Symmetric Transformation Research Articles

A spatiotemporal symmetrical transformer structure for EEG emotion recognition

In the field of brain-computer interface, automatic recognition of emotions based on electroencephalogram (EEG) signals is of great significance. At present, deep learning can deeply mine the information in the data, especially the convolutional neural network (CNN) and the recurrent neural network (LSTM), which has remarkably improved the accuracy in numerous fields, hence it is applied by researchers to EEG-based emotional identification research. Nonetheless, existing CNN and LSTM-based models still rely on data preprocessing and feature extraction. Furthermore, CNNs have limitations in perceiving global dependencies while LSTMs have problems such as vanishing gradients in the case of long sequences. In this paper, we proposed the Spatiotemporal Symmetric Transformer Model (STS-Transformer), an effective EEG emotion recognition model, to overcome the current problems. STS-Transformer is an end-to-end framework that directly recognizes emotion from raw EEG signals without data preprocessing and feature extraction. This method achieves 89.86% and 86.83% accuracy respectively in the binary classification of valence and arousal in the DEAP dataset; in the DREAMER dataset, the binary classification accuracy of valence and arousal is 85.09% and 82.32%. Therefore, our method exhibits remarkable advantages over other end-to-end models in similar studies.

SMiT: symmetric mask transformer for disease severity detection.

The application of deep learning methods to the intelligent diagnosis of diseases has been the focus of intelligent medical research. When dealing with image classification tasks, if the lesion area is small and uneven, the background image involved in the training will affect the ultimate accuracy in determining the extent of the lesion. We did not follow the traditional approach of building an intelligent system to assist physicians in diagnosis from the perspective of CNN models, but instead proposed a pure transformer framework that can be used for diagnostic grading of pathological images. We propose a Symmetric Mask Pre-Training vision Transformer SMiT model for grading pathological cancer images. SMiT performs a symmetrically identical high probability sparsification of the input image token sequence at the first and last encoder layer positions to pre-train visual transformers, and the parameters of the baseline model are fine-tuned after loading the pre-training weights, allowing the model to concentrate more on extracting detailed features in the lesion region, effectively getting rid of the potential feature dependency problem. SMiT achieved 92.8% classification accuracy on 4500 histopathological images of colorectal cancer processed by Gaussian filter denoising. We validated the effectiveness and generalizability of this study's methodology on the publicly available diabetic retinopathy dataset APTOS2019 from Kaggle and achieved quadratic Cohen Kappa, accuracy and F1-score of 91.9%, 86.91% and 72.85%, respectively, which were 1-2% better than previous studies based on CNN models. SMiT uses a simpler strategy to achieve better results to assist physicians in making accurate clinical decisions, which can be an inspiration for making good use of the visual transformers in the field of medical imaging.

N-Quasi-m-Complex Symmetric Transformations

Our aim in this study is to consider a generalization of the concept of m-complex symmetric transformations to n-quasi-m-complex symmetric transformations. A map S∈B(Y) is said to be an n-quasi-m-complex symmetric transformation if there exists a conjugation C on Y such that S satisfies the condition S*n∑0≤k≤m(−1)m−kmkS*kCSm−kCSn=0, for some positive integers n and m. This class of transformation contains the class of m-complex symmetric transformations as a proper subset. Some basic structural properties of n-quasi-m-complex symmetric linear transformations are established with the help of transformation matrix representation. In particular, we obtain that a power of an n-quasi-m-complex symmetric is again an n-quasi-m-complex symmetric operator. Moreover, if T and S are such that T is an n1-quasi-m1-complex symmetric and S is an n2-quasi-m2-complex symmetric, their product TS is an max{n1,n2}-quasi-(m1+m2−1)-complex symmetric under suitable conditions. We examine the stability of n-quasi-m-complex symmetric operators under perturbation by nilpotent operators.

Adjacency matrices over a finite prime field and their direct sum decompositions

In this paper, we discuss the adjacency matrices of finite undirected simple graphs over a finite prime field Fp. We apply symmetric (row and column) elementary transformations to the adjacency matrix over Fp in order to get a direct sum decomposition by other adjacency matrices. In this paper, we give a complete description of the direct sum decomposition of the adjacency matrix of any graph over Fp for any odd prime p. Our key tool is quadratic residues of Fp.

