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1. Neural efficiency and spatial task difficulty: A road forward to mapping students’ neural engagement in spatial cognition

   Snowden, Ariel W. ; Warren, Christopher M. ; Goodridge, Wade ; Fang, Ning ( January 2021 , Engineering design graphics journal)

   The current study examined the neural correlates of spatial rotation in eight engineering undergraduates. Mastering engineering graphics requires students to mentally visualize in 3D and mentally rotate parts when developing 2D drawings. Students’ spatial rotation skills play a significant role in learning and mastering engineering graphics. Traditionally, the assessment of students’ spatial skills involves no measurements of neural activity during student performance of spatial rotation tasks. We used electroencephalography (EEG) to record neural activity while students performed the Revised Purdue Spatial Visualization Test: Visualization of Rotations (Revised PSVT:R). The two main objectives were to 1) determine whether high versus low performers on the Revised PSVT:R show differences in EEG oscillations and 2) identify EEG oscillatory frequency bands sensitive to item difficulty on the Revised PSVT:R.  Overall performance on the Revised PSVT:R determined whether participants were considered high or low performers: students scoring 90% or higher were considered high performers (5 students), whereas students scoring under 90% were considered low performers (3 students). Time-frequency analysis of the EEG data quantified power in several oscillatory frequency bands (alpha, beta, theta, gamma, delta) for comparison between low and high performers, as well as between difficulty levels of the spatial rotation problems.   Although we did not find any significant effects of performance type (high, low) on EEG power, we observed a trend in reduced absolute delta and gamma power for hard problems relative to easier problems. Decreases in delta power have been reported elsewhere for difficult relative to easy arithmetic calculations, and attributed to greater external attention (e.g., attention to the stimuli/numbers), and consequently, reduced internal attention (e.g., mentally performing the calculation). In the current task, a total of three spatial objects are presented. An example rotation stimulus is presented, showing a spatial object before and after rotation. A target stimulus, or spatial object before rotation is then displayed. Students must choose one of five stimuli (multiple choice options) that indicates the correct representation of the object after rotation. Reduced delta power in the current task implies that students showed greater attention to the example and target stimuli for the hard problem, relative to the moderate and easy problems. Therefore, preliminary findings suggest that students are less efficient at encoding the target stimuli (external attention) prior to mental rotation (internal attention) when task difficulty increases.  Our findings indicate that delta power may be used to identify spatial rotation items that are especially challenging for students. We may then determine the efficacy of spatial rotation interventions among engineering education students, using delta power as an index for increases in internal attention (e.g., increased delta power). Further, in future work, we will also use eye-tracking to assess whether our intervention decreases eye fixation (e.g., time spent viewing) toward the target stimulus on the Revised PSVT:R. By simultaneously using EEG and eye-tracking, we may identify changes in internal attention and encoding of the target stimuli that are predictive of improvements in spatial rotation skills among engineering education students.  

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2. Optothermal rotation of micro-/nano-objects

   https://doi.org/10.1039/D2CC06955E  

   Ding, Hongru ; Chen, Zhihan ; Ponce, Carolina ; Zheng, Yuebing ( February 2023 , Chemical Communications)

   Due to its contactless and fuel-free operation, optical rotation of micro-/nano-objects provides tremendous opportunities for cellular biology, three-dimensional (3D) imaging, and micro/nanorobotics. However, complex optics, extremely high operational power, and the applicability to limited objects restrict the broader use of optical rotation techniques. This Feature Article focuses on a rapidly emerging class of optical rotation techniques, termed optothermal rotation. Based on light-mediated thermal phenomena, optothermal rotation techniques overcome the bottlenecks of conventional optical rotation by enabling versatile rotary control of arbitrary objects with simpler optics using lower powers. We start with the fundamental thermal phenomena and concepts: thermophoresis, thermoelectricity, thermo-electrokinetics, thermo-osmosis, thermal convection, thermo-capillarity, and photophoresis. Then, we highlight various optothermal rotation techniques, categorizing them based on their rotation modes ( i.e. , in-plane and out-of-plane rotation) and the thermal phenomena involved. Next, we explore the potential applications of these optothermal manipulation techniques in areas such as single-cell mechanics, 3D bio-imaging, and micro/nanomotors. We conclude the Feature Article with our insights on the operating guidelines, existing challenges, and future directions of optothermal rotation. 

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3. F1FO ATP synthase molecular motor mechanisms

   https://doi.org/10.3389/fmicb.2022.965620  

   Frasch, Wayne D. ; Bukhari, Zain A. ; Yanagisawa, Seiga ( August 2022 , Frontiers in Microbiology)

