MATH 485/585 - Spring 2012 - Modeling Projects
Math 485 modeling projects should be on one of the topics listed below. The articles or web sites given as references must make the basis of each project and be used as the starting point for bibliographical searches.
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Modeling the formation of sand dunes
The first paper discusses a discrete model describing the time evolution of the height of the sand bed. The second and third papers discuss a continuous model and stress the solitary-wave behavior of barchan dunes.- Computer simulation of aeolian sand ripples and dunes by T.-D. Miao, Q.-S. Mu and S.-Z. Wu
- A model of Barchan dunes including lateral shear stress by V. Schwämmle and H.J. Hermann
- Solitary behavior of sand dunes by V. Schwämmle and H.J. Hermann
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Modeling diseases and epidemics
- Resistance to antibiotics
- A model of antibiotic-resistant bacterial epidemics in hospitals by G.F. Webb, E.M.C. D'Agata, P. Magal and S. Ruan
- Modeling the Hong Kong SARS epidemics using a small world network
The first link points to the main article. The second link is a general discussion on the use of multiscale models to describe epidemics.- Clustering model for transmission of the SARS virus: application to epidemic control and risk assessment by M. Small and C.K. Tse
- Multiscale, resurgent epidemics in a hierarchical metapopulation model by D.J. Watts, R. Muhamad, D.C. Medina and P.S. Dodds
- Modeling leukaemia chemotherapy
The first link points to a news article in Nature. The second link points to the article describing the model.- Cancer biology: Summing up cancer stem cells by J.P. Huntly and D.G. Gilliland
- Dynamics of chronic myeloid leukaemia by F. Michor, T.P. Hughes, Y. Iwasa, S. Branford, N.P. Shah, C.L. Sawyers and M.A. Nowak
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Adding human adaptation to disease spread models
- Adaptive human behavior in epidemiological models by E. Fenichel et al
- Resistance to antibiotics
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Modeling the dream team
The first link points to a perspective article published in Science. The second link points to the article describing the model of team formation.- Network Theory - the emergence of the creative enterprise by A.-L. Barabási
- Team assembly mechanisms determine collaboration network structure and team performance by R. Guimerà, B. Uzzi, J. Spiro and L.A. Amaral
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Modeling in Economics
- Modeling the distribution of retail stores in a city
- Aggregation of retail stores by P. Jensen, J. Boisson and H. Larralde
- Individual versus systemic risk and the Regulator's Dilemma by N. Beale, D. Rand, H. Battey, K. Croxson, R. May and M. Nowak
- Modeling the distribution of retail stores in a city
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Modeling collective behaviors of living organisms
The first link points to a general discussion of schooling behaviors and the second to the main article for the project. The third link describes Boids, which are simulated creatures that can collectively reproduce flocking behaviors.- Complexity, Pattern, and Evolutionary Trade-Off in Animal Aggregation by J.K. Parrish & L. Edelstein-Keshet
- Effective leadership and decision-making in animal groups on the move by I.D. Couzin, J. Krause, N.R. Franks and S.A. Levin
- C. Reynolds Boids page.
- Different dispersal abilities allow reef fish to coexist by M. Bode, L. Bode and P. Armsworth
- How simple rules determine pedestrian behavior and crowd disasters by M. Moussaid, D. Helbing, and G. Theraulaz
Modeling evolution
- Sex-ratio control erodes sexual selection, revealing evolutionary feedback from adaptive plasticity by T. Fawcett, B. Kuijper, F. Weissing and I. Pen
- Evolution of direct reciprocity under uncertainty can explain human generosity in one-shot encounters by A. Delton, M. Krasnow, L. Cosmides and J. Tooby
Math 585 modeling projects may either be on one of the topics listed above or be based on the student's graduate thesis work.