Pair Of Planes Research Articles

Equiangular lines in ℂ3

Abstract A p-set of equiangular lines in ℂ3 is a set of p lines spanning ℂ3 each pair of which has the same nonzero angle arccos c, where 0 < c < 1. It is known that via a real matrix representation, a pair of lines in ℝ3 with angle arccos c yields a pair of isoclinic planes in ℝ6 with angle arccos c. In this article we characterize all p-tuples of equi-isoclinic planes in ℝ6 which come via our real matrix representation from p-tuples of equiangular lines in ℂ3. More precisely, we describe quadruples, quintuples up to nine-tuples of equiangular lines in ℂ3.

Algebraic fundamental groups of fake projective planes

Fundamental groups of fake projective planes fall into fifty distinct isomorphism classes, one for each complex conjugate pair. We prove that this is not the case for their algebraic fundamental groups: there are only forty-six isomorphism classes. We show that there are four pairs of complex conjugate pairs of fake projective planes that are \operatorname{Aut}(\mathbb{C}) -equivalent and hence have mutually isomorphic algebraic fundamental groups. All other pairs of algebraic fundamental groups are shown to be distinct through explicit finite étale covers. As a by-product, this provides the first examples of commensurable but nonisomorphic lattices in a rank one semisimple Lie group that have isomorphic profinite completions.

Hopcroft’s Problem, Log* Shaving, Two-dimensional Fractional Cascading, and Decision Trees

We revisit Hopcroft’s problem and related fundamental problems about geometric range searching. Given n points and n lines in the plane, we show how to count the number of point-line incidence pairs or the number of point-above-line pairs in O ( n 4/3 ) time, which matches the conjectured lower bound and improves the best previous time bound of \(n^{4/3}2^{O(\log ^*n)}\) obtained almost 30 years ago by Matoušek [ 58 ]. We describe two interesting and different ways to achieve the result: The first is randomized and uses a new two-dimensional version of fractional cascading for arrangements of lines; the second is deterministic and uses decision trees in a manner inspired by the sorting technique of Fredman [42]. The second approach extends to any constant dimension. Many consequences follow from these new ideas: For example, we obtain an O ( n 4/3 )-time algorithm for line segment intersection counting in the plane, O ( n 4/3 )-time randomized algorithms for distance selection in the plane and bichromatic closest pair and Euclidean minimum spanning tree in three or four dimensions, and a randomized data structure for halfplane range counting in the plane with O ( n 4/3 ) preprocessing time and space and \(O(n^{1/3})\) query time.

Orientation Relationship of the Intergrowth Al13Fe3 and Al13Fe4 Intermetallics Determined by Single-Crystal X-ray Diffraction

In the Al-Fe binary system, the Al13Fe3 phase as well as the Al13Fe4 phase has similar icosahedral building blocks like those appearing in quasicrystals. Therefore, it is of vital importance to clarify the formation process of these two phases. Coexistence of the Al13Fe3 and Al13Fe4 phases was discovered from the educts obtained with a nominal atomic ratio of Al/Fe of 9:2 by high-pressure sintering for the first time. Firstly, single crystal X-ray diffraction (SXRD) combined with a scanning electron microscope (SEM) with energy dispersive X-ray spectroscopy (EDX) measurement capabilities were adopted to determine the detailed crystal structures of both phases, which were sharply refined with regard to Al13Fe3 and Al13Fe4. Secondly, the orientation relationship between Al13Fe3 and Al13Fe4 was directly deduced from the SXRD datasets and the coexistence structure model was consequently constructed. Finally, seven pairs of parallel atomic planes and their unique orientation relations were determined from the reconstructed reciprocal space precession images. In addition, the real space structure model of the intergrowth crystal along with one kind of interfacial atomic structure were constructed from the determined orientation relations between two phases.

