Transformation Matrix Research Articles

Optimal Design Problem of Dragon Dance Team Path Based on Rotation Matrix

In this paper, an accurate collision detection method is proposed for the collision problem during the traveling of the traditional event - Bench Dragon Dance Team. It needs to consider the collision problem when the Bench Dragons are traveling, but the existing literature has not provided an effective detection means for this specific model. Through geometric analysis, this paper reveals the mechanism of collision occurrence, models the dragon body approximately as a rectangle, and utilizes the rotation matrix transformation for collision detection. In order to further improve the detection accuracy, this paper adopts an iterative search algorithm to optimize and calibrate the model. This paper analyzes the critical termination moment, at this moment, the Dragon Dance Team cannot continue coiling along the isometric spiral. With this model, collisions among the benches can be accurately predicted and avoided. Eventually, when the time t = 566.2 s, the Dragon Dance Team's coiling-in maneuver is completed, and no collision occurs between the benches, at which time the coordinates of the dragon's head position are (0.01, -3.42). The model proposed in this paper effectively solves the collision problem during the traveling process of the bench dragon, and provides a scientific collision detection method for similar scenarios.

Noninvasive megapixel fluorescence microscopy through scattering layers by a virtual incoherent reflection matrix.

Optical-resolution fluorescence imaging through and within complex samples presents a major challenge due to random light scattering, with substantial implications across multiple fields. While considerable advancements in coherent imaging through severe multiple scattering have been recently introduced by reflection matrix processing, approaches that tackle scattering in incoherent fluorescence imaging have been limited to sparse targets, require high-resolution control of the illumination or detection wavefronts, or require a very large number of measurements. Here, we present an approach that allows the adaptation of well-established reflection matrix techniques to scattering compensation in incoherent fluorescence imaging. We experimentally demonstrate that a small number of conventional wide-field fluorescence microscope images acquired under unknown random illuminations can effectively be used to construct a virtual fluorescence-based reflection matrix. Processing this matrix by an adapted matrix-based scattering compensation algorithm allows reconstructing megapixel-scale images from <150 acquired frames, without any spatial light modulators or computationally intensive processing.

A Versatile Gyro Inclinometer, Adaptive to the Borehole Trajectory, Based on a Uniaxial Angular Rate Sensor

Introduction. An approach to designing a gyroscopic inclinometer (GI) based on a single uniaxial angular rate sensor (ARS) is developed. It is argued that such an ARS should be considered a modification of a longitudinal GI scheme, preserving the well-known disadvantages of its performance characteristics. The latter include a lack of adaptability to the trajectory, i.e., commensurability of GI errors at different zenith angles. This work sets out to develop a scheme with one ARS in order to achieve a multiple increase in the accuracy of azimuth measurements for vertical and adjacent-to-the-vertical boreholes when the GI is operated in continuous mode.Aim. To make a GI based on a uniaxial angular velocity sensor more adaptive to the borehole trajectory thought its design modification and a comparative analysis of errors.Materials and methods. Algorithms for ideal operation of the proposed scheme in continuous mode are synthesized based on matrix transformations of coordinates and Euler equations. The properties of orientation errors are examined using linearization methods, integral calculus, fundamentals of the calculus of variations, and the theory of linear differential equations.Results. The adaptivity of the modified GI scheme to the borehole trajectory was achieved by means of a structurally provided deviation of the ARS sensitivity axis by a certain angle of non-orthogonality to the GI longitudinal axis. When designing a GI based on the developed approach, it is possible to realize the value of this angle of 20°. For this angle, the increase in the compassing error does not exceed the uncertainty of the ARS drift statistical characteristics, while achieving an effective level of adaptivity to the borehole trajectory in continuous mode.Conclusion. The developed scheme makes it possible to significantly reduce the influence of the ARS drift on the accuracy of azimuth calculation in the transitional zenith angles area (from vertical to directional boreholes) in comparison with the well-known longitudinal scheme, thereby maintaining an increased initial azimuth accuracy during movement in the initial alignment at the wellhead.

