research
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Essay
A monoid-aggregated summary evaluates a finite rooted cop-labeled tree bottom-up through a finite state set and a finite commutative child-aggregation monoid. Once the multiplicity observation map and the monoid are fixed, context equivalence has finite index and is exactly equality of a finite behavior vector. This note sharpens the resulting pumping and normal-form theory: the crude pigeonhole bound in the product monoid is replaced by an exact index–period bound on each behavior type’s child contribution, isolating support, modular, and saturation counting in the Boolean, cyclic, and threshold families. Combining exact sibling pumping with a size-minimality argument — no behavior vector may repeat along a root-to-leaf path — yields a finite universe of normal representatives, and an external tie-break selects one canonical representative per class. Worked computations for one-node trees, stars, unary chains, and split-versus-concentrated examples make the bounds concrete.
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Essay
We study a local team-chase problem in a -regular graph whose ball of large radius around the robber is a tree. We isolate the right local invariant — the deep load along a nonbacktracking path tube — and prove a coordinated package of positive and negative results: (i) sharp counts of geodesic cones and their truncations, (ii) a one-round universal branch-persistence lemma, (iii) a -round generalization with depth budget , (iv) a sampling barrier showing that any proof relying on the path-tube certificate requires cops, and (v) a finite-order potential-degeneration barrier showing that any local invariant depending only on order- tube data is strictly insufficient to certify even -round persistence. Together, these results form a double pincer: certifying -round persistence by an order- local invariant requires , and order- resolution requires cops to occupy by uniform sampling. This rules out order- branch-aggregated potentials (for any fixed ) as a route to -round chase from polylogarithmic cops, and identifies the precise structural reason why the natural iteration of the one-round argument fails.
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Essay
3D pose-estimation and kinematic-analysis system for neurological-recovery research, developed in Liqi Shu’s laboratory at the Brown University Department of Neurology. Python/TensorFlow inference, MATLAB-based statistical post-processing, Rust backend with HTML/JS frontends. Four externally-funded sub-projects since 2023; clinical-implications manuscript in preparation.
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Essay
A deep learning model using ICD-10-CM diagnosis codes with a permutation-invariant Deep Sets aggregator improved 30-day unplanned readmission (AUC 0.7496 vs 0.6553 for CCI) and 30-day postdischarge in-hospital mortality (AUC 0.8557 vs 0.7844 for age-adjusted CCI) compared with Charlson and Elixhauser comorbidity-index benchmarks in a national claims database of over 113 million adult hospitalizations.
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Essay
We systematically decompose the sources of SIMD speedup for ML-KEM (Kyber) on Intel x86-64 AVX2. By benchmarking four compilation variants, we demonstrate that GCC’s auto-vectorizer provides negligible benefit, and that hand-written AVX2 assembly delivers a – performance increase for core arithmetic operations. This drives an end-to-end KEM speedup of –.
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Essay
A compendium of years of informal, empirical experiments aimed at extending the efficacy of Anki beyond rote memorization to more intricate levels of learning.