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1. Oriented and Non-Oriented Cubical Surfaces in the Penteract

   Estévez, Manuel; Roldán, Érika; Segerman, Henry (August 2024, Bridges Conference Proceedings)

   Which surfaces can be realized with two-dimensional faces of the five-dimensional cube (the penteract)? How can we visualize them? In recent work, Aveni, Govc, and Roldán show that there exist 2690 connected closed cubical surfaces up to isomorphism in the 5-cube. They give a classification in terms of their genus 𝑔 for closed orientable cubical surfaces, and their demigenus 𝑘 for a closed non-orientable cubical surface. In this paper we present the definition of a cubical surface and we visualize the projection to $R^3$ of a torus, a genus two torus, the projective plane, and the Klein bottle. We use reinforcement learning techniques to obtain configurations optimized for 3D-printing. 

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2. General and own-species attentional face biases

   https://doi.org/10.3758/s13414-020-02132-w  

   Jakobsen, Krisztina V.; White, Cassidy; Simpson, Elizabeth A. (October 2020, Attention, Perception, & Psychophysics)

   null (Ed.)

   Humans demonstrate enhanced processing of human faces compared with animal faces, known as own-species bias. This bias is important for identifying people who may cause harm, as well as for recognizing friends and kin. However, growing evidence also indicates a more general face bias. Faces have high evolutionary importance beyond conspecific interactions, as they aid in detecting predators and prey. Few studies have explored the interaction of these biases together. In three experiments, we explored processing of human and animal faces, compared with each other and to nonface objects, which allowed us to examine both own-species and broader face biases. We used a dot-probe paradigm to examine human adults’ covert attentional biases for task-irrelevant human faces, animal faces, and objects. We replicated the own-species attentional bias for human faces relative to animal faces. We also found an attentional bias for animal faces relative to objects, consistent with the proposal that faces broadly receive privileged processing. Our findings suggest that humans may be attracted to a broad class of faces. Further, we found that while participants rapidly attended to human faces across all cue display durations, they attended to animal faces only when they had sufficient time to process them. Our findings reveal that the dot-probe paradigm is sensitive for capturing both own-species and more general face biases, and that each has a different attentional signature, possibly reflecting their unique but overlapping evolutionary importance. 

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3. Surface Registration with Eigenvalues and Eigenvectors

   Hamidian, Hajar; Zhong, Zichun; Fotouhi, Farshad; Hua, Jing (January 2019, IEEE transactions on visualization and computer graphics)

   This paper presents a novel surface registration technique using the spectrum of the shapes, which can facilitate accurate localization and visualization of non-isometric deformations of the surfaces. In order to register two surfaces, we map both eigenvalues and eigenvectors of the Laplace-Beltrami of the shapes through optimizing an energy function. The function is defined by the integration of a smoothness term to align the eigenvalues and a distance term between the eigenvectors at feature points to align the eigenvectors. The feature points are generated using the static points of certain eigenvectors of the surfaces. By using both the eigenvalues and the eigenvectors on these feature points, the computational efficiency is improved considerably without losing the accuracy in comparison to the approaches that use the eigenvectors for all vertices. In our technique, the variation of the shape is expressed using a scale function defined at each vertex. Consequently, the total energy function to align the two given surfaces can be defined using the linear interpolation of the scale function derivatives. Through the optimization of the energy function, the scale function can be solved and the alignment is achieved. After the alignment, the eigenvectors can be employed to calculate the point-to-point correspondence of the surfaces. Therefore, the proposed method can accurately define the displacement of the vertices. We evaluate our method by conducting experiments on synthetic and real data using hippocampus, heart, and hand models. We also compare our method with non-rigid Iterative Closest Point (ICP) and a similar spectrum-based methods. These experiments demonstrate the advantages and accuracy of our method 

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4. Thurston norms of tunnel number-one manifolds

   https://doi.org/10.1142/S0218216519500561  

   Pacheco-Tallaj, Natalia; Schreve, Kevin; Vlamis, Nicholas G. (August 2019, Journal of Knot Theory and Its Ramifications)

   null (Ed.)

   The Thurston norm of a three-manifold measures the complexity of surfaces representing two-dimensional homology classes. We study the possible unit balls of Thurston norms of three-manifolds [Formula: see text] with [Formula: see text], and whose fundamental groups admit presentations with two generators and one relator. We show that even among this special class, there are three-manifolds such that the unit ball of the Thurston norm has arbitrarily many faces. 

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5. Surface Registration with Eigenvalues and Eigenvectors

   https://doi.org/10.1109/TVCG.2019.2915567  

   Hamidian, Hajar; Zhong, Zichun; Fotouhi, Farshad; Hua, Jing (May 2019, IEEE Transactions on Visualization and Computer Graphics)

   This paper presents a novel surface registration technique using the spectrum of the shapes, which can facilitate accurate localization and visualization of non-isometric deformations of the surfaces. In order to register two surfaces, we map both eigenvalues and eigenvectors of the Laplace-Beltrami of the shapes through optimizing an energy function. The function is defined by the integration of a smoothness term to align the eigenvalues and a distance term between the eigenvectors at feature points to align the eigenvectors. The feature points are generated using the static points of certain eigenvectors of the surfaces. By using both the eigenvalues and the eigenvectors on these feature points, the computational efficiency is improved considerably without losing the accuracy in comparison to the approaches that use the eigenvectors for all vertices. After the alignment, the eigenvectors can be employed to calculate the point-to-point correspondence of the surfaces. Therefore, the proposed method can accurately define the displacement of the vertices. We evaluate our method by conducting experiments on synthetic and real data using hippocampus, heart, and hand models. We also compare our method with non-rigid ICP and a similar spectrum-based methods. These experiments demonstrate the advantages and accuracy of our method. 

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