Dimensional Transformation Research Articles

Power Domain Superimposed Modulation Method Based on Dimensional Level Transformation and 5D Constellation Shaping

Power Domain Superimposed Modulation Method Based on Dimensional Level Transformation and 5D Constellation Shaping

Volume and Euler classes in bounded cohomology of transformation groups

Abstract Let $M$ be an oriented smooth manifold and $\operatorname{Homeo}\!(M,\omega )$ the group of measure preserving homeomorphisms of $M$ , where $\omega$ is a finite measure induced by a volume form. In this paper, we define volume and Euler classes in bounded cohomology of an infinite dimensional transformation group $\operatorname{Homeo}_0\!(M,\omega )$ and $\operatorname{Homeo}_+\!(M,\omega )$ , respectively, and in several cases prove their non-triviality. More precisely, we define: • Volume classes in $\operatorname{H}_b^n(\operatorname{Homeo}_0\!(M,\omega ))$ , where $M$ is a hyperbolic manifold of dimension $n$ . • Euler classes in $\operatorname{H}_b^2(\operatorname{Homeo}_+(S,\omega ))$ , where $S$ is an oriented closed hyperbolic surface. We show that Euler classes have positive norms for any closed hyperbolic surface and volume classes have positive norms for all hyperbolic surfaces and certain hyperbolic $3$ -manifolds; hence, they are non-trivial.

Exploring high-order correlation for hyperspectral image denoising with hypergraph convolutional network

High-order correlation is an important property of hyperspectral images (HSIs) and has been widely investigated in model-based HSI denoising. However, the existing deep learning-based HSI denoising approaches have not fully utilized the high-order correlation. Hypergraph convolutional networks have shown great potential in capturing the high-order correlation. Therefore, in this paper, we propose a novel HSI denoising method by employing hypergraph convolution to characterize the high-order correlation at the patch level. Specifically, our framework is a symmetrically skip-connected 3D encoder–decoder architecture, which enhances the extraction and utilization of local features. Furthermore, to integrate competently the hypergraph convolutional modules into the 3D framework, we devise a dimensional transformation module that facilitates the fusion of 3D convolution and hypergraph convolution. Notably, in the hypergraph convolution operation, we use a data-driven technique to acquire the incidence matrix of a hypergraph, efficiently constructing the HSI into a high-order structure. Our proposed method excels in HSI denoising performance compared to state-of-the-art approaches, evidenced by extensive experiments on synthetic and real-world noisy HSIs.

Application of two dimensional correlation Fourier Transform Infrared spectroscopy (2D-COS-FTIR) to the quantification of carbohydrates in milk powder

The importance of milk and its products accelerated their adulteration as well as their characterization in term of techniques used, composition determination and adulteration quantification. Fourier Transform Infrared spectroscopy (FTIR) is one of the most widely used and increasingly developed methods to identify chemical contaminations and determine their concentrations. This study employs FTIR and two dimensional correlation (2D-COS) spectroscopies to detect milk powder adulteration with sucrose, lactose and starch in the concentrations range from 0.0 % to 6.0 % w/w. With the help of synchronous 2D-COS-FTIR spectra, the FTIR regions from 830 to 930 and 930–1200 cm−1 were determined as the qualified regions for the detection and carrying out quantitative analysis of milk adultered carbohydrates. Based on the area beneath the corresponding region or the height of a specific band limits of detection were determined as 0.25, 1.2 and 1.5 % for sucrose, starch and lactose respectively. The method was applied on commercial milk powder samples and one sample was assigned to have been adultered with 4 % sucrose. FTIR spectroscopy combined with 2D-COS offers an advanced tool for rapid screening and quantification of milk adulteration.

NLNet: A narrow-channel lightweight network for finger multimodal recognition

Multimodal biometric recognition has attracted more and more attention in recent years because of its security and accuracy. Compared with the single use of fingerprint or finger vein feature recognition, the multi-modal feature recognition method based on fingerprint and finger vein significantly improves the recognition performance. However, most of the multi-modal feature recognition networks have the disadvantages of large number of parameters and high training cost. In this paper, a narrow-channel lightweight network NLNet for fingerprint and finger vein recognition is proposed. The network adopts asymmetric narrow channel structure for lightweight design, and combines shallow network to improve the discriminating nature of the extracted features, which significantly reduces the model parameters and computation. In addition, a lightweight feature extraction module for building feature extraction branches is designed for NLNet. This module takes dimensional transformation feature extraction as the backbone, and the joint extension module and attention mechanism obtain low-redundancy multi-scale feature information. In terms of feature fusion, a feature fusion method based on PatchPooling is proposed. This method combines the characteristics of modal images, and uses Spatial dimension local mapping to increase the utilization rate of low-dimensional features, which effectively improves the richness of classified features. In this paper, experiments were carried out on the SDUMLA-HMT, NUPT-FPV, FVCHKP and HDPR-310 multimodal finger datasets, and the recognition accuracy was high as 97.72 %, 99.10 %, 99.67 % and 99.74 %, respectively. In addition, the effectiveness of the model is verified by comparing with other advanced methods.

