arXiv subjects

David Xiang

Publications and source records attributed to David Xiang.

6 recordsLinked to original sources

arXiv2024

Impact of Road Infrastructure and Traffic Scenarios on E-scooterists' Riding and Gaze Behavior

The growing adoption of e-scooters has raised significant safety concerns, particularly due to a surge in injuries and fatalities. This study explores the relationship between road infrastructure, traffic scenarios, and e-scooterists' riding and gaze behaviors to improve road safety and user experience. A naturalistic study was conducted using instrumented e-scooters, capturing gaze patterns, fixation metrics, and head movement data across various road layouts and traffic scenarios. Key findings reveal that bike lanes offer a stable environment with reduced horizontal head movement and focused attention on the road, while shared roads and sidewalks lead to more dispersed gaze and increased head movement, indicating higher uncertainty and complexity. Interactions with other road users, such as navigating intersections, passing buses, riding near cars, and descending on downhill paths, demand greater cognitive load. Intersections require heightened visual focus and spatial awareness, reflected in increased horizontal eye and head movements. Interactions with vehicles prioritize visual scanning over head movement to maintain stability and avoid collisions, while high-speed and downhill riding demand focused attention on obstacles and the road surface. The results provide insights into e-scooter riders' behavior and physiological response analysis, paving the way for safer riding experiences and improved understanding of their needs.

cs.CY↗

arXiv2021

Quantitatively improved finite-size criteria for spectral gaps

Finite-size criteria have emerged as an effective tool for deriving spectral gaps in higher-dimensional frustration-free quantum spin systems. We quantitatively improve the existing finite-size criteria by introducing a novel subsystem weighting scheme. The approach applies to Euclidean lattices of any dimension, the honeycomb lattice, and the triangular lattice.

math-ph↗

arXiv2021

Elementary analysis of isolated zeroes of a polynomial system

Wooley ({\em J. Number Theory}, 1996) gave an elementary proof of a Bezout like theorem allowing one to count the number of isolated integer roots of a system of polynomial equations modulo some prime power. In this article, we adapt the proof to a slightly different setting. Specifically, we consider polynomials with coefficients from a polynomial ring $\mathbb{F}[t]$ for an arbitrary field $\mathbb{F}$ and give an upper bound on the number of isolated roots modulo $t^s$ for an arbitrary positive integer $s$. In particular, using $s=1$, we can bound the number of isolated roots of a system of polynomials over an arbitrary field $\mathbb{F}$.

math.NT↗

arXiv2020

A nonuniform Littlewood-Offord inequality for all norms

Let $\mathbf{v}_i$ be vectors in $\mathbb{R}^d$ and $\{\varepsilon_i\}$ be independent Rademacher random variables. Then the Littlewood-Offord problem entails finding the best upper bound for $\sup_{\mathbf{x} \in \mathbb{R}^d} \mathbb{P}(\sum \varepsilon_i \mathbf{v}_i = \mathbf{x})$. Generalizing the uniform bounds of Littlewood-Offord, Erd\H{o}s and Kleitman, a recent result of Dzindzalieta and Ju\v{s}kevi\v{c}ius provides a non-uniform bound that is optimal in its dependence on $\|\mathbf{x}\|_2$. In this short note, we provide a simple alternative proof of their result. Furthermore, our proof demonstrates that the bound applies to any norm on $\mathbb{R}^d$, not just the $\ell_2$ norm. This resolves a conjecture of Dzindzalieta and Ju\v{s}kevi\v{c}ius.

math.CO↗

arXiv2019

A Self-contained Analysis of the Lempel-Ziv Compression Algorithm

This article gives a self-contained analysis of the performance of the Lempel-Ziv compression algorithm on (hidden) Markovian sources. Specifically we include a full proof of the assertion that the compression rate approaches the entropy rate of the chain being compressed.

cs.IT↗

arXiv2017

The facets of the matroid polytope and the independent set polytope of a positroid

A positroid is a special case of a realizable matroid that arose from the study of the totally nonnegative part of the Grassmannian by Postnikov. In this paper, we study the facets of its matroid polytope and the independent set polytope. This allows one to describe the bases and independent sets directly from the decorated permutation, bypassing the use of the Grassmann necklace. We also describe a criterion for determining whether a given cyclic interval is a flat or not using the decorated permutation, then show how it applies to checking the concordancy of positroids.

math.CO↗