4 papers · 1 filter
Explicit Separators for Consecutive Levels of Parrilo's Sum-of-Squares Hierarchy over the Copositive Cone
Jiachen Shen, Hui Zhong
Parrilo's cones $\Kc{n}{r}$ form a nested sequence of semidefinite-representable inner approximations of the copositive cone $\COP_n$. For their union is all of $\COP_5$, yet…
A conditional no-go for resource-free magic-axis measurement on a static surface code
Jiachen Shen, Hui Zhong
Under stated assumptions, a static surface-code patch that adds no fold or \mbox{self-dual} structure cannot perform the magic-axis check that magic-state cultivation relies on whi…
Grid-Interactive Thermal Management of AI Data Centers via Contextual Distributionally Robust Optimization
Jiachen Shen, Jian Shi, Yijie Yang +4
Thermal management in AI data centers is increasingly challenged by bursty workloads and uncertain heat generation. To prevent thermal violations, existing cooling strategies eithe…
Strategic Decision-Making Under Uncertainty through Bi-Level Game Theory and Distributionally Robust Optimization
Jiachen Shen, Jian Shi, Lei Fan +4
In strategic scenarios where decision-makers operate at different hierarchical levels, traditional optimization methods are often inadequate for handling uncertainties from incompl…