Interpretations of Discrete Diffusion and Their Consequences on Turing
Instabilities* presented at the MAA Seaway Section’s 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.

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

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

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

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

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

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

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