Rotational Invariance Research Articles

A statistical-based automatic detection of a low-contrast object in the ACR CT phantom for measuring contrast-to-noise ratio of CT images

Purpose. This study aimed to develop a new method for automated contrast-to-noise ratio (CNR) measurement using the low-contrast object in the ACR computed tomography (CT) phantom.Methods. The proposed method for CNR measurement was based on statistical criteria. A region of interest (ROI) was placed in a specific radial location and was then rotated around 360° in increments of 2°. At each position, the average CT number within the ROI was calculated. After one complete rotation, a profile of the average CT number around the full rotation was obtained. The center coordinate of the low-contrast object was determined from the maximum value of the profile. The CNR was calculated based on the average CT number and noise within the ROI in the low-contrast object and the ROI in the background, i.e., at the center of the phantom. The proposed method was used to evaluate CNR from images scanned with various phantom rotations, images with various noise levels (tube currents), and images from 25 CT scanners. The results were compared to a previous method based on a threshold approach.Results. The proposed method successfully placed the ROI properly in the center of a low-contrast object for variations of phantom rotation and tube current, whereas was not properly located in the center of the low-contrast object using the previous method. In addition, from 325 image samples of the 25 CT scanners, the proposed method successfully (100%) located the ROI within the low-contrast objects of all images used. The success rate of the previous method was only 58%.Conclusion. A new method for measuring CNR in the ACR CT phantom has been proposed and implemented. It is more powerful than a previous method based on a threshold approach.

Robust block tensor PCA with F-norm projection framework

Tensor principal component analysis (TPCA), also known as Tucker decomposition, ensures that the extracted “core tensor” maximizes the variance of the sample projections. Nevertheless, this method is particularly susceptible to noise and outliers. This is due to the utilization of the squared F-norm as the distance metric. In addition, it lacks constraints on the discrepancies between the original tensors and the projected tensors. To address these issues, a novel tensor-based trigonometric projection framework is proposed using F-norm to measure projection distances. Tensor data are first processed utilizing a blocking recombination technique prior to projection, thus enhancing the representation of the data at a local spatio-temporal level. Then, we present a block TPCA with the F-norm metric (BTPCA-F) and develop an iterative greedy algorithm for solving BTPCA-F. Subsequently, regarding the F-norm projection relation as the “Pythagorean Theorem”, we provide three different objective functions, namely, the tangent, cosine and sine models. These three functions directly or indirectly achieve the two objectives of maximizing projection distances and minimizing reconstruction errors. The corresponding tangent, cosine and sine solution algorithms based on BTPCA-F (called tan-BTPCA-F, cos-BTPCA-F and sin-BTPCA-F) are presented to optimize the objective functions, respectively. The convergence and rotation invariance of these algorithms are rigorously proved theoretically and discussed in detail. Lastly, extensive experimental results illustrate that the proposed methods significantly outperform the existing TPCA and the related 2DPCA algorithms.

Robust Multimodal Image Matching Based on Radiation Invariant Phase Correlation

Abstract. Due to the influence of nonlinear radiation distortion and geometric deformation, achieving multimodal image matching remains a challenging task. To address these issues, this paper proposes a method called radiation invariant phase correlation (RIPC) to simultaneously estimate the rotation, scale, and displacement changes of multimodal image pairs. Firstly, based on the local structure characteristics of the image itself, we harness the nonlinear invariance of kernel canonical correlation analysis to devise the multimodal local self-correlation (MLSC) descriptor. This descriptor is resilient to nonlinear radiative differences, as well as local rotation and scale variations. Subsequently, we incorporate the log-polar coordinate transformation to capture the overall rotation and scale changes in the image, enabling independent representation of these factors on the Cartesian coordinate system. Finally, drawing upon the continuity of displacement estimation, as well as rotation and scale estimation, we construct a five-dimensional descriptor tailored for phase correlation. Extensive experiments conducted on five open-source datasets demonstrate that our proposed method surpasses state-of-the-art (SOTA) techniques in matching performance. Furthermore, our RIPC method achieves matching accuracy within 2-pixel threshold, which underscores its effectiveness in multimodal remote sensing image matching.

Robust Symbol Detection Based on Quaternion Neural Networks in Wireless Polarization-Shift-Keying Communications.

