arXiv subjects

Ziyi Dai

Publications and source records attributed to Ziyi Dai.

3 recordsLinked to original sources

arXiv2026

Counting Lattice Points in Minkowski Sums of Cross Polytopes

Motivated by Postnikov's study of lattice-point enumeration in Minkowski sums of simplices, we investigate lattice points in Minkowski sums of cross polytopes and establish analogous results, together with several related consequences. In particular, we introduce the support-enumerator associated with Postnikov's notion of draconian sequences and show that it coincides with the $h^*$-polynomial of the corresponding root polytope. This provides a new interpretation of the $h^*$-polynomial and yields a simple method for computing the volume of the corresponding polytope. By exploiting the symmetry of these root polytopes, we further establish a duality property for support-enumerators, which in turn provides a proof of a conjecture by Athanasiadis and Chapoton concerning the $h$-polynomials of preorders. Consequently, we obtain a formula for the number of lattice points in Minkowski sums of cross polytopes in terms of draconian sequences and show that these polytopes are Ehrhart positive. Furthermore, this formula leads to analogous expressions for the number of lattice points on their boundaries and for their surface volumes.

math.CO↗

arXiv2023

Single channel based interference-free and self-powered human-machine interactive interface using eigenfrequency-dominant mechanism

The recent development of wearable devices is revolutionizing the way of human-machine interaction (HMI). Nowadays, an interactive interface that carries more embedded information is desired to fulfil the increasing demand in era of Internet of Things. However, present approach normally relies on sensor arrays for memory expansion, which inevitably brings the concern of wiring complexity, signal differentiation, power consumption, and miniaturization. Herein, a one-channel based self-powered HMI interface, which uses the eigenfrequency of magnetized micropillar (MMP) as identification mechanism, is reported. When manually vibrated, the inherent recovery of the MMP caused a damped oscillation that generates current signals because of Faraday's Law of induction. The time-to-frequency conversion explores the MMP-related eigenfrequency, which provides a specific solution to allocate diverse commands in an interference-free behavior even with one electric channel. A cylindrical cantilever model was built to regulate the MMP eigenfrequencies via precisely designing the dimensional parameters and material properties. We show that using one device and two electrodes, high-capacity HMI interface can be realized when the MMPs with different eigenfrequencies have been integrated. This study provides the reference value to design the future HMI system especially for situations that require a more intuitive and intelligent communication experience with high-memory demand.

physics.app-ph↗

arXiv2019

Can WiFi Estimate Person Pose?

WiFi human sensing has achieved great progress in indoor localization, activity classification, etc. Retracing the development of these work, we have a natural question: can WiFi devices work like cameras for vision applications? In this paper We try to answer this question by exploring the ability of WiFi on estimating single person pose. We use a 3-antenna WiFi sender and a 3-antenna receiver to generate WiFi data. Meanwhile, we use a synchronized camera to capture person videos for corresponding keypoint annotations. We further propose a fully convolutional network (FCN), termed WiSPPN, to estimate single person pose from the collected data and annotations. Evaluation on over 80k images (16 sites and 8 persons) replies aforesaid question with a positive answer. Codes have been made publicly available at https://github.com/geekfeiw/WiSPPN.

cs.CV↗