Research
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Research
Research
3,998+ open-access research outputs.
Understanding human actions is critical for advancing behavior analysis in human-robot interaction. Particularly in tasks that demand quick and proactive feedback, robots must recognize human actions …
Take a compact Sasakian threefold $M$ and consider the associated irreducible $\text{SL}(r,{\mathbb C})$-character variety ${\mathcal R} := \text{Hom}(\pi_1(M, x_0), \text{SL}(r, {\mathbb C}))^{ir}/ \…
We introduce equivariant localization as a method for computing the action of probe branes in supergravity backgrounds. We apply it to supersymmetric probe D3-branes in type IIB supersymmetric spaceti…
We introduce an explicit class of tempered Laurent polynomials in the sense of Villegas and Doran--Kerr in $n \leqslant 4$ variables including all Landau--Ginzburg models for smooth Fano threefolds wi…
We obtain a complete classification of components of strata of holomorphic and meromorphic k-differentials. We show that, when genus is at least two and outside of explicit exceptions when k < 4, ther…
We showed a positive energy theorem for asymptotically flat initial data sets with the concept of spectral PSC by He-Shi-Yu, Bi-Hao-He-Shi-Zhu and Brendle-Wang. Then, we proved a quantitative shieldin…
We develop a Koszul-theoretic framework for comparing classical Alexander-type invariants with infinitesimal invariants arising from finite-type commutative differential graded algebra models. The cen…
Extreme Mass Ratio Inspirals (EMRIs) are among the key targe sources for the space-based gravitational wave (GW) detectors. The waveforms of the EMRIs are highly sensitive to the types of the central …
Semi-discrete (differential-difference) matrix Lax representations (Lax pairs) play an essential role in the theory of integrable differential-difference equations. Fix a (1+1)-dimensional evolution…
In this paper, we study Hardy-type uncertainty principles and unique continuation properties for linear covariant Schrodinger equations with variable coefficients in the presence of bounded electric a…
In this paper, we consider the global spherically symmetric strong solution to the compressible Navier-Stokes equations with far-field vacuum and density-denpendent degenerate viscosity which is refer…
We present a search for small Kochen-Specker (KS) sets in dimension 3, specifically targeting extensions of the 13-ray Yu-Oh set, which has been proven to be the minimal witness to state-independent c…
The standard cosmological model is challenged by an ever-growing collection of observations, which invites (and stimulates) inquiry into possible additions and/or alterations. One such alteration come…
Generating high-quality videos from complex temporal descriptions that contain multiple sequential actions is a key unsolved problem. Existing methods are constrained by an inherent trade-off: using m…
We extend the Hodge atoms framework of Katzarkov--Kontsevich--Pantev--Yu to one-parameter conifold degenerations of Calabi--Yau threefolds. For a degeneration $\pi\colon X \to \Delta$ whose central fi…
We show that the very general Verra fourfold is irrational, using the Hodge atom framework of Katzarkov--Kontsevich--Pantev--Yu. Two novel points are: a refined analysis of Hodge atoms, based on the i…
Let $F_n$, $W_n$, and $\widehat{K}_n$ be the graphs obtained by joining a vertex to $n$ independent edges, a cycle and a path of order $n-1$, respectively. In this paper, we give new bounds for the Ra…
We study transversely K\"ahler almost contact metric Lie algebras $(\mathfrak{g},\varphi,\xi,\eta,g)$ such that the structure $1$-form $\eta$ is a contact form. They include both quasi Sasakian and an…
We give an independent eta-product derivation of the level-8 Apery limit lim B_n^{(8)}/s_n = (7/32) zeta(3), where s_n = sum_{k=0}^n C(n,k)^2 C(2k,n)^2 and B_n^{(8)} is the rational companion sequence…
Large Language Models (LLMs) face prominent security risks from jailbreaking, a practice that manipulates models to bypass built-in security constraints and generate unethical or unsafe content. Among…
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