Quaternion neural networks (QNNs) form a class of neural networks constructed with quaternion numbers. They are suitable for processing 3-D features with fewer trainable free parameters than real-valued neural networks (RVNNs). This article proposes symbol detection in wireless polarization-shift-keying (PolSK) communications by employing QNNs. We demonstrate that quaternion plays a crucial role in the symbol detection of PolSK signals. Existing artificial-intelligence communication studies mainly focus on RVNN-based symbol detection in digital modulations having constellations in complex plane. However, in PolSK, information symbols are represented as the state of polarization, which can be mapped on the Poincare sphere and thus its symbols have a 3-D data structure. Quaternion algebra offers a unified representation to process 3-D data with rotational invariance and, therefore, it keeps the internal relationship among three components of a PolSK symbol. Hence, we can expect that QNNs learn the distribution of received symbols on the Poincare sphere with higher consistency to detect the transmitted symbols more efficiently than RVNNs. We compare PolSK symbol detection accuracy of two types of QNNs, RVNN, existing methods such as least-square and minimum-mean-square-error channel estimations, as well as detection knowing perfect channel state information (CSI). Simulation results including symbol error rate show that the proposed QNNs outperform the existing estimation methods and that they reach better results with two to three times fewer free parameters than the RVNN. We find that QNN processing will bring practical use of PolSK communications.

Biokinetic modeling approach to investigate the impact of rotational speed variations in modified rotating biological contactors for palm oil mill effluent treatment

Palm oil mill effluent (POME) contains high organic content, posing significant environmental challenges that demand effective treatment solutions. Conventional rotating biological contactor (RBC) used for POME treatment are limited by insufficient surface area for microbial growth and inefficient oxygen transfer, limiting their effectiveness. This study enhances RBC systems by incorporating bioballs to increase microbial attachment surfaces and improve treatment performance. Experiments were conducted at various rotational speeds, and biokinetic modeling was applied under unsteady-state conditions. The results showed that the RBC operated at 3 rpm achieved the highest removal efficiencies, with 67.4 % for SCOD, 92.4 % for TSS, and 73 % for NH3. The biokinetic model revealed that rotational speed did not significantly impact oxygen transfer, mainly during the aeration phase. Lower speeds optimized substrate degradation and microbial growth, while higher speeds caused biofilm detachment. The innovative use of bioballs improves POME treatment efficiency at lower speeds, offering a cost-effective solution.

Automated production of batched unclonable micro-patterns anti-counterfeiting labels with strong robustness and rapid recognition speed

Anti-counterfeiting technologies are indeed crucial for information security and protecting product authenticity. Traditional anti-counterfeiting methods have their limitations due to their clonable nature. Exploring new technologies, particularly those based on pixel-level textures, is a promising avenue to address the clonable issue due to high encoding capacity. However, research in this field is still in its early stages. This work introduces a new fluorescent anti-counterfeiting label technology with four key characteristics: efficient laser etching, high-throughput fabrication and segmentation, robustness aided by data augmentation, and an exceptionally high recognition speed. Specifically, the etching achieves a speed of 1,200 labels/3s, the high-throughput procedures yield a rate of 2,400 labels/4 min, and the total count is about 5.2 × 104 labels. The number of labels is further augmented to about 5.2 × 106 by implementing arbitrary rotation and brightness variation to enhance the robustness in the recognition procedure. We divide these labels into 44 categories based on differences in patterns. Utilizing machine learning methods, we have achieved a total recognition (including extraction and search process) time per label averaging 421.96 ms without classification, and 40.13 ms with classification. Specifically, the search process with classification is nearly fiftieth times shorter than the non-classification method, reaching 8.52 ms in average. The overall recognition time is much faster than previous works, and achieves an accuracy of over 98.7%. This work significantly increases the practical significance of pixel-level anti-counterfeiting labels.

