Two-dimensional Matrices Research Articles

Ultrafast quasi-three-dimensional imaging

Understanding laser induced ultrafast processes with complex three-dimensional (3D) geometries and extreme property evolution offers a unique opportunity to explore novel physical phenomena and to overcome the manufacturing limitations. Ultrafast imaging offers exceptional spatiotemporal resolution and thus has been considered an effective tool. However, in conventional single-view imaging techniques, 3D information is projected on a two-dimensional plane, which leads to significant information loss that is detrimental to understanding the full ultrafast process. Here, we propose a quasi-3D imaging method to describe the ultrafast process and further analyze spatial asymmetries of laser induced plasma. Orthogonally polarized laser pulses are adopted to illuminate reflection-transmission views, and binarization techniques are employed to extract contours, forming the corresponding two-dimensional matrix. By rotating and multiplying the two-dimensional contour matrices obtained from the dual views, a quasi-3D image can be reconstructed. This successfully reveals dual-phase transition mechanisms and elucidates the diffraction phenomena occurring outside the plasma. Furthermore, the quasi-3D image confirms the spatial asymmetries of the picosecond plasma, which is difficult to achieve with two-dimensional images. Our findings demonstrate that quasi-3D imaging not only offers a more comprehensive understanding of plasma dynamics than previous imaging methods, but also has wide potential in revealing various complex ultrafast phenomena in related fields including strong-field physics, fluid dynamics, and cutting-edge manufacturing.

Magnetic stimulation of chemical reactions in coal

Purpose. To identify a mechanism in terms of which a signal of weak magnetic field is transformed into response of some components of nanostructure of a carbonaceous matter with further formation of chemical bonds. Methodology. Physical and mathematical modelling procedures of elementary chemical acts have been applied. Regularities of quantum mechanics and dynamics of chemical bonds were also used in addition to a magnetic isotope theory, a diffusion theory of recombination of radical pairs taking into consideration triplet-singlet transit, and nuclear-spin selectivity of chemical reactions. Findings. The physical mechanism of the magnetic scenario of interradial reactions is considered from the viewpoint of their energy stimulation through magnetic fields, i.e. the idea has been implemented according to which the number of radical pairs, able to be recombined into stable molecules, increases significantly if the weak magnetic field exercises certain influence. In addition to stimulation of interradial reactions, the magnetic field impact on organic coal mass-radicals results in stabilization of carbonaceous structures with regular atomic arrangement (being two-dimensional matrices, chains etc.) and their increase. Originality. A physical model of structural and phase changes in coal, depending upon the effect by external weak magnetic field, has been developed. It has been shown that the weak magnetic field signal, being incomparably smaller energetically to compare with the energy of thermal molecular motion, can initiate triplet-singlet transitions, i. e. transform radicals into reactive state. A mechanism has been proposed to form chemical bonds between movable radicals and non-complete bonds of atoms at the surfaces of solid phases of carbonaceous matter. Practical value. Implementation of the obtained results, concerning magnetic coal processing, may be connected with the development of a new procedure to avoid explosive conditions in coal seams. Progress in the field of magnetic processing should involve studies concerning calculation and selection of coal processing parameters (i.e. magnetic field density, frequency, energy, and a processing period) to control efficiently the chemical reactions in the carbonaceous matter. A substantiation degree of coal processing will influence greatly both efficiency of chemical processes and expediency of practical use of the results.

The Evolution of the Collaborative Environmental Governance Network in Guizhou Province, China

China has successively set goals of carbon peaking and carbon neutrality, aiming to transform to a green and low-carbon economy. Collaborative environmental governance (CEG) is an important way to achieve this transformation. To improve collaborative environmental governance, the study of the evolution of the collaborative environmental governance network (CEGN) is necessary. In this study, the CEGNs in different periods in Guizhou Province, China are established based on social network analysis. Then, the evolution of environment governance policy implementers’ functions in the network is investigated by two-dimensional (breadth and intensity) matrices. Moreover, the evolution of core implementers’ functions and its impacts on the operation of the network are analyzed based on the network stability. The results show that the network size, frequency of collaboration, and cohesion have gradually increased, and the network structure has changed from a loose pattern to an expanded and balanced system. Implementers such as the governments of municipalities (prefectures) (MGs) and counties (districts) (CGs), urban management committee (UMCs), and municipal (prefecture) ecological environment bureaus (MBEEs) have played leading and coordinating roles at different phases. However, the cohesion of the network is low, indicating a low level of collaboration. This study integrates the collaborative governance theory and social network analysis, which provides a new way for the study of CEG. In addition, the CEG effect is evaluated by analyzing the evolution of the CEGN, which provides a reference for the CEG policy making in developing regions.