Dual-quaternion-based iterative algorithm of the three dimensional coordinate transformation

Nowadays a unit quaternion is widely employed to represent the three-dimensional (3D) rotation matrix and then applied to the 3D similarity coordinate transformation. A unit dual quaternion can describe not only the 3D rotation matrix but also the translation vector meanwhile. Thus it is of great potentiality to the 3D coordinate transformation. The paper constructs the 3D similarity coordinate transformation model based on the unit dual quaternion in the sense of errors-in-variables (EIV). By means of linearization by Taylor's formula, Lagrangian extremum principle with constraints, and iterative numerical technique, the Dual Quaternion Algorithm (DQA) of 3D coordinate transformation in weighted total least squares (WTLS) is proposed. The algorithm is capable to not only compute the transformation parameters but also estimate the full precision information of computed parameters. Two numerical experiments involving an actual geodetic datum transformation case and a simulated case from surface fitting are demonstrated. The results indicate that DQA is not sensitive to the initial values of parameters, and obtains the consistent values of transformation parameters with the quaternion algorithm (QA), regardless of the size of the rotation angles and no matter whether the relative errors of coordinates (pseudo-observations) are small or large. Moreover, the DQA is advantageous to the QA. The key advantage is the improvement of estimated precisions of transformation parameters, i.e. the average decrease percent of standard deviations is 18.28%, and biggest decrease percent is 99.36% for the scaled quaternion and translations in the geodetic datum transformation case. Another advantage is the DQA implements the computation and precision estimation of traditional seven transformation parameters (which still are frequent used yet) from dual quaternion, and even could perform the computation and precision estimation of the scaled quaternion.Graphical

Human activity recognition through deep learning: Leveraging unique and common feature fusion in wearable multi-sensor systems

With the progress in IoT and AI technologies, multi-sensor fusion for human activity recognition (HAR) has garnered considerable attention. As a result of integrating diverse information from different sensors, individuals employ sensors to monitor their daily activities. However, identifying crucial features for classification and assigning suitable weights to sensors is a complex task. On the other side, varied data structures pose challenges in establishing a unified format for the fusion of diverse data. To address these challenges, this paper presents UC Fusion, a method focusing on the fusion of unique and common features in wearable multi-sensor systems for HAR. First, UC Fusion merges the unique feature of each sensor with the common features of all sensors. Second, it tackles the challenge of handling heterogeneous data by unifying the data format through segmentation and dimensional transformation. Extensive experiments on the UCI HAR and WISDM datasets were conducted to evaluate UC Fusion’s performance. The results demonstrate that our proposed method secured an average recognition accuracy of 96.84% and 98.85%. Furthermore, ablation studies were performed on each module of UC Fusion to assess their impact on accuracy, confirming the effectiveness of the proposed method.

Reconstruction of Supersonic Flowfield Using Physical Neural Network Based on Channel Interaction

The evolution of shock waves in a combustor is a complex process comprising multiple time series, which results in a long computational cycle for unsteady numerical simulations. Current data-driven methods integrating physical information provide novel opportunities to rapidly and accurately predict the flowfield in the combustor. In this study, we construct a dataset under Mach numbers from 2 to 5 based on a self-designed scramjet combustor model and propose a physical convolutional neural network flowfield reconstruction method based on channel interaction (PICNNCI). This method embeds Euler equations that characterize the flow characteristics of inviscid fluids as physical constraints to solve the low-accuracy problem of traditional convolutional neural networks arising due to insufficient prior information. The model first performs dimensional transformations on temporal and spatial information input and converts a one-dimensional column vector into a two-dimensional vector to meet the convolution operation rules. Then, convolution is used for feature extraction to output the predicted flowfield, including velocity, pressure, and density fields. Finally, the predicted flowfield is optimized using the Euler equation and compared with the results obtained by numerical calculation and traditional neural network methods. The average peak signal-to-noise ratio of PICNNCI reaches 34.01 dB, and the linear correlation reaches 0.994.

In Situ Single Particle Reconstruction Reveals 3D Evolution of PtNi Nanocatalysts During Heating.

