Papers -- Daniel Irving Bernstein

Expository

  1. Matroids on graphs in applied algebraic geometry. Guest post on the Matroid Union blog.

Submitted papers and preprints

  1. Generic symmetry-forced infinitesimal rigidity: translations and rotations. 2003.10529
  2. On Alignment in Deep Linear Neural Networks (with Adityanarayanan Radhakrishnan, Eshaan Nichani, and Caroline Uhler). 2003.06340

Journal papers

  1. Typical ranks in symmetric matrix completion (with Greg Blekherman and Kisun Lee). Journal of Pure and Applied Algebra, to appear. 1909.06593
  2. The algebraic matroid of the funtf variety (with Cameron Farnsworth and Jose Israel Rodriguez). Journal of Pure and Applied Algebra, Volume 224, Issue 8, August 2020. 1812.10353 Supplementary Materials
  3. L-Infinity optimization to Bergman fans of matroids with an application to phylogenetics. SIAM Journal on Discrete Mathematics 34, no. 1 (2020): 701-720. 1702.05141
  4. The tropical Cayley-Menger variety (with Robert Krone). SIAM Journal on Discrete Mathematics. 33 (2019) no.3, pp. 1725–1742. 1812.09370
  5. Typical and generic ranks in matrix completion (with Greg Blekherman and Rainer Sinn). Linear algebra and its applications, Volume 585, 15 January 2020, pp. 71-104 1802.09513
  6. Unimodular hierarchical models and their Graver bases (with Christopher O'Neill). Journal of Algebraic Statistics. 8 (2017) no.2. 1704.09018 Supplementary Materials
  7. Completion of tree metrics and rank 2 matrices. Linear Algebra and its Applications. 533 (2017), pp. 1-13. 1612.06797
  8. 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
  9. Unimodular binary hierarchical models (with Seth Sullivant). Journal of Combinatorial Theory, Series B. 123 (2017) pp. 97–125. 1502.06131 Supplementary Materials
  10. Normal binary hierarchical models (with Seth Sullivant). Experimental Mathematics. 26 (2017), no. 2, pp. 153-164. 1508.05461
  11. 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
  12. On Three Sets with Nondecreasing Diameter (with Carl Yerger and David J. Grynkiewicz) Discrete Mathematics. 338 (2015) no.8 pp. 1328-1344. 1407.5122

Refereed conference proceedings

  1. Ordering-Based Causal Structure Learning in the Presence of Latent Variables (with Basil Saeed, Chandler Squires, and Caroline Uhler). The 23rd International Conference on Artificial Intelligence and Statistics (AISTATS 2020). 1910.09014

Theses:

  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