Research
Research
Research
Research
1,928+ open-access research outputs.
This paper proposes an algorithm for clipping line segment against an axis-aligned rectangular window. The conventional algorithms for line segment clipping treat the clipping boundary and/or the line…
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…
In 1965 Kraichnan pointed out that a sufficiently strong background magnetic field, i.e. the case of small Alfv\'en number, will reduce the nonlinear interaction and inhibit the formation of strong gr…
Reider's Theorem on the very ampleness of adjoint linear series on a complex projective algebraic surface is extended in two new directions. First, Reider-type inequalities are shown to imply nefness …
We describe how the spacetime positive energy theorem in dimension $n \geq 4$ follows from our recent work on the Riemannian version of the positive mass theorem. Our proof builds on the fundamental w…
The ensemble Kalman filter (EnKF) is widely used for nonlinear and high-dimensional state estimation because it replaces complex covariance propagation with simple ensemble statistics. However, conven…
The development of general-purpose agents requires a shift from executing simple instructions to completing complex, real-world productivity workflows. However, current tool-use benchmarks remain misa…
The proliferation of financial misinformation poses a severe threat to market stability and investor trust, misleading market behavior and creating critical information asymmetry. Detecting such misle…
Reinforcement learning (RL) paradigms have demonstrated strong performance on reasoning-intensive tasks such as code generation. However, limited trajectory diversity often leads to diminishing return…
The maximum score method (Manski, 1975, 1985) is a powerful approach for binary choice models, yet it is known to face both practical and theoretical challenges. In particular, the estimator converges…
Davis, Drusvyatskiy, and Jiang showed that gradient descent with an adaptive stepsize converges locally at a nearly-linear rate for smooth functions that grow at least quartically away from their mini…
A classical result of Steinitz from 1913 \cite{Ste13}, answering an earlier question of Riemann and L\'evy (e.g., \cite{Lev05}), states that for any norm $\|\cdot\|$ in $\mathbb{R}^d$ and any set of v…
Let $\mathcal{V}^c(\mathfrak{gl}_N)$ be Etingof--Kazhdan's quantum affine vertex algebra associated with the trigonometric $R$-matrix. We establish a connection between suitably generalized deformed $…
For positive integers $n$, $d$, $k$ and $h$, let $[n]^d$ be the $d$-dimensional grid of order $n$, and we refer to the equation $\sum_{i=1}^{h}x_{1,i}=\cdots =\sum_{i=1}^{h}x_{k,i}$ as the {\it $B_{k,…
Large language models (LLMs) produce responses rated as highly empathic in single-turn settings (Ayers et al., 2023; Lee et al., 2024), yet they are also known to be formulaic generators that reuse th…
We introduce a new type of generating theorems in General Relativity for anisotropic, static, spherically symmetric solutions of the Einstein field equations. The results are used to derive a class of…
The maximum score estimator of Manski (1975) provides an elegant approach to estimate slope coefficient in binary choice models without requiring parametric assumptions on the error distribution. Howe…
Ensuring safety and reliability in human-robot interaction (HRI) requires the timely detection of unexpected events that could lead to system failures or unsafe behaviours. Anomaly detection thus play…
With the rise of LLMs, there is an increasing need for intelligent recommendation assistants that can handle complex queries and provide personalized, reasoning-driven recommendations. LLM-based recom…
AI agents are increasingly deployed in real-world applications, including systems such as Manus, OpenClaw, and coding agents. Existing research has primarily focused on server-side efficiency, proposi…
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