Tailoring nanoparticles' composition and morphology is of particular interest for improving their performance for catalysis. A challenge of this approach is that the nanoparticles' optimized initial structure often changes during use. Visualizing the three dimensional(3D) structural transformation in situ is therefore critical, but often prohibitively difficult experimentally. Although electron tomography provides opportunities for 3D imaging, restrictions in the tilt range of in situ holders together with electron dose considerations limit the possibilities for in situ electron tomography studies. Here, an in situ 3D imaging methodology is presented using single particle reconstruction (SPR) that allows 3D reconstruction of nanoparticles with controlled electron dose and without tilting the microscope stage. This in situ SPR methodology is employed to investigate the restructuring and elemental redistribution within a population of PtNi nanoparticles at elevated temperatures. The atomic structure of PtNi is further examined and a heat-induced transition is found from a disordered to an ordered phase. Changes in structure and elemental distribution are linked to a loss of catalytic activity in the oxygen reduction reaction. The in situ SPR methodology employed here can be extended to a wide range of in situ studies employing not only heating, but gaseous, aqueous, or electrochemical environments to reveal in-operando nanoparticle evolution in 3D.

LKDA-GAN: Cross-modality image synthesis via Generative Adversarial Network aggregating large kernel decomposable attention bottleneck block

Background and Objective:Mainstream image synthesis methods fail to capture local contextual information long-range dependence, and adaptability, especially under the influence of computation overload and random noise distribution, leading to the loss of contrast and detailed information. Approach:To alleviate these issues, we propose a Generative Adversarial Network aggregating large kernel decomposable attention (LKDA-GAN) bottleneck block for cross-modality image synthesis. Initially, a novel LKDA module is proposed by combining a spatial local convolution, a spatial long-range convolution, and a channel convolution, which aims to balance the local contextual information and the long-range dependence, and enhance the channel adaptability by enlarging the receptive field. Subsequently, a bottleneck block is designed and integrated into the LKDA module by feature dimensional transformation to capture rich semantic information and alleviate computational overhead. Ultimately, an auxiliary registration network (ARN) based on the noise transition matrix is put forward to learn the prior knowledge of the noise distribution and produce the unique optimal solution. Furthermore, it is based on Res-UNet to avoid network degradation. Main results:By analyzing qualitative assessment and quantitative measurement, extensive experiments demonstrate the proposed approach outperforms the state-of-the-art methods, and ablation studies also show the superiority of LKDA. Significance:LKDA-GAN provides a suitable way to synthesize images between different modalities, which is conductive to indicate disease areas and improve diagnosis accuracy.

Dimensional Transformation of Percolation Structure in Mixed-Matrix Membranes (MMMs).

A large number of studies of mixed-matrix membranes (MMMs) have confirmed the possibility of obtaining new materials with unique transport properties, including for solving specific problems in the separation of mixtures of liquids and gases. The choice of particles with a given affinity for the matrix and separable components allows researchers to adjust the selective properties of MMMs in a wide range, which changes the properties of MMMs in a wide range. However, even within the framework of the most complex percolation mechanism of the formation of the MMM structure, it is possible to explain only some of the observed effects. In particular, questions about the required particle concentration and fluctuation of properties in various MMM samples are still the subject of research. The results of the numerical modeling of such structures presented in this paper determined the possible causes of the observed deviations of the experimental results, for example, particle size dispersion, agglomeration, and interaction with the matrix. According to our research, the key factor that qualitatively changes the parameters of percolation structures is the ratio of the geometric dimensions of the system. We have confirmed in a wide range a significant change in the conditions of cluster formation and its power at different particle diameters and lengths (traditional parameters in percolation studies). But in our work, we additionally studied the effect on the cluster parameters of the interfacial layer and the anisotropy of the matrix (the transition from the cube to the film). The results obtained show that changing the parameters of the matrix-particle interaction affects agglomeration, and the degradation of the percolation structure is possible. That is, with an increase in concentration, the parameters of the percolation cluster, its power, and the probability of formation, may decrease. But even more negative changes in percolation structures are observed during the transition from a volumetric matrix to films. The anisotropy of space leads to the formation of percolation through the film in certain areas at low concentrations of particles. At the same time, in a significant part of the matrix, percolation between the film surfaces will be absent, and the effect of changing the properties of MMMs in the matrix as a whole decreases. Our study explains the observed instability of MMM properties at fixed concentrations and parameters of embedded particles, including the effect of reducing the influence of particles with increasing concentration.