Comparison of deep-learning and conventional machine learning algorithms for salary prediction

Salary is an integral part of contemporary life. With the large-scale use of machine learning, it has become possible to predict salaries with machine learning. Previous researchers have used random forest algorithms to solve this problem, however, there is a research gap in using a neural network to solve this problem. Therefore, the research topic of this paper is to use convolutional neural networks (CNN) and datasets on Kaggle to predict salary. The research methodology of this paper is as follows. First, the Kaggle dataset is divided into the train-dataset and the test-dataset. After preprocessing the data, two kinds of features are obtained. The features will be transformed into two two-dimensional matrices. Next, the matrices were used to train two CNNs separately. These two CNNs will be connected together to get the predicted salary by fully connected layers and Relu activation functions. After training the CNN, the study called the test dataset to verify the accuracy of the model. Similarly, the study used a random forest model for prediction. Finally, the comparison of the two results showed which algorithm was better. The study found that the error rate of the CNN was 0.0732 and its variance was 0.1899. The error rate of the random forest was 0.2437 and its variance was 0.8285. From the results, CNN is better than random forest in terms of accuracy and stability. Therefore, using CNN for salary prediction has a high probability of getting better results.

Alpha-divergence two-dimensional nonnegative matrix factorization for biomedical blind source separation

An alpha-divergence two-dimensional nonnegative matrix factorization (NMF2D) for biomedical signal separation is presented. NMF2D is a popular approach for retrieving low-rank approximations of nonnegative data such as image pixel, audio signal, data mining, pattern recognition and so on. In this paper, we concentrate on biomedical signal separation by using NMF2D with alpha-divergence family which decomposes a mixture into two-dimensional convolution factor matrices that represent temporal code and the spectral basis. The proposed iterative estimation algorithm (alpha-divergence algorithm) is initialized with random values, and it updated using multiplicative update rules until the values converge. Simulation experiments were carried out by comparing the original and estimated signal in term of signal-to-distortion ratio (SDR). The performances have been evaluated by including and excluding the sparseness constraint which sparseness is favored by penalizing nonzero gains. As a result, the proposed algorithm improved the iteration speed and sparseness constraints produce slight improvement of SDR.

Intelligent fault diagnosis of planetary gearboxes under time-varying conditions based on dynamic adversarial balance adaptation with multi-label information confusion

Intelligent diagnosis methods based on big data have been extensively applied in the fault diagnosis of rotating equipment such as planetary gearboxes. Most of these methods usually satisfy the condition of independent identically distribution among the training and diagnosis data. However, the data distribution in the actual diagnosis task struggles to satisfy the above conditions due to the lack of fault data, missing label information and the feature differences within different signals, thus increasing the difficulty of cross-condition fault diagnosis in small sample sets. Therefore, we propose a dynamic adversarial balance adaptation method with multi-label information confusion (MLC-DABA) for diagnosing planetary gearbox faults under time-varying conditions. In the signal preprocessing process, we transform the nonstationary timing signals into two-dimensional time-frequency matrices for the feature learning of networks, which avoids the frequency characteristic mess caused by frequency overlap. Moreover, we adopt a balance adaptation algorithm to dynamically evaluate the feature distribution between source and target tasks through the domain labels and category labels, thus establishing a balanced adaptation relationship between the feature distributions of both tasks. This dynamic adversarial training mechanism can tap more domain-invariant feature information to measure the distribution distance among tasks, thus closing the feature differences in different tasks and increasing the generalization of source tasks to the data distribution in target tasks. The proposed method is verified in planetary gearbox experiments. Experimental analysis results indicate that the diagnostic performance of MLC-DABA outperforms other comparison methods in terms of accuracy and training robustness.