Network model for magnetic higher-order topological phases

We propose a network-model realization of magnetic higher-order topological phases (HOTPs) in the presence of the combined space-time symmetry C4T—the product of a fourfold rotation and time-reversal symmetry. We show that the system possesses two types of HOTPs. The first type, analogous to Floquet topology, generates a total of eight corner modes at 0 or π eigenphase, while the second type, hidden behind a weak topological phase, yields a unique phase with eight corner modes at ±π/2 eigenphase (after gapping out the counterpropagating edge states), arising from the product of particle-hole and phase-rotation symmetry. By using a bulk Z4 topological index (Q), we found both HOTPs have Q=2, whereas Q=0 for the trivial and the conventional weak topological phase. Together with a Z2 topological index associated with the reflection matrix, we are able to fully distinguish all phases. Our work motivates further studies on magnetic topological phases and symmetry-protected 2π/n boundary modes, as well as suggesting that such phases may find their experimental realization in coupled-ring-resonator networks. Published by the American Physical Society 2024

Fast Type-II Hartley Transform Algorithms for Short-Length Input Sequences

This paper presents the type-II fast discrete Hartley transform (DHT-II) algorithms for input data sequences of lengths from 2 to 8. The starting point for developing the eight algorithms is the representation of DHT-II as a matrix–vector product. The underlying matrices usually have a good block structure. These matrices must then be successfully factorized to obtain a computational procedure that reduces the number of operations in computing the matrix–vector product. In some cases, it is necessary to pre-decompose the original matrices into submatrices and rearrange the rows and/or columns of the resulting matrices to find the factorizations that would substantially save the arithmetic operations. As a result of applying the pointed transformations, we synthesized the final algorithms with reduced computational complexity. The correctness of the obtained algorithmic solutions was theoretically justified using the rigorous mathematical background of each of them. Then, the complex algorithms were further tested using the MATLAB R2023b software to confirm their performance. Finally, an evaluation of the computational complexity for each obtained solution was compared with the computational complexity of the direct calculation of the matrix–vector product and existing fast DHT-II algorithms. The obtained factorizations of the DHT-II transformation matrices on average reduce the number of additions by 5% and the number of multiplications by 73% compared with the direct calculation of the matrix–vector product.

Automated image registration of RGB, hyperspectral and chlorophyll fluorescence imaging data

BackgroundThe early and specific detection of abiotic and biotic stresses, particularly their combinations, is a major challenge for maintaining and increasing plant productivity in sustainable agriculture under changing environmental conditions. Optical imaging techniques enable cost-efficient and non-destructive quantification of plant stress states. Monomodal detection of certain stressors is usually based on non-specific/indirect features and therefore is commonly limited in their cross-specificity to other stressors. The fusion of multi-domain sensor systems can provide more potentially discriminative features for machine learning models and potentially provide synergistic information to increase cross-specificity in plant disease detection when image data are fused at the pixel level.ResultsIn this study, we demonstrate successful multi-modal image registration of RGB, hyperspectral (HSI) and chlorophyll fluorescence (ChlF) kinetics data at the pixel level for high-throughput phenotyping of A. thaliana grown in Multi-well plates and an assay with detached leaf discs of Rosa × hybrida inoculated with the black spot disease-inducing fungus Diplocarpon rosae. Here, we showcase the effects of (i) selection of reference image selection, (ii) different registrations methods and (iii) frame selection on the performance of image registration via affine transform. In addition, we developed a combined approach for registration methods through NCC-based selection for each file, resulting in a robust and accurate approach that sacrifices computational time. Since image data encompass multiple objects, the initial coarse image registration using a global transformation matrix exhibited heterogeneity across different image regions. By employing an additional fine registration on the object-separated image data, we achieved a high overlap ratio. Specifically, for the A. thaliana test set, the overlap ratios (ORConvex) were 98.0 ± 2.3% for RGB-to-ChlF and 96.6 ± 4.2% for HSI-to-ChlF. For the Rosa × hybrida test set, the values were 98.9 ± 0.5% for RGB-to-ChlF and 98.3 ± 1.3% for HSI-to-ChlF.ConclusionThe presented multi-modal imaging pipeline enables high-throughput, high-dimensional phenotyping of different plant species with respect to various biotic or abiotic stressors. This paves the way for in-depth studies investigating the correlative relationships of the multi-domain data or the performance enhancement of machine learning models via multi modal image fusion.