A Base-Map-Guided Global Localization Solution for Heterogeneous Robots Using a Co-View Context Descriptor

With the continuous advancement of autonomous driving technology, an increasing number of high-definition (HD) maps have been generated and stored in geospatial databases. These HD maps can provide strong localization support for mobile robots equipped with light detection and ranging (LiDAR) sensors. However, the global localization of heterogeneous robots under complex environments remains challenging. Most of the existing point cloud global localization methods perform poorly due to the different perspective views of heterogeneous robots. Leveraging existing HD maps, this paper proposes a base-map-guided heterogeneous robots localization solution. A novel co-view context descriptor with rotational invariance is developed to represent the characteristics of heterogeneous point clouds in a unified manner. The pre-set base map is divided into virtual scans, each of which generates a candidate co-view context descriptor. These descriptors are assigned to robots before operations. By matching the query co-view context descriptors of a working robot with the assigned candidate descriptors, the coarse localization is achieved. Finally, the refined localization is done through point cloud registration. The proposed solution can be applied to both single-robot and multi-robot global localization scenarios, especially when communication is impaired. The heterogeneous datasets used for the experiments cover both indoor and outdoor scenarios, utilizing various scanning modes. The average rotation and translation errors are within 1° and 0.30 m, indicating the proposed solution can provide reliable localization support despite communication failures, even across heterogeneous robots.

Research on the Registration of Aerial Images of Cyclobalanopsis Natural Forest Based on Optimized Fast Sample Consensus Point Matching with SIFT Features

The effective management and conservation of forest resources hinge on accurate monitoring. Nonetheless, individual remote-sensing images captured by low-altitude unmanned aerial vehicles (UAVs) fail to encapsulate the entirety of a forest’s characteristics. The application of image-stitching technology to high-resolution drone imagery facilitates a prompt evaluation of forest resources, encompassing quantity, quality, and spatial distribution. This study introduces an improved SIFT algorithm designed to tackle the challenges of low matching rates and prolonged registration times encountered with forest images characterized by dense textures. By implementing the SIFT-OCT (SIFT omitting the initial scale space) approach, the algorithm bypasses the initial scale space, thereby reducing the number of ineffective feature points and augmenting processing efficiency. To bolster the SIFT algorithm’s resilience against rotation and illumination variations, and to furnish supplementary information for registration even when fewer valid feature points are available, a gradient location and orientation histogram (GLOH) descriptor is integrated. For feature matching, the more computationally efficient Manhattan distance is utilized to filter feature points, which further optimizes efficiency. The fast sample consensus (FSC) algorithm is then applied to remove mismatched point pairs, thus refining registration accuracy. This research also investigates the influence of vegetation coverage and image overlap rates on the algorithm’s efficacy, using five sets of Cyclobalanopsis natural forest images. Experimental outcomes reveal that the proposed method significantly reduces registration time by an average of 3.66 times compared to that of SIFT, 1.71 times compared to that of SIFT-OCT, 5.67 times compared to that of PSO-SIFT, and 3.42 times compared to that of KAZE, demonstrating its superior performance.

Efficient Semantic Segmentation for Large-Scale Agricultural Nursery Managements via Point Cloud-Based Neural Network

Remote sensing technology has found extensive application in agriculture, providing critical data for analysis. The advancement of semantic segmentation models significantly enhances the utilization of point cloud data, offering innovative technical support for modern horticulture in nursery environments, particularly in the area of plant cultivation. Semantic segmentation results aid in obtaining tree components, like canopies and trunks, and detailed data on tree growth environments. However, obtaining precise semantic segmentation results from large-scale areas can be challenging due to the vast number of points involved. Therefore, this paper introduces an improved model aimed at achieving superior performance for large-scale points. The model incorporates direction angles between points to improve local feature extraction and ensure rotational invariance. It also uses geometric and relative distance information for better adjustment of different neighboring point features. An external attention module extracts global spatial features, and an upsampling feature adjustment strategy integrates features from the encoder and decoder. A specialized dataset was created from real nursery environments for experiments. Results show that the improved model surpasses several point-based models, achieving a Mean Intersection over Union (mIoU) of 87.18%. This enhances the precision of nursery environment analysis and supports the advancement of autonomous nursery managements.