Research on Symmetrical Integrated Matrix Transformer Applied to Full-Bridge LLC Resonant Converter for CM Noise Cancellation

The planar transformer is widely used in DC-DC power converters due to the small leakage inductance and low height. However, the big overlapping area between primary and secondary windings in the planar transformer generates large parasitic capacitance, which brings serious common-mode (CM) noise problems. The full-bridge LLC resonant converter can meet the premise of CM noise cancellation since the noise sources on the primary and secondary sides have same magnitudes and opposite phases. Therefore, the symmetrical planar transformer design is more conducive to the attenuation of CM noise. This paper analyses symmetrical winding arrangements with minimal winding loss for the transformer in the full-bridge LLC resonant converter. Based on this, the symmetry of the reverse integrated matrix transformer (RIMT) and forward integrated matrix transformer (FIMT) composed of two elemental transformers is investigated. The scattering parameter <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">21</sub> is used to evaluate the symmetry of RIMT and FIMT. It is found that the two CM <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">21</sub> curves of RIMT are not consistent even though the windings have been arranged symmetrically. In contrast, the CM <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">21</sub> curves for FIMT are almost overlapped. This implies that FIMT is symmetrical and capable of CM current cancellation. Finally, the CM noises of the full-bridge LLC resonant converter using RIMT, RIMT with a balance capacitor, and FIMT are tested. Experimental results show that the CM noise for the converter using FIMT is lowest. Especially at the switching frequency, the CM noise is reduced by more than 20 dBμV.

A Fully Symmetric High-Performance Transformer Balun Based on TSV for RF Applications

A Fully Symmetric High-Performance Transformer Balun Based on TSV for RF Applications

Ukrainian National Encryption Standards for FPGA Based Embedded Systems

The paper presents the hardware implementation based on FPGA of the main cryptographic transformations of the symmetric transformation algorithm of DSTU 7624:2014 and the stream cipher of DSTU 8845:2019, which are the national encryption standards of Ukraine. In the case of DSTU 7624: 2014 developed and implemented a hardware implementation for multiplication of two polynomials modulo x8+x4+x3+x2+1 in the form of a combinational circuit that allows to execute the MixColumn transformation by one cycle. SubBytes transformation is implemented based on asynchronous read-only memory. For stream cipher, DSTU 8845:2019 the nonlinear function T are implemented as subtitution byte operation in the form of precalculated cells of ROM memory. The multiplication function by α and α-1 in Galois field arithmetic GF (2 64) is realized based on ROM and combinational logic. The control of the modes of operation of the shift register with linear feedback is performed based on a FSM. Both hardware implementations of encryption standards have been verified by the authors according to the specified data in the standard, and their HDL code can be provided by the authors for further research to interested parties.

3D Assembly Completion

Automatic assembly is a promising research topic in 3D computer vision and robotics. Existing works focus on generating assembly (e.g., IKEA furniture) from scratch with a set of parts, namely 3D part assembly. In practice, there are higher demands for the robot to take over and finish an incomplete assembly (e.g., a half-assembled IKEA furniture) with an off-the-shelf toolkit, especially in human-robot and multi-agent collaborations. Compared to 3D part assembly, it is more complicated in nature and remains unexplored yet. The robot must understand the incomplete structure, infer what parts are missing, single out the correct parts from the toolkit and finally, assemble them with appropriate poses to finish the incomplete assembly. Geometrically similar parts in the toolkit can interfere, and this problem will be exacerbated with more missing parts. To tackle this issue, we propose a novel task called 3D assembly completion. Given an incomplete assembly, it aims to find its missing parts from a toolkit and predict the 6-DoF poses to make the assembly complete. To this end, we propose FiT, a framework for Finishing the incomplete 3D assembly with Transformer. We employ the encoder to model the incomplete assembly into memories. Candidate parts interact with memories in a memory-query paradigm for final candidate classification and pose prediction. Bipartite part matching and symmetric transformation consistency are embedded to refine the completion. For reasonable evaluation and further reference, we design two standard toolkits of different difficulty, containing different compositions of candidate parts. We conduct extensive comparisons with several baseline methods and ablation studies, demonstrating the effectiveness of the proposed method.

