Complex Mathematical Operations Research Articles

Cell-nanoparticle stickiness and dose delivery in a multi-model in silico platform: DosiGUI

BackgroundIt is well-known that nanoparticles sediment, diffuse and aggregate when dispersed in a fluid. Once they approach a cell monolayer, depending on the affinity or “stickiness” between cells and nanoparticles, they may adsorb instantaneously, settle slowly – in a time- and concentration-dependent manner - or even encounter steric hindrance and rebound. Therefore, the dose perceived by cells in culture may not necessarily be that initially administered. Methods for quantifying delivered dose are difficult to implement, as they require precise characterization of nanoparticles and exposure scenarios, as well as complex mathematical operations to handle the equations governing the system dynamics. Here we present a pipeline and a graphical user interface, DosiGUI, for application to the accurate nano-dosimetry of engineered nanoparticles on cell monolayers, which also includes methods for determining the parameters characterising nanoparticle-cell stickiness.ResultsWe evaluated the stickiness for 3 industrial nanoparticles (TiO2 – NM-105, CeO2 – NM-212 and BaSO4 – NM-220) administered to 3 cell lines (HepG2, A549 and Caco-2) and subsequently estimated corresponding delivered doses. Our results confirm that stickiness is a function of both nanoparticle and cell type, with the stickiest combination being BaSO4 and Caco-2 cells. The results also underline that accurate estimations of the delivered dose cannot prescind from a rigorous evaluation of the affinity between the cell type and nanoparticle under investigation.ConclusionAccurate nanoparticle dose estimation in vitro is crucial for in vivo extrapolation, allowing for their safe use in medical and other applications. This study provides a computational platform – DosiGUI – for more reliable dose-response characterization. It also highlights the importance of cell-nanoparticle stickiness for better risk assessment of engineered nanomaterials.

Predictive coding networks for temporal prediction.

One of the key problems the brain faces is inferring the state of the world from a sequence of dynamically changing stimuli, and it is not yet clear how the sensory system achieves this task. A well-established computational framework for describing perceptual processes in the brain is provided by the theory of predictive coding. Although the original proposals of predictive coding have discussed temporal prediction, later work developing this theory mostly focused on static stimuli, and key questions on neural implementation and computational properties of temporal predictive coding networks remain open. Here, we address these questions and present a formulation of the temporal predictive coding model that can be naturally implemented in recurrent networks, in which activity dynamics rely only on local inputs to the neurons, and learning only utilises local Hebbian plasticity. Additionally, we show that temporal predictive coding networks can approximate the performance of the Kalman filter in predicting behaviour of linear systems, and behave as a variant of a Kalman filter which does not track its own subjective posterior variance. Importantly, temporal predictive coding networks can achieve similar accuracy as the Kalman filter without performing complex mathematical operations, but just employing simple computations that can be implemented by biological networks. Moreover, when trained with natural dynamic inputs, we found that temporal predictive coding can produce Gabor-like, motion-sensitive receptive fields resembling those observed in real neurons in visual areas. In addition, we demonstrate how the model can be effectively generalized to nonlinear systems. Overall, models presented in this paper show how biologically plausible circuits can predict future stimuli and may guide research on understanding specific neural circuits in brain areas involved in temporal prediction.

Revolutionizing Robotic Depalletizing: AI-Enhanced Parcel Detecting with Adaptive 3D Machine Vision and RGB-D Imaging for Automated Unloading.

Detecting parcels accurately and efficiently has always been a challenging task when unloading from trucks onto conveyor belts because of the diverse and complex ways in which parcels are stacked. Conventional methods struggle to quickly and accurately classify the various shapes and surface patterns of unordered parcels. In this paper, we propose a parcel-picking surface detection method based on deep learning and image processing for the efficient unloading of diverse and unordered parcels. Our goal is to develop a systematic image processing algorithm that emphasises the boundaries of parcels regardless of their shape, pattern, or layout. The core of the algorithm is the utilisation of RGB-D technology for detecting the primary boundary lines regardless of obstacles such as adhesive labels, tapes, or parcel surface patterns. For cases where detecting the boundary lines is difficult owing to narrow gaps between parcels, we propose using deep learning-based boundary line detection through the You Only Look at Coefficients (YOLACT) model. Using image segmentation techniques, the algorithm efficiently predicts boundary lines, enabling the accurate detection of irregularly sized parcels with complex surface patterns. Furthermore, even for rotated parcels, we can extract their edges through complex mathematical operations using the depth values of the specified position, enabling the detection of the wider surfaces of the rotated parcels. Finally, we validate the accuracy and real-time performance of our proposed method through various case studies, achieving mAP (50) values of 93.8% and 90.8% for randomly sized and rotationally covered boxes with diverse colours and patterns, respectively.

