arXiv subjects

Lin Ge

Publications and source records attributed to Lin Ge.

22 records · Page 2Linked to original sources

arXiv2021

Phyllotaxis-inspired Nanosieves with Multiplexed Orbital Angular Momentum

Nanophotonic platforms such as metasurfaces, achieving arbitrary phase profiles within ultrathin thickness, emerge as miniaturized, ultracompact and kaleidoscopic optical vortex generators. However, it is often required to segment or interleave independent subarray metasurfaces to multiplex optical vortices in a single nano device, which in turn affects the compactness and channel capacity of the device. Here, inspired by phyllotaxis patterns in pine cones and sunflowers, we theoretically prove and experimentally report that multiple optical vortices can be produced in a single compact phyllotaxis nanosieve, both in free space and on a chip, where one metaatom may contribute to many vortices simultaneously. The time resolved dynamics of on chip interference wavefronts between multiple plasmonic vortices was revealed by ultrafast time-resolved photoemission electron microscopy. Our nature inspired optical vortex generator would facilitate various vortex related optical applications, including structured wavefront shaping, free space and plasmonic vortices, and high capacity information metaphotonics.

physics.optics↗

arXiv2021

Metadata-based Multi-Task Bandits with Bayesian Hierarchical Models

How to explore efficiently is a central problem in multi-armed bandits. In this paper, we introduce the metadata-based multi-task bandit problem, where the agent needs to solve a large number of related multi-armed bandit tasks and can leverage some task-specific features (i.e., metadata) to share knowledge across tasks. As a general framework, we propose to capture task relations through the lens of Bayesian hierarchical models, upon which a Thompson sampling algorithm is designed to efficiently learn task relations, share information, and minimize the cumulative regrets. Two concrete examples for Gaussian bandits and Bernoulli bandits are carefully analyzed. The Bayes regret for Gaussian bandits clearly demonstrates the benefits of information sharing with our algorithm. The proposed method is further supported by extensive experiments.

cs.LG↗

arXiv2021

Variable bandwidth kernel regression estimation

In this paper we propose a variable bandwidth kernel regression estimator for $i.i.d.$ observations in $\mathbb{R}^2$ to improve the classical Nadaraya-Watson estimator. The bias is improved to the order of $O(h_n^4)$ under the condition that the fifth order derivative of the density function and the sixth order derivative of the regression function are bounded and continuous. We also establish the central limit theorems for the proposed ideal and true variable kernel regression estimators. The simulation study confirms our results and demonstrates the advantage of the variable bandwidth kernel method over the classical kernel method.

math.ST↗

arXiv2017

Further Refinement of Self-normalized Cram\a'{e}r-type moderate Deviations

In this paper, we study the self-normalized Cram\a'{e}r-type moderate deviations for centered independent random variables $X_1, X_2,...$ with $0<E |X_i|^3 <\infty$. The main results refine Theorems 1.1 and 1.2 of Wang (2011), the Berry-Esseen bound (2.11) and Corollaries 2.2 and 2.3 of Jing, Shao and Wang (2003) under stronger moment conditions.

math.PR↗