Orientation Relationship of Intergrowth Al2Fe and Al5Fe2 Intermetallics Determined by Single-Crystal X-ray Diffraction

Although the Al2Fe phase has similar decagonal-like atomic arrangements as that of the orthorhombic Al5Fe2 phase, no evidence for intergrowth samples of Al2Fe and Al5Fe2 has been reported. In the present work, the co-existence of Al2Fe and Al5Fe2 phases has been discovered from the educts obtained with a nominal atomic ratio of Al:Fe of 2:1 by arc melting. First, single-crystal X-ray diffraction (SXRD) as well as scanning electron microscope (SEM) equipped with energy-dispersive X-ray spectroscopy (EDX) measurements have been utilized to determine the exact crystal structures of both phases, which are refined to be Al12.48Fe6.52 and Al5.72Fe2, respectively. Second, the orientation relationship between Al2Fe and Al5Fe2 has been directly deduced from the SXRD data sets, and the co-existence structure model has been constructed. Finally, four pairs of parallel atomic planes and their unique orientation relations have been determined from the reconstructed reciprocal-space precession images of (0kl), (h0l), and (hk0) layers. In addition, one kind of interface atomic structure model is constructed by the orientation relations between two phases, correspondingly.

A transmission electron microscopy study of the crystallographic characteristics of magnetite needles in plagioclase

The correct and precise crystal forms and the crystallographic orientation relationships (CORs) of ten main magnetite needle groups in the plagioclase host were unequivocally determined by transmission electron microscopy from >100 selected magnetite needles with well defined shape orientations in petrographic thin sections of a gabbro core sample drilled from the Mid-Atlantic Ridge. The as-observed CORs of magnetite in plagioclase are in accordance with the optimal matching in the oxygen sublattices of the two structures via the close alignment between two sets of close-packed (c.p.) oxygen arrays parallel to {111}m in magnetite (m) and two sets of quasi-c.p. oxygen arrays parallel to (150)p, (150)p, (112)p, (312)p, (021)p or (121)p in plagioclase (p), as demonstrated for the first time in the accumulated oxygen number versus normal distance [from the (hkl) plane] plots. Such a simple oxygen sublattice matching principle does not rely on the length matching for the specific pair of lattice directions or on the d-spacing matching for the specific pair of lattice planes of the two structures, and therefore must be generally applicable for any mineral/oxide inclusions with a c.p. or quasi-c.p. oxygen sublattice formed via precipitation in open or closed systems. The topotaxial nuclei then undergo extended growth along the kinetically fast growth direction of the two structures with the most similar oxygen distribution patterns, i.e. along the normal direction of the aligned pair of oxygen arrays, thereby yielding the pronounced shape orientations such as magnetite needles in plagioclase.

Camera–LiDAR Calibration Using Iterative Random Sampling and Intersection Line-Based Quality Evaluation

This paper proposes a novel camera–LiDAR calibration method that utilizes an iterative random sampling and intersection line-based quality evaluation using a foldable plane pair. Firstly, this paper suggests using a calibration object consisting of two small planes with ChArUco patterns, which is easy to make and convenient to carry. Secondly, the proposed method adopts an iterative random sampling to make the calibration procedure robust against sensor data noise and incorrect object recognition. Lastly, this paper proposes a novel quality evaluation method based on the dissimilarity between two intersection lines of the plane pairs from the two sensors. Thus, the proposed method repeats random sampling of sensor data, extrinsic parameter estimation, and quality evaluation of the estimation result in order to determine the most appropriate calibration result. Furthermore, this method can also be used for the LiDAR–LiDAR calibration with a slight modification. In experiments, the proposed method was quantitively evaluated using simulation data and qualitatively assessed using real-world data. The experimental results show that the proposed method can successfully perform both camera–LiDAR and LiDAR–LiDAR calibrations while outperforming the previous approaches.

A Simulation-Based Approach to Evaluate the Performance of Automated Surveillance Camera Systems for Smart Cities

A surveillance camera is the typical device that makes up a surveillance camera system in a modern city. It will still be a representative surveillance unit in future scenarios such as in smart cities. Furthermore, as the demand for public safety increases, a massive number of surveillance cameras will be in use in the future, and an automated system that controls surveillance cameras intelligently will also be required. Meanwhile, installing a surveillance system without any verification system might not be cost-effective, so a simulation that evaluates the system’s performance is required in advance. For this reason, we introduce how to simulate a surveillance area and evaluate surveillance performance in this paper to assess a surveillance system consisting of large amounts of surveillance cameras. Our simulator defined the surveillance area as a pair of two-dimensional planes, which depend on various camera-related configurations. Both surveillance areas are used to determine if the moving object belongs to the coverage of a surveillance camera. In addition, our simulator adopts several performance indices to evaluate a surveillance camera system in terms of target detection and quality. The simulation study provides comprehensive results on how various components of the surveillance system affect the performance of the surveillance system, leading to the conclusion that building a sophisticated scheme to control a large number of surveillance cameras can provide a cost-effective and reliable surveillance system for smart cities.

