Browsing Mathematics & Statistics Department by Subject "Mathematical modeling"

Now showing items 1-5 of 5

    • Analyzing collective motion with machine learning and topology 

      Bhaskar, Dhananjay; Manhart, Angelika; Milzman, Jesse; Nardini, John T.; Topaz, Chad M.; Ziegelmeier, Lori (American Institute of Physics, 2019-12-18)
      We use topological data analysis and machine learning to study a seminal model of collective motion in biology [M. R. D’Orsogna et al., Phys. Rev. Lett. 96, 104302 (2006)]. This model describes agents interacting nonlinearly ...

    • Building context with tumor growth modeling projects in differential equations 

      Gevertz, Jana L.; Beier, Julie C.; Howard, Keith E. (Taylor & Francis, 2015)
      The use of modeling projects serves to integrate, reinforce, and extend student knowledge. Here we present two projects related to tumor growth appropriate for a first course in differential equations. They illustrate the ...

    • Evaluating optimal therapy robustness by virtual expansion of a sample population, with a case study in cancer immunotherapy 

      Barish, Syndi; Ochs, Michael F.; Sontag, Eduardo D.; Gevertz, Jana L. (National Academy of Sciences, 2017)
      Cancer is a highly heterogeneous disease, exhibiting spatial and temporal variations that pose challenges for designing robust therapies. Here, we propose the VEPART (Virtual Expansion of Populations for Analyzing Robustness ...

    • Mathematical Model of Real-Time PCR Kinetics 

      Gevertz, Jana L.; Dunn, Stanley M.; Roth, Charles M. (Wiley Periodicals, Inc, 2005)
      Several real-time PCR (rtPCR) quantification techniques are currently used to determine the expression levels of individual genes from rtPCR data in the form of fluorescence intensities. In most of these quantification ...

    • Stability of twisted states on lattices of Kuramoto oscillators 

      Goebel, Monica; Mizuhara, Matthew S.; Stepanoff, Sofia (American Institute of Physics, 2021-10)
      Real world systems comprised of coupled oscillators have the ability to exhibit spontaneous synchronization and other complex behaviors. The interplay between the underlying network topology and the emergent dynamics remains ...