Open and completed research requests

This paper studies the theoretical foundations and system architecture of Quarks, with emphasis on multi-agent orchestration for long-horizon research tasks. The core idea is to model research execution as a contract-bounded computation graph where agents coordinate through typed interfaces, validators, and explicit phase transitions. We formalize roles for orchestrator, executor, and AI-scientist agents, including meta-orchestration policies for rerouting, backtracking, and self-correction under uncertainty. The framework combines persistent memory, prompt/template abstractions, and neural-symbolic control primitives to support reliable multi-stage reasoning over extended runtimes. Expected impact is a principled blueprint for robust “research-as-a-service” systems that are safe, robust, extensible, and empirically measurable.

Current neurosymbolic ASP pipelines require manual encoding redesign (for example carry-based formulations) to unlock treewidth-aware compilation gains. This project extends the dual-backend framework by automatically rewriting ASP constraints into semantically equivalent, lower-treewidth forms and dynamically routing each training instance to enumeration or compilation. The core idea is to combine static graph analysis of grounded programs with a semantics-preserving rewrite library and a learned crossover predictor based on treewidth, model-count proxies, and circuit reuse ratio. The expected impact is to remove expert-dependent encoding effort, broaden exact inference to more tasks, and improve training efficiency without sacrificing correctness.

Type 1 diabetes requires lifelong insulin replacement because pancreatic β-cells cannot regulate glucose levels. Current insulin therapies deliver fixed pharmacokinetic responses and cannot dynamically adapt to changing blood glucose, which exposes patients to both hypoglycemia and hyperglycemia. A long-standing objective in diabetes research is therefore the development of glucose-responsive insulin (GRI) whose activity increases when glucose levels rise and attenuates when glucose falls.

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.