Vector Method Research Articles

Higher order angular kinematic quantities computed with dual numbers

We present a comprehensive methodology for calculating angular kinematic quantities up to the fourth order using automatic differentiation with dual numbers. Two approaches are employed: the vector method, which uses position vectors and derivatives of three non-collinear points, and the body-fixed frame (BFF) method, which differentiates an attached basis to the rigid body. The BFF method avoids indeterminacy and divergence issues. Numerical examples, drawn from robotics and classical mechanics, validate the methodology and demonstrate its robustness. Our approach effectively addresses challenging inverse problems of acceleration, jerk, and jounce/snap.

Next frontier in cancer treatment: an iPSC supported CAR-T cell therapies

The spread of cancer and huge number of cancer related deaths has made it imperative for scientist to search new diagnostic, prognostic and treatment tools for its effective management. Chimeric Antigen Receptor (CAR) T-cell (CAR-T) therapy has been brought into limelight as novel treatment strategy for cancer. In this review we briefly introduced the CAR-T therapy highlighting its successful application for various cancers along with the possibility of integrating the induced pluripotent stem cell (iPSC) technology with CAR-T technology to overcome its intrinsic limitation. The mechanism of CAR-T technology is based on the isolation of white blood cells through leukapheresis from patients’ blood or healthy donors followed by the isolation of T-cells (a type of immune cells). The isolated T-cells are engineered through using a viral vector or other methods to incorporate the CAR gene and expanded in the lab. This modification enables T cells to distinguish and attack antigens on the surfaces of cancer cells. However, this approach is not without its inherent limitations. CAR-T cell therapy notable limitation is the exhaustible availability of T cells within the donor or patient system, which can restrict the feasibility and effectiveness of therapeutic intervention. A potential solution to this limitation may lie in synergizing CAR-T technology with the induced pluripotent stem cell (iPSC) technology. The inherent potential of iPSC technology lies in its ability to provide an endless supply of T-cell resources. A substantial amount of research revealed the production of various human CAR-T cells using iPSC technology. Therefore, such combinatorial approach utilizing CAR-T technology for mounting an immunological attack against cancer with continues supply of T-cells through iPSCs technology can prove revolutionary in designing novel and pragmatic methods for cancer treatment.

Automation of quantum dot measurement analysis via explainable machine learning

Abstract The rapid development of quantum dot (QD) devices for quantum computing has necessitated more efficient and automated methods for device characterization and tuning. Many of the measurements acquired during the tuning process come in the form of images that need to be properly analyzed to guide the subsequent tuning steps. By design, features present in such images capture certain behaviors or states of the measured QD devices. When considered carefully, such features can aid the control and calibration of QD devices. An important example of such images are so-called triangle plots, which visually represent current flow and reveal characteristics important for QD device calibration. While image-based classification tools, such as convolutional neural networks (CNNs), can be used to verify whether a given measurement is good and thus warrants the initiation of the next phase of tuning, they do not provide any insights into how the device should be adjusted in the case of bad images. This is because CNNs sacrifice prediction and model intelligibility for high accuracy. To ameliorate this trade-off, a recent study introduced an image vectorization approach that relies on the Gabor wavelet transform [1]. Here we propose an alternative vectorization method that involves mathematical modeling of synthetic triangles to mimic the experimental data. Using explainable boosting machines, we show that this new method offers superior explainability of model prediction without sacrificing accuracy. This work demonstrates the feasibility and advantages of applying explainable machine learning techniques to the analysis of quantum dot measurements, paving the way for further advances in automated and transparent QD device tuning.

