Algebraic, Geometric, and Combinatorial Aspects of Unique Model Identification
Brandilyn Stigler
Southern Methodist University
Preliminaries
Different bases => (potentially) different models
Unique Reduced Gröbner Bases�for All Monomial Orders
| GB | LT | SM |
1 | | | |
2 | | | |
3 | | | |
Dimitrova, He, Robbiano, Stigler. Small Gröbner Fans of Ideals of Points. J of Algebra and its Applications. 2019.
Dimitrova, He, Robbiano, Stigler. Small Gröbner Fans of Ideals of Points. J of Algebra and its Applications. 2019.
He, Dimitrova, Stigler, Zhang. Geometric characterization of data sets with unique reduced Gröbner bases. Bull of Math Bio. 2019.
Bicondition for URGB�algebraic property
Dimitrova, Fredrickson, Rondoni, Stigler, Veliz-Cuba. Algebraic Experimental Design: Theory and Computation. Submitted. 2022.
Necessary Condition for URGB�geometric property
Dimitrova, Fredrickson, Rondoni, Stigler, Veliz-Cuba. Algebraic Experimental Design: Theory and Computation. Submitted. 2022.
Necessary Condition for URGB�geometric property
Dimitrova, Fredrickson, Rondoni, Stigler, Veliz-Cuba. Algebraic Experimental Design: Theory and Computation. Submitted. 2022.
Necessary Condition for URGB�geometric property
Dimitrova, Fredrickson, Rondoni, Stigler, Veliz-Cuba. Algebraic Experimental Design: Theory and Computation. Submitted. 2022.
Minsets �fewest inputs needed to define a function
Jarrah, Laubenbacher, Stigler, Stillman. Reverse Engineering of Polynomial Dynamical Systems. Adv in Applied Mathematics. 2007.
Computing minsets �with known outputs
(3 minsets)
Computing minsets�with unknown outputs
Computing minsets�with unknown outputs
inconsistent
inconsistent
Computing minsets�with unknown outputs
Computing minsets�with unknown outputs
Summary
Acknowledgments
Recent joint work with
Computational Mathematics Award #1419023
Algebraic Experimental Design:
Theory and Computation
E Dimitrova | C Fredrickson | N Rondoni | A Veliz-Cuba |
Cal Poly | Cal Poly | Cal Poly | Univ Dayton |