Abacus Algorithms: A Pure Mathematical Approach to Ancient Calculation Tools

The abacus is one of the oldest calculating tools still in use today. Despite its simplicity, the bead-based interface allows users to conduct complex mathematical operations through a system of sliding beads along wires or rods. While the physical abacus itself provides an intuitive and visual approach to calculation, the underlying operations rely on fundamental mathematical principles. This paper provides a comprehensive mathematical framework that formally describes the algorithms behind abacus calculations. Beginning with basic abacus configuration, we define key components like rods, beads, and bead values required to model abacus states. We then characterize the core abacus algorithms for addition, subtraction, multiplication, and division through set notation, recurrence relations, and state transition diagrams. Our formalized abacus algorithms leverage concepts from number theory, modular arithmetic, combinatorics, and algebra. In addition to offering new mathematical insights into ancient technologies, our work helps bridge connections between the tangible abacus interface and the abstract algorithms powering it. Through examples and proofs, we show how bead manipulations precisely correspond to mathematical transformations. This level of formalization not only helps explain the effectiveness of the abacus, but also illustrates how even rudimentary calculation tools utilize profound mathematical ideas. Our mathematical abacus framework lays the foundation for further analysis as well as modifications and extensions of the classic abacus approach.

General Curve Model for Evaluating Mechanical Properties of Concrete at Different Ages

During the process of pouring and solidification of concrete, the compressive strength and elastic modulus of concrete exhibit dynamic growth patterns. The mechanical properties of concrete usually remain stable in the later stage (28 days after pouring). Studying appropriate curve models to accurately evaluate the changes in early mechanical properties of concrete has always been an important topic in the field of concrete materials. This work proposes a new dual parameter curve model for accurately evaluating the growth pattern of early compressive strength and elastic modulus of concrete. A comparative study was conducted between the proposed new curve model and existing curve models using 18 sets of experimental data from 10 literature sources. The research results indicate that the fitting average error and standard deviation of this new curve model are significantly smaller than the existing curve models. For some examples, the fitting error and standard deviation of the new model are only about 20%–30% of those of the existing models. The main advantages of this new curve model lie in two aspects. The first advantage is that this new curve model only contains two unknown parameters, so only a small amount of experimental data is required for data fitting and does not require complex mathematical operations. The second advantage is that this new curve model has a wide range of applications, which include compressive strength evaluation and elastic modulus evaluation and can also be extended to the evaluation of the mechanical properties of other materials similar to concrete.

Neural Network-Enhanced Fault Diagnosis of Robot Joints

Industrial robots play an indispensable role in flexible production lines, and the faults caused by degradation of equipment, motors, mechanical system joints, and even task diversity affect the efficiency of production lines and product quality. Aiming to achieve high-precision multiple size of fault diagnosis of robotic arms, this study presents a back propagation (BP) multiclassification neural network-based method for robotic arm fault diagnosis by taking feature fusion of position, attitude and acceleration of UR10 robotic arm end-effector to establish the database for neural network training. The new algorithm achieves an accuracy above 95% for fault diagnosis of each joint, and a diagnostic accuracy of up to 0.1 degree. It should be noted that the fault diagnosis algorithm can detect faults effectively in time, while avoiding complex mathematical operations.

Direct Heterogeneous Causal Learning for Resource Allocation Problems in Marketing

Marketing is an important mechanism to increase user engagement and improve platform revenue, and heterogeneous causal learning can help develop more effective strategies. Most decision-making problems in marketing can be formulated as resource allocation problems and have been studied for decades. Existing works usually divide the solution procedure into two fully decoupled stages, i.e., machine learning (ML) and operation research (OR) --- the first stage predicts the model parameters and they are fed to the optimization in the second stage. However, the error of the predicted parameters in ML cannot be respected and a series of complex mathematical operations in OR lead to the increased accumulative errors. Essentially, the improved precision on the prediction parameters may not have a positive correlation on the final solution due to the side-effect from the decoupled design. In this paper, we propose a novel approach for solving resource allocation problems to mitigate the side-effects. Our key intuition is that we introduce the decision factor to establish a bridge between ML and OR such that the solution can be directly obtained in OR by only performing the sorting or comparison operations on the decision factor. Furthermore, we design a customized loss function that can conduct direct heterogeneous causal learning on the decision factor, an unbiased estimation of which can be guaranteed when the loss convergences. As a case study, we apply our approach to two crucial problems in marketing: the binary treatment assignment problem and the budget allocation problem with multiple treatments. Both large-scale simulations and online A/B Tests demonstrate that our approach achieves significant improvement compared with state-of-the-art.

