11 papers
Copositive Matrices with Ordered Off-Diagonal Entries
Grigoriy Blekherman, Santanu S. Dey, Alex Dunbar +1
We study copositive matrices which admit a decomposition into a sum of a positive semidefinite matrix and a matrix with nonnegative entries. Our main result shows that if the off-d…
Unifying Sidewinding and Rolling: A Wave-Based Framework for Self-Righting in Elongated Limbless and Multi-Legged Robots
Hangjun Liu, Jiarui Geng, Jinxuan Ding +7
Centipede-like robots offer unique locomotion advantages due to their small cross-sectional area for accessing confined spaces, and their redundant legs enhance robustness in clutt…
Nonnegative Polynomials and Moment Problems on Algebraic Curves
Lorenzo Baldi, Grigoriy Blekherman, Rainer Sinn
The cone of nonnegative polynomials is of fundamental importance in real algebraic geometry, but its facial structure is understood in very few cases. We initiate a systematic stud…
Stubborn Polynomials
Lorenzo Baldi, Grigoriy Blekherman, Khazhgali Kozhasov +3
The relationship between nonnegative polynomials and sums of squares is a classical topic in real algebraic geometry. We study \emph{stubborn polynomials} on a real variety …
Moments, Sums of Squares, and Tropicalization
Grigoriy Blekherman, Felipe Rincón, Rainer Sinn +2
We use tropicalization to study the duals to cones of nonnegative polynomials and sums of squares on a semialgebraic set . The truncated cones of moments of measures supported o…
On Domination Exponents for Pairs of Graphs
Grigoriy Blekherman, Annie Raymond, Alexander Razborov +1
Understanding graph density profiles is notoriously challenging. Even for pairs of graphs, complete characterizations are known only in very limited cases, such as edges versus cli…