Classification for GM and Non-GM Maize Kernels Based on NIR Spectra and Deep Learning

The classification of GM and non-GM maize kernels is fundamental for further analysis of the gene action in maize. Therefore, a complete and novel detection scheme based on near-infrared spectra was designed to distinguish GM and non-GM maize kernels. Hyperspectral images (935–1720 nm) of 777 maize kernels from 3 kinds were captured, and the average spectra of the maize kernels were extracted for modeling analysis. The classical modeling methods based on feature engineering were first studied, and the backpropagation neural network–genetic algorithm model showed the best performance with a prediction accuracy of 0.861. Then, novel modeling methods based on deep learning were developed. To dig out the interactive information between different bands and match the application scenarios, the original spectra were transformed into two-dimensional matrices before establishing the deep learning models. A modified convolution neural network (i.e., VGG net) with dilated convolution was finally constructed to classify the maize kernels, and the prediction accuracy reached 0.961. This research provides a referential and novel way to detect GM maize kernels. Future research will improve the detection scheme for monitoring unauthorized GM organisms by introducing the visualization technology of deep learning.

Modeling of Composite Structures in Fire Using a Coupled Skeletal Frame and Floor System Analysis: Slab Panel Method

This paper presents a proposed design methodology which combines the fire beam element (FBE) for skeletal frame analysis with the slab panel method (SPM) for floor experiencing catenary action. The methodology enables the two systems to interact with each other to provide a simplistic manner to design a full composite structure. The design methodology consists of an iterative process in which (1) the SPM is used to design the composite slab and provides the loads on the support beams of the skeletal structure, and then (2) the FBE analysis, implemented in OpenSees version 2.5.0, determines the deflection of the edge support beams which are used to update the SPM calculations. The existing two-dimensional (2D) FBE finite-element matrices are updated for a three-dimensional FBE, while the SPM is modified to allowing the interaction between the FBE analysis and the SPM. Three validation studies of the FBE analysis show that the FBE analysis is able to capture the behavior of the skeletal structure adequately, as long as the support edge beams of the slab panel have sufficient strength to support the slab panel. The application of the design methodology to an office building serves as a proof on concept and demonstrates that the deflection of the edge beams does have a significant impact on the predicted ultimate load-carrying capacity of the slab panel.

Lagrange’s Theorem in Group Theory

The structure and behavior of molecules and crystals depend on their different symmetries. Thus, group theory is an essential technique in some fields of chemistry. Within mathematics itself, group theory is very closely linked to symmetry in geometry. Lagrange’s theorem is a statement in group theory that can be viewed as an extension of the number theoretical result of Euler’s theorem. It is seen as a significant lemma for proving more complicated results in group theory. The main intention of this dissertation is to prove Lagrange’s theorem which illustrates that every quadratic irrationality has a periodic continued fraction. Conversely, every periodic continued fraction is a quadratic irrationality. The first part of this paper is the research of so-called Dirichlet groups, which are subgroups of preserving certain pairs of lines. These groups are closely related to the periodicity of sails. The structure of a Dirichlet group is induced by the structure of the group of units in order. Taking n-th roots of two-dimensional matrices using Gauss’s reduction theory will also be shown. Finally, the solutions of Pell’s equation and Lagrange’s theorem will be proved.

Intelligent fault diagnosis of helical gearboxes with compressive sensing based non-contact measurements

