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Jamie Bell

Publications and source records attributed to Jamie Bell.

10 recordsLinked to original sources
arXiv2026

Nonamenable groups whose reduced group C*-algebras are not pure

We exhibit nonamenable groups whose reduced group C*-algebras are not pure. More precisely, if $\Gamma$ is any countably infinite discrete group, then the reduced group C*-algebra of the restricted wreath product $(\mathbb{Z}/2\mathbb{Z}) \wr \Gamma$ has an ideal-quotient isomorphic to $\mathcal{K}(\ell^2(\Gamma))$. It is therefore not nowhere scattered and, in particular, not pure. Taking $\Gamma$ nonamenable gives a negative answer to a question of Thiel concerning pureness of reduced group C*-algebras.

math.OA↗
arXiv2026

Nonnuclear Bunce-Deddens algebras

We introduce nonnuclear Bunce-Deddens algebras, defined as reduced crossed product C*-algebras associated with free odometer actions of nonamenable countable discrete residually finite groups on a Cantor space. These are nonnuclear counterparts to the generalised Bunce-Deddens algebras introduced by Orfanos. For large classes of groups, we show that they share many regularity properties, including real rank zero, stable rank one, strict comparison of positive elements, and admitting a unique tracial state. In many cases, we deduce that they are even selfless and hence pure. Finally, we compute the K-theory of Bunce-Deddens algebras over nonabelian free groups.

math.OA↗
arXiv2026

Crossed product C*-algebras associated with non-minimal actions on the circle

We examine crossed product C*-algebras associated with free non-minimal actions of countably infinite discrete abelian groups on the circle, extending the work of Putnam, Schmidt, and Skau. We obtain a large class of unital separable nuclear and non-simple C*-algebras that are quasidiagonal, have stable rank one, and admit a unique tracial state. We determine their ideal structure and establish an improved uniform upper bound for their nuclear dimension. Finally, in the case $G = \mathbb{Z}^d$, we compute the K-theory and trace pairing map.

math.OA↗
arXiv2025

Stable rank one in nonnuclear crossed products

We initiate an investigation into the local structure of simple nonnuclear C$^*$-crossed products by showing that stable rank one is generic within two natural classes of minimal actions of free groups on the Cantor set. The arguments also apply to some other free product groups. Our approach is inspired by Li and Niu's stable rank one theorem in the amenable setting and also yields a streamlined argument in that case, along with a generalization to product actions.

math.OA↗
arXiv2025

Robots for Kiwifruit Harvesting and Pollination

This research was a part of a project that developed mobile robots that performed targeted pollen spraying and automated harvesting in pergola structured kiwifruit orchards. Multiple kiwifruit detachment mechanisms were designed and field testing of one of the concepts showed that the mechanism could reliably pick kiwifruit. Furthermore, this kiwifruit detachment mechanism was able to reach over 80 percent of fruit in the cluttered kiwifruit canopy, whereas the previous state of the art mechanism was only able to reach less than 70 percent of the fruit. Artificial pollination was performed by detecting flowers and then spraying pollen in solution onto the detected flowers from a line of sprayers on a boom, while driving at up to 1.4 ms-1. In addition, the height of the canopy was measured and the spray boom was moved up and down to keep the boom close enough to the flowers for the spray to reach the flowers, while minimising collisions with the canopy. Mobile robot navigation was performed using a 2D lidar in apple orchards and vineyards. Lidar navigation in kiwifruit orchards was more challenging because the pergola structure only provides a small amount of data for the direction of rows, compared to the amount of data from the overhead canopy, the undulating ground and other objects in the orchards. Multiple methods are presented here for extracting structure defining features from 3D lidar data in kiwifruit orchards. In addition, a 3D lidar navigation system -- which performed row following, row end detection and row end turns -- was tested for over 30 km of autonomous driving in kiwifruit orchards. Computer vision algorithms for row detection and row following were also tested. The computer vision algorithm worked as well as the 3D lidar row following method in testing.

cs.RO↗
arXiv2024

A Note on the Growth of Sha in Dihedral Extensions

We provide a formula for the order of the Tate--Shafarevich group of elliptic curves over dihedral extensions of number fields of order $2n$, up to $4^{th}$ powers and primes dividing $n$. Specifically, for odd $n$ it is equal to the order of the Tate--Shafarevich group over the quadratic subextension. A similar formula holds for even $n$.

math.NT↗
arXiv2022

p-Selmer ranks of CM abelian varieties

For an elliptic curve with complex multiplication over a number field, the $p^{\infty}$--Selmer rank is even for all $p$. \v{C}esnavi\v{c}ius proved this using the fact that $E$ admits a $p$-isogeny whenever $p$ splits in the complex multiplication field, and invoking known cases of the $p$-parity conjecture. We give a direct proof, and generalise the result to abelian varieties.

math.NT↗
arXiv2020

Kiwifruit detection in challenging conditions

Accurate and reliable kiwifruit detection is one of the biggest challenges in developing a selective fruit harvesting robot. The vision system of an orchard robot faces difficulties such as dynamic lighting conditions and fruit occlusions. This paper presents a semantic segmentation approach with two novel image prepossessing techniques designed to detect kiwifruit under the harsh lighting conditions found in the canopy. The performance of the presented system is evaluated on a 3D real-world image set of kiwifruit under different lighting conditions (typical, glare, and overexposed). Alone the semantic segmentation approach achieves an F1_score of 0.82 on the typical lighting image set, but struggles with harsh lighting with an F1_score of 0.13. Utilising the prepossessing techniques the vision system under harsh lighting improves to an F1_score 0.42. To address the fruit occlusion challenge, the overall approach was found to be capable of detecting 87.0% of non-occluded and 30.0% of occluded kiwifruit across all lighting conditions.

cs.CV↗
arXiv2020

Deep Neural Network Based Real-time Kiwi Fruit Flower Detection in an Orchard Environment

In this paper, we present a novel approach to kiwi fruit flower detection using Deep Neural Networks (DNNs) to build an accurate, fast, and robust autonomous pollination robot system. Recent work in deep neural networks has shown outstanding performance on object detection tasks in many areas. Inspired this, we aim for exploiting DNNs for kiwi fruit flower detection and present intensive experiments and their analysis on two state-of-the-art object detectors; Faster R-CNN and Single Shot Detector (SSD) Net, and feature extractors; Inception Net V2 and NAS Net with real-world orchard datasets. We also compare those approaches to find an optimal model which is suitable for a real-time agricultural pollination robot system in terms of accuracy and processing speed. We perform experiments with dataset collected from different seasons and locations (spatio-temporal consistency) in order to demonstrate the performance of the generalized model. The proposed system demonstrates promising results of 0.919, 0.874, and 0.889 for precision, recall, and F1-score respectively on our real-world dataset, and the performance satisfies the requirement for deploying the system onto an autonomous pollination robotics system.

cs.CV↗