arXiv subjects

Ethan Liu

Publications and source records attributed to Ethan Liu.

4 recordsLinked to original sources

arXiv2026

PHD-Hand: A Printable Humanoid Dexterous Hand with Linkage-Driven 3-DOA Digits

Currently, dexterous humanoid robot hands are widely considered the final hardware bottleneck that hampers generalist robots from physically assisting people at home and work. As conventional tendon-driven designs suffer from high cost, demanding maintenance, poor reliability, and short durability, alternative linkage-driven designs have increasingly gained attention. Despite their potential to avoid the weaknesses of tendon-driven hands, integrating multiple degrees of actuation (DOA) in a single digit with linkage drivetrains is a challenge for design and fabrication. Only a few studies have managed to present functional humanoid hands that are completely linkage-driven and have at least three DOAs per digit without compromising actuator placement and other design preferences. Our work introduces a new linkage-driven hand featuring a unique flexure hinge. Together with elastic drive rods made of spring steel, the linkage drivetrains are significantly simplified. Unlike other linkage-driven designs of similar dexterity, our design does not require many miniature moving parts. As a result, the hand can be fabricated easily with a budget 3D printer. This not only significantly lowers the barrier to entry for using and developing dexterous humanoid robot hand functions, but also allows the hands to be sized much closer to regular human hands. The design offers desirable kinematic advantages as well. A prototype is evaluated for grasping and object manipulation. In addition, this paper presents our latest findings on kinematics and control of the hand.

cs.RO↗

arXiv2025

Multi-LLM Text Summarization

In this work, we propose a Multi-LLM summarization framework, and investigate two different multi-LLM strategies including centralized and decentralized. Our multi-LLM summarization framework has two fundamentally important steps at each round of conversation: generation and evaluation. These steps are different depending on whether our multi-LLM decentralized summarization is used or centralized. In both our multi-LLM decentralized and centralized strategies, we have k different LLMs that generate diverse summaries of the text. However, during evaluation, our multi-LLM centralized summarization approach leverages a single LLM to evaluate the summaries and select the best one whereas k LLMs are used for decentralized multi-LLM summarization. Overall, we find that our multi-LLM summarization approaches significantly outperform the baselines that leverage only a single LLM by up to 3x. These results indicate the effectiveness of multi-LLM approaches for summarization.

cs.CL↗

arXiv2023

The Ideal of Vanishing Polynomials and the Ring of Polynomial Functions

Vanishing polynomials are polynomials over a ring which output $0$ for all elements in the ring. In this paper, we study the ideal of vanishing polynomials over specific types of rings, along with the closely related ring of polynomial functions. In particular, we provide several results on generating vanishing polynomials. We first analyze the ideal of vanishing polynomial over $\mathbb{Z}_n$, the ring of the integers modulo $n$. We then establish an isomorphism between the vanishing polynomials of a ring and the vanishing polynomials of the constituent rings in its decomposition. Lastly, we generalize our results to study the ideal of vanishing polynomials over arbitrary commutative rings.

math.AC↗

arXiv2023

Results on Vanishing Polynomials and Polynomial Root Counting

We study the set of algebraic objects known as vanishing polynomials (the set of polynomials that annihilate all elements of a ring) over general commutative rings with identity. These objects are of special interest due to their close connections to both ring theory and the technical applications of polynomials, along with numerous applications to other mathematical and engineering fields. We first determine the minimum degree of monic vanishing polynomials over a specific infinite family of rings of a specific form and consider a generalization of the notion of a monic vanishing polynomial over a subring. We then present a partial classification of the ideal of vanishing polynomials over general commutative rings with identity of prime and prime square orders. Finally, we prove some results on rings that have a finite number of roots and propose a technique that can be utilized to restrict the number of roots polynomials can have over certain finite commutative rings.

math.AC↗