Helical gearboxes play a critical role in power transmission of industrial applications. They are vulnerable to various faults due to long-term and heavy-duty operating conditions. To improve the safety and reliability of helical gearboxes, it is necessary to monitor their health conditions and diagnose various types of faults. The conventional measurements for gearbox fault diagnosis mainly include lubricant analysis, vibration, airborne acoustics, thermal images, electrical signals, etc. However, a single domain measurement may lead to unreliable fault diagnosis and the contact installation of transducers is not always accessible, especially in harsh and dangerous environments. In this article, a Compressive Sensing (CS)-based Dual-Channel Convolutional Neural Network (CNN) method was proposed to accurately and intelligently diagnose common gearbox faults based on two complementary non-contact measurements (thermal images and acoustic signals) from a mobile phone. The raw acoustic signals were analysed by the Modulation Signal Bispectrum (MSB) to highlight the coupled modulation components relating to gear faults and suppress the irrelevant components and random noise, which generates a series of two-dimensional matrices as sparse MSB magnitude images. Then, CS was used to reduce the image redundancy but retain key information owing to the high sparsity of thermal images and acoustic MSB images, which significantly accelerates the CNN training speed. The experimental results convincingly demonstrate that the proposed CS-based Dual-Channel CNN method significantly improves the diagnostic accuracy (99.39% on average) of industrial helical gearbox faults compared to the single-channel ones.

Assessing alignment between curriculum standards and teachers’ instructional practices in China’s school music education

Alignment between curriculum standards and teachers’ classroom instructional practices is critical in assessing curriculum implementation effectiveness and students’ learning. Using a modified version of the Surveys of Enacted Curriculum (SEC) for music, this study explored the alignment between the enacted curriculum and the national curriculum standards in the Chinese school system. Curriculum standards and classroom instructional practices were represented using sets of two-dimensional matrices that comprised content themes and five learning domains: Cognitive, Affective, Psychomotor, Social, and Cultural (the CAPSCt model). The results showed an overall high level of alignment (0.81–0.90). It was also suggested that the degree of alignment gradually decreased from the low grade to high grade band. Individual variations were evident in both the learning content and learning objectives, in which more emphasis was put on cognitive, affective, and psychomotor development than on social and cultural aspects. Methodological challenges and implications of the CAPSCt model for assessing curriculum enactment are also discussed.

Spiral waves of divergence in the Barkley model of nilpotent matrices

A new type of a spiral wave is presented in this paper. It is shown that spiral waves of divergence can be generated by the discrete Barkley model when all scalar nodal variables are replaced by two-dimensional nilpotent matrices of variables. However, spiral waves of divergence do not exist if scalar nodal variables of the Barkley model are replaced by idempotent matrices instead. Computational experiments demonstrate that spiral waves diverge along the centerline of the rotating bands, starting from the tip of the spiral wave – but the numerical values of the field stay bounded around zero in the regions between the rotating bands. Spiral waves of divergence are classified into five different classes according to their transient behavior. The formation of transient anti-phase clusters and Wada boundaries of five different types of spiral waves in the parameter plane of the Barkley model are examined in detail. Potential applications of spiral waves of divergence in hiding secret digital images are also discussed.

Short-Term Probability Density Function Forecasting of Industrial Loads Based on ConvLSTM-MDN

Load forecasting for industrial customers is essential for reliable operation decisions in the electric power industry. However, most of the load forecasting literature has been focused on deterministic load forecasting (DLF) without considering information on the uncertainty of industrial load. This article proposes a probabilistic density load forecasting model comprising convolutional long short-term memory (ConvLSTM) and a mixture density network (MDN). First, a sliding window strategy is adopted to convert one-dimensional (1D) data into two-dimensional (2D) matrices to reconstruct input features. Then the ConvLSTM is utilized to capture the deep information of the input features. At last, the mixture density network capable of directly predicting probability density functions of loads is adopted. Experimental results on the load datasets of three different industries show the accuracy and reliability of the proposed method.

Sentiment classification of delta robot trajectory control using word embedding and convolutional neural network

