432 citations · 1.5k across the 11 of their papers we have counts for
3 papers · 1 filter
On the asymptotic minimum number of monochromatic 3-term arithmetic progressions
Pablo A. Parrilo, Aaron Robertson, Dan Saracino
Let V(n) be the minimum number of monochromatic 3-term arithmetic progressions in any 2-coloring of {1,2,...,n}. We show that (1675/32768) n^2 (1+o(1)) <= V(n) <= (117/2192) n^2(1+…
Improved quantum algorithms for the ordered search problem via semidefinite programming
Andrew M. Childs, Andrew J. Landahl, Pablo A. Parrilo
One of the most basic computational problems is the task of finding a desired item in an ordered list of N items. While the best classical algorithm for this problem uses log_2 N q…
Stability and Robustness Analysis of Nonlinear Systems via Contraction Metrics and SOS Programming
Erin M. Aylward, Pablo A. Parrilo, Jean-Jacques E. Slotine
Contraction analysis is a stability theory for nonlinear systems where stability is defined incrementally between two arbitrary trajectories. It provides an alternative framework i…