Probing the effects of broken symmetries in machine learning

Abstract Symmetry is one of the most central concepts in physics, and it is no surprise that it has also been widely adopted as an inductive bias for machine-learning models applied to the physical sciences. This is especially true for models targeting the properties of matter at the atomic scale. Both established and state-of-the-art approaches, with almost no exceptions, are built to be exactly equivariant to translations, permutations, and rotations of the atoms. Incorporating symmetries—rotations in particular—constrains the model design space and implies more complicated architectures that are often also computationally demanding. There are indications that unconstrained models can easily learn symmetries from data, and that doing so can even be beneficial for the accuracy of the model. We demonstrate that an unconstrained architecture can be trained to achieve a high degree of rotational invariance, testing the impacts of the small symmetry breaking in realistic scenarios involving simulations of gas-phase, liquid, and solid water. We focus specifically on physical observables that are likely to be affected—directly or indirectly—by non-invariant behavior under rotations, finding negligible consequences when the model is used in an interpolative, bulk, regime. Even for extrapolative gas-phase predictions, the model remains very stable, even though symmetry artifacts are noticeable. We also discuss strategies that can be used to systematically reduce the magnitude of symmetry breaking when it occurs, and assess their impact on the convergence of observables.

Joint range and velocity super-resolution estimation with Doppler effects for innovative OFDM-based RFA RadCom system

Conventional radar and communication signals face challenges when integrating for accurate sensing in dense electromagnetic environments, especially in scenarios involving high-velocity targets estimation. To address this issue, we propose the random frequency agile-orthogonal frequency division multiplexing-based radar and communication (RFA-OFDM-based RadCom) signal, a novel framework that combines RFA hopping radar signal and OFDM signal. This framework effectively handles high-velocity Doppler scenarios, enhancing electronic countermeasure capabilities. In high-velocity scenarios, achieving accurate range and velocity estimation is crucial. We introduce a comprehensive received signal model that considers intrapulse and intersubcarrier Doppler effects, often overlooked in traditional high-velocity contexts. The proposed two-phase hierarchical perceptual methodology enables joint super-resolution estimation using the shared signal. We transform the shared signal echo model into a uniform linear array-like model and employ the matrix decomposition algorithm based on bidirectional weighted frequency smoothing (BWFS-MD) for decoherence processing. Subsequently, the estimation of signal parameters via rotational invariance techniques (ESPRIT)-complementary integrated subspace fitting (E-CISF) algorithm accurately estimates joint range and velocity. Meanwhile, the contrastive analysis of the mutual impacts between radar and communication functions is conducted. Theoretical analysis and simulation results robustly validate the superior performance of the proposed BWFS-MD algorithm. Furthermore, considering the precision of joint range-velocity estimation, real-time constraints, and super-resolution capability (which is emphasized), the E-CSIF algorithm demonstrates the best overall performance from a comprehensive perspective.

Design and architecting of a broadband bullet-diamond shaped integrated frequency selective meta-surface absorber for aero-stealth platform.

The work report on architecture of integrated frequency selective meta-surface (IFSMS) absorbers for aerospace stealth applications. Fabricated IFSMS comprised of a pattern metasurface integrated with dielectric interlayer and conducting ground. Initially, a supercell (2 × 2-unit cell: 24 × 24 mm2) was designed with a fourfold topological symmetry. Supercell produces impedances (R), inductances (L), and capacitances (C) in tune with design on its interaction with microwave. RC performance was tested at variable incident transverse electric/magnetic (TE/TM) modes over, Θ, 0°-60° and at the normal incidence (TE), against a planer, clockwise rotation over, Φ, 0°-90°. The mode stability and rotational invariance was analyzed for displacement current- and power-density distributions. The impedance behavior and phase reversal S11 reflection coefficient studies revealed the emergence of mid-band Fabry-Perot mode distinguishing LC behavior of the circuit. The meta-pattern was manufactured by mask lithography using a customized resistive micro-carbon ink and imprinted onto dielectric/ground tile (dimension: 30 × 30 cm2). Structure-property relationship of the ink material was investigated using SEM, XRD, FTIR, UV-visible spectroscopy to reveled surface properties of imprinted material. The absorber was subjected to the free space measurements over C (4-8), X (8-12), and Ku (12-18GHz) bands, including pristine interlayer dielectrics. The simulated and experimental RC data was found to be in excellent agreement. The proposed IFSMS design is a potential candidate for the stealth application.

