arXiv subjects

Luke Kelly

Publications and source records attributed to Luke Kelly.

4 recordsLinked to original sources

arXiv2026

Biomechanically Accurate Gait Analysis: A 3d Human Reconstruction Framework for Markerless Estimation of Gait Parameters

This paper presents a biomechanically interpretable framework for gait analysis using 3D human reconstruction from video data. Unlike conventional keypoint based approaches, the proposed method extracts biomechanically meaningful markers analogous to motion capture systems and integrates them within OpenSim for joint kinematic estimation. To evaluate performance, both spatiotemporal and kinematic gait parameters were analysed against reference marker-based data. Results indicate strong agreement with marker-based measurements, with considerable improvements when compared with pose-estimation methods alone. The proposed framework offers a scalable, markerless, and interpretable approach for accurate gait assessment, supporting broader clinical and real world deployment of vision based biomechanics

eess.IV↗

arXiv2009

Cycles Of Given Length In Oriented Graphs

We show that for each \ell\geq 4 every sufficiently large oriented graph G with δ^+(G), δ^-(G) \geq \lfloor |G|/3 \rfloor +1 contains an \ell-cycle. This is best possible for all those \ell\geq 4 which are not divisible by 3. Surprisingly, for some other values of \ell, an \ell-cycle is forced by a much weaker minimum degree condition. We propose and discuss a conjecture regarding the precise minimum degree which forces an \ell-cycle (with \ell \geq 4 divisible by 3) in an oriented graph. We also give an application of our results to pancyclicity and consider \ell-cycles in general digraphs.

math.CO↗

arXiv2009

Arbitrary Orientations Of Hamilton Cycles In Oriented Graphs

We use a randomised embedding method to prove that for all α>0 any sufficiently large oriented graph G with minimum in-degree and out-degree δ^+(G),δ^-(G)\geq (3/8+α)|G| contains every possible orientation of a Hamilton cycle. This confirms a conjecture of Häggkvist and Thomason.

math.CO↗

arXiv2008

A Dirac type result on Hamilton cycles in oriented graphs

We show that for each α>0 every sufficiently large oriented graph G with δ^+(G),δ^-(G)\ge 3|G|/8+ α|G| contains a Hamilton cycle. This gives an approximate solution to a problem of Thomassen. In fact, we prove the stronger result that G is still Hamiltonian if δ(G)+δ^+(G)+δ^-(G)\geq 3|G|/2 + α|G|. Up to the term α|G| this confirms a conjecture of Häggkvist. We also prove an Ore-type theorem for oriented graphs.

math.CO↗