Linear Transformation Research Articles

Robust active vibration control of flexible smart beam by μ-synthesis

This paper presents a comprehensive method for designing a robust active vibration control system to suppress low-frequency vibrations in smart structures. A novel finite element method based on the first-order shear deformation theory is used to calculate the dynamic response of a smart beam. Through a comprehensive system identification process, the uncertain model of the smart beam is extracted considering both the magnitude and phase. The model fits the experimental data successfully. In addition, a generalized low-frequency vibration control performance function is designed for the piezoelectric smart beam. Using a linear fractional transformation, the system is converted into a standard μ-synthesis control framework, and the controller K is synthesized using structural singular values μ. The effectiveness of the proposed method is experimentally validated using a setup with a piezoelectric smart beam. The experimental results suggest that the proposed control method exhibits robust stability and robust performance, effectively enhancing the performance of smart structure control in various scenarios. The proposed control framework utilizes structured singular value analysis to provide optimal robust stability margins and superior robust control performance, effectively addressing system uncertainties and non-linearities.

A model-based design approach for low-pressure axial fan blades considering the air flow system characteristics

The paper puts forward a computer methodology for designing low-pressure axial fan blades for small-capacity refrigeration applications. Based on the blade element theory (BET), the airfoil efficiency of the airfoil, the principles of mass and momentum conservation together with empirical correlations for the flow irreversibilities, a mathematical model was devised for screening the blade geometric parameters (e.g., radial chord and pitch variation, and hub radius) by varying the induction coefficient distribution for a given fan diameter, motor speed, and airflow system characteristic curve. The best blade configuration is selected by means of a tailor-made optimization algorithm and undergoes a series of linear transformations for translating the fan parametrization into a CAD drawing. Two new fan blades were designed, one for maximum blade efficiency (MBE) and another for maximum airflow rate (MAR). In comparison with the free-swirl design approach, a standard procedure adopted in the open literature, the proposed blades showed an efficiency and an airflow by 20 % (MBE) and 14 % (MAR) higher than the reference. The airflow characteristics of the new designs were also assessed by means of wind-tunnel testing, which confirmed an increase of 11 % in the case of MBE design, while an enhancement of 10 % was observed in the case of MAR design.

A calibration method for telecentric line-scan cameras with an enhanced dynamic imaging model and initial estimates derived from direct linear transformation

This study presents a calibration method for telecentric line-scan cameras, incorporating a dynamic imaging model and initial estimates derived from direct linear transformation. The enhanced dynamic imaging model includes an inclination parameter instead of velocities in three orthogonal spatial directions. It is applicable to any direction of motion, considers lens distortion, and accommodates the line sensor at an arbitrary position relative to the optical axis. Employing the enhanced camera model, the initial values of telecentric line-scan camera parameters are determined derived from direct linear transformation. Sensitivity of our method with respect to the noise level of image points and the number of pattern planes are assessed through numerical simulations, while effectiveness and robustness are validated through experiments using real-world data, achieving a reprojection error of 0.6386 pixels and a standard deviation of 0.0160 pixels. The versatility of the proposed method can be extended to measurement applications utilizing flatbed scanners.

State Observer Synchronization of Three-dimensional Chaotic Oscillatory Systems Based on DNA Strand Displacement.

Currently, DNA strand displacement (DSD) as the theoretical basis of DNA chemical reaction networks (CRNs) has promoted the development of chaotic synchronization technique. This paper introduces the synchronization technology of two isomorphic three-dimensional chaotic systems based on DNA strand displacement under state observer. By studying the theoretical knowledge of DNA molecules, multiple DSD reactions are used to construct three-dimensional chaotic system. Based on two isomorphic chaotic systems, the linear transformation system and the state observer system are designed according to the theory of state observer construction. In addition, in order to realize the synchronization of chaotic systems, a coupling controller is designed between the drive system and the linear transformation system, and a soft variable-structure controller is designed between the state observer system and the response system. Through multiple DSD reactions, the chemical reaction networks of four chaotic systems and two controllers are constructed, and they are cascaded to realize the synchronization of two isomorphic three-dimensional chaotic systems. Numerical simulations verify the effectiveness and robustness of the scheme. Our work will extend and provide a reference for new methods to achieve synchronization of chaotic systems using DSD.