Crystal plasticity model of BCC metals from large-scale MD simulations

Accurate crystal plasticity models that faithfully capture the behavior of single crystals under a wide range of loading conditions, such as loading direction, strain rate, and temperature, are still lacking. Here we introduce a novel approach in which a crystal plasticity (CP) model is informed directly from and calibrated to large-scale quantum-accurate MD simulations in which single crystal BCC Ta serves as a testbed material. By analyzing our large set of MD simulations several key insights are obtained leading us to modify constitutive assumptions in order to address deficiencies of existing CP models. Importantly, we observe that the standard notion of fixed slip systems – pairs of slip directions and slip planes – is inadequate for describing high-rate plasticity in BCC tantalum at room temperature. Instead, pencil glide defined as dislocation motion in the maximum resolved shear stress planes (MRSSP) of each Burgers vector is fully consistent with our MD simulation data while providing significant simplifications of the constitutive relations. Our resulting new CP model closely matches the behavior of single crystals observed in high-rate MD simulations while being fully consistent with lower rate experimental results.

Optical and thermal performance-cost evaluation for different segmentation of a novel equal-length multi-section compound parabolic concentrator

To solve the problems of high production and maintenance cost, poor substitutability and low standardization level of the compound parabolic concentrators (CPCs) with glass mirror curved concentrator for building integrated solar system, an alternative equal-length multi-section planar splicing concentrator is introduced. This work mainly focuses on how to realize higher performance-cost ratio through different planar segmentation of the curved concentrating surface. Based on optical and thermal modelling, spatial energy flux density distribution, optical efficiency, photothermal efficiency of the CPCs whose concentrating surface containing 15, 13, 11, 9, 7, 5 and 3 pairs of equal-length planes were investigated. Results show that the average output temperature of the CPC containing 15 planes is 364.4 K, and the photothermal efficiency is 61.63%. With the decrease of the number of segments, the photothermal efficiency gradually decreases. However, it brings benefits that the peak of energy flux density becomes gradually smaller, the thermal stress in the glass tube gets reduced, and the CPC manufacturing cost is greatly reduced. Considering comprehensive photothermal performance and cost, CPCs containing 9–15 equal-length planes could trade off between the performance and cost. The findings can promote the planarization and standardization of CPCs for building integrated solar system.

Brain Age Prediction With Improved Least Squares Twin SVR.

Alzheimer's disease (AD) is the prevalent form of dementia and shares many aspects with the aging pattern of the abnormal brain. Machine learning models like support vector regression (SVR) based models have been successfully employed in the estimation of brain age. However, SVR is computationally inefficient than twin support vector machine based models. Hence, different twin support vector machine based models like twin SVR (TSVR), ε-TSVR, and Lagrangian TSVR (LTSVR) models have been used for the regression problems. ε-TSVR and LTSVR models seek a pair of ε-insensitive proximal planes for generation of end regressor. However, SVR and TSVR based models have several drawbacks- i) SVR model is computationally inefficient compared to the TSVR based models. ii) Twin SVM based models involve the computation of matrix inverse which is intractable in real world scenario's. iii) Both TSVR and LTSVR models are based on empirical risk minimization principle and hence may be prone to overfitting. iv) TSVR and LTSVR assume that the matrices appearing in their formulation are positive definite which may not be satisfied in real world scenario's. To overcome these issues, we formulate improved least squares twin support vector regression (ILSTSVR). The proposed ILSTSVR modifies the TSVR by replacing the inequality constraints with the equality constraints and minimizes the slack variables using squares of L2 norm instead of L1. Also, we introduce a different Lagrangian function to avoid the computation of matrix inverses. We evaluated the proposed ILSTSVR model on the subjects including cognitively healthy, mild cognitive impairment and Alzheimer's disease for brain-age estimation. Experimental evaluation and statistical tests demonstrate the efficiency of the proposed ILSTSVR model for brain-age prediction.

