Papers -- Daniel Irving Bernstein

Expository

  1. Matroid representability and non-rational polytopes. Editor post on the Matroid Union blog.
  2. Matroids on graphs in applied algebraic geometry. Guest post on the Matroid Union blog.

Submitted papers and preprints

  1. Maximum likelihood thresholds of generic linear concentration models (with Steven J. Gortler and Louis Theran). 2305.06280

Journal papers

  1. Matroid lifts and representability (with Zach Walsh). Electronic journal of combinatorics, to appear. 2306.12543
  2. Computing maximum likelihood thresholds using graph rigidity (with Sean Dewar, Steven J. Gortler, Anthony Nixon, Meera Sitharam, and Louis Theran). Algebraic statistics, to appear. 2210.11081
  3. Maximum likelihood thresholds via graph rigidity (with Sean Dewar, Steven J. Gortler, Anthony Nixon, Meera Sitharam, and Louis Theran). Annals of applied probability, to appear. 2108.02185
  4. K_{5,5} is fully reconstructable in C^3 (with Steven J. Gortler). Discrete Applied Mathematics, 322 (2022):442-447. 2110.10224 Supplementary Materials
  5. Generic symmetry-forced infinitesimal rigidity: translations and rotations. SIAM Journal on Applied Algebra and Geometry, 6 (2), 190-215. 2003.10529
  6. Typical ranks in symmetric matrix completion (with Greg Blekherman and Kisun Lee). Journal of Pure and Applied Algebra, Volume 225, Issue 7, July 2021. 1909.06593
  7. 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
  8. 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
  9. The tropical Cayley-Menger variety (with Robert Krone). SIAM Journal on Discrete Mathematics. 33 (2019) no.3, pp. 1725–1742. 1812.09370
  10. 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
  11. Unimodular hierarchical models and their Graver bases (with Christopher O'Neill). Journal of Algebraic Statistics. 8 (2017) no.2. 1704.09018 Supplementary Materials
  12. Completion of tree metrics and rank 2 matrices. Linear Algebra and its Applications. 533 (2017), pp. 1-13. 1612.06797
  13. 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
  14. Unimodular binary hierarchical models (with Seth Sullivant). Journal of Combinatorial Theory, Series B. 123 (2017) pp. 97–125. 1502.06131 Supplementary Materials
  15. Normal binary hierarchical models (with Seth Sullivant). Experimental Mathematics. 26 (2017), no. 2, pp. 153-164. 1508.05461
  16. 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
  17. On Three Sets with Nondecreasing Diameter (with Carl Yerger and David J. Grynkiewicz) Discrete Mathematics. 338 (2015) no.8 pp. 1328-1344. 1407.5122

Conference products

  1. On Alignment in Deep Linear Neural Networks (with Adityanarayanan Radhakrishnan, Eshaan Nichani, and Caroline Uhler). Companion paper to a poster presented at ICML Workshop on "Over-Parameterization: Pitfalls and Opportunities" (ICML 2021). 2003.06340
  2. 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