Research
Research
Research
Research
1,972+ 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…
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…
The authors previously formulated the hybrid conjecture, unifying Andr\'e-Pink-Zannier and Andr\'e-Oort conjectures, and proved it in Shimura varieties of abelian type. We study its analogue for mixed…
We demonstrate robust programmable state preparation in small VCSEL arrays with optical feedback using transient optical injection in the form of Gaussian pulses. In Lang--Kobayashi type models of del…
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 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…
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…
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…
Modern Security Operations Centers struggle with alert fatigue, fragmented tooling, and limited cross-source event correlation. Challenges that current Security Information Event Management and Extend…
In 1998, Bremner conjectured that elliptic curves over the rationals having long sequences of different rational points whose $x$-coordinates are in arithmetic progression, have large rank. This conje…
This paper identifies a structural limitation in current multimodal AI architectures that is topological rather than parametric. Contrastive alignment (CLIP), cross-attention fusion (GPT-4V/Gemini), a…
We extend AMM trade functions to negative inputs via the \textit{concave continuation}, derived from the invariance of the local conservation law under allocation direction flips. This unifies routing…
Recently, Jiang et al. [2026] developed Leon, a practical variant of One-sided Shampoo [Xie et al., 2025a, An et al., 2025] algorithm for online convex optimization, which does not require computing a…
We study structured abstraction-based reasoning for the Abstraction and Reasoning Corpus (ARC) and compare its generalization to test-time approaches. Purely neural architectures lack reliable combina…
Given a graph $F$, the random Tur\'an problem asks to determine the maximum number of edges in an $F$-free subgraph of $G_{n,p}$. Prior to this work, the only bipartite graphs $F$ with known tight bou…
We give a linear algebraic classification of Auslander regular acyclic monomial algebras via the Bruhat factorisation of the Coxeter matrix. Namely, we show under mild assumptions that a monomial acyc…
Denoising generative models deliver high-fidelity generation but remain bottlenecked by inference latency due to the many iterative denoiser calls required during sampling. Training-free acceleration …
For an elliptic curve $E$ over $\mathbb{Q}$ without complex multiplication, Lang and Trotter conjectured that the number of primes $p <X$ at which $E$ has a supersingular reduction is asymptotically e…
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