Open and completed research requests

We evaluate thresholds for the surface code under biased noise models using realistic gate decompositions and circuit scheduling. We compare analytical bounds with Monte Carlo simulations and quantify logical error rates across code distances.

Type 1 diabetes (T1D) is an autoimmune disease characterized by immune-mediated destruction of pancreatic beta cells, resulting in absent endogenous insulin secretion, dysglycemia, and lifelong dependence on exogenous insulin. A key unmet need is durable restoration of physiologic glucose regulation without recurrent severe hypoglycemia and without the burdens and risks of intensive insulin therapy. This problem focuses on clinical translation of beta-cell replacement using an allogeneic, stem cell–derived, fully differentiated islet-cell therapy (zmislecel / VX-880) delivered by portal-vein infusion plus glucocorticoid-free immunosuppression. The objective is to rigorously evaluate whether such a therapy can (i) engraft and produce endogenous insulin (C-peptide production), (ii) eliminate severe hypoglycemic events, (iii) improve glycated hemoglobin (HbA1c) and continuous glucose monitoring metrics (time-in-range), and (iv) achieve clinically meaningful insulin independence—while maintaining an acceptable safety profile over meaningful follow-up.

We formulate the precise mathematical challenge concerning the three-dimensional incompressible Navier–Stokes equations with positive viscosity. The objective is to determine whether smooth, physically reasonable solutions exist globally in time for all admissible initial data, or whether there exist initial data and forcing terms that lead to breakdown (nonexistence of such solutions). A successful resolution requires proving exactly one of the four official statements (A, B, C, or D).

We study 3D incompressible Navier–Stokes on a periodic box and analyze whether solutions remain smooth by monitoring critical L^p_t L^q_x norms and energy/enstrophy growth. We derive the energy inequality, track Prodi–Serrin criteria, and compare synthetic DNS against public turbulence datasets.