Achieving Eco-Balance in Translating Non-Fiction Literature: An Approach through Adaptation and Selection—With Shark’s Fin and Sichuan Pepper as a Case

This paper aims to provide valuable insights for future translators dealing with the English-to-Chinese translation of non-fiction literature, employing principles from Eco-Translatology. The research focuses on the translation of Shark’s Fin and Sichuan Pepper, utilizing the framework of Translation as Adaptation and Selection. By evaluating the degree of multi-dimensional transformations, reader’s feedback, and translator quality in the existing Chinese version, the paper assesses eco-balance within the translated work, considering the hybrid nature of non-fiction literature and its linguistic, cultural, and communicative aspects. Based on the analysis, the paper suggests that translators should strive for comprehensive dimensional transformations, with emphasis on the communicative dimension, while considering other dimensions based on the content type (informative, literary, or hybrid). Additionally, constant attention to the target readership is essential throughout the translation process. These findings contribute to enhancing the quality of English-to-Chinese translations of non-fiction literature.

A node elimination algorithm for cubature of high-dimensional polytopes

Node elimination is a numerical approach for obtaining cubature rules for the approximation of multivariate integrals. Beginning with a known cubature rule, nodes are selected for elimination, and a new, more efficient rule is constructed by iteratively solving the moment equations. This paper introduces a new criterion for selecting which nodes to eliminate that is based on a linearization of the moment equation. In addition, a penalized iterative solver is introduced, that ensures that weights are positive and nodes are inside the integration domain. A strategy for constructing an initial cubature rule for various polytopes in several space dimensions is described. High efficiency rules are presented for two, three and four dimensional polytopes. The new rules are compared with rules that are obtained by combining tensor products of one dimensional quadrature rules and domain transformations, as well as with known analytically constructed cubature rules.

Continuous and Discrete ZND Models with Aid of Eleven Instants for Complex QR Decomposition of Time-Varying Matrices

The problem of QR decomposition is considered one of the fundamental problems commonly encountered in both scientific research and engineering applications. In this paper, the QR decomposition for complex-valued time-varying matrices is analyzed and investigated. Specifically, by applying the zeroing neural dynamics (ZND) method, dimensional reduction method, equivalent transformations, Kronecker product, and vectorization techniques, a new continuous-time QR decomposition (CTQRD) model is derived and presented. Then, a novel eleven-instant Zhang et al discretization (ZeaD) formula, with fifth-order precision, is proposed and studied. Additionally, five discrete-time QR decomposition (DTQRD) models are further obtained by using the eleven-instant and other ZeaD formulas. Theoretical analysis and numerical experimental results confirmed the correctness and effectiveness of the proposed continuous and discrete ZND models.

Learning Spatial–Spectral-Dimensional-Transformation-Based Features for Hyperspectral Image Classification

Recently, deep learning tools have made significant progress in hyperspectral image (HSI) classification. Most of existing methods implement a patch-based classification manner which may cause training test information leakage or waste labeled information for non-central pixels of image patches. Therefore, it is challenging to achieve remarkable classification performance via the traditional convolutional neural networks (CNN) in the absence of label information. Moreover, due to the limitation of convolutional kernel sizes and convolution operations, the spectral information of HSI cannot be fully utilized with a traditional CNN framework. In this paper, we implement pixel-based classification by a special data division strategy and propose a novel spatial–spectral dimensional transformation (SSDT) to obtain spectral features containing more spectral information. Then, we construct a fully convolutional network (FCN) with two branches based on 3D-FCN and 2D-FCN to achieve broader spatial and spectral information interaction. Finally, the fused features are utilized to realize accurate pixel-based classification. We verify our proposed method on three classic publicly available datasets; the overall classification accuracy and average accuracy reach 82.27%/87.85%, 83.81%/81.55%, and 85.97%/83.89%. Compared with the latest proposed method SS3FCN in the no-information-leakage scenario, the overall classification accuracy of our proposed method is improved by 1.72%, 4.95% and 0.2%, and the average accuracy is improved by 0.95%, 3.92% and 2.67% on the three databases, respectively. Experimental results demonstrate the effectiveness of the proposed SSDT and the proposed CNN framework.

Automated two-dimensional geometric model reconstruction from point cloud data for construction quality inspection and maintenance

Despite the availability of 3D digital models, 2D floor plans remain extensively used for quality inspection and maintenance as they offer firsthand information. While laser scanners enable efficient capture and reconstruction of real-world scenes, challenges arise in accurately extracting building geometry from laser scanning data due to the loss of geometric features. This paper describes a method for accurately reconstructing 2D geometric drawings of built facilities using laser scanning data. These techniques involve transforming the dimension of 3D data into 2D and displaying the registered data as pixels to extract solid lines that represent wall structures. By employing dimensionality transformation and pixelation techniques, the method supports reliable quality inspection and maintenance processes, overcoming the challenges of extracting precise geometry from laser scanning data. This paper contributes to the automated extraction of geometric features from point clouds and inspires the future development of fully automated 2D CAD and 3D BIM in alignment with Scan-to-BIM.