Differentials of the basis in Clifford Geometric Algebra

In this paper we discuss the dynamic effects of the varying frames. The differential of frame or basis vectors is always equivalent to a linear transformation of the frame, and the linear transformation is not the same in different contexts. In differential geometry, the linear transformation is the connection operator. While in quantum mechanics, the operator algebra corresponds to the differentials of matrices. Corresponding to the variation of the metric, the variation of the frame contains a unusual fourth-order tensor. We also derive the Lie differential of the frame corresponding to the Lorentz transformation group. The definition of differential of the frame is different, so the corresponding linear transformation is also different. In this paper, the unified point of view to deal with the variation of frame or basis vectors will bring great convenience to the research and application of Clifford algebras.

Neutron-producing gas puff Z-pinch experiments on a fast, low-impedance, 0.5 MA linear transformer driver

A study on the neutron production from single and double gas puff Z-pinches on the CESZAR linear transformer driver with ∼0.45 MA current and 170 ns rise time is presented. Total neutron yield measurements made with a LaBr activation detector are compared for three configurations, using a double nozzle setup. When a single, hollow, deuterium gas shell was used, reliable implosions could only be attained at higher load mass than the optimal value to match implosion time with the driver rise time, with neutron yields of ∼106 per pulse. The use of a double gas puff configuration with a deuterium center jet allowed a reduction in the shell density and operation closer to machine-matched conditions, recording up to (4.1 ± 0.3) × 107 neutrons/pulse when either Kr or D2 was used in the shell. For a comparable mass and implosion time, using a higher atomic-number gas in the outer shell results in more unstable plasma surface and smaller plasma radius at the location of instability bubbles, which, however, do not seem to consistently correlate with a higher neutron yield. Comparing implosion dynamics with models and neutron yields with literature scaling suggests that the machine current is not well coupled to the plasma during the final stages of compression. Optimizing current and energy coupling to the pinched plasma is critical to improving performance, particularly in low-impedance drivers.

Enhancing analysis of diadochokinetic speech using deep neural networks

Diadochokinetic speech tasks (DDK) involve the repetitive production of consonant-vowel syllables. These tasks are useful in detecting impairments, differential diagnosis, and monitoring progress in speech-motor impairments. However, manual analysis of those tasks is time-consuming, subjective, and provides only a rough picture of speech. This paper presents several deep neural network models working on the raw waveform for the automatic segmentation of stop consonants and vowels from unannotated and untranscribed speech. A deep encoder serves as a features extractor module, replacing conventional signal processing features. In this context, diverse deep learning architectures, such as convolutional neural networks (CNNs) and large self-supervised models like HuBERT, are applied for the extraction process. A decoder model uses derived embeddings to identify frame types. Consequently, the paper studies diverse deep architectures, ranging from linear layers, LSTM, CNN, and transformers. These architectures are assessed for their ability to detect speech rate, sound duration, and boundary locations on a dataset of healthy individuals and an unseen dataset of older individuals with Parkinson’s Disease. The results reveal that an LSTM model performs better than all other models on both datasets and is comparable to trained human annotators.

Insulator Defect Detection Based on YOLOv5s-KE

To tackle the issue of low detection accuracy in insulator images caused by intricate backgrounds and small defect sizes, as well as the requirement for real-time detection on embedded and mobile devices, this research introduces the YOLOv5s-KE model. Integrating multiple strategies, YOLOv5s-KE aims to boost detection accuracy significantly. Initially, an enhanced anchor generation method utilizing the K-means++ algorithm is proposed to generate more appropriate anchor boxes for insulator defects. Moreover, an attention mechanism is integrated into both the backbone and neck networks to enhance the model’s capacity to focus on defect features and resist interference. To improve the detection of small defects, the EIoU loss function is implemented in place of the original CIoU loss function. In order to meet the real-time detection needs on embedded and mobile devices, the model is further refined through the integration of Ghost convolution for lightweight feature extraction and a linear transformation to reduce the computational burden of standard convolution. A channel pruning strategy is deployed to optimize the sparsely trained network, diminishing redundancy, and improving model generalization. Additionally, the CARAFE operator replaces the original upsampling operator to minimize model parameters and elevate detection speed. Experimental outcomes demonstrate that YOLOv5s-KE achieves a detection accuracy of 92.3% on the Chinese transmission line insulator dataset, marking a 5.2% enhancement over the original YOLOv5s. The streamlined version of YOLOv5s-KE achieves a detection speed of 94.3 frames per second, indicating an improvement of 30.1 frames per second compared to the original model. Model parameters are condensed to 9.6 M, resulting in a detection accuracy of 91.1%. This study underscores the precision and efficiency of the proposed approach, suggesting that the advanced strategies explored introduce novel possibilities for insulator defect detection.

