Research
Research
Research
Research
34,585+ open-access research outputs.
Long-context large language models (LLMs)-for example, Gemini-3.1-Pro and Qwen-3.5-are widely used to empower many real-world applications, such as retrieval-augmented generation, autonomous agents, a…
In this paper, we investigate the existence of fixed-point-free automorphisms for finite-dimensional Lie algebras. By a result of Jacobson, a Lie algebra admitting a fixed-point-free automorphism is s…
We study scale-invariant geometric quantities associated with embedded closed curves in Euclidean three-space, with an emphasis on their behavior under optimization within a fixed knot type. Given a E…
The full-field reconstruction of three-dimensional (3D) turbulent flows from sparse experimental measurements remains a significant challenge, particularly for flows exhibiting complex 3D flow separat…
There is a Lie algebra structure on the tensor product of a Leibniz algebra and a Zinbiel algebra for the operads of Leibniz algebras and Zinbiel algebras are Koszul dual. In this paper, we extend suc…
In this paper, we utilize our previous results on mod p monodromy of cyclic coverings of the projective line to realize a large series of groups of the form PSL(n, q) and PSU(n, q) as Galois groups ov…
We study properties of the following four classes of operators on the Fock space in $\mathbb C^n:$ 1) weakly localized operators; 2) sufficiently localized operators in the sense of Xia and Zheng; 3) …
Topological entanglement entropy (TEE) is a key diagnostic of long-range entanglement in two-dimensional gapped phases of matter, but it can suffer from spurious contributions that overestimate the to…
Differential-difference matrix Lax representations (Lax pairs), gauge transformations, and discrete Miura-type transformations (MTs) belong to the main tools in the theory of (nonlinear) integrable di…
We show that under $\mathsf{ZF} + \mathsf{CC}_{\mathbb R}$, if the Ramsey property holds for all sets in a good pointclass $\Gamma$, then there is no MAD family in $\Gamma$, proving a long-standing co…
The rapid growth of molecular foundation models and general-purpose large language models has encouraged a scale-centric view of artificial intelligence in drug discovery, in which larger pretrained m…
We develop a geometric-phase framework for time-bin photonic qudits and propose a practical calibration and feed-forward algorithm for separating and compensating geometric (Pancharatnam-Berry), dynam…
Brualdi and Hoffman proposed a well-known problem of determining the graph with maximum adjacency spectral radius among all graphs with given size $m$. Early work by Friedland and Stanley addressed so…
In this paper, we investigate non-abelian extensions of Lie algebras with derivations using several different approaches. We show that the theory of non-abelian extensions of a Lie algebra with a deri…
Given a holomorphic Lie algebroid $(V, \phi)$ on a compact connected Riemann surface $X$, we give a necessary and sufficient condition for a parabolic vector bundle on $X$, with parabolic structure ov…
This paper presents a method for incorporating control analysis into design optimization for highly-maneuverable aircraft. By studying reachable sets for aircraft dynamics, we ensure that the optimize…
Accurate quantification of protein-nanoparticle interactions is essential for applications in nanobiotechnology, nanomedicine, and drug delivery. Motivated by recent computational and experimental wor…
The Quantum Approximate Optimization Algorithm (QAOA) follows a single, fixed evolution path, overlooking the potential computational advantage of coherently superposing multiple trajectories. Here we…
Binary spike coding enables sparse and event-driven computation in spiking neural networks (SNNs), yet its 1-bit-per-timestep representation fundamentally limits information throughput. This bottlenec…
In a previous paper, we introduce and study formal manifolds, which generalize smooth manifolds. In this paper, we establish the basic theory of formal Lie groups, which are group objects in the categ…
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