MODEL OF THREE-PHASE ASYNCHRONOUS MOTOR WITH SHORT CIRCUIT ROTOR IN MATLAB PACKAGE

The presented paper examines the specifics of researching the mathematical apparatus of the model of a three-phase АМ with a short-circuited rotor in the matlab package. It has been proven that three-phase АМ with a short-circuited rotor form the basis of a modern electric drive in many branches of industry, agro-industrial complex and transport. A model was developed in the matlab package, which describes the operation of a frequency-regulated electric drive, taking into account theoretical analysis and experimental studies. In the scientific work, the task of combining mathematical modeling and modern computer technologies, which are based on application packages, is fulfilled, which gives the researcher the opportunity to deeply study the processes that occur in all links of the electric drive. With the help of the proposed model, quantitative and qualitative analysis of electromagnetic and electromechanical processes in transient and established modes of operation, research of dynamic mechanical and operational characteristics, analysis of spectral composition and hodographs of spatial vectors of phase voltage and current of an АМ can be carried out. The considered model can be applied not only when powering an asynchronous motor from a three-phase source with a sinusoidal form of voltage, but also when powering it from power semiconductor converters. The scheme of a virtual installation for modeling and researching processes in a three-phase АМ with a short-circuited rotor was developed in the work. The analyzed installation includes the following blocks: three-phase AC voltage source, three-phase AC voltage meter, Selector block, Voltage Measurement block, three-phase АМ under investigation, static torque assignment block, active and reactive power meter, Subsystem block. An analysis of electromagnetic processes in static and electromechanical converters of electrical energy was carried out using the spatial vector method, which has found wide use. With the help of software packages, instantaneous values of symmetrical three-phase variables such as voltage, current, flux linkage were mathematically transformed into one vector.

From Fact Drafts to Operational Systems: Semantic Search in Legal Decisions Using Fact Drafts

This research paper presents findings from an investigation in the semantic similarity search task within the legal domain, using a corpus of 1172 Hungarian court decisions. The study establishes the groundwork for an operational semantic similarity search system designed to identify cases with comparable facts using preliminary legal fact drafts. Evaluating such systems often poses significant challenges, given the need for thorough document checks, which can be costly and limit evaluation reusability. To address this, the study employs manually created fact drafts for legal cases, enabling reliable ranking of original cases within retrieved documents and quantitative comparison of various vectorization methods. The study compares twelve different text embedding solutions (the most recent became available just a few weeks before the manuscript was written) identifying Cohere’s embed-multilingual-v3.0, Beijing Academy of Artificial Intelligence’s bge-m3, Jina AI’s jina-embeddings-v3, OpenAI’s text-embedding-3-large, and Microsoft’s multilingual-e5-large models as top performers. To overcome the transformer-based models’ context window limitation, we investigated chunking, striding, and last chunk scaling techniques, with last chunk scaling significantly improving embedding quality. The results suggest that the effectiveness of striding varies based on token count. Notably, employing striding with 16 tokens yielded optimal results, representing 3.125% of the context window size for the best-performing models. Results also suggested that from the models having 8192 token long context window the bge-m3 model is superior compared to jina-embeddings-v3 and text-embedding-3-large models in capturing the relevant parts of a document if the text contains significant amount of noise. The validity of the approach was evaluated and confirmed by legal experts. These insights led to an operational semantic search system for a prominent legal content provider.

Precise beam control in optical phased arrays using the four steps rotating element electric field vector method

The integrated optical phase arrays (OPAs) possess the capability for rapid modulation and precise control of output beam deflection, making it widely applicable in fields such as three-dimensional terrain reconstruction, autonomous driving, and holographic imaging. However, the unknown initial phase introduced during the manufacturing and packaging processes of current OPAs results in low beam alignment quality and random output beam phases, significantly limiting the development and application of OPAs. To address these challenges, this paper proposes a precise control technology for OPA output beams, utilizing a beam calibration method we have developed, known as the Four Steps Rotating Element Electric Field Vector Method. This method enables rapid and accurate calibration, achieving precise phase control for each antenna on the OPA chip by calibrating the phase shift and controlling the voltage relationship. It overcomes the challenges of unknown phase distributions common in passive calibration methods, aligning the calibrated phase distribution more closely with theoretical expectations. The proposed method further enhances control over the OPA output beam. Based on this technology, we constructed an experimental platform to achieve a main lobe with a PSLR of 15.98 dB and successfully generated vortex beams using a 4×4 OPA. This innovation not only addresses the initial phase issues caused by manufacturing errors but also significantly enhances the precise control of OPA phases, expanding its applications in LiDAR systems.