Sharper Hardy Uncertainty Relations on Signal Concentration in Terms of Linear Canonical Transform

Sharper Hardy Uncertainty Relations on Signal Concentration in Terms of Linear Canonical Transform

Higher Order Polynomial Transformer for Fine-Grained Freezing of Gait Detection.

Freezing of Gait (FoG) is a common symptom of Parkinson's disease (PD), manifesting as a brief, episodic absence, or marked reduction in walking, despite a patient's intention to move. Clinical assessment of FoG events from manual observations by experts is both time-consuming and highly subjective. Therefore, machine learning-based FoG identification methods would be desirable. In this article, we address this task as a fine-grained human action recognition problem based on vision inputs. A novel deep learning architecture, namely, higher order polynomial transformer (HP-Transformer), is proposed to incorporate pose and appearance feature sequences to formulate fine-grained FoG patterns. In particular, a higher order self-attention mechanism is proposed based on higher order polynomials. To this end, linear, bilinear, and trilinear transformers are formulated in pursuit of discriminative fine-grained representations. These representations are treated as multiple streams and further fused by a cross-order fusion strategy for FoG detection. Comprehensive experiments on a large in-house dataset collected during clinical assessments demonstrate the effectiveness of the proposed method, and an area under the receiver operating characteristic (ROC) curve (AUC) of 0.92 is achieved for detecting FoG.

Viscosity of deep eutectic solvents: Predictive modeling with experimental validation

Viscosity, the measure of a fluid's resistance to deformation, is a critical parameter in many industries. Being able to accurately predict viscosity is essential for the successful design and optimization of technological processes. In this research, regression models were created to predict the viscosity of deep eutectic solvents (DESs). Machine learning models were trained using a data set of 3440 data points for two component DESs. Different algorithms, such as Multiple Linear Regression, Random Forest, CatBoost, and Transformer CNF, were employed alongside a variety of structural representations like fingerprints, σ-profiles, and molecular descriptors. The effectiveness of the models was assessed for interpolation tasks within the training data and extrapolation outside of it. The results indicate that a rigorous splitting of the dataset into subsets is necessary to accurately evaluate the performance of the models. Two new choline chloride-based DESs were prepared and their viscosities were measured to evaluate the predictive capabilities of the models. The CatBoost algorithm with CDK molecular descriptors was chosen as the recommended model. The average absolute relative deviations (AARD) of this model exhibited fluctuations during 5-fold cross-validation, ranging from 10.8 % when interpolating within the dataset to 88 % when extrapolating to new mixture components. The open access model was presented in this study (http://chem-predictor.isc-ras.ru/ionic/des/).

FORMULATION OF THE CORRELATION ON THE REDUCED LINEAR BIQUATERNION CANONIC TRANSFORMATION

This research aims to formulate a correlation theorem on the canonical transformation of reduced linear biquaternion (RBLCT).This research is a literature review conducted at the Department of Industrial Technology, Makassar PSDKU Graphics Engineering Study Programme, Politeknik Negeri Media Kreatif.The definition of reduced biquaternion linear canonical transformation (RBLCT) is obtained by first constructing the definition of reduced biquaternion Fourier transform (FTRB) and investigating its properties by replacing the kernel of Fourier Transform with the kernel of FTRB in the definition of Linear Canonical Transformation (LCT). The proposed Correlation Theorem for RBLCT is an extension of the correlation theorem of linear canonical transform to the domain of RBLCT. A different proof of the Parseval formula for RBLCT is also given whose proof is much simpler by using the conjugacy property of the RBLCT kernel. As an application of the obtained results, the RBLCT correlation theorem is briefly discussed to study frequency-swift filters in general.

On Laplace invariants of two-dimensional nonlinear equations of the second order with homogeneous polynomial

We study two-dimensional nonlinear partial differential equations of the second order with variable coefficients. The left-hand side of these equations is a homogeneous polynomial of the second degree in unknown function and its derivatives. We consider a set of linear multiplicative transformations of the unknown function which keep the form of the initial equation. By analogy with linear equations, the Laplace invariants are determined as the invariants of this transformation. The expressions for the Laplace invariants in terms of the coefficients of the equation and their first derivatives are obtained. For the considered equations, we found the equivalent systems of the first order equations containing the Laplace invariants. It is shown that if one of the Laplace invariants equals zero, the corresponding system is reduced to one equation of the first order. Also in this case, the solution of the initial equation can be obtained in quadratures if some additional conditions on the coefficients are met. The investigations are executed for a hyperbolic equation with a mixed derivative and for a nonlinear second order equation of the general form with a homogeneous polynomial of the second degree in unknown function and its derivatives. We obtained for these cases the Laplace invariants and equivalent systems of the first order equations.