Implementation and analysis of symmetrical signals in the sequency domain

Every transform has unique attributes and traits that are crucial to reducing computing costs and offering simple solutions. Many different frequency domain transformations, for instance, have properties that can be used in a variety of signal processing applications and analyses. Some of the Complex Hadamard Transform's variants' sequencies can be compared to those of the Discrete Fourier Transforms. It is proven the characteristics of the Conjugate Symmetric Sequency-Ordered Complex Hadamard Transform symmetry. These qualities are crucial for signal analysis and image processing. Due to duplicate spectra across the origin, it reduces computational complexity, makes an analytical analysis for symmetric signals simpler, and needs less storage. Its analysis shows that the Discrete Fourier Transform and this Complex Hadamard Transform version exhibit similar symmetry tendencies. By using elementary signals in the time domain to connect the positive and negative sequencies with their associated phasor conceptions, sequency domain spectra are used to highlight these properties. As a result of image representation, relative spectra are represented in related domains. Transform can be used to extract and analyze various aspects from a wide range of medical images.

Application of double core symmetrical phase shifting transformer in power flow regulation of UHV power grid

With the development of society, the demand for electric energy is growing day by day. However, the energy centers and load centers are geographically distributed in a reverse direction, so the power supply and demand are unbalanced. High voltage transmission lines are characterized by long distance and large capacity, and the power flow problems are increasingly prominent. In order to flexibly adjust the line power flow, improve the comprehensive utilization of grid assets, and improve the transmission capacity of the system, this paper analyzes the principle of double core symmetrical phase-shift transformer (DS-PST) and the application of power flow regulation. Firstly, the basic principle of phase shifting transformer is analyzed in detail, and the equivalent mathematical model of DS-PST and the calculation of main parameters are derived. Impedance coefficient and excitation coefficient are introduced to modify the parameter design of DS-PST. Then, an electromagnetic simulation model is established to verify the effectiveness of the design method. Finally, a system simulation model is built to verify the power flow regulation effect of DS-PST by taking 500 kV UHV power grid and IEEE standard multi-node system as examples. DS-PST can transfer the active power transmitted by the lines with high load rate to the lines with low load rate, which makes the power flow distribution of the system more balanced and effectively improves the transmission capacity of the power system.

A lossless compression method for random integer based on three-dimensional product- triangular chaotic iterative sequences

Using the ergodicity of chaotic iterative sequences to realize data compression is a new research perspective. We find that, under suitable initial conditions, one or more local segments that are numerically identical to random integer sequences appear on the iterative sequence, which is a prerequisite for compression. Based on this, this paper designs a random integer lossless compression method based on three-dimensional product-triangular chaotic iterative sequences. The method proposed only needs to input a small amount of iterative initial information to compress a large amount of data through an iterative sequence of limited length. The key lies in three aspects. First, according to the characteristics of the data to be compressed, the iterative initial conditions suitable for compression are obtained by screening. Secondly, map the traversal results into a sequence of binary integers to complete the recording of key information. Finally, this binary integer sequence is rapidly compressed using a designed parity symmetric transformation algorithm, and decompression is achieved in its reverse process. As a new way to achieve compression, this approach is not only simple, but also requires less computation time. The experimental results show that the compression effect achieved by this method has obvious advantages in terms of compression ratio, data reconstruction quality, and compression and decompression speed.

Nonlocal symmetries and interaction solutions for the (n + 1)-dimensional generalized Korteweg–de Vries equation

The (n + 1)-dimensional generalized KdV equation is presented in this paper, and we further investigate its nonlocal symmetries by different methods. It can be seen that the symmetrical transformations obtained by different nonlocal symmetries are usually equivalent. Based on the obtained Lie point symmetry as well as the mth finite symmetrical transformations, we obtain its soliton molecules and multiple soliton solutions. Additionally, for the case of n = 4 various types of interaction solutions among solitons and periodic waves are obtained by the similarity reduction method.