ANSYS Modelling of Piezoelectric Smart Beam using Ritz Vector Method and Sub-structuring Analysis

Abstract Finite element analysis (FEA) is an important tool for smart structure modelling, particularly in the context of piezoelectric beams. A key challenge in such modelling is the derivation of electro-elastic coupling, which explains how these structures respond mechanically to electrical loading. Traditional methods rely on intricate shape functions that encompass both electrical and mechanical degrees of freedom, rendering the process complex. In this study, an innovative approach—the so-called Ritz vector method— which facilitates modelling of the system based on loading effect is implemented to simplify electro-elastic coupling calculations. The method previously applied in MSC Nastran with a thermal analogy system and validated experimentally is now implemented in the widely accessible ANSYS software. By harnessing ANSYS’ robust piezoelectric capabilities and sub-structuring analysis for matrix extraction, the essential piezoelectric coupling and dielectric matrices are derived for piezoelectric stack and patch actuator driven cantilevered beams. Subsequently, state space models of these smart structures are constructed using MATLAB and results are compared with ANSYS FEA static and dynamic response. Active Disturbance Rejection Control (ADRC) was implemented on the modelled beams and results show significant suppression of free vibration due to impulse excitation of the tip. This work portrays the potential of the Ritz vector method, a powerful yet underexplored tool that simplifies electro-elastic coupling calculations for piezoelectric smart structures.

DEVELOPMENT OF A CREDIT SCORING MODEL USING MACHINE LEARNING FOR COMMERCIAL BANKS IN VIETNAM

In an increasingly competitive financial market, developing an accurate and efficient credit scoring model is crucial for banks to make informed credit decisions, and to help customers obtain credit products that match their financial capabilities. This study aims to develop a credit scoring model for individual customers of Vietnamese banks using machine learning techniques. This article will use a set of financial and non-financial indicators as inputs for various machine learning models such as Logistic Regression, K-nearest Neighbor, Decision Tree, Random Forest, LightGBM, and Support Vector Method. The obtained results from these models will be carefully compared and evaluated to ultimately select the best credit scoring model for the bank. This study leverages Google Colab, a cloud-based platform, for comprehensive data analysis and model development, ensuring a robust and data-driven approach. This study hopes to provide a useful solution for Vietnamese banks in managing credit risk and improving their business performance.

Phased Array Antenna Calibration Based on Autocorrelation Algorithm.

The problem of calibrating phased array antennas in a noisy environment using an autocorrelation algorithm is investigated and a mathematical model of the autocorrelation calibration method is presented. The proposed calibration system is based on far-field scanning of the phased array antenna in an environment with internal noise and external interference. The proposed method is applied to a phased array antenna and compared with traditional rotating-element electric-field vector methods, which involve identifying the maximum and minimum vector-sum points (REVmax and REVmin, respectively). The proposed calibration system is verified for a phased array antenna at 3 GHz. Experimental verification of the mathematical model of the proposed method demonstrates that the autocorrelation method is more accurate than the rotating-element electric-field vector methods in determining the amplitude and phase shifts. The measured peak gain of the combined beam in the E-plane increased from 7.83 to 8.37 dB and 3.57 to 4.36 dB compared to the REVmax and REVmin methods, respectively, and the phase error improved from 47° to 55.48° and 19.43° to 29.16°, respectively. The proposed method can be considered an effective solution for large-scale phase calibration at both in-field and in-factory levels, even in the presence of external interference.

