Research
Research
Research
Research
39,707+ open-access research outputs.
We study geodesic motion of a test particle in Schwarzschild spacetime. Bound and scattering geodesics are commonly described using Darwin variables, which provide a convenient parametrization of the …
We provide a unified framework for independence and mean independence tests based on the Hilbert-Schmidt independence criterion, extending some previous results in the literature to hold in general to…
Let $M$ be a smooth manifold without boundary and let $\mathcal{T}$ be a countable collection of manifolds with corners, each equipped with a smooth map to $M$. We show that the singular simplicial se…
In this paper, we study the $L^p$-boundedness of Stein's square function $\mathfrak{S}^{\alpha}(\mathcal{L})$ associated with the sub-Laplacian $\mathcal{L}$ on M\'etivier group $G$. A key aspect of o…
AI-generated images are becoming increasingly realistic and diverse, posing significant challenges for generalizable detection. While Vision Foundation Models (VFMs) provide rich semantic representati…
The choice of loss function in classification involves a fundamental trade-off: smooth losses (like Cross-Entropy) enable fast optimization rates but yield slow square-root consistency bounds, while p…
Preference learning has become the foundation of aligning Large Language Models (LLMs) with human intent. Popular methods, such as Direct Preference Optimization (DPO), minimize surrogate losses as pr…
Learning algorithms can be significantly improved by routing complex or uncertain inputs to specialized experts, balancing accuracy with computational cost. This approach, known as learning to defer, …
This paper proposes a bitwise over-parameterized neural network (ONN) decoder for polar-coded transmission and develops a tractable theoretical performance analysis framework. By modeling each synthes…
We give a unified proof of property $R_\infty$ for the Higman groups $H_n$ ($n\ge 4$) and for their generalizations studied by Martin and Horbez--Huang. As a key step, we prove that the automorphism g…
We present fast-vollib, an open-source Python library that provides high-performance European option pricing, implied volatility (IV) computation, and Greeks under the Black-76, Black-Scholes, and Bla…
We demonstrate a micro-Fabry-P\'erot cavity array through laser etching of high-surface-quality mirrors onto a single fused silica substrate. A cavity finesse of $4750\pm 200$ was achieved with a simp…
We study embeddings between reproducing kernel Hilbert spaces $H(K)$ of functions of $d \in \mathbb{N} \cup \{\infty\}$ variables. The kernels $K$ are superpositions of weighted finite tensor products…
This paper proposes a novel algorithm for semisupervised learning. This algorithm learns graph cuts that maximize the margin with respect to the labels induced by the harmonic function solution. We mo…
Uncertainty estimation is essential for robust decision-making in the presence of ambiguous or out-of-distribution inputs. Gaussian Processes (GPs) are classical kernel-based models that offer princip…
Deep learning compilers and vendor libraries deliver strong baseline performance but are bounded by finite, engineer-curated catalogs. When these omit needed optimizations, practitioners substitute ha…
Face Recognition (FR) is used in a variety of application domains, from entertainment and banking to security and surveillance. Such applications rely on the FR model to be robust and perform well in …
Speech Sound Disorders (SSD) affect roughly five percent of children, yet speech-language pathologists face severe staffing shortages and unmanageable caseloads. We test a hierarchical approach to SSD…
We address the joint detection-and-attribution problem in cross-border financial contagion through a two-stage framework. The first stage applies wavelet-quantile transfer entropy across time-scales a…
The Fock-Darwin (FD) quantum system describes the motion on the plane of a charged particle under the action of an isotropic oscillator potential together with a perpendicular constant magnetic field.…
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