공간 감각 신장을 지원하는 초등수학 교수․학습의 방향성 탐색

This study aims to explore the direction of elementary mathematics teaching and learning to support the development of spatial sense. For this purpose, tasks in elementary mathematics textbooks dealing with spatial sense were analyzed from the perspectives of spatial sense and levels of cognitive demands. The results showed that Korean textbooks provided tasks related to mental rotation, mental transformation, mental dimensional transformation, and positional sense in terms of spatial sense, and PNC, PWC, and DM tasks in terms of the levels of cognitive demands. In order to explore the direction of teaching and learning related to the spatial sense of three-dimensional shapes, we analyzed publicly available teaching and learning materials from IREM in France as an example of a task with distinctive features from the Korean textbooks tasks. Based on this analysis and discussion, implications were drawn for the direction of elementary mathematics teaching and learning that supports the development of spatial sense in terms of task development, curriculum, and teaching and learning methods.

FPLA: A Flexible Physical Layer Authentication Mechanism for Distributing Quantum Keys Securely via Wireless 5G Channels

Quantum Key Distribution (QKD) is popular for establishing a native secure quantum communication network. However, existing QKD networks are built via classical wired fiber channels; it is difficult to distribute quantum keys directly into mobile phones, and no effective candidate solution is available yet. This paper presents a novel Flexible Physical Layer Authentication (FPLA) mechanism that exploits the unique characteristic of wireless signals from mobile phones to securely distribute quantum keys via wireless 5G channels. In particular, a 5G Up-Link Sounding Reference Signal (SRS)-based transmission model is developed to capture and extract the unique characteristic, which is then used to distribute quantum keys. Moreover, the model could lose accuracy due to SRS variations introduced by 5G Multiuser Multiple-Input Multiple-Output (MU-MIMO), so a dimensional transformation residual network is designed to classify legitimate and malicious user equipment (UE). An average authentication accuracy of 96.8% is proved by FPLA in multiple experiments in a 3 dB Signal-to-Noise Ratio (SNR) test environment with a training dataset of 300 samples per malicious UE. Simulation results show that FPLA is able to adapt to antenna diversity in 5G MU-MIMO systems.

Traffic Monitoring System for Vehicle Detection in Day and Night Conditions

Abstract In this work, a day and night time vehicle detection system for traffic surveillance is proposed. Our system is composed of two main processes, day time and night time processes. In the night time, the vehicles are detected based on their taillights and headlights. First of all, the 2D-DWT (Two Dimensional Discrete Wavelet Transform) and the background subtraction are applied to the input image. Then, the connected component technique is used to extract the region of interest. If it is the daytime, the connected component candidates are taken as potential vehicles after applying a pre-processing algorithm to improve the result. If it is the night-time, a filtering operation is used to keep only the bright white and red connected component candidates (which represent potential headlights and taillights, respectively). Finally, potential lamp sets are formed by grouping the extracted components on the basis of their positions, sizes, and colours. The potential extracted vehicles are classified as a vehicle or non-vehicle by using a pre-trained CNN (Convolutional Neural Network) classifier. The proposed system was tested and evaluated using different works from the literature. The experiments show that our proposed system has reached a high accuracy in terms of vehicle detection process whether in day or night time. The experiments were performed using four different videos and were implemented using the C++ language, which facilitates mathematical computation, and its OpenCV library, which is used to run the image processing algorithms used, as well as the TensorFlow library, which facilitates transfer learning of pre-trained CNN models.

Use of hydraulic radius to estimate the permeability of coarse-grained materials using a new geodatabase

This paper reviews commonly used parameters and prediction models for assessing the permeability of granular soils. Following a review of published models for prediction of soil permeability, a dimensional homogenous transformation model for a-priori estimation of soil permeability was calibrated using a large database (CG/KSAT/7/1278) comprising permeability data for a wide range of granular soils sourced from over 50 publications. The new transformation model requires knowledge of the void ratio and gradation of the material to make estimates of the soil permeability. The prediction accuracy of the calibrated model was then assessed alongside that of other empirical and semi-empirical models also calibrated using CG/KSAT/7/1278. The potential influences of void ratio, key gradation parameters and permeability test type on the prediction accuracy of the proposed model are also examined. The paper shows that while the fitted constants in the proposed transformation model are affected to varying extents by the aforementioned parameters, it does offer reasonable predictions of permeability with only knowledge of the void ratio and material gradation required.