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1. A theory of pitch for the hydrodynamic properties of molecules, helices, and achiral swimmers at low Reynolds number

   https://doi.org/10.1063/5.0152546  

   Duraes, Anderson D.; Gezelter, J. Daniel (October 2023, The Journal of Chemical Physics)

   We present a theory for pitch, a matrix property that is linked to the coupling of rotational and translational motion of rigid bodies at low Reynolds numbers. The pitch matrix is a geometric property of objects in contact with a surrounding fluid, and it can be decomposed into three principal axes of pitch and their associated moments of pitch. The moments of pitch predict the translational motion in a direction parallel to each pitch axis when the object is rotated around that axis and can be used to explain translational drift, particularly for rotating helices. We also provide a symmetrized boundary element model for blocks of the resistance tensor, allowing calculation of the pitch matrix for arbitrary rigid bodies. We analyze a range of chiral objects, including chiral molecules and helices. Chiral objects with a Cn symmetry axis with n > 2 show additional symmetries in their pitch matrices. We also show that some achiral objects have non-vanishing pitch matrices, and we use this result to explain recent observations of achiral microswimmers. We also discuss the small but non-zero pitch of Lord Kelvin’s isotropic helicoid. 

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2. Learning Orientation Distributions for Object Pose Estimation

   Okorn, Brian; Xu, Mengyun; Hebert, Martial; Held, David (January 2020, Proceedings of the IEEERSJ International Conference on Intelligent Robots and Systems)

   null (Ed.)

   For robots to operate robustly in the real world, they should be aware of their uncertainty. However, most methods for object pose estimation return a single point estimate of the object’s pose. In this work, we propose two learned methods for estimating a distribution over an object’s orientation. Our methods take into account both the inaccuracies in the pose estimation as well as the object symmetries. Our first method, which regresses from deep learned features to an isotropic Bingham distribution, gives the best performance for orientation distribution estimation for non-symmetric objects. Our second method learns to compare deep features and generates a non-parametric histogram distribution. This method gives the best performance on objects with unknown symmetries, accurately modeling both symmetric and non-symmetric objects, without any requirement of symmetry annotation. We show that both of these methods can be used to augment an existing pose estimator. Our evaluation compares our methods to a large number of baseline approaches for uncertainty estimation across a variety of different types of objects. Code available at https://bokorn.github.io/orientation-distributions/ 

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3. Graph Topology Inference Benchmarks for Machine Learning

   https://doi.org/10.1109/MLSP49062.2020.9231794  

   Lassance, Carlos; Gripon, Vincent; Mateos, Gonzalo (September 2020, 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP))

   null (Ed.)

   Graphs are nowadays ubiquitous in the fields of signal processing and machine learning. As a tool used to express relationships between objects, graphs can be deployed to various ends: (i) clustering of vertices, (ii) semi-supervised classification of vertices, (iii) supervised classification of graph signals, and (iv) denoising of graph signals. However, in many practical cases graphs are not explicitly available and must therefore be inferred from data. Validation is a challenging endeavor that naturally depends on the downstream task for which the graph is learnt. Accordingly, it has often been difficult to compare the efficacy of different algorithms. In this work, we introduce several ease-to-use and publicly released benchmarks specifically designed to reveal the relative merits and limitations of graph inference methods. We also contrast some of the most prominent techniques in the literature. 

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4. Rotational Self-motion Cues Improve Spatial Learning when Teleporting in Virtual Environments

   https://doi.org/10.1145/3385959.3418443  

   Lim, Alex F.; Kelly, Jonathan W.; Sepich, Nathan C.; Cherep, Lucia A.; Freed, Grace C.; Gilbert, Stephen B. (October 2020, Symposium on Spatial User Interaction)

   null (Ed.)

   Teleporting interfaces are widely used in virtual reality applications to explore large virtual environments. When teleporting, the user indicates the intended location in the virtual environment and is instantly transported, typically without self-motion cues. This project explored the cost of teleporting on the acquisition of survey knowledge (i.e., a ”cognitive map”). Two teleporting interfaces were compared, one with and one without visual and body-based rotational self-motion cues. Both interfaces lacked translational self-motion cues. Participants used one of the two teleporting interfaces to find and study the locations of six objects scattered throughout a large virtual environment. After learning, participants completed two measures of cognitive map fidelity: an object-to-object pointing task and a map drawing task. The results indicate superior spatial learning when rotational self-motion cues were available. Therefore, virtual reality developers should strongly consider the benefits of rotational self-motion cues when creating and choosing locomotion interfaces. 

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5. Sign and Basis Invariant Networks for Spectral Graph Representation Learning

   D. Lim, J. D. (May 2023, International Conference on Learning Representations (ICLR))

   We introduce SignNet and BasisNet---new neural architectures that are invariant to two key symmetries displayed by eigenvectors: (i) sign flips, since if v is an eigenvector then so is -v; and (ii) more general basis symmetries, which occur in higher dimensional eigenspaces with infinitely many choices of basis eigenvectors. We prove that under certain conditions our networks are universal, i.e., they can approximate any continuous function of eigenvectors with the desired invariances. When used with Laplacian eigenvectors, our networks are provably more expressive than existing spectral methods on graphs; for instance, they subsume all spectral graph convolutions, certain spectral graph invariants, and previously proposed graph positional encodings as special cases. Experiments show that our networks significantly outperform existing baselines on molecular graph regression, learning expressive graph representations, and learning neural fields on triangle meshes. Our code is available at https://github.com/cptq/SignNet-BasisNet. 

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