The horizontal tensor complementarity problem

This article explores a new type of nonlinear complementarity problem, namely the horizontal tensor complementarity problem (HTCP), which is a natural extension of the horizontal linear complementarity problem studied in Sznajder [Degree-theoretic analysis of the vertical and horizontal linear complementarity problems [Ph.D. Thesis]. University of Maryland Baltimore County; 1994]. We extend the concepts of R 0 , R and P pairs from a pair of linear transformations given in Chi et al. [The weighted horizontal linear complementarity problem on a Euclidean Jordan algebra. J Global Optim. 2019;73:153–169] to a pair of tensors. When a given pair of tensors has these properties, we use degree-theoretic tools to discuss the existence and boundedness of solutions to the HTCP. Finally, we study a uniqueness result of the solution of the HTCP.

Enhancing capacity estimation of retired electric vehicle lithium-ion batteries through transfer learning from electrochemical impedance spectroscopy

The low economic feasibility caused by inefficient testing and inaccurate performance estimation is one of the main bottlenecks in the echelon utilization of large-scale retired batteries. This study proposes a fast and accurate capacity estimation method for retired batteries based on electrochemical impedance spectroscopy (EIS). Firstly, the EIS of the batteries that experience multi-condition aging in the laboratory are collected. EIS characteristic parameter sequences highly related to battery performance, including real part and magnitude, are directly extracted to establish a base bi-directional long short-term memory model. Secondly, a transfer learning method based on feature matching is designed, which applies a linear transformation layer to map the features between the source and target domains. The proposed transfer learning method has been effectively validated on laboratory battery data measured at different temperatures and retired battery datasets of different material types. The improvements are especially notable for retired batteries. The detection time has been reduced, with each cell requiring only 1.67 min. And using only a small amount of data as input for transfer learning can achieve an accuracy improvement of over 90 %, indicating an effective transfer channel from the base model established on laboratory small-capacity battery aging data to large-capacity retired battery data is successfully established for the first time. For retired nickel-cobalt-manganese batteries, the mean absolute percentage error (MAPE) and the root mean square percentage error (RMSPE) are 2.33 % and 2.75 %, respectively, while for retired lithium-iron-phosphate batteries, the MAPE and RMSPE reached 4.12 % and 5.04 %, respectively. The results demonstrate the proposed method reduces the cost of repeated testing, modeling, and training for specific retired batteries while maintaining the accuracy of capacity estimation. This advancement helps to improve the efficiency of large-scale retired battery grading, and injects new momentum into facilitating more effective decision-making processes.

A novel algorithm developed using machine learning and a J-ACCESS database can estimate defect scores from myocardial perfusion single-photon emission tomography images.

Stress myocardial perfusion single-photon emission computed tomography (SPECT) imaging (MPI) has been used to diagnose and predict the prognoses of patients with coronary artery disease (CAD). An ongoing multicenter collaboration established a Japanese database (J-ACCESS) in 2001 that includes a risk model and expert interpretations. The present study aimed to develop a novel algorithm using machine learning (ML) and resources from the J-ACCESS database to aid SPECT image interpretation. We analyzed data from 1288 patients in J-ACCESS 3 and 4 databases. Three-dimensional (3D) stereoscopic images of left ventricular myocardial perfusion were reconstructed with linear transformation from the original short-axis data. Segments were extracted from U-Net, then features were extracted from each segment during the ML process. We estimated segmental scores based on weighted features obtained from fully connected layers. Correlations between segment scores interpreted by nuclear cardiology experts and estimated by ML were evaluated using a 17-segment model, summed stress (SSS), summed rest (SRS), and summed difference (SDS) scores, and ratios (%) of summed different scores (%SDS). The complete concordance rate of scores assessed by the experts and estimated by ML was 79.6%. The underestimated and overestimated rates were 10.3% and 10.0%, respectively. Associations between defect scores assessed by experts and ML were close, with correlation coefficients (r) of 0.923, 0.917, 0.842 and 0.853 for SSS, SRS, SDS, %SDS, respectively (p < 0.0001 for all). We created a new algorithm to estimate MPI scores using ML and the J-ACCESS database. This algorithm should provide accurate MPI interpretation even in facilities without specialist nuclear cardiologists, and might facilitate therapeutic decision-making and predict prognoses.

