Charlie Brummitt

PhD candidate in Applied Mathematics

Department of Mathematics       
University of California
One Shields Avenue                   CV
Davis, CA 95616-8633
USA

I am a third-year graduate student in the Graduate Group in Applied Mathematics, advised by Prof. Raissa D'Souza.

Much of my current work concerns cascades in networks. The three main projects aim to answer the following questions, using both theoretical and empirical mathematical models:

1. What amount of interdependence among infrastructure optimally reduces systemic risk?
2. People interact using more social media, and banks lend in more and more ways; how do these trends affect how easily things go viral and how easily default spreads?
   
3. What makes some social groups innovative?

I also work on more abstract models of emergence in complex systems, such as cellular automata.

Research interests: cascades in networks, dynamical systems, branching processes, game theory, with applications to critical infrastructure, viral marketing and financial markets

Publications:

• Multiplexity-facilitated cascades on networks. Phys. Rev. E 85, 045102(R) (2012). arXiv:1112.0093
  C. D. Brummitt, K.-M. Lee, K.-I. Goh
  
  
  • Poster at CompleNet 2012 in Melbourne, FL and at the 2012 SIAM conference in Davis, CA.
    
  • Talk at McCann Universal, a marketing agency in San Francisco.
    
  • 177-word press summary
    

  As people interact in more ways, things go viral more easily. Buying a new phone or car often requires decisions. Apple or Android? Hybrid or electric? Many such decisions are influenced by contacts of many types, such as friends and family, colleagues and bloggers, friends on Facebook and on Twitter. As more of a person's social contacts choose a certain alternative, such as buying an electric car, that person becomes more likely to choose it as well, because of peer influence and compatible technology. Simple models of this behavior adoption due to peer influence have recently garnered attention. Most such models lump together contacts of different types, such as friends and colleagues and Twitter followers. Here we show that distinguishing types of contacts can make things spread virally through a population more easily. As we participate in more social spheres and use more online social media platforms like Facebook and Twitter, behavior change can more easily spread. This could offer tools for marketers trying to make their products go viral. But it also hints at why the financial system has grown more vulnerable with each new lending mechanism



• Suppressing cascades of load in interdependent networks. Proc. Natl. Acad. Sci. USA 109 (12) E680–E689 (2012).
  C. D. Brummitt, R. M. D'Souza, E. A. Leicht
  
  
  • Author summary (2 page PDF)
    
• Media coverage in Slashdot, NetworkWorld/ComputerWorld/PCWorld/InfoWorld/TechWorld/CIO, Ilsussidiario, UC Davis College of Engineering News.
  
• Simulation code on GitHub.
  
  
• A search for the simplest chaotic partial differential equation. Physics Letters A 373 (31), 2717–2721 (2009).
  C. D. Brummitt, J. C. Sprott.
  
  
• Packard Snowflakes on the von Neumann Neighborhood. Journal of Cellular Automata 3 (1), 57–80 (2008).
  C. D. Brummitt, H. Delventhal, M. Retzlaff.

Preprints:

• Boundary growth in one-dimensional cellular automata. arXiv:1204.2172 (April 10, 2012)
  C. D. Brummitt, E. Rowland
  
  
  • Packages: CellularAutomatonBoundaries.m, CellularAutomatonData.m
    
  • Talk by Eric at Joint Mathematics Meeting 2012
    

Recent long-term activities:

• Santa Fe Institute Complex Systems Summer School, June 2012
• NSF EAPSI: During summer 2011, I did research with Prof. Kwang-Il Goh and PhD student Kyu-Min Lee at the statistical physics group at Korea University in Seoul. Here is the NSF Project Outcomes Report and our first paper together.
• During spring 2011, I visited SAMSI in Research Triangle, NC, for the 2010-11 Program on Complex Networks. The first paper from this collaboration is coming soon.
  

Other research and class projects:

• A network model of heterosis. Joint work with Tal Levy for Prof. Vladimir Filkov's Computational Understanding of Biological Networks, Winter 2011. [pdf]
• The evolution of foresight and strategic teaching. Poster with Prof. Burkhard C. Schipper (UC Davis) at the Davis SIAM Conference, May 2010. [pdf]
• Automated defect detection: computational methods to detect flaws in industrial parts. Mathematical Problems in Industry Workshop, June 2010. Report for General Electric with Prof. Peter Kramer and six other students. [pdf]
  
• Networks formed by chaotic Units. Final project for Prof. Jim Crutchfield's NCASO/NLP classes, Spring 2010. [pdf]

Selected awards:

• National Defense Science & Engineering Graduate Fellowship (NDSEG), 2011-14
  
• National Science Foundation Graduate Research Fellowship (NSF GRF), 2011 (declined in order to accept NDSEG)
  
• Graduate Assistance in Areas of National Need (GAANN) Fellowship, 2010-11
• UC Davis Graduate Scholars Fellowship, 2009-10
  

• Cycling (UCD, DBC)
• Climbing (Rocknasium)
• Running (GVH)
  
• Music (Davis/Sac, SF)
  
• Blog (for keeping in touch with family & friends)