Diophantine analysis of the orbits of any given point under a family of diagonal matrix transformations

Diophantine analysis of the orbits of any given point under a family of diagonal matrix transformations

Analysis of the Radial Force of a Piezoelectric Actuator with Interdigitated Spiral Electrodes.

The actuator is a critical component of the micromanipulator. By utilizing the properties of expansion and contraction, the piezoelectric actuator enables the manipulator to handle and grasp miniature objects during micromanipulation. However, in piezoelectric ceramic disc actuators with conventional surface electrode configurations, the actuating force generated in the radial direction is relatively limited. When used as the actuation element of the manipulator, achieving regulation over a wide range of operating strokes becomes challenging. Therefore, altering the electrode structure is necessary to generate a greater radial force, thus enhancing the positioning and grasping capabilities of the operating arm. This paper investigates a piezoelectric actuator with interdigitated spiral electrodes, featuring a constant pitch between adjacent electrodes. The radial force was tested under mechanical clamping conditions, and the influence of the electrical signal was examined. The characteristics of the electrode structure were described, and the working principles of the piezoelectric actuators were analyzed. Theoretical equations were derived for the macroscopic characterization of the radial clamping force of the actuator, based on the piezoelectric constitutive equation, geometric principles, and Bond matrix transformation relationships. A finite element model was developed, reflecting the features of the electrode structure, and finite element simulations were employed to verify the theoretical equations for radial force. To prepare the samples, encircled interdigitated spiral electrode lines were printed on the PZT-52 piezoelectric ceramic disc using a screen printing method. The clamping force experimental platform was established, and experiments on the clamping radial force were conducted with electrical signals of varying waveforms, frequencies, and voltages. The experimental results show that the piezoelectric ceramic disc actuator with an interdigitated spiral electrode line structure, when excited by a stable sine wave operating at 200 V and 0.2 Hz, generated a peak force of 0.37 N. It was 1.76 times greater than that produced by a previously utilized piezoelectric disc with conventional electrode structures.

Fundamental theorems of summability theory for double sequences via stretching by blocks

This paper extends fundamental theorems of summability theory to double sequences using stretching by blocks technique. We prove Steinhaus- and Buck-type theorems for double sequences, characterizing sequences that resist summability by RH-regular matrices and providing conditions for P-convergence. The preservation of P-divergence under block stretching is demonstrated, and a characterization of P-limit points via this method is established. We also show the impossibility of summing all block stretchings with a single RH-regular matrix. These results provide a more comprehensive framework for analyzing double sequences under matrix transformations.

Achieving High Piezoelectric Performance Across Multidomains Design in K(Ta,Nb)O3-Based Lead-free Single Crystals.

In light of environmental issues, the lead-free ferroelectric single crystal K(Ta1-xNbx)O3 (KTN) has attracted considerable interest due to its excellent piezoelectric properties. This research focus on improving the piezoelectric performance of KTN by engineering domains through polarization in the [011]c direction. The full-matrix parameters of KTN crystals after polarization along the [011] direction were determined. The finding reveal that KTN polarized in the nonspontaneous polarization direction [011]c exhibits higher piezoelectric constants (d33 = 156 pC/N, d15 = 155 pC/N) and dielectric constants (ε33T ∼ 2337). Additionally, tensor matrix transformation techniques were utilized to analyze the directional dependence of the piezoelectric (d33*), dielectric (ε33T*), elastic (s33E*) constants, and electromechanical coupling coefficient (k33*). The results indicate that these constants reach their maximum values along the polarized [011]c direction. A comparison of the experimental polarization values in the [011]c direction with those calculated for a single-domain state, demonstrates that ferroelectric domains in KTN crystals contribute significantly to the piezoelectric properties. Finally, polarized light microscopy was used to conduct a detailed analysis of the domain structure in KTN single crystals, revealing various orientations and sizes of domain walls. This research offers strategies for optimizing piezoelectric performance.