RP-Net: A Robust Polar Transformation Network for rotation-invariant face detection

Face detection is challenging in unconstrained environments, where it encounters various challenges such as orientation, pose, and occlusion. Deep convolutional neural networks, particularly cascaded ones, have greatly improved detection performance but still struggle with rotating objects due to limitations in the Cartesian coordinate system. Although data augmentation can mitigate this issue, it also increases computational demands. This paper introduces the Robust Polar Transformation Network (RP-Net) for rotation-invariant face detection. RP-Net converts the complex rotational problem into a simpler translational one to enhance feature extraction and computational efficiency. Additionally, the Advanced Spatial-Channel Restoration (ASCR) module optimizes facial landmark detection within polar domains and restores critical details lost during transformation. Experimental results on benchmark datasets show that RP-Net significantly improves rotation invariance over traditional CNNs and surpasses several state-of-the-art rotation-invariant face detection methods.

Validating Gaia DR3 Pulsating Variable Classifications with TESS. II. 360+ Eclipsing Binaries with δ Scuti and γ Doradus Components

A comprehensive analysis of 75,369 stars from Gaia DR3 has led to the serendipitous discovery of 380 eclipsing binaries featuring δ Scuti and γ Doradus pulsators, 45 eclipsing binaries exhibiting rotational variability, and 8 new RR Lyrae stars. Moreover, this study has confirmed 12,145 δ Scuti stars (including 8710 new) and 8192 γ Doradus stars (including 7531 new). These findings substantially expand the existing catalogs of δ Scuti and γ Doradus stars, now encompassing 98,968 and 19,466 stars, respectively, providing a valuable resource for future studies. The remarkable number of newly identified pulsating binaries underscores the significance of this project in validating Gaia variables.

Representing Noisy Image Without Denoising.

A long-standing topic in artificial intelligence is the effective recognition of patterns from noisy images. In this regard, the recent data-driven paradigm considers 1) improving the representation robustness by adding noisy samples in training phase (i.e., data augmentation) or 2) pre-processing the noisy image by learning to solve the inverse problem (i.e., image denoising). However, such methods generally exhibit inefficient process and unstable result, limiting their practical applications. In this paper, we explore a non-learning paradigm that aims to derive robust representation directly from noisy images, without the denoising as pre-processing. Here, the noise-robust representation is designed as Fractional-order Moments in Radon space (FMR), with also beneficial properties of orthogonality and rotation invariance. Unlike earlier integer-order methods, our work is a more generic design taking such classical methods as special cases, and the introduced fractional-order parameter offers time-frequency analysis capability that is not available in classical methods. Formally, both implicit and explicit paths for constructing the FMR are discussed in detail. Extensive simulation experiments and robust visual applications are provided to demonstrate the uniqueness and usefulness of our FMR, especially for noise robustness, rotation invariance, and time-frequency discriminability.

A High-Precision, Ultra-Short Baseline Positioning Method for Full Sea Depth

To fulfill the demand for high-precision underwater acoustic positioning at full sea depth, an ultra-short baseline (USBL) positioning method with the square array based on the least squares estimating signal parameters via rotational invariance techniques (LS-ESPRIT) algorithm is presented in this paper. A combination of beam tracking and beamforming is employed to improve the accuracy of direction-of-arrival (DOA) estimation and, consequently, enhance overall positioning accuracy. In order to mitigate the issue of position jumping resulting from phase ambiguity in traditional four-element cross arrays, we have improved the stability of the positioning algorithm by utilizing a multi-element square array and employing the LS-ESPRIT algorithm for DOA estimation. Furthermore, the signal detection method integrating the correlation coefficient and ascending/descending chirp signals is employed to enhance the reliability of the location algorithm. Simulation analysis and experimental results demonstrate that the proposed algorithm effectively enhances positioning accuracy and improves the problem of jumping in positioning results.

Rotation-invariant image recognition using interconnected floating-gate phototransistor

