Latest papers
In general relativity, the motion of a test mass around a rotating black hole is described by Kerr geodesics. Owing to the symmetries of the Kerr spacetime, these geodesics possess four constants of motion, rendering the associated…
A correlated equilibrium is information-value-free if every player has an action that yields the same payoff as their equilibrium strategy when all other players follow their respective equilibrium strategies. An equilibrium is learnable if…
We present stellarator optimization algorithms for designing the edge magnetic structure in vacuum fields, together with the vacuum vessel. First, we introduce a numerical method that robustly computes periodic-orbit fixed points of any…
Persistence Diagram (PD) is known to capture point cloud topology effectively, but its computation has high time complexity. Expected Persistence Diagram (EPD) has been developed to reduce the time cost by studying the topology of multiple…
Amateur badminton players increasingly record matches, yet existing tools provide only aggregate statistics or generic summaries, leaving most unable to extract tactical insights without expert guidance. A formative study (N=8) reveals the…
In the theory of spectral algebraic geometry, few objects receive as much study as the spectrum of topological modular forms. In this paper, we compute the strict units of topological modular forms, defined as the connective cover of the…
Erasure-error detection can improve the efficiency of quantum error correction by revealing the times and locations of their error events. In this work, we demonstrate erasure conversions and mid-circuit erasure detections in a single…
Gastrointestinal (GI) endoscopic image analysis has shifted from single-label classification toward visual question answering (VQA), where a model must answer free-form clinical questions about an image. While recent vision-language models…
We develop a global differential calculus on the $L^2$-Wasserstein space over a closed Riemannian manifold, based on derivations of cylinder functions rather than on the standard pointwise approach. Within this framework we define some…
Let $\Omega\subset\mathbb H^2$ be a bounded smooth horoconvex domain and let $\psi_1>0$ be its first Dirichlet eigenfunction. We prove that \[ \operatorname{Hess}_{\mathbb H^2}(-\log\psi_1)>0 \] throughout $\Omega$, with no restriction on…
We obtain novel integral representations, expressed as contour integrals in the complex Fourier plane, for the solution of fully nonhomogeneous initial-boundary-value as well as interface problems for the Barenblatt-Zheltov-Kochina…
In this paper, we show the $L^2$ contraction property of the planar oscillatory or monotone dispersive shock profiles of the dissipative Kadomtsev-Petviashvili (KP) equation modelling water waves and the multi-dimensional Korteweg-de Vries…
We give an algorithm which, given $n = O(d^2 \cdot (\log\log(d)/\log(d))^2)$ copies of $\rho$, estimates the eigenvalues of $\rho$ to constant error in total variation distance. Thus, we can learn the eigenvalues of a quantum state with…
We provide a short proof of a Ky Fan-type majorization relation for the singular values of a sum of binary tensor products of matrices. This generalizes Alhejji's result (arXiv:2410.18254) from two summands to arbitrary sums and from…
We consider the $k$-generalized Korteweg-de Vries equation \begin{equation*} \partial_{t}v+\partial_{x}^{3}v +\partial_{x}(v^{k+1})=0, \qquad (t,x)\in\mathbb R\times\mathbb R, \qquad k\in\mathbb Z_{+}, \end{equation*} emphasizing the…
We resolve a conjecture of Guy David and Svitlana Mayboroda. We show that if $\Omega \subset \mathbb{R}^n$ is a uniform domain with $(n-1)$-dimensional Ahlfors David regular boundary $E = \partial \Omega$, and if $E$ satisfies the Weak…
The growing capability of image generation models has made synthetic images a routine presence in open media, making robust and generalizable AI-Generated Image (AIGI) detection increasingly essential. While multi-modal large language…
It has been well established that the orbital magnetization of interacting electrons can be simply evaluated by applying the single-particle formula to self-consistent HF bands. However, we show that such procedure fails qualitatively for…
High-fidelity quantum control relies on accurate models of driven dynamics. We examine this re- quirement for single-qubit gates in superconducting transmons by comparing control pulses derived from the standard Duffing approximation and…
Autoregressive video diffusion models enable real-time streaming video generation. However, errors introduced during self-rollout accumulate over long horizons, manifesting as color drift, motion stagnation, and eventual visual collapse. In…