Research
Research
Research
Research
2,055+ open-access research outputs.
The Airborne Collision Avoidance System Xu (ACAS-Xu) relies on large certified Look-Up Tables (LUTs) that encode the exact decision logic used in operation. Neural-network-based approximations have be…
We propose a novel Phase I intra-patient dose-escalation design tailored for multi-cycle immunotherapy settings, in which toxicity at a fixed dose level is clinically expected to decrease over success…
We continue studies on phase retrieval for continuous and discrete Fourier transforms in multidimensions. Using finite difference operators, we give a large class of unexpected examples of non-uniquen…
We prove that normal projective stable families of maximal variation, of fixed dimension, and with bounded adjoint volume are birationally bounded. This is a consequence of a substantially stronger st…
The problem of probabilistic verification of a neural network investigates the probability of satisfying the safe constraints in the output space when the input is given by a probability distribution.…
We present a uniform framework for constructing $3$-designs from $\mathrm{GL}_2(\mathbb F_q)$-invariant subspaces of $\mathbb F_q[X,Y]_k$, the space of homogeneous polynomials of degree $k$. Given suc…
In this paper, we study the following quasi-linear elliptic inequality $\Delta_m u +u^p |\nabla u|^q \leqslant 0$ on weighted graphs, where $(m,p,q)\in (1,\infty)\times\mathbb{R}\times\mathbb{R}$. Acc…
It is generally believed that quantum fluctuations collaborate with thermal fluctuations, effectively reducing transition temperatures (e.g. for melting of charge order). We show that this is not alwa…
In long-context decoding for LLMs and LMMs, attention becomes increasingly memory-bound because each decoding step must load a large amount of KV-cache data from GPU memory. Existing acceleration stra…
Large Reasoning Models (LRMs) achieve strong performance on complex tasks through extended chains of thought but suffer from high inference latency due to autoregressive reasoning. Recent work explore…
We prove a lower bound on the Calabi functional for degenerations of polarized varieties, involving the difference of CM degrees between generically isomorphic families. This may be viewed as a discre…
The challenge of 3D multi-object tracking is achieving robustness in real-world applications, for example under adverse conditions and maintaining consistency as distance increases. To overcome these …
We provide a new characterization of law-invariant backward stochastic differential equations (i.e. BSDEs) with quadratic growth. This answers the open question raised in Xu--Xu--Zhou (2022) on necess…
Let $C_k$ denote the cycle of length $k$, $S_t$ be a star with $t$ edges. And let $B_t$ be the graph consisting of $t$ copies of $C_4$ sharing one fixed edge. Equivalently, $B_t=K_2 \mathbin{\square…
In this paper, we investigate the relationship between positive definite functions on the unit sphere $\sph$ and on the Euclidean space $\RR^d$. For the dimension $d$ to be odd, a new technique is dev…
Relying on the Classification of Finite Simple Groups it was shown by Feng and Xu (Discrete Math., 2005) that every quartic Cayley graph of a regular $p$-group, $p \neq 2,5$, is normal. In this paper …
In this paper, we first establish the localization of the Bergman kernels for unbounded pseudoconvex domains near a D'Angelo finite type boundary point. This result was proved by Engli\v{s} more than …
Large Language Models (LLMs) have shown a high capability in answering questions on a diverse range of topics. However, these models sometimes produce biased, ideologized or incorrect responses, limit…
Agentic AI systems capable of autonomous goal setting and proactive intervention introduce new challenges for regulating moral-emotional processes in learning environments. Existing frameworks typical…
Ping Xu generalized Drinfeld 2-cocycles from bialgebras to associative bialgebroids over noncommutative base algebras. Any counital Drinfeld--Xu 2-cocycle twists the base algebra of the bialgebroid an…
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