FDBR: Ultra-fast and data-efficient behavior recognition of port vessels using a statistical framework

Accurate recognition of maritime vessel behavior is essential for ensuring safety and optimizing port operations. Traditional methods often focus on isolated behaviors, like identifying individual stops or avoiding collisions between encountering vessels, without adopting a systematic approach. Single-vessel behavior recognition typically relies on clustering or deep learning techniques, which face challenges in adapting to diverse scenarios or require extensive data annotation. Moreover, current research on multi-vessel behavior tends to overlook cooperative interactions within port areas, which limits the potential for enhancing port efficiency. To address these challenges, this paper introduces a novel ultra-fast and data-efficient systematic statistical framework for port vessel behavior recognition (FDBR). For single-vessel behavior, we present a vectorized stop identification method with sliding window correction, enabling real-time recognition without the need for data annotation. For multi-vessel behavior, we employ a non-linear logistic regression model that incorporates dynamic vessel features to recognize cooperative behaviors with minimal data annotation. Our method achieves 98.738% accuracy in stop recognition, surpassing most deep learning approaches, and 93.930% accuracy in cooperation recognition. Additionally, recognizing different vessel behaviors at the Port of Los Angeles enables accurate extraction of various functional and high-risk areas, contributing to the optimization of port operations and enhancement of maritime safety.

An improved vector method for simultaneous analysis of removability and kinematics in block theory

Block theory is an important and commonly used method for addressing stability problems in rock engineering, and it is very meaningful to simplify its analysis procedure and improve its computational efficiency. In this paper, an improved vector method capable of simultaneously analyzing block removability and kinematics that works well for both convex and concave blocks is proposed. This improved approach is based on rigorously proven theorems. Compared to the original vector method in block theory, it is simpler and more efficient because it skips the removability analysis and simplifies some of the judgment conditions in kinematic analysis. With the results of kinematic analysis, the improved vector method can also determine the removability of the block. The validity of the improved vector method is verified by analyzing a series of individual convex or concave blocks with different removability and failure modes. Finally, the improved vector method is applied to the block progressive failure analysis of an engineering slope, which again validates the effectiveness of the improved vector method. The advantages of the improved vector method are highlighted through a comparison with existing methods, especially its high computational efficiency, ease of understanding and implementation.

Enhanced Subspace Iteration Technique for Probabilistic Modal Analysis of Statically Indeterminate Structures

In structural stochastic dynamic analysis, the consideration of the randomness in the physical parameters of the structure necessitates the establishment of numerous stochastic finite element models and the subsequent computation of their corresponding vibration modes. When the complete analysis is applied to calculate the vibration modes for each sample of the stochastic finite element model, a substantial computational expense is incurred. To enhance computational efficiency, this work presents an extended subspace iteration method aimed at rapidly determining the vibration modal parameters of statically indeterminate structures. The essence of this proposed method revolves around efficiently constructing reduced basis vectors during the subspace iteration process, utilizing flexibility disassembly perturbation and the Krylov subspace. This extended subspace iteration method proves particularly advantageous for the modal analysis of finite element models that incorporate a multitude of random variables. The proposed modal random analysis method has been validated using both a truss structure and a beam structure. The results demonstrate that the proposed method achieves substantial savings in computational time. Specifically, for the truss structure, the calculation time of the proposed method is approximately 1.2% and 65% of that required by the comprehensive analysis method and the combined approximation method, respectively. For the beam structure, on average, the computational time of the proposed method is roughly 2.1% of a full analysis and approximately 48.2% of the Ritz vector method’s time requirement. Compared to existing stochastic modal analysis algorithms, the proposed method offers improved computational accuracy and efficiency, particularly in scenarios involving high-discreteness random analyses.