Model Predictive PI Circulating Current Control for Modular Multilevel Converter

Significant circulating currents in the modular multilevel converter (MMC) increase system losses and complicate heat-sink design. Conventional PI and PR controllers can achieve steady-state error adjustment, but are sensitive to parameter changes and model uncertainty, heavily relying on coordinate transformations and careful design of model parameters. Model predictive control (MPC) has the characteristics of simple design, good robustness, and excellent dynamic response; however, it encountered the complexity of adjusting weighting factors. This paper proposed circulating the current model predictive proportional integral control (MPPIC) method in abc reference frame. This hybrid control solution utilized the predictive model and traditional PI algorithm to combine the advantages of nonlinear and linear control. Compared with existing suppression methods, this method avoided complex mathematical operations and a selection of weight coefficients, was easy to implement, and can effectively suppress circulating currents under different modulation ratios. Simulations were conducted on MATLAB/Simulink to verify the effectiveness of the proposed control strategy. MPPIC can not only distinctly suppress the circulating currents, but also reduce the overall voltage fluctuation of sub-modules capacitors under different modulation ratios, and had almost no any adverse effect on the performance of MMC.

An Authenticated Group Shared Key Mechanism Based on a Combiner for Hash Functions over the Industrial Internet of Things

The Industrial Internet of Things (IIoT) provides internet connectivity for instruments, digital machines, and any other manufactured object to enable intelligent industrial operations to achieve high productivity. Securing communications between IIoT devices remains a critical and challenging issue due to the resource-constrained and processing capabilities of sensing devices. Moreover, the traditional group shared key might implement complex mathematical operations that are not suitable for the limited recourse capability of the IIoT device. Furthermore, the standard Diffie–Hellman (DH) and elliptic curve Diffie–Hellman (ECDH), which are the most suited for tiny devices, only work between a pair of IIoT devices, while they are not designed to work among a group of IIoT devices. This paper proposes an authenticated group shared key (AGSK) mechanism that allows a set of industrial objects to establish a common session key over the IIoT. The proposed AGSK utilizes the combiner for the hash function and digital signature, which is implemented in IIoT devices. Additionally, the random oracle model has been used to prove the security of AGSK, while the IIoT adversary model has been used to analyze the AGSK countermeasures against cyberattacks. The results of the performance evaluation showed that the efficiency of the AGSK was reduced by 41.3% for CPU computation time, 45.7% for storage cost, and 40% less power consumption compared to the baseline group key management algorithms.

Predictive Control of Four-Legged Inverter Using Sliding-Window Discrete Fourier Transform Computation for Harmonic Recession

—Shunt active power filters are the most promising solution for power quality challenges. It injects compensating current at the point of common coupling to recede harmonic content and to attain unity power factor. The proposed control strategy comprises of (a) Model predictive control (MPC) for switching state selection and (b) Sliding-window Discrete fourier transform (SDFT) technique for computing reference compensating current in a four-legged shunt active power filter. This paper incorporates MPC and SDFT control as a single-step algorithm for a four-leg inverter. The absence of modulator, look-up tables and complex mathematical operations support the easy implementation of the proposed controller digitally. The proposed scheme involves unique features like improved cost function in MPC, flexible sampling window size in SDFT, reduced computational complexity and execution time. Also, the compensation principle of the controller requires only line current measurement in contrast to the classical compensation techniques which require the distortion level and reactive power demand of the load. The efficacy of the proposed control method is tested for steady-state, dynamic conditions and parameter uncertainties. The system is validated by simulation using level-2 S-function block in MATLAB/Simulink for various case studies.

Simple Method for Optical Detection and Characterization of Surface Agents on Conjugated Gold Nanoparticles.