Sentiment classification (SC) is an important research field in natural language processing (NLP) <span lang="EN-US">that classifying, extracting and recognizing subjective information from unstructured text, including opinions, evaluations, emotions, and attitudes. Human-robot interaction (HRI) also involves natural language processing, knowledge representation, and reasoning by utilizing deep learning, cognitive science, and robotics. However, sentiment classification for HRI is rarely implemented, especially to navigate a robot using the Indonesian Language which semantically dynamics when written in text. This paper proposes a sentiment classification of Bahasa Indonesia that supports the delta robot to move in particular trajectory directions. Navigation commands of the delta robot were vectorized using a word embedding method containing two-dimensional matrices to propose the classifier pattern such as convolutional neural network (CNN). The result compared the particular architecture of CNN, GloVe-CNN, and Word2Vec-CNN. As a classifier method, CNN models trained, validated, and tested with higher accuracy are 98.97% and executed in less than a minute. The classifier produces four navigation labels: right means </span><em><span lang="EN-US">'kanan'</span></em><span lang="EN-US">, left means </span><em><span lang="EN-US">'kiri</span></em><span lang="EN-US">', top means </span><em><span lang="EN-US">'atas</span></em><span lang="EN-US">', bottom means </span><em><span lang="EN-US">'bawah</span></em><span lang="EN-US">', and multiplier factor. The classifier result is utilized to transform any navigation commands into direction along with end-effector coordinates.</span>

Self-Calibrated AC Zero Potential Circuit for Two-Dimensional Impedimetric Sensor Matrices

Zero potential circuits (ZPC) can be used for reducing cross-talk effects within the 2-Dmatrices. ZPC using AC excitation signals (AC-ZPC) with different frequencies in every row can address all the sensors in a matrix simultaneously. The main challenge thereby is the remaining deviations. To analyze the reasons for this, an analytical model of the column-side output voltages is elaborated, which takes into account the non-ideal characteristics of the operational amplifiers, including the input impedance, finite open-loop gain factor, leakage current, output impedance, and load impedance. Based on this model, a novel method is proposed to realize a higher AC measurement accuracy by suppressing the matrix row side impedance through voltage followers and compensating the matrix column side non-ideal amplifiers through reference units. For compensation, one row and one column of given impedimetric units are included in the target matrix as reference elements. The measurement deviations are reduced by comparing the output differences between the targeted sensor and the reference elements. In a simulation for a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$4\times 4$ </tex-math></inline-formula> impedimetric sensor matrix composed of RC elements from <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$1.9\,k\Omega \vert \vert 361.7\,pF$ </tex-math></inline-formula> to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$100.4\,k\Omega \vert \vert 7.3\,pF$ </tex-math></inline-formula> , this new method achieves measurement deviations below 0.1%, which is a significant improvement over previous works that reached deviations above 1%.

Binary Matrix Method to Enumerate, Hierarchically Order, and Structurally Classify Peptide Aggregation.

Protein aggregation is a common and complex phenomenon in biological processes, yet a robust analysis of this aggregation process remains elusive. The commonly used methods such as center-of-mass to center-of-mass (COM-COM) distance, the radius of gyration (Rg), hydrogen bonding (HB), and solvent accessible surface area do not quantify the aggregation accurately. Herein, a new and robust method that uses an aggregation matrix (AM) approach to investigate peptide aggregation in a MD simulation trajectory is presented. An nxn two-dimensional AM is created by using the interpeptide Cα-Cα cutoff distances, which are binarily encoded (0 or 1). These aggregation matrices are analyzed to enumerate, hierarchically order, and structurally classify the aggregates. Comparison of the present AM method suggests that it is superior to the HB method since it can incorporate nonspecific interactions and the Rg and COM-COM methods since the cutoff distance is independent of the length of the peptide. More importantly, the present method can structurally classify the peptide aggregates, which the conventional Rg, COM-COM, and HB methods fail to do. The unique selling point of this method is its ability to structurally classify peptide aggregates using two-dimensional matrices.

One-Body Two-Dimensional Switching Matrices With a Triangular Lattice of Beams

This letter presents a numerical design method of one-body two-dimensional (2-D) switching matrices with a triangular lattice of an arbitrary number of beams in each of horizontal and vertical directions, improving the overlap between the beams in a 2-D multiple-beam coverage. With the proposed matrix configuration, the minimum number of cascaded units consisting of a mix of 1-D and 2-D couplers and phase shifters is found to be smaller than that of the conventional cascade of 1-D matrices when the number of beams is larger than three in either of horizontal or vertical directions. The proposed solution is of interest for millimeter-wave applications requiring spatial diversity.