ФОРМИРОВАНИЕ СТРУКТУРНОЙ СХЕМЫ РАДИООБМЕНА С ПРИМЕНЕНИЕМ ПСП

The structure of the radio exchange demonstrates the interconnection pattern of the drones with the control center. To protect against unauthorized access to control and navigation channels it is necessary to hide such data and increase their noise immunity. The aim of the work is to use signals with a pseudorandom sequence and duplicate control and navigation blocks in the information channel of a small-scale aerial vehicle. Thus, at the beginning of the paper, a general structural diagram of radio communication between the unmanned aerial vehicle and the control center is presented. The model of 2-element antenna array consisting of two non-directional antenna elements is considered. On the basis of which it is possible to conclude about the signal arrival with a phase shift, taking into account which it is possible to determine the output signal of the array. An important factor is the synchronization and encryption of the signal. Data synchronization can be used by synchronous signal transmission between the drone and the control center. To reduce the probability of interception of the synchronous signal, the data packets containing it are transmitted in a pseudo-random sequence. Synchronization is achieved by using a micronavigation system through continuous radio transmissions from a ground source and simultaneous reception and recording of the signal on the drone. A one-time encryption or scrambler with a reversible symmetric transformation of the encoded information can be used as an encryption or scrambler. A random number generator is used to generate a sequence of random data, from which an array of key information tied to a specific period of use is created. The phase method can be used to process the signal. By measuring the phase shift with a phase detector, you can determine the location of the radio source with respect to the base normal. Measurements can be made with a digital receiving antenna array. Signal processing with digital receiving antenna array is performed by the diagramming device and the adaptive processor unit. As a result, all data using this approach is entered into the information block with the use of a pseudo-random coding change scheme, pseudo-random permutation of the navigation and control blocks.

Optimal distribution of the fundamental non-efficient load current terms between the energy gateways connected in grid-tied microgrids

Main objective of this paper is the optimal distribution of the fundamental non-efficient load current terms between the inverters —Energy Gateways (EGs)— connected in grid-tied microgrids (MGs). The main feature of the presented approach is the use of the EGs as controlled current sources that can compensate fundamental non-efficient load current terms in addition to the generation of fundamental positive-sequence active current, avoiding the use of shunt active power filters. The approach relies on the so-called System of Constant References (SoCR) that is based on the symmetrical components decomposition and dq0 transformation. SoCR procedure decouples efficient and non-efficient components of the instantaneous load currents, transforming all of them into six constant references. The optimization algorithm uses a new approach for the calculation of the peak currents in each phase, avoiding non-convex problems when determining the currents of the EGs considering their operating limits. A medium-power size MG that includes photovoltaic and wind generators, as well as, a battery energy storage system is considered to evaluate the capabilities of the proposal. There were evaluated four scenarios: baseline, balanced distribution, proportional distribution, and optimal distribution. All scenarios, except optimal distribution scenario, surpass the current limits for the EGs connected. The results highlight the benefits of using the EGs as active agents in MG efficient operation and demonstrate how the optimization approach achieves the goal of maintaining the generation capabilities of EGs at the same time that compensates the non-efficient current terms demanded by the load.

Anti-windup ADRC design for temperature control systems with output delay against asymmetric input constraint

To tackle the asymmetric input constraint typically involved with industrial temperature control systems, e.g., there is a tuning range from 0 to 100% in the heating power, an anti-windup active disturbance rejection control (ADRC) is proposed for the practical application, in particular for dealing with output delay. Based on an artificial symmetric transformation for the asymmetric input constraint along with a delay-free output prediction, an anti-windup extended state observer (AESO) is firstly constructed to simultaneously estimate the delay-free system state and external disturbance for control design. When the input saturation constraint occurs, the proposed AESO could also offer anti-windup compensation. Then, a feedback controller is analytically derived by assigning repetitive-type poles for the characteristic equation of the closed-loop structure, followed by a set-point prefilter design to ensure no overshoot and output tracking deviation. Tractable linear matrix inequality based conditions are rigorously established to guarantee the asymptotic stability of the resulting closed-loop system under a specified initial condition. A benchmark example from a recent reference is used to verify the superiority of the proposed control method over some existing anti-windup control designs. Moreover, a real application to the temperature control of a jacketed crystallizer is shown in comparison with a recently developed control method with no anti-windup compensation.

A symmetric prior knowledge based deep learning model for intracerebral hemorrhage lesion segmentation.

