Performance Evaluation Of Algorithms Research Articles

Channel Prediction for Underwater Acoustic Communication: A Review and Performance Evaluation of Algorithms

Underwater acoustic (UWA) channel prediction technology, as an important topic in UWA communication, has played an important role in UWA adaptive communication network and underwater target perception. Although many significant advancements have been achieved in underwater acoustic channel prediction over the years, a comprehensive summary and introduction is still lacking. As the first comprehensive overview of UWA channel prediction, this paper introduces past works and algorithm implementation methods of channel prediction from the perspective of linear, kernel-based, and deep learning approaches. Importantly, based on available at-sea experiment datasets, this paper compares the performance of current primary UWA channel prediction algorithms under a unified system framework, providing researchers with a comprehensive and objective understanding of UWA channel prediction. Finally, it discusses the directions and challenges for future research. The survey finds that linear prediction algorithms are the most widely applied, and deep learning, as the most advanced type of algorithm, has moved this field into a new stage. The experimental results show that the linear algorithms have the lowest computational complexity, and when the training samples are sufficient, deep learning algorithms have the best prediction performance.

Machine learning modeling of base flow generation potential: A case study of the combined application of BWM and Fallback bargaining algorithm

The study of base flow is essential for sustainable water management. By understanding the dynamics of base flow, policymakers can make informed decisions to ensure the long-term health and availability of water resources. This study was conducted with the aim of modeling the spatial changes of Base Flow Generation Potential (BFGP) using integrated Machine Learning Algorithms (MLAs) including Decision