Restoring trilinearity with the purpose of advanced modeling: towards a more effective analysis of Pericarpium Citri Reticulatae during storage periods

To accurately quantify Pericarpium Citri Reticulatae samples, trilinear structure was restored in the stacked fingerprints for more robust modeling. Initially, liquid chromatography - diode array detector - mass spectrometry (LC-DAD-MS) and head space-solid phase micro extraction coupled to gas chromatography - mass spectrometry (HS-SPME/GC-MS) were utilized to analyze Pericarpium Citri Reticulatae. Faced with the time-shifts in two-dimensional (2D) matrices across different samples, three algorithms were developed to synchronize them. Furthermore, bilinear and trilinear models were used to realize the quantifications with different principles. Through real cases based on LC-DAD, the advantages and disadvantages of trilinear decomposition over multivariate curve resolution-alternating least-squares can be clarified in the quantification of raw or synchronized fingerprints. Also in the data processing, a modification version of multi-scale peak alignment (mMSPA) was proved to be more suitable for trilinearity restoring than the other two algorithms. Recognizing these facts, restoring trilinearity were developed for more robust modeling in the application of the Pericarpium Citri Reticulatae fingerprints from different storage periods. After effective analysis, the upward/downward trend of 13 flavonoids were drawn accurately; and several flavour components having the highest contribution rate during storage were outlined reasonably. In conclusion, more robust modeling can be realized in trilinear data synchronized by appropriate algorithms, leading to an accurate quantification in herbal quality researches.

Highly undersampling dynamic cardiac MRI based on low-rank tensor coding

Dynamic cardiac magnetic resonance imaging (CMRI) is an important tool for the non-invasive assessment of cardiovascular disease. However, dynamic CMRI suffers from long acquisition times due to the need of obtaining images with high temporal and spatial resolution, whole-heart coverage. Conventionally, a multidimensional dataset in dynamic CMRI is treated as a series of two-dimensional matrices, and then various matrix/vector transforms are used to explore the sparsity of MR images. In this paper, we propose a low-rank tensor coding (LRTC) model with tensor sparsity for the application of compressive sensing (CS) in dynamic CMRI. In this framework, each group of 3D similar patches extracted from high-dimensional images is considered to be a low-rank tensor. LRTC can better capture the sparse part of dynamic CMRI and make full use of the redundancy between the feature vectors of adjacent positions. ADMM technique is introduced to tackle the proposed model, where soft threshold operator is used to solving the l1 norm relaxation. Higher-order singular value decomposition (HOSVD) is exploited to process high-dimensional tensors and mine correlations in space-time dimensions. Validations based on cardiac cine and myocardial perfusion datasets indicate that the proposed method achieved comparable reconstruction accuracy with the low-rank matrix recovery methods, and outperformed the conventional sparse recovery methods.

Sudoku-inspired high-Shannon-entropy alloys

Current definition of high-entropy alloys (HEAs) is commonly based on the configurational entropy. But this definition depends only on the chemical composition of a HEA and therefore cannot distinguish the information content that is encoded in various local atomic arrangements and measurable by the Shannon entropy in information theory. Here, inspired by the finding that two-dimensional (2D) Sudoku matrices exhibit higher average Shannon entropy than 2D random matrix counterparts, we propose high-Shannon-entropy alloys (HSEA), whose structures are based on 3D Sudoku matrices. Despite the constraints on the atomic arrangements to form a 3D Sudoku 4 × 4 × 4 matrix, we find that, a prototypical HSEA, NbMoTaW has a lower energy than the same HEA with a random structure due to the smaller lattice distortion. We compute the electronic structures and mechanical properties and find that the HSEA exhibits enhanced average Fermi velocity and ductility over the random NbMoTaW HEA. Finally, we evaluate the formation energies of single vacancies and a vacancy cluster in the HSEA, whose configurations mimic Sudoku puzzles with one and several missing numbers, respectively. We find that a range of large energies are required to generate such vacancies, which depend on the location and species of missing atoms. Our work shows that introducing the Shannon entropy to HEAs offers a useful metric to reveal more atomic details of HEAs and that HSEAs represent an uncharted domain in the complicated energy landscape of HEAs which may be endowed with improved properties.