In this article, we propose a simple method to calculate electrical permittivity and refractive index of surface agents of gold nanoparticles (Au NPs), in which it is possible to find the refractive index of surface agents shell by using the absorption peak of the gold nano-colloid. One of the usual tests for detection of surface agents is colorimetric methods based on the change of color of Au NPs. The color change is mainly due to the shift of localized surface plasmon resonance which is related to electrical interactions of surface agents. Although there are many mathematical models for simulating the absorption spectrum and calculating the plasmonic peak, using them is not simple and possible for everyone due to the need for programming. Here, the necessary simulations have been performed for different values ​​of refractive index of surface agents and particle size, and absorption peaks have been obtained. Using numerical methods, a simple formula is obtained between the wavelength of plasmonic peak, the ratio of hydrodynamic diameter to Feret size of the particles, and the refractive index of the surface agents. This method can help researchers to obtain the refractive index and consequently the type or concentration of surface agents around Au NPs without the need for programming or complex mathematical operations. It can also open new horizons in analyzing colorimetric diagnosis of biological agents such as viral antibodies, antigens, and other biological agents.

High-level synthesis assisted, low-latency, area- and power-optimized FPGA implementation of MUSIC algorithm for direction-of-arrival estimation

For multiple signal-processing applications, estimating the target’s speed, distance, and elevation angle by using applications running in real time and consequently, fast data rates is important. Custom hardwares, such as field programmable gate arrays (FPGAs), are often used to prototype and deploy such signal-processing algorithms. Multiple signal classification (MUSIC) is typically used for direction-of-arrival (DOA) estimation. It involves complex mathematical operations such as covariance matrix computation, eigen value decomposition, and peak value search for signal values. With a novel high-level synthesis (HLS)-based design approach that optimizes the bit widths for the eigen value decomposition logic, this study presents an area and speed-optimal implementation of MUSIC algorithm on FPGA. The final implementation involving the covariance matrix computation, eigen value decomposition, and peak search was implemented on Xilinx Zynq (XC7Z020) FPGA. Because of its optimum bit widths, area utilization was minimized and operation frequency on the target FPGA was maximized. The proposed design works in real time to estimate the DOA in less than 1.7 µs (15 % faster than reported values) and uses up to 30 % less resources on the target FPGA compared with other reported implementations.

Mathematical Model for Early-Aged UHPFRC Compressive Strength Changes

Compressive strength is the most important mechanical index of ultra-high performance fiber-reinforced concrete (UHPFRC). The rule of changes in compressive strength in early-aged UHPFRC is of great significance to guide concrete curing, formwork removal, and prestress stretching. Therefore, it is very necessary to study an accurate mathematical model to describe the change in compressive strength of UHPFRC at an early age. For this purpose, a new mathematical model of compressive strength age is proposed in this work for predicting the long-term strength of UHPFRC according to a few test data from early-aged UHPFRC. This new model can overcome the shortcomings of the existing models, such as the exponential model, logarithmic model, and polynomial model. The proposed model is first demonstrated by using four groups of compressive strength test data compiled from previous research studies. Subsequently, an experiment of early-aged UHPFRC compressive strength was carried out to further verify the proposed mathematical model. The mixed proportion used in the UHPFRC compressive strength test was 10.87:0.82:1 (powder:steel fiber:water), and the design strength grade was 120 MPa. Based on the UHPFRC experimental data, it was shown that the average fitting error and standard deviation of the new model were about 10%~20% of that of the logarithmic model and the polynomial model. The proposed model can precisely predict the compressive strength of UHPFRC, with a determination coefficient (R2) of 0.9974. The research results show that the average fitting error and standard deviation of this new model were significantly reduced when compared to the existing models, and the predicted compressive strength by the new model on the 60th day is the closest to the actual design strength grade of concrete. The greatest advantage of the proposed method lies in its simple formula, fast implementation, and no need for complex mathematical operations. It has been shown that the proposed model is superior to the existing models due to its higher fitting accuracy and prediction accuracy, and it can be better used to predict the later strength of UHPFRC by using only a few compressive strength test data taken at the early age stage.

A nonunit two-stage protection scheme for DC transmission lines in high-voltage DC grids

Nonunit protection is suitable for the primary protection of DC lines in high-voltage DC (HVDC) grids because of its rapidity. However, most existing nonunit protections are not sensitive enough for remote-end high-resistance faults. To solve this problem, a novel nonunit two-stage protection capable of tolerating high-resistance faults is proposed in this paper. First, the propagation process of a traveling wave (TW) generated by the fault is presented, revealing the insufficiency of fault TW-based protections to tolerate remote-end high-resistance faults. Then, the TW generated by the DC circuit breaker (DCCB) located on the opposite end is analyzed, and its characteristic difference between the internal and external faults is discussed. Moreover, the nonunit two-stage protection scheme that contains stage-I and stage-II protections is proposed. Stage-I protection rapidly identifies the closed-end and remote-end low-resistance faults using the fault TW. Stage-II protection identifies the remote-end high-resistance fault using the TW generated by the DCCB, and the fault clearing time is reduced by combining the DCCB operation. The protection criteria, setting principle and operation process of the proposed protection scheme are presented in detail. Finally, a large number of PSCAD/EMTDC simulations validate the excellent performance of the proposed scheme, including a high fault resistance tolerance, quick fault clearing time, and no requirements of excessive sampling frequency and complex mathematical operations.