   The F-ATP synthase, consisting of F 1 and F O motors connected by a central rotor and the stators, is the enzyme responsible for synthesizing the majority of ATP in all organisms. The F 1 (αβ) 3 ring stator contains three catalytic sites. Single-molecule F 1 rotation studies revealed that ATP hydrolysis at each catalytic site (0°) precedes a power-stroke that rotates subunit-γ 120° with angular velocities that vary with rotational position. Catalytic site conformations vary relative to subunit-γ position (β E , empty; β D , ADP bound; β T , ATP-bound). During a power stroke, β E binds ATP (0°–60°) and β D releases ADP (60°–120°). Årrhenius analysis of the power stroke revealed that elastic energy powers rotation via unwinding the γ-subunit coiled-coil. Energy from ATP binding at 34° closes β E upon subunit-γ to drive rotation to 120° and forcing the subunit-γ to exchange its tether from β E to β D , which changes catalytic site conformations. In F 1 F O , the membrane-bound F O complex contains a ring of c-subunits that is attached to subunit-γ. This c-ring rotates relative to the subunit-a stator in response to transmembrane proton flow driven by a pH gradient, which drives subunit-γ rotation in the opposite direction to force ATP synthesis in F 1 . Single-molecule studies of F 1 F O embedded in lipid bilayer nanodisks showed that the c-ring transiently stopped F 1 -ATPase-driven rotation every 36° (at each c-subunit in the c 10 -ring of E. coli F 1 F O ) and was able to rotate 11° in the direction of ATP synthesis. Protonation and deprotonation of the conserved carboxyl group on each c-subunit is facilitated by separate groups of subunit-a residues, which were determined to have different pKa’s. Mutations of any of any residue from either group changed both pKa values, which changed the occurrence of the 11° rotation proportionately. This supports a Grotthuss mechanism for proton translocation and indicates that proton translocation occurs during the 11° steps. This is consistent with a mechanism in which each 36° of rotation the c-ring during ATP synthesis involves a proton translocation-dependent 11° rotation of the c-ring, followed by a 25° rotation driven by electrostatic interaction of the negatively charged unprotonated carboxyl group to the positively charged essential arginine in subunit-a. 

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4. Flattening and surface-brightness of the fast-rotating star δ Persei with the visible VEGA/CHARA interferometer

   https://doi.org/10.1051/0004-6361/201629934  

   Challouf, M. ; Nardetto, N. ; Domiciano de Souza, A. ; Mourard, D. ; Tallon-Bosc, I. ; Aroui, H. ; Farrington, C. ; Ligi, R. ; Meilland, A. ; Mouelhi, M. ( August 2017 , Astronomy & Astrophysics)

   null (Ed.)

   Context. Rapid rotation is a common feature for massive stars, with important consequences on their physical structure, flux distribution and evolution. Fast-rotating stars are flattened and show gravity darkening (non-uniform surface intensity distribution). Another important and less studied impact of fast-rotation in early-type stars is its influence on the surface brightness colour relation (hereafter SBCR), which could be used to derive the distance of eclipsing binaries. Aims. The purpose of this paper is to determine the flattening of the fast-rotating B-type star δ Per using visible long-baseline interferometry. A second goal is to evaluate the impact of rotation and gravity darkening on the V − K colour and surface brightness of the star. Methods. The B-type star δ Per was observed with the VEGA/CHARA interferometer, which can measure spatial resolutions down to 0.3 mas and spectral resolving power of 5000 in the visible. We first used a toy model to derive the position angle of the rotation axis of the star in the plane of the sky. Then we used a code of stellar rotation, CHARRON, in order to derive the physical parameters of the star. Finally, by considering two cases, a static reference star and our best model of δ Per, we can quantify the impact of fast rotation on the surface brightness colour relation (SBCR). Results. We find a position angle of 23 ± 6 degrees. The polar axis angular diameter of δ Per is θ p = 0.544 ± 0.007 mas, and the derived flatness is r = 1.121 ± 0.013. We derive an inclination angle for the star of i = 85 + 5 -20 degrees and a projected rotation velocity V sin i = 175 + 8 -11 km s -1 (or 57% of the critical velocity). We find also that the rotation and inclination angle of δ Per keeps the V − K colour unchanged while it decreasing its surface-brightness by about 0.05 mag. Conclusions. Correcting the impact of rotation on the SBCR of early-type stars appears feasible using visible interferometry and dedicated models. 

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5. A Functional Approach to Rotation Equivariant Non-Linearities for Tensor Field Networks

   Poulenard, Adrien ; Guibas, Leonidas ( January 2021 , Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition)

   null (Ed.)

   Learning pose invariant representation is a fundamental problem in shape analysis. Most existing deep learning algorithms for 3D shape analysis are not robust to rotations and are often trained on synthetic datasets consisting of pre-aligned shapes, yielding poor generalization to unseen poses. This observation motivates a growing interest in rotation invariant and equivariant methods. The field of rotation equivariant deep learning is developing in recent years thanks to a well established theory of Lie group representations and convolutions. A fundamental problem in equivariant deep learning is to design activation functions which are both informative and preserve equivariance. The recently introduced Tensor Field Network (TFN) framework provides a rotation equivariant network design for point cloud analysis. TFN features undergo a rotation in feature space given a rotation of the input pointcloud. TFN and similar designs consider nonlinearities which operate only over rotation invariant features such as the norm of equivariant features to preserve equivariance, making them unable to capture the directional information. In a recent work entitled "Gauge Equivariant Mesh CNNs: Anisotropic Convolutions on Geometric Graphs" Hann et al. interpret 2D rotation equivariant features as Fourier coefficients of functions on the circle. In this work we transpose the idea of Hann et al. to 3D by interpreting TFN features as spherical harmonics coefficients of functions on the sphere. We introduce a new equivariant nonlinearity and pooling for TFN. We show improvments over the original TFN design and other equivariant nonlinearities in classification and segmentation tasks. Furthermore our method is competitive with state of the art rotation invariant methods in some instances. 

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