A Linear time shrinking-SL(t)-ViT approach for brain tumor identification and categorization

Automated brain tumor detection and classification systems have gained popularity in recent years because traditional diagnosis procedures are time-consuming and costly in nature. Deep learning(DL) methods, specifically pre-trained convolutional neural networks (CNNs), have shown promising results in accurately and rapidly classifying brain tumors. However, the lack of diverse magnetic resonance imaging (MRI) datasets has hindered the ability of DL algorithms to generalize effectively. To address this issue, this paper proposes a DL model using generative adversarial networks (GANs) in conjunction with data augmentation strategies and a structural similarity loss function employed for generating annotated images. A novel DL model inspired from Vision Transformer, Shrinking Linear Time Vision Transformer (SL(t)-ViT) network model is proposed for disease data classification. The model underwent extensive evaluation across multiple datasets, employing standard performance metrics to assess its efficacy in brain tumor identification. The proposed model achieved remarkable testing accuracies of 0.995, 0.996, 0.9954, 0.998, and 0.997 for binary classification tasks across multiple datasets, and 0.986, 0.982, 0.985, and 0.993 for multi-class classification tasks. These results underscore the superior performance of our proposed model, showcasing its capability to outperform state-of-the-art techniques. Specifically, it demonstrated a substantial margin of improvement, ranging from 1-2% for binary classification and 9-10% for multi-class classification, solidifying its position as a leading approach in brain tumor identification. Results demonstrate the efficacy of the proposed model, outperforming other models. Overall, this study highlights the potential of SL(t)-ViT and GANs in improving the accuracy, resource consumption, and efficiency of brain tumor diagnosis.

Quantum Attacks on MIBS Block Cipher Based on Bernstein–Vazirani Algorithm

Because of the substantial progress in quantum computing technology, the safety of traditional cryptologic schemes is facing serious challenges. In this study, we explore the quantum safety of the lightweight cipher MIBS and propose quantum key-recovery attacks on the MIBS cipher by utilizing Grover’s algorithm and Bernstein–Vazirani algorithm. We first construct linear-structure functions based on the 5-round MIBS cipher according to the characteristics of the linear transformations, and then we obtain a quantum distinguisher of the 5-round MIBS cipher by applying Bernstein–Vazirani algorithm to the constructed functions. Finally, utilizing this distinguisher and Grover’s algorithm, we realize a 7-round key-recovery attack on the MIBS cipher, and then we expand the attack to more rounds of MIBS based on a similar idea. The quantum attack on the 7-round MIBS requires 156 qubits and has a time complexity of 210.5. An 8-round attack requires 179 qubits and has a time complexity of 222. Compared with existing quantum attacks, our attacks have better time complexity when attacking the same number of rounds.

A map neuron with piezoelectric membrane, energy regulation and coherence resonance

The cell membrane has a layered structure, which separates the intracellular and extracellular ions for developing gradient electromagnetic field, and its flexible property enables the capacitance dependence on the shape deformation due to external stimuli. Therefore, piezoelectric membrane can be suitable to describe the biophysical characteristic of cell membrane and equivalent circuit approach becomes important. In this paper, two capacitors are connected via a piezoelectric ceramic and two additive memristive channels are combined to mimic the neural activity response with exact energy description. Furthermore, linear transformation is applied to obtain an equivalent piezoelectric map neuron and energy function is provided to explore the adaptive energy regulation on mode selection in neural activities. Coherence resonance is detected and analyzed. The map neuron can also be considered as an auditory neuron for perceiving acoustic signals and its membrane property is considered from physical aspect.

Multiparameter cascaded quantum interferometer

We theoretically propose a multiparameter cascaded quantum interferometer in which a two-input and two-output setup is obtained by concatenating 50:50 beam splitters with n independent and adjustable time delays. A general method for deriving the coincidence probability of such an interferometer is given based on the linear transformation of the matrix of beam splitters. As examples, we analyze the interference characteristics of one-, two-, and three-parameter cascaded quantum interferometers with different frequency correlations and input states. Some typical interferograms of such interferometers are provided to reveal richer and more complicated two-photon interference phenomena. This work offers a general theoretical framework for designing versatile quantum interferometers and provides a convenient method for deriving the coincidence probabilities involved. In principle, arbitrary two-input and two-output experimental setups can be designed with the framework. Potential applications can be found in the complete spectral characterization of two-photon states, multiparameter estimation, and quantum metrology.