Lie symmetry method to discuss the optimal system of Lie subalgebras and similarity solutions for shock propagation in a perfectly conducting dusty gas with magnetic field in rotating medium

In this paper, the similarity solutions for the shock wave propagation in a perfectly conducting dusty gas under the effect of axial or azimuthal magnetic field in the case of rotating medium by using Lie symmetry method have been discussed. The optimal system of one-dimensional Lie subalgebras related to the hyperbolic system of nonlinear partial differential equations had been constructed by using general invariant function and general adjoint transformation matrix. The optimal system is the collection of inequivalent optimal classes, which provides crucial information regarding different types of the similarity solutions. On the basis of the optimal system, we have discussed all possible similarity solutions for inequivalent optimal classes individually. Also, we have found that the similarity solutions exist in two cases for power law shock path and in one case with exponential law shock path. The shock wave decay is due to an increment in the physical parameter such as shock Cowling number or non-idealness parameter or adiabatic exponent or rotational parameter. For smaller value of the ratio of density of solid particles to initial species density of the gas i.e. [Formula: see text], the shock strength decreases with an increment in the mass fraction of solid particles in the mixture [Formula: see text], but the shock strength decreases as [Formula: see text] increases for [Formula: see text]. Also, the shock strength increases with an increment in [Formula: see text] at constant [Formula: see text]. It is observed that the shock wave is stronger in the presence of axial magnetic field as compared to azimuthal magnetic field.

LGSur‐Net: A Local Gaussian Surface Representation Network for Upsampling Highly Sparse Point Cloud

AbstractWe introduce LGSur‐Net, an end‐to‐end deep learning architecture, engineered for the upsampling of sparse point clouds. LGSur‐Net harnesses a trainable Gaussian local representation by positioning a series of Gaussian functions on an oriented plane, complemented by the optimization of individual covariance matrices. The integration of parametric factors allows for the encoding of the plane's rotational dynamics and Gaussian weightings into a linear transformation matrix. Then we extract the feature maps from the point cloud and its adjoining edges and learn the local Gaussian depictions to accurately model the shape's local geometry through an attention‐based network. The Gaussian representation's inherent high‐order continuity endows LGSur‐Net with the natural ability to predict surface normals and support upsampling to any specified resolution. Comprehensive experiments validate that LGSur‐Net efficiently learns from sparse data inputs, surpassing the performance of existing state‐of‐the‐art upsampling methods. Our code is publicly available at https://github.com/Rangiant5b72/LGSur-Net.

A Matrix-Based Approach to Unified Synthesis of Planar Four-Bar Mechanisms for Motion Generation With Position, Velocity, and Acceleration Constraints

Abstract This paper introduces a novel matrix-based approach for the simultaneous type and dimensional synthesis of planar four-bar linkage mechanisms, accommodating various practical constraints, including position, velocity, acceleration, and joint placements. Traditional design processes segregate type synthesis, the determination of joint and link configurations, from dimensional synthesis, which involves specifying link sizes and pivot locations. This segregation often leads to complexities in addressing the complete design challenge. The novel methodology proposed in this paper departs from the conventional sequential design approach by concurrently evaluating type and dimensional parameters using a data-driven matrix formulation. The crux of the paper’s methodology involves formulating a singular design equation through a transformation matrix, parameterized by the Cartesian parameters of the mechanism’s dyads. This formulation linearly expresses a broad range of constraints, facilitating the identification of viable solutions through singular value decomposition and null space analysis. This integrated approach not only simplifies the synthesis process but also provides direct insights into the mechanism’s parameters, encompassing both type and dimensions, thereby obviating the need for further interpretative steps common to the use of quaternions and kinematic mapping. In essence, the paper presents two main contributions: the development of a unified design equation capable of encompassing a wide array of constraints within the mechanism synthesis process, and the introduction of an algorithm that effectively identifies all potential planar four-bar linkage mechanisms by accurately satisfying up to five constraints. This approach promises to enhance the design and optimization of mechanical systems by offering a more holistic and efficient pathway to mechanism synthesis.

