PhD, Applied Mathematics, University of Colorado, Boulder

Networks are  widespread in technology, biology, and society. Moreover, they can encode similarity between arbitrary objects (i.e., images, videos, etc.) and thus play a crucial role for data-analysis methodology in general. I develop mathematical, statistical and machine learning tools to study network representations of complex systems and data. My work falls under two broad groups:

• Network-Data Analytics — methodology development for community detection, ranking systems, network inference, and manifold learning;
• Dynamics on and of Networks — nonlinear and stochastic systems including social contagions, oscillator synchronization, and network evolution.
  

Importantly, these two groups are closely intertwined. That is, realistic modeling of dynamical systems typically requires assimilation with empirical data. At the same, data-analysis methodology often stems from the study of dynamics. Random walks, for example, are central to algorithms including PageRank, Infomap, and Diffusion Map. I study network dynamics and network data as a synergistic pursuit.

• Z Li, PJ Mucha and D Taylor (2017) Network-ensemble comparisons with stochastic rewiring and von Neumann entropy. arXiv preprint.
  
  
• D Taylor, JG Restrepo and FG Meyer (2016) Ensemble-based estimates of eigenvector error for empirical covariance matrices. arXiv preprint.
  
  
• D Taylor, RS Caceres and PJ Mucha (2017)  Super-resolution community detection for layer-aggregated multilayer networks. Physical Review X, in press. arXiv preprint.

• D Taylor, SA Myers, A Clauset, MA Porter and PJ Mucha (2017)  Eigenvector-based centrality measures for temporal networks. Multiscale Modeling and Simulation 15(1), 537-574.
  
  
• D Taylor, PS Skardal and J Sun (2016) Synchronization of heterogeneous oscillators under network modifications: Perturbation and optimization of the synchrony alignment function. SIAM Journal on Applied Mathematics 76(5), 1984-2008.
  
  
• D Taylor, S Shai, N Stanley and PJ Mucha (2016) Enhanced detectability of community structure in multilayer networks through layer aggregation. Physical Review Letters 116, 228301.