Rotational invariance is fundamental for robust image recognition systems, ensuring accurate analysis irrespective of image orientation. However, existing systems predominantly reliant on software often encounter challenges such as increased computational demands and compromises between processing speed and accuracy. In this study, we propose leveraging the interconnected floating-gate (FG) structure as an effective hardware-level solution to achieve rotational invariance in image recognition. Our design features a reconfigurable two-dimensional material FG phototransistor array, where each processing unit integrates four sensory devices sharing a common FG. This configuration facilitates uniform distribution of stored charges across the interconnected FG layer, which is typically made of metal, enabling consistent application of a single weight matrix to images across varied rotational conditions. The photoactive material, tungsten diselenide (WSe2), possesses a distinctive bipolar property that facilitates both hole and electron tunneling into the FG layer. This property directly contributes to the efficiency of state transition within the setup and improves its overall adaptability. In this manner, our design achieves stable and predictable outputs in recognizing identical digital numbers regardless of their rotation, while also demonstrating variable performance essential for accurately distinguishing between different digital numbers. This dual capability guarantees both the adaptability and precision required for rotation-invariant image recognition, suggesting that our work may open up a promising venue for exploring advanced hardware designs, such as optimized interconnected FG architectures, tailored for enhancing recognition accuracy and efficiency in the field of intelligent visual systems.

Representing crystal potential energy surfaces via a stationary-point network

A cornerstone of materials physics is the principle that all properties of crystalline systems are fundamentally determined based on the underlying potential energy surface (PES), which affects the structural stability and structure–property relations. Finding a proper representation of the PES is essential for the implementation of this principle, which has attracted considerable interest over the past decades; however, progress has been impeded by the lack of a firm theoretical basis for effectively exploring the vast configurational space. Here, we introduce a new method for constructing a crystal PES by using a solution landscape with an improved high-index saddle dynamic scheme, in which generalized coordinates are introduced to encode crystals that satisfy translational and rotational invariance. To represent the PES of periodic crystalline structures, we devise an advanced graph-based stationary-point network to visualize and analyze complex PES terrains, with nodes and edges representing stationary points and their connections, respectively. Crystalline GaN and Si are considered as exemplary case studies, and our newly devised approach leads to the discovery of several hidden transition paths with low enthalpy barriers associated with multistep processes; thus, the effectiveness of the approach is validated. Our method combined with the first-principles calculations offers a viable solution to long-standing problems associated with crystal PESs, such as the kinetics of activated processes, materials stability and synthesizability. These findings represent a notable advancement and offer a basis for future research.

Heavy flavor production under a strong magnetic field

The magnetic field created in high energy nuclear collisions will affect the QCD dynamical processes, such as the heavy quark production which happens in the initial stage of the collisions. We calculate in a strong magnetic field the heavy quark production cross section of the process gg→QQ¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ gg\ o Q\\overline{Q} $$\\end{document} at leading order and the corresponding transverse momentum distribution in nucleus-nucleus collisions. In comparison to the QED process, the heavy quark production is dominated by the unique QCD channel with gluon self-interaction. Due to the dimension reduction of quark phase space in a strong magnetic field, the production is concentrated in a very narrow energy region above the threshold. Since the rotational invariance is broken in a magnetic field, the production becomes anisotropic.

Decoding Substrate Selectivity of an Archaeal RlmCD-like Methyltransferase Through Its Salient Traits.

5-Methyluridine (m5U) rRNA modifications frequently occur at U747 and U1939 (Escherichia coli numbering) in domains II and IV of the 23S rRNA in Gram-negative bacteria, with the help of S-adenosyl-l-methionine (SAM)-dependent rRNA methyltransferases (MTases), RlmC and RlmD, respectively. In contrast, Gram-positive bacteria utilize a single SAM-dependent rRNA MTase, RlmCD, to modify both corresponding sites. Notably, certain archaea, specifically within the Thermococcales group, have been found to possess two genes encoding SAM-dependent archaeal (tRNA and rRNA) m5U (Arm5U) MTases. Among these, a tRNA-specific Arm5U MTase (PabTrmU54) has already been characterized. This study focused on the structural and functional characterization of the rRNA-specific Arm5U MTase from the hyperthermophilic archaeon Pyrococcus horikoshii (PhRlmCD). An in-depth structural examination revealed a dynamic hinge movement induced by the replacement of the iron-sulfur cluster with disulfide bonds, obstructing the substrate-binding site. It revealed distinctive characteristics of PhRlmCD, including elongated positively charged loops in the central domain and rotational variations in the TRAM domain, which influence substrate selectivity. Additionally, the results suggested that two potential mini-rRNA fragments interact in a similar manner with PhRlmCD at a positively charged cleft at the interface of domains and facilitate dual MTase activities akin to the protein RlmCD. Altogether, these observations showed that Arm5U MTases originated from horizontal gene transfer events, most likely from Gram-positive bacteria.