Broadband Magnetoelectric Dipole Filtering Antenna for 5G Application

A magnetoelectric (ME) dipole filtering antenna with high out-of-band suppression level and high selectivity is proposed in this letter. The intrinsic radiation null of the traditional ME dipole antenna is used, which produces a good filtering response at the edge of the lower passsband. A pair of vertical parasitic metal planes are introduced between the shorted walls and fed through slot coupling, which can be equivalent to an additional magnetic dipole. The radiated electric field of the magnetic dipole is opposite to that of the original antenna at higher frequency, forming a wide stopband radiation null, which greatly improves the high-frequency stopband suppression level of the antenna. Furthermore, a pair of T-shaped coupling stubs are inserted between the shorted wall and electric dipole, producing another radiation null with high roll-off rate at higher frequency. The measurement results show that the −10 dB impedance bandwidth of the proposed antenna is 49.4% (3.2–5.3 GHz). Its low-frequency stopband suppression level is greater than 16.6 dB and high-frequency stopband suppression level is greater than 26.0 dB. Moreover, the antenna radiation pattern is stable and symmetrical in the whole operating passband, and the filtering response is desirable.

Parameter adaptive unit-linking pulse coupled neural network based MRI–PET/SPECT image fusion

Medical image fusion has many applications to healthcare that is accomplished by extracting and then combining the complementary information from multiple medical images into a single image. The pulse coupled neural network (PCNN) is greatly applied to image fusion due to its efficient coupling of surrounding neurons, but suffers from network complexity and manual parameter settings. This paper proposes a novel parameter adaptive unit-linking PCNN (PAULPCNN) model, whose parameters are automatically obtained from the external stimulus and exhibits a simpler structure than the original PCNN. The multi-scale decomposition-based methods, particularly based on the non-subsampled shearlet transform (NSST), are widely employed by researchers to perform medical image fusion due to their efficient separation of spatial details at different scales. Motivated by the advantages of the PCNN and multi-scale decomposition-based methods, a hybrid medical image fusion method based on the PAULPCNN model is introduced in the NSST domain that merges the salient complementary details from a gray-scale and the corresponding pseudo-color medical image captured at different modalities to produce a more informative image that is more useful to medical experts in computer-aided diagnosis of diseases. The proposed method first employs NSST to transform the source images into a low-pass and several high-pass sub-bands, respectively. The high-pass sub-bands are combined using the firing times of the proposed PAULPCNN model, whereas a new distance-weighted regional energy-based rule is applied to construct the fused low-pass sub-band, which while estimating regional energy, assigns weight to different neighboring pixels depending on their distance from the central pixel. Finally, inverse NSST is applied on the fused sub-bands to construct the fused image. The effectiveness of the proposed technique is shown using the fusion results of eleven state-of-the-art methods on thirty gray-scale and pseudo-color brain medical image pairs comprising mild Alzheimer’s disease, Huntington’s disease, motor neuron disease, sagittal plane, coronal plane, transaxial plane, and glioma image pairs, where eight objective metrics are considered for the quantitative assessment. Experimental results demonstrate that the proposed method is competitive with the state-of-the-art methods, which even outperforms some of these methods by providing fused images with better visual quality and greater objective performance, which are more suitable for specialists to diagnose brain diseases.

Experimental investigation and theoretical evaluation on the leakage mechanisms of seawater hydraulic axial piston pump under sea depth circumstance

Seawater hydraulic axial piston pump (SHAPP) is an important component of underwater hydraulic system. However, due to the particularity of the deep-sea high-pressure environment, the precise measurement of the SHAPP has not been carried out in the past, and there is a lack of performance evaluation of piston pump based on deep-sea test. In this paper, a testing system of the SHAPP in deep sea environment was designed and established, and the leakage mechanisms of the SHAPP is mainly studied by methods of experimental research and theoretical evaluation. The results indicated that the piston and piston bush produce micron deformation under sea depth circumstance. The compaction coefficient of plane pair (slippers/swashplate and port plate/valve plate) decreases gradually with the increase of sea depth. The main reasons why the leakage increases with the increase of sea depth under a certain load are that the clearance of the piston/piston bush becomes larger, and that the sealing of the plane pair gradually deteriorates due to the reduction of the compaction coefficient. Finally, the method of reducing leakage is given, this paper will provide theoretical and experimental reference for the design and application of the SHAPP in deep-sea environment.

