Papers -- Daniel Irving Bernstein

Submitted Papers and Preprints

  1. The tropical Cayley-Menger variety (with Robert Krone). 1812.09370
  2. The algebraic matroid of the funtf variety (with Cameron Farnsworth and Jose Israel Rodriguez). 1812.10353 Supplementary Materials
  3. Typical and generic ranks in matrix completion (with Greg Blekherman and Rainer Sinn). 1802.09513
  4. L-Infinity optimization to Bergman fans of matroids with an application to phylogenetics. 1702.05141

Papers in Press and Print

  1. Unimodular hierarchical models and their Graver bases (with Christopher O'Neill). Journal of Algebraic Statistics. 8 (2017) no.2. 1704.09018 Supplementary Materials
  2. Completion of tree metrics and rank 2 matrices. Linear Algebra and its Applications. 533 (2017), pp. 1-13. 1612.06797
  3. L-infinity optimization to linear spaces and phylogenetic trees (with Colby Long). SIAM Journal on Discrete Mathematics. 31 (2017) no.2  pp. 875-889. 1702.05127 Supplementary Materials
  4. Unimodular binary hierarchical models (with Seth Sullivant). Journal of Combinatorial Theory, Series B. 123 (2017) pp. 97–125. 1502.06131 Supplementary Materials
  5. Normal binary hierarchical models (with Seth Sullivant). Experimental Mathematics. 26 (2017), no. 2, pp. 153-164. 1508.05461
  6. Bounds on the expected size of the maximum agreement subtree (with Lam Ho, Colby Long, Mike Steel, Katherine St. John, and Seth Sullivant) SIAM Journal on Discrete Mathematics. 29 (2015) no. 4 pp. 2065–2074. 1411.7338
  7. On Three Sets with Nondecreasing Diameter (with Carl Yerger and David J. Grynkiewicz) Discrete Mathematics. 338 (2015) no.8 pp. 1328-1344. 1407.5122


  1. Matroids in Algebraic Statistics, 2018 (Ph.D. Dissertation, North Carolina State University) link
  2. Algorithmic Definitions of Singular Functions, 2013. (Undergraduate Honors Thesis, Davidson College) pdf