Papers -- Daniel Irving Bernstein

** Expository **

- Algebraic matroids. Matroid Union blog post.
- Matroid representability and non-rational polytopes. Matroid Union blog post.
- Matroids on graphs in applied algebraic geometry. Matroid Union blog post.

** Submitted papers and preprints**

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

**Journal papers**

- Matroid lifts and representability (with Zach Walsh).
*Electronic journal of combinatorics*, to appear. 2306.12543 - 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 - Maximum likelihood thresholds via graph rigidity (with Sean Dewar, Steven J. Gortler, Anthony Nixon, Meera Sitharam, and Louis Theran).
*Annals of applied probability*2024, Vol. 34, No. 3, 3288-3319. 2108.02185 - K_{5,5} is fully reconstructable in C^3 (with Steven J. Gortler).
*Discrete Applied Mathematics*, 322 (2022):442-447. 2110.10224 Supplementary Materials - Generic symmetry-forced infinitesimal rigidity: translations and rotations.
*SIAM Journal on Applied Algebra and Geometry*, 6 (2), 190-215. 2003.10529 - 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 - 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 - 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 - The tropical Cayley-Menger variety (with Robert Krone).
*SIAM Journal on Discrete Mathematics*.**33**(2019) no.3, pp. 1725–1742. 1812.09370 - 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 - Unimodular hierarchical models and their Graver bases (with Christopher O'Neill).
*Journal of Algebraic Statistics*.**8**(2017) no.2. 1704.09018 Supplementary Materials - Completion of tree metrics and rank 2 matrices.
*Linear Algebra and its Applications.*1612.06797**533**(2017), pp. 1-13. - 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 - Unimodular binary hierarchical models (with Seth Sullivant).
*Journal of Combinatorial Theory, Series B.***123**(2017) pp. 97–125. 1502.06131 Supplementary Materials - Normal binary hierarchical models (with Seth Sullivant).
*Experimental Mathematics.***26**(2017), no. 2, pp. 153-164. 1508.05461 - 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 - 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**

- 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 - 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:**