A New Encryption Algorithm Utilizing DNA Subsequence Operations for Color Images

The computer network has fundamentally transformed modern interactions, enabling the effortless transmission of multimedia data. However, the openness of these networks necessitates heightened attention to the security and confidentiality of multimedia content. Digital images, being a crucial component of multimedia communications, require robust protection measures, as their security has become a global concern. Traditional color image encryption/decryption algorithms, such as DES, IDEA, and AES, are unsuitable for image encryption due to the diverse storage formats of images, highlighting the urgent need for innovative encryption techniques. Chaos-based cryptosystems have emerged as a prominent research focus due to their properties of randomness, high sensitivity to initial conditions, and unpredictability. These algorithms typically operate in two phases: shuffling and replacement. During the shuffling phase, the positions of the pixels are altered using chaotic sequences or matrix transformations, which are simple to implement and enhance encryption. However, since only the pixel positions are modified and not the pixel values, the encrypted image’s histogram remains identical to the original, making it vulnerable to statistical attacks. In the replacement phase, chaotic sequences alter the pixel values. This research introduces a novel encryption technique for color images (RGB type) based on DNA subsequence operations to secure these images, which often contain critical information, from potential cyber-attacks. The suggested method includes two main components: a high-speed permutation process and adaptive diffusion. When implemented in the MATLAB software environment, the approach yielded promising results, such as NPCR values exceeding 98.9% and UACI values at around 32.9%, demonstrating its effectiveness in key cryptographic parameters. Security analyses, including histograms and Chi-square tests, were initially conducted, with passing Chi-square test outcomes for all channels; the correlation coefficient between adjacent pixels was also calculated. Additionally, entropy values were computed, achieving a minimum entropy of 7.0, indicating a high level of randomness. The method was tested on specific images, such as all-black and all-white images, and evaluated for resistance to noise and occlusion attacks. Finally, a comparison of the proposed algorithm’s NPCR and UAC values with those of existing methods demonstrated its superior performance and suitability.

Research on High Power Density Flyback Converter With a New Passive Lossless Snubber

ABSTRACTThis paper proposes a flyback converter with a new passive lossless snubber. It eliminates the power dissipation of the traditional RCD snubber, while providing protection against MOS breakdown from energy stored in the power‐transformer leakage. This energy is used to power the power chip, which simplifies the design of the transformer. Meanwhile, an optimal design method for high power density planar transformers is presented. Applying the principle of flux cancellation, a matrix transformer that originally needed an independent magnetic core was integrated into a single magnetic core to reduce the volume of the core. This method effectively reduces the printed circuit board (PCB) layer number of the planar transformer and increases the possibility of the application of the planar transformer in the flyback converter. The detailed operation principle and design considerations are presented. Finally, a multi‐output flyback converter with a frequency of 100 kHz is designed to verify the practical performance of the structure.

“What Treasure is Hid in Milk”?: Transforming Bodily Fluids in the English Early Modern Receipt Book

Abstract: Early modern scholars have traced the use of milk as a culinary metaphor in Renaissance drama. Milk was understood to be an already transformed and actively transforming fluid. Sixteenth-century receipt books from the Folger Shakespeare Library help contextualize these symbolic resonances in milk’s material substance as it manifests in the receipt book’s utilitarian prescriptions. This paper uses genre studies to argue that milk offers an additional node on the receipt book’s matrices of transformation and to highlight the early modern receipt book as a valuable site of inquiry for ecofeminist and new materialist scholarship.