Polar duality between pairs of transversal Lagrangian planes; applications to uncertainty principles

We extend the notion of polar duality to pairs (ℓ,ℓ′) of transversal Lagrangian planes in the standard symplectic space. (R2n,ω). This allows us to show that polar duality has a natural symplectic interpretation. Our main results are the following: we first show that the oblique projections Ωℓ and Ωℓ′ on ℓ and ℓ′ of a centrally symmetric convex body Ω containing a symplectic ball with radius one satisfy the duality relation Ωℓo⊂Ωℓ′. We thereafter show that if, conversely, (Ωℓ,Ωℓ′)⊂ℓ×ℓ′ is such that Ωℓo=Ωℓ′ then Ωℓ and Ωℓ′ are the projections of a symplectic ball with radius one which is the John ellipsoid of Ωℓ×Ωℓ′o. We apply these results to the quantum principle of indeterminacy, which contains as a particular case the usual uncertainty principle.

EVALUATION OF UAV-BORNE PHOTOGRAMMETRY AND LASER SCANNING FOR 3D TOPOGRAPHIC CHANGE ANALYSIS AT AN ACTIVE ROCK GLACIER

Abstract. Point clouds derived from UAV-borne laser scanning and UAV-borne photogrammetry provide new opportunities for 3D topographic monitoring in geographic research. The airborne acquisition strategy overcomes common challenges of ground-based techniques, such as limited spatial coverage or heterogeneous measurement distribution, and allows flexible repeated acquisitions at high temporal and spatial resolution. While UAV-borne 3D sensing techniques are expected to thereby enhance geographic monitoring, their specific potential for methods and algorithms of 3D change analysis is yet to be investigated. In our study, we assess point clouds originating from UAV-borne photogrammetry using dense image matching (DIM) and UAV-borne laser scanning (ULS) as input for 3D topographic change analysis at an active rock glacier in the Austrian Alps. We analyse surface change by using ULS and DIM point clouds of 2019 and 2021 as input for two state-of-the-art methods for pairwise surface change analysis: (1) The Multiscale Model to Model Cloud Comparison (M3C2) algorithm and (2) a recent M3C2-based approach (CD-PB M3C2) using plane correspondences to reduce the uncertainty of quantified change. We evaluate ULS-based and DIM-based change analysis regarding their performance in (1) achieving high spatial coverage of derived changes, (2) accurately quantifying magnitudes and uncertainty of change, and (3) detecting significant change (change magnitudes > associated uncertainty). As reference we use change quantified between two terrestrial laser scanning (TLS) surveys undertaken simultaneously with the ULS and DIM data acquisitions. Our study shows the improved spatial coverage of M3C2 achieved with point clouds acquired with UAVs (+ 60% of core points used for change analysis). For CD-PB M3C2, ULS and DIM point clouds enabled a spatially more uniform distribution of plane pairs used for change quantification and a slightly higher spatial coverage (+6% – +7% of core points used for change analysis) compared to the TLS reference. Magnitudes of M3C2 change were closer to the TLS reference for ULS-ULS (mean difference: 0.04 m; std. dev.: 0.05 m) compared to ULS-DIM (mean difference: 0.12 m; std. dev.: 0.08 m). Similar results were obtained for CD-PB M3C2 using ULS-ULS (mean difference: 0.02 m; std. dev.: 0.01 m) and ULS-DIM (mean difference: 0.06 m; std. dev.: 0.01 m). Moreover, magnitudes of change were above the associated uncertainty in 82% – 89% (M3C2) and 89% – 90% (CD-PB M3C2) of the area of change analysis. Our findings demonstrate the potential of ULS and DIM point clouds as input for accurate 3D topographic change analysis for the study at hand and can support the design and setup of 3D/4D Earth observation systems for rock glaciers and natural scenes with complex topography, such as landslides or debris covered glaciers.

Noise mitigation in high-speed PCB applications: experimental verification and validation of electromagnetic band gap filters

Electromagnetic noise (EMI) affects efficiency of a gadget, proximity devices and human beings, necessitating the noise mitigation. Introduction of Electromagnetic Band Gap (EBG) structure in PCB as plane pairs helps for high-speed operations. In this paper, the planar L-bridge embedded pattern-type EBG structure is designed to mitigate the noise. Experimental verification of the designed EBG type with various geometrical parameters is carried out by altering the geometrical parameters of the unit cell with 18 cases. All the cases are simulated for the frequency sweep 0.1–10 GHz. Simulation results are compared with theoretical calculations and measurement results. It is found that they are in good agreement. The depth in noise levels can be efficiently altered by changing air gap, line length and unit cell width. In order to validate the EBG, a continuous plane is considered and found that EBG helps to mitigate the noise level in the higher frequency.