Deep least squares one-class classification

One-class classification refers to a distinctive type of classification problem in which data originating from a single class, referred to as the target class, are exclusively available for training a specialized classifier known as the one-class classifier. This type of classification is encountered in various real-world applications when the characterization of outliers is challenging. Three primary methods—density estimation, boundary methods, and reconstruction methods—are used to solve one-class classification problems. This research is focused on boundary methods, particularly the popular support vector methods. Recently, the integration of deep neural networks with support vector methods has shown promise in one-class classification. This article proposes a new deep learning–based method called deep least squares support vector data description (DLS-SVDD), which combines the deep network’s feature extraction capability with the one-class objective to detect anomalies in complex data sets. The superior efficiency and performance of the proposed method over some one-class classifiers are illustrated through simulations and real-world data sets.

Research on Pose Error Modeling and Compensation of Posture Adjustment Mechanism Based on WOA-RBF Neural Network

This paper is aimed to address the issue of decreased accuracy in the ship block docking caused by the structural errors of posture adjustment mechanism. First, inverse kinematic analysis is performed to investigate the sources of static errors in the mechanism. Subsequently, based on the closed-loop vector method, a pose error model for the moving platform is established, which includes eight categories of error terms. The impact of various structural errors on the pose accuracy of the moving platform is then compared and analyzed under both single-limb and multi-limb configurations. Therefore, a compensation method based on the whale optimization algorithm optimized radial basis function neural network is proposed. By transforming pose errors into actuator length errors, it establishes a predictive model between the theoretical pose of the dynamic platform and actuator length errors. After optimizing the network parameters, it yields the actuator length compensation to correct the actual pose of the dynamic platform. Simulation and experimental results validate the effectiveness of this method in enhancing the motion accuracy of the parallel mechanism. The mean pose accuracy of the moving platform is improved by 85.07%, demonstrating a significant compensation effect.

Revisiting each fracture size and spatial pattern: Inference from rock mass surface to interior

Estimating fracture size is a fundamental aspect of rock engineering. However, determining the most probable diameter (MPD) from a fracture’s surface trace remains challenging in the scientific community. The prevailing methodologies typically infer statistical distributions of fracture sizes rather than specific values. This research presents a novel approach to inferring the MPD and the true spatial distribution pattern of each fracture. The challenge lies in linking the inference process with the trace length of each fracture and the statistical characteristics of the entire outcrop. Additionally, it is necessary to address the non-unique inverse problem. The methodology comprises several key steps. Firstly, the issue of censoring bias is addressed by considering the lengths of the traces contained. Secondly, the orientation bias is corrected using the vector method, and the true mean trace length and standard deviation are estimated and derived. Thirdly, assuming a lognormal distribution for fracture sizes, the mean and standard deviation of diameters are derived through a high-order moment relationship between trace lengths and diameters, validated by Crofton’s theorem. Finally, the MPDs of all trace samples are determined by relating MPDs to trace lengths and the standard deviation of diameters using stereology techniques. Furthermore, the true fracture spatial patterns are inverted based on spatial geometric relationships. The proposed methodology is validated through rigorous Monte Carlo simulation and applied in a practical engineering case study, demonstrating its potential for use in rock engineering applications.

Unconstrained measurement method and verification of thrust vector in small solid propulsion system

In response to the inherent limitations of traditional thrust vector measurement methods for small solid rocket motors(SRM), this paper proposes an innovative method based on flight attitude inversion. Flight measurement tests were conducted. Firstly, a six-degree-of-freedom (6-DOF) data inversion algorithm for solving the dynamic data of the three-axis thrust vector was constructed based on the Euler transformation method and the 6-DOF flight motion mathematical model of the flight measurement platform under the action of a three-axis thrust vector. Then, an unconstrained experimental platform was established, obtaining 6-DOF data during the operation of the experimental SRM through an inertial measurement unit(IMU). Finally, the thrust vector data were obtained from the recorded data. During the stable working phase, the average main thrust was 845 N, and the average thrust eccentricity angle was 0.018°, with a main thrust error of 0.6 %, thereby validating the feasibility of the measurement method.

Quantum support vector machines: theory and applications

Abstract. Quantum Support Vector Machines (QSVMs) combine the fundamental principles of quantum computing and classical Support Vector Machines (SVMs) to improve machine learning performance. In this paper, the author will further explore QSVM. Firstly, introduce the basics of classical SVM, including hyperplane, margin, support vector, and kernel methods. Then, introduce the basic theories of quantum computing, including quantum bits, entanglement, quantum states, superposition, and some related quantum algorithms. Focuses on the concept of QSVM, quantum kernel methods, and how SVM runs on a quantum computer. Key topics include quantum state preparation, measurement, and output interpretation. Theoretical advantages of QSVMs, such as faster computation speed, stronger performance to process high-dimensional data, and kernal computation. In addition, the author discussed the implementation of QSVM, quantum algorithms, quantum gradient descent, and optimization techniques for SVM training. The article also discusses practical issues such as error mitigation and quantum hardware requirements. The purpose of this paper is to show the advantages of QSVM by comparing SVM and QSVM.

Increasing irrigation-triggered landslide activity caused by intensive farming in deserts on three continents

Population growth and agricultural intensification lead to stress on landscapes that are highly sensitive to land-use changes. An increase in irrigation-triggered landslides (ITL) in dry climates has negative impacts on local communities. However, evolution and global impacts of ITL are little-known. Here, we use Multi-Temporal Interferometric Synthetic Aperture Radar (MT-InSAR), vectorization, and differential method to study surface deformation, ground displacement, and changes in headscarp morphology and topography in regions prone to ITL, aiming to uncover the evolution and spatiotemporal distribution of ITL. Findings show that the most severe surface deformation of ITL occurs on the landslide body. Meanwhile, the ITL displacement curve indicates the ITL will maintain continuous movement for at least 7 years, while ancient ITL also poses a threat. Moreover, the headscarp of ITL shows lateral expansion and longitudinal retrogression on the horizontal ground, whereby the scale of expansion is greater than that of retrogression, which transforms landslides into landslide clusters. Finally, the topographic changes further reveal that the main development pattern of ITL is lateral expansion. We suggest that the frequency and disaster-causing ability of ITL will increase greatly with further population growth and related intensification in the agricultural sector.

Effect of Three-Dimensional auxetic honeycomb core on behavior of sound transmission loss in shallow sandwich cylindrical shell

The primary objective of this research is to examine the sound transmission loss (STL) in a shallow sandwich cylindrical shell featuring a 3D auxetic honeycomb core. Initially, the 3D elasticity theory was employed by applying the state vector method and extracting both local and global transfer matrices to calculate STL relations for the cylindrical shell, including the auxetic honeycomb core. Subsequently, boundary conditions were applied to calculate the unknowns, eventually leading to a relationship for calculating STL within the structure. The derived equations were numerically solved using MATLAB software. The validity of the results obtained using this method was examined by comparing them with the findings of other researchers. Moreover, a comparison was conducted involving a large ratio of the curvature radius to thickness, considering both the auxetic honeycomb core and aluminum with equal mass. The results demonstrate a significant increase in STL when utilizing this auxetic honeycomb core compared to a material with the same mass. Specifically, at a frequency of 2 Hz, a significant enhancement of about 29.44 % in STL is observed when increasing the core thickness from 10.39 mm to 20.39 mm. Furthermore, STL results have been obtained for various thicknesses, radius of curvature, and incident angles.

The Information content of annual report and cost of equity capital: Based on Text Vectorization Method

Taking Chinese A-share listed companies in Shanghai and Shenzhen from 2017 to 2021 as the research sample, the method of text vectorization is used to construct an index of information content of annual report, and empirically test the impact of information content on the cost of equity capital. The results show that the information content is negatively related to the cost of equity capital, and the degree of information asymmetry plays a mediating role between them. This article is the first to verify the effect of information content on the cost of equity capital, and it is expected to provide theoretical guidance for regulators, enterprises and investors.