Background: Accurate localization and classification of intracerebral hemorrhage (ICH) lesions are of great significance for the treatment and prognosis of patients with ICH. The purpose of this study is to develop a symmetric prior knowledge based deep learning model to segment ICH lesions in computed tomography (CT). Methods: A novel symmetric Transformer network (Sym-TransNet) is designed to segment ICH lesions in CT images. A cohort of 1,157 patients diagnosed with ICH is established to train (n = 857), validate (n = 100), and test (n = 200) the Sym-TransNet. A healthy cohort of 200 subjects is added, establishing a test set with balanced positive and negative cases (n = 400), to further evaluate the accuracy, sensitivity, and specificity of the diagnosis of ICH. The segmentation results are obtained after data pre-processing and Sym-TransNet. The DICE coefficient is used to evaluate the similarity between the segmentation results and the segmentation gold standard. Furthermore, some recent deep learning methods are reproduced to compare with Sym-TransNet, and statistical analysis is performed to prove the statistical significance of the proposed method. Ablation experiments are conducted to prove that each component in Sym-TransNet could effectively improve the DICE coefficient of ICH lesions. Results: For the segmentation of ICH lesions, the DICE coefficient of Sym-TransNet is 0.716 0.031 in the test set which contains 200 CT images of ICH. The DICE coefficients of five subtypes of ICH, including intraparenchymal hemorrhage (IPH), intraventricular hemorrhage (IVH), extradural hemorrhage (EDH), subdural hemorrhage (SDH), and subarachnoid hemorrhage (SAH), are 0.784 0.039, 0.680 0.049, 0.359 0.186, 0.534 0.455, and 0.337 0.044, respectively. Statistical results show that the proposed Sym-TransNet can significantly improve the DICE coefficient of ICH lesions in most cases. In addition, the accuracy, sensitivity, and specificity of Sym-TransNet in the diagnosis of ICH in 400 CT images are 91.25%, 98.50%, and 84.00%, respectively. Conclusion: Compared with recent mainstream deep learning methods, the proposed Sym-TransNet can segment and identify different types of lesions from CT images of ICH patients more effectively. Moreover, the Sym-TransNet can diagnose ICH more stably and efficiently, which has clinical application prospects.

Miniature and Symmetrical Transformer Based on Through-Silicon Vias

A high-density symmetrical transformer based on through-silicon via (TSV) is proposed in this article. The primary winding and secondary winding have strong symmetry, and the inductance mismatch is less than 0.1%, so the transformer structure is suitable for differential circuit. Compared with transformers in other literatures, the proposed transformer has advantages in area and efficiency, which is reflected in that the on-chip area is greatly reduced by 58% to 89%, and the coupling coefficient can reach more than 0.92.

The aesthetics of frieze patterns: Effects of symmetry, motif, and element size.

Frieze patterns appear frequently in architectural designs and ornamental patterning but their aesthetic qualities have never been studied experimentally. In the first experiment, 39 undergraduates used a seven-point rating scale to assess the perceived beauty of the seven basic frieze types presented at a horizontal orientation. The friezes consisted of individual curved and linear motifs as well as random textures. Friezes that filled the entire pattern region and which contained emergent global features were preferred the most. In a second experiment, we utilized horizontal texture friezes that were completely filled and which varied in size and number of elements. Participants preferred patterns with larger features, probably because they make detection of the symmetric transformations more visible. The frieze with the greatest number of symmetries was preferred most but symmetric complexity by itself could not completely account for the predicted preference ordering. In both studies, friezes containing horizontal mirrors (translation, 180° rotation, horizontal mirror, vertical mirror, and glide reflection and translation, horizontal mirror, and glide reflection) were preferred far more than any other condition. Horizontal symmetry may enhance perceived beauty in these cases because it runs parallel to and so emphasizes the overall frieze orientation.

Lie symmetry analysis, exact solutions and power series solutions of the logarithmic Monge–Ampère flow evolution equation

In this paper, the logarithmic Monge–Ampère flow evolution equation is studied by the classical Lie symmetry analysis method. First, the optimal system was obtained by the adjoint representation table. Second, by performing symmetric transformation on the optimal system, the corresponding ordinary differential equations are obtained, and the Jacobian elliptic function solution, the periodic solution and the power series solution are constructed. Finally, the dynamical behaviors of the solutions are described by choosing arbitrary parameters.

Cascaded Transformers-Based Multilevel Inverters With NPC

The basic structure and generalization of two cascaded transformer multilevel inverters (CTMIs) are proposed in this paper. Such configurations are based on cascaded symmetrical transformers coupled to two-level (2L) legs and three-level (3L) neutral-point clamped (NPC) legs. One configuration has a shared 2L leg, connected to all transformers. The other configuration consists of multiple shared legs, where each is connected between two transformers. A modulation technique is also presented that allows only one leg of the proposed inverters operates at high frequency, while all other legs operate at low frequency. Compared to three conventional CTMIs, the proposed structures can produce more output voltage levels using a smaller number of switches and transformers, offering a better power quality, less weight, volume, and cost of the system. Moreover, the proposed inverters offer a natural balancing property that can self-regulate the dc-link capacitor voltages. Simulation and experimental results are presented in order to demonstrate the performance and feasibility of the proposed configurations.