MCB-DPO: Multiport Constrained Barrier Method-Based Decoupling Capacitor Placement Optimization on Irregularly Shaped Planes

A multi-port constrained optimization methodology is presented for the optimal placement of decoupling capacitors in power distribution networks (PDNs) of printed circuit boards (PCBs). The proposed method is based on barrier methods and can simultaneously handle multiple ball grid array (BGA) devices and capacitor ports on practical power/ground plane pairs of polygonal shapes without restriction in the problem geometry. Semi-analytical expressions are developed for the magnitude of device port impedance that is set as the objective function. The placement optimization problem including constraints of planar boundaries and impedance specifications is cast into a matrix expression that meets Karush–Kuhn Tucker (KKT) conditions and solved through Newton–Raphson (N–R) iterations. The convergence of iterations is ensured by guaranteeing the positive definiteness of the system matrix through the Levenberg–Marquardt algorithm. Mutual coupling among multiple ports and discrete components of the problem domain is accounted for via matrix calculus techniques applied to the partial derivatives of optimization variables. The derivatives are evaluated accurately exploiting the semi-analytical relations developed for the distributed planar impedance. The proposed method is tested with several examples, and the results are observed to be in good agreement with those obtained from a numerical electromagnetic (EM) simulator while yielding significant speed-up.

Boundary plane-oriented grain boundary model generation

This study proposes algorithms for building tilt grain boundary (GB) models with a boundary plane-oriented approach that does not rely on existence of a coincidence site lattice (CSL). As conventional GB model generation uses the CSL of superimposed grains as the starting point, our totally different approach allows systematic treatment of diverse grain boundary systems that was previously not possible. Candidates of a pair of GB planes for a selected rotation axis, constituting a symmetrical or asymmetrical tilt GB, are thoroughly obtained by computational search that is applicable to any crystal structure. A GB interface for feasible computational analysis would have two-dimensional (2D) periodicity shared by the 2D lattices of the two GB planes, hence surface-slab supercells (slab-and-vacuum models) with common in-plane basis vectors of the shared 2D lattice are obtained. Finally, a procedure to obtain a GB-model supercell with alternately stacking such slabs is given. Symmetry operations of each slab may be considered such that the iterated interfaces are symmetrically equivalent, which is beneficial in ab initio calculations. The proposed algorithms allow streamlined generation of GB models, both symmetric and asymmetric, with or without an exact 3D-CSL relation.

Interphase misorientation as a tool to study metamorphic reactions and crystallization in geological materials

AbstractInterphase boundaries are planar defects that separate two different minerals, which in general have different compositions and/or crystalline structures; they may play an important role as a pathway for fluids in rocks and affect their physical properties. To completely characterize interphase boundaries, one needs to define the misorientation between adjacent grains and the orientation of the grain boundary plane. The analysis performed here is limited to the misorientation characterization and the trace of the interphase boundary. Although the determination of possible orientation relationships between the two adjacent phases is routinely performed by selected-area electron diffraction in a transmission electron microscope, this method lacks statistical representativeness. With the advent of techniques like electron backscatter diffraction (EBSD), it is possible to calculate orientation relationships not only in single pairs of crystals of the same phase but in full thin sections and between different minerals. The interphase misorientation is calculated from two orientations of two adjacent crystals of different phases. A set of single misorientations is then used to calculate the misorientation distribution function (MDF), from where it is possible to identify a maximum and its crystallographic interpretation. If we then know the misorientation and the unit-cell parameters of the individual phases, the crystal-lographic relationships between the different phases can be described with the pairs of parallel crystal-lographic planes and the pairs of crystallographic directions. In this paper, I present examples of the use of interphase misorientation analysis on the transformation of calcite-aragonite, olivine-antigorite, magnetite-hematite, and on the study of orientation relationships between plagioclase-olivine-ilmenite in mid-ocean ridges gabbros (ODP Hole 735).