Uncovering SPP1+ Macrophage, Neutrophils and Their Related Diagnostic Biomarkers in Intracranial Aneurysm and Subarachnoid Hemorrhage.

Intracranial aneurysms (IA) frequently cause subarachnoid hemorrhage (SAH) and have poor prognosis. However, the molecular mechanisms and diagnostic biomarkers associated with IA and ruptured IA (rIA) remain poorly understood. In this study, single-cell and transcriptome datasets were obtained from the GEO database. The cell populations were annotated to identify potential pathogenic subpopulations, followed by intercellular communication, pseudotime, and SCENIC analyses. Proteome-wide and transcriptome-wide Mendelian randomization (MR) analyses were conducted to identify risk factors for IA and SAH. The major pathological changes and diagnostic biomarkers of IA and SAH were identified based on the transcriptome datasets. A clinical cohort was established to identify the diagnostic biomarkers and validate the results. Macrophages and neutrophils were predominantly increased in IA and rIA tissues, and neutrophils were markedly upregulated in the blood of SAH patients. SPP1+ Macrophage was progressively elevated in aneurysms, promoting vascular smooth muscle cell (VSMC) phenotypic transformation and collagen matrix remodeling through the SPP1 and TGF-β pathways. Furthermore, HIF1α regulon was enriched in SPP1+ Macrophage, mediating inflammation and metabolic reprogramming, which contributed to IA progression. Integrated MR analysis identified CD36 as a risk factor for both IA and SAH, and it has been recognized as an effective blood biomarker for SAH. Neutrophils and their related indicators have emerged as excellent biomarkers of SAH in clinical cohorts. This study highlighted the detrimental role of SPP1+ Macrophage in IA and SAH using single-cell sequencing and MR analyses. CD36 was identified as a risk factor for IA and SAH and was also an efficient blood biomarker for SAH. In a clinical cohort, neutrophils and related indicators were valuable for the early diagnosis of SAH.

Efficient conversion of Euler angles to quaternion for practical aerospace applications

Abstract Current methods for converting Euler angles to a rotation quaternion are computationally intensive and have limited practical applications in aerospace. This study introduces an efficient approach that directly converts Euler angles in any desired sequence to a rotation quaternion, eliminating the need for intermediate Euler angle transformation matrices, which leads to a significant improvement in computational efficiency. Moreover, it is general because it works with all 12 possible sequences of rotations. A case study is presented, demonstrating the application of the algorithm in converting between the launch frame and the missile frame of a vertical takeoff vertical landing (VTVL) rocket. The results show more than a ninefold improvement in computational efficiency compared to the classical Euler angle method while maintaining consistency of results.

New sequence spaces derived from the Catalan–Motzkin matrix and related matrix transformations

UDC 512.6 We consider the domain of a conservative matrix involving Catalan and Motzkin numbers in the sequence spaces c and c 0 . Moreover, the α -, β -, and γ -duals are given and some matrix mappings are presented on the resulting spaces.

Scene Measurement Method Based on Fusion of Image Sequence and Improved LiDAR SLAM

To address the issue that sparse point cloud maps constructed by SLAM cannot provide detailed information about measured objects, and image sequence-based measurement methods have problems with large data volume and cumulative errors, this paper proposes a scene measurement method that integrates image sequences with an improved LiDAR SLAM. By introducing plane features, the positioning accuracy of LiDAR SLAM is enhanced, and real-time odometry poses are generated. Simultaneously, the system captures image sequences of the measured object using synchronized cameras, and NeRF is used for 3D reconstruction. Time synchronization and data registration between the LiDAR and camera data frames with identical timestamps are achieved. Finally, the least squares method and ICP algorithm are employed to compute the scale factor s and transformation matrices R and t between different point clouds from LiDAR and NeRF reconstruction. Then, the precise measurement of the objects could be implemented. Experimental results demonstrate that this method significantly improves measurement accuracy, with an average error within 10 mm and 1°, providing a robust and reliable solution for scene measurement.