Bézier Coefficients Matrix for ElGamal Elliptic Curve Cryptosystem

It is well-known that cryptography is a branch of secrecy in science and mathematics, which usually preserves the confidentiality and authenticity of the information, where its growth is parallel with the rapid evolution of the internet and communication. As one of the prominent public key cryptosystems, the Elliptic Curve Cryptosystem (ECC) offers efficiency and complex mathematical operations with a smaller bit compared to other types of public key schemes. Throughout the evolution of cryptography, ElGamal Elliptic Curve Cryptosystem (ElGamal ECC) revolved from ElGamal public key scheme for user efficiency and privacy. In this study, an improved method will be introduced using ElGamal ECC as the foundation with the incorporation of the Bézier curve coefficient matrix, where the ElGamal ECC value is considered as the control point of the Bézier curve during the encryption and decryption processes. The proposed method is designed to develop a robust ciphertext system algorithm for better efficiency and to increase the level of protection in ElGamal ECC. In this paper, the performance of the proposed method is compared with the normal ElGamal ECC. The results of this study show that the proposed method offers no significant difference in terms of the implementation time during the encryption and decryption process. However, it does offer extra layers of protection when operated with complex mathematical operations.

A method for reducing implementation complexity in linear parameter-varying controllers

Gain-scheduling is a popular control technique to deal with nonlinear and time varying systems. The linear parameter-varying (LPV) system approach offers systematic tools to design gain-scheduled controllers. However, the implementation of these controllers might demand complex mathematical operations to be performed in real-time. This limits the hardware and the applications in which LPV controllers can be used. In this article, we analyze these limitations and propose a design methodology to reduce the implementation complexity of gain-scheduled LPV controllers. The methodology is illustrated with a nonlinear bicycle model used in electric vehicle control.

Elasto-dynamic performance evaluation of a 6-DOF hybrid polishing robot based on kinematic modeling and CAE technology

By taking a 6-DOF hybrid polishing robot as an example, this paper presents a generalized methodology for elasto-dynamic analysis of hybrid robots in an easy, accurate and rapid manner. The approach can be implemented by three steps: (1) creating an inverse kinematic model for calculating the configuration parameters of the body-fixed frame of each substructure and the coordinates of the joint frames with respect to the reference frame of the fixed platform; (2) building a parameterized Finite Element (FE) model at the home pose by using the modal reduction techniques and Parametric Design Languages (PDL) embedded in the CAE system; (3) driving the FE model to specified poses using the calculated configuration parameters of substructures and coordinates of joint frames in the batch mode, and evaluating the elasto-dynamic performance of the robot over its entire workspace. The merit of this approach lies in that parallel or hybrid robots having different topologies can be modeled without complex mathematical derivation and operation, allowing the lower-order dynamic performance to be rapidly predicted with sufficient accuracy.

Modified Advanced Encryption Standard for Boost Image Encryption

Cryptography is a field of study that deals with converting data from a readable to an unreadable format. It can provide secrecy, data integrity, authenticity, and non-repudiation services. Security has become a concern for the community because of the technology’s potential use in numerous sectors of any company, market, agency, or governmental body, information. The cryptosystems ensure that data are transported securely and only authorized individuals have access to it. Deeply encrypted data that cannot be deciphered through cryptanalysis are in high demand right now. There are a variety of encryption algorithms that can guarantee the confidentiality of data. For multimedia data, standard symmetric encryption algorithms (AES) can give superior protection. However, using the symmetric key encryption approach on more complicated multimedia data (mainly photos) may result in a computational issue. To address this issue, the AES has been modified to satisfy the high computing requirements due to the complex mathematical operations in MixColumns transformation, which slow down the encryption process. The modified AES uses bit permutation to replace the MixColumns transformation in AES because it is simple to construct and does not require any complex mathematical computation. This research focuses on using the Modified Advanced Encryption Standard (MAES) algorithm with 128 and 256 bit key sizes to encrypt and decrypt image data. The algorithms were implemented using the Python programming language without complex mathematical computation. By comparing the MAES algorithm with the original AES algorithm, the results showed that the MAES requires less encrypting and decryption time with higher efficiency for all file sizes.

