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We investigate $L^p$ estimates for the $\bar{\partial}$-problem on rational Hartogs triangles $\mathbb{H}_{m/n} = \{ (z_1, z_2) \in \mathbb{C}^2 : |z_1|^m < |z_2|^n < 1 \}$. For $p \in (1, \infty)$, we establish the existence of a solution…

We study CC-geodesic Kakeya sets in the first Heisenberg group, defined by requiring a left translate of every unit-speed CC-geodesic segment issuing from the identity. The natural analogue of the Kakeya conjecture would predict full…

The coexistence of quantum and classical signals in the same optical fiber is a critical challenge for the deployment of quantum networks. Indeed, selecting an optimal channel for quantum signal transmission is crucial to minimize noise…

This paper is concerned with Remez-type inequalities and their applications in observability inequality. Our aim is twofold. First, we establish the following fractal Remez's inequality on the unit sphere $\mathbb{S}^{n-1}$ \begin{align*}…

The key bottleneck in embodied AI is not model architecture but data. Although billions of human manipulation videos exist online, robots cannot directly learn from them due to the embodiment gap between human morphology and robot hardware.…

Differences in nuclear charge distributions between isotopes lead to small changes in atomic spectra known as the field shift. While largely proportional to the change in the mean-square nuclear radius, the field shift also contains…

Convex Collision-Free Regions (CCFR) is a collision handling method that explicitly represents local convex feasible regions to enforce non-penetration. Each feasible region is constructed from surrounding mesh primitive configurations,…

Let $S_n(32\text{-}1)$ and $S_n(3\text{-}21)$ denote the sets of $n$-permutations avoiding the vincular patterns $32\text{-}1$ and $3\text{-}21$, respectively. Using Lehmer codes, we realize these families as weighted posets…

Diverse human groups produce diverse ideas, the raw material of innovation. Generative AI challenges this engine twice over: everyday AI assistance may homogenize what diverse people create, and AI-simulated diversity may replace the people…

Structural asymmetry combined with optical nonlinearity often leads to nonreciprocal light transport. We explore the mechanism by which 1-photon interference effects can revive reciprocity in such nonlinear models. To this end, we study…

Classical discrepancy quantifies the irregularity of the distribution of a sequence in the unit interval. In this paper, we study the analogous notion for sequences in the ring of $p$-adic integers with a focus on the dynamically generated…

Intermittency in turbulence manifests as intense vortices and sharp peaks of dissipation. Causing the breakdown of Kolmogorov's simple self-similar theory, it leads to anomalous scaling, multifractality and so far remains beyond the scope…

We prove that the full group \(\SL(3,\R)\) occurs as the set of one-particle deformation gradients of periodic, unforced, single-shell solutions of both the three-dimensional Euler and Navier--Stokes equations. More precisely, given a…

Many real-life systems can be found as examples of stochastic matching on hypergraphs, such as production lines or assemble-to-order systems. Two common features are the number of items required may vary between matchings, and there may…

Recent advances in LLM-based user simulation have shown promise for offline evaluation of recommendation and advertising systems. However, existing simulators typically infer user preferences from single-domain interaction histories and are…

We address the problem of locating a chemical source in a flow. Based on the duality between the concentration field and Lagrangian tracer trajectories, we interpret concentration detections as evidence of paths connecting the source to the…

Sequence labeling is a fine-grained information extraction task, yet existing large language model-based approaches suffer from insufficient domain alignment and low inference efficiency. To address these issues, we propose DIRECT, a…

Let $M$ be a smooth compact manifold, and $g$ a smooth non-degenerate symmetric bilinear form on $TM$. We prove that every smooth vector field can be written as a finite linear combination of iterated Lie brackets of gradient vector fields.

Reconstructing articulated objects with multiple movable parts is essential for understanding object structure and enabling physical interaction. However, this reconstruction task poses significant challenges due to the entanglement of…

High-entropy alloys (HEAs), with their unique compositional-complexity and tunable surface chemistry, have emerged as promising electrocatalysts for energy conversion. The catalytic activity of HEA often arises from the interplay between…