Аналитическое решение первой задачи динамики манипуляторов с вращательными сочленениями

The problem of complexity of derivation and the cumbersome analytical form of equations of mathematical models of controlled body systems with explicit structural, kinematic, static and dynamic parameters is solved. First of all, this applies to the equations of dynamics on which the control systems are based. Our practical experience and theoretical results indicate that solutions to this problem should be sought in two directions. Firstly, in the direction of classifying body systems and using peculiarities of the representatives of the considered classes of body systems in terms of simplifying formalisms for deriving their equations of dynamics, as well as reducing the number of mathematical operations in the analytical representation of the equations of dynamics. Second, and in the direction of choosing the parameters of the state of bodies in which the analytical scalar-coordinate types of the equations of dynamics are written down. In this connection, it should be noted that the vast majority (more than 90 %) of industrial robots, as well as special-purpose robots, have a single open branch structure in which the bodies form rotational kinematic pairs of the fifth class (rotational articulations) with each other. If in such systems the poles of the bodies are chosen on the axes of their relative rotation, the interpole distances will be constant, which greatly simplifies the solution of the above problem. Regarding the choice of state parameters explicitly included in the equations of dynamics, it should be noted that quasi-velocities, i.e. projections of absolute angular velocities of bodies on the axes of their coupled coordinate systems, are the most suitable for these purposes. The point is that in the equations of kinematics, which close the equations of dynamics to a complete set of equations for solving a problem, one can always express quasi-velocities through any other parameters, for example, relative angles of rotation of bodies and their time derivatives, guiding cosines and their derivatives, quaternions, etc. If projections of absolute angular velocities of bodies on their axes are measured, for example, by gyroscopes on bodies, and the first problem of dynamics is solved, the solution formulas contain a minimum number of addition and multiplication operations. Thus, the goal of the study is to develop a simple method for deriving the analytical form of the equations of dynamics of manipulators with rotational joints in quasi-velocity, in which geometric, kinematic, static and inertial parameters of bo¬dies are explicitly expressed. The used research methods (vector and analytical mechanics of body systems, vector algebra, system analysis and methods of identity transformations) made it possible to reduce the derivation of the equations of dynamics of manipulators to formal actions of writing them out without performing complex mathematical operations of differentiation, magnification, calculation of vector operations, etc. The results of the study contain a proof of the general vector form of the equations of dynamics of manipulators in quasi-velocity with explicitly expressed interpole distances and parameters of mass distribution of bodies. Scalar-coordinate formulas and their simple special formulas for the case of parallel rotation axes of neighboring joints are derived for writing out the moments of driving forces in joints. As a special case, the formulas for writing out the equations of dynamics of manipulators on the plane were obtained. For them, the process of writing out the equations of dynamics is reduced to the specification of the number of bodies, their geometric and inertial parameters. Conclusion. The effectiveness of the outlined methods and the obtained formulas have been demonstrated by examples of deriving the equations of dynamics of a body with a single fixed point, a gyroscope in a gimbal, and an angular manipulator with three and six degrees of freedom in space. These results allow us to expect that the number of users of the proposed methods will grow. The positive experience of using these methods in the educational process in the disciplines “Fundamentals of Mechanics of Body Systems”, “Electromechanical Systems” and “Mechatronics” justifies our expectations.

A review of optimisation and least-square problem methods on field programmable gate array-based orthogonal matching pursuit implementations

Orthogonal matching pursuit (OMP) is the most efficient algorithm used for the reconstruction of compressively sampled data signals in the implementation of compressive sensing. OMP operates in an iteration-based nature, which involves optimisation and least-square problem (LSP) as the main processes. However, optimisation and LSP processes comprise complex mathematical operations that are computationally demanding, and software-based implementations are slow, power-consuming, and unfit for real-time applications. To fill the research gap, we reviewed the optimisation and LSP techniques implemented on the FPGA platform as the hardware accelerator. Aspects that contributed to the performance, algorithm, and methods involved in the implemented works were discussed and compared. The methods were found to be improved when modified or combined. However, the best approach still depends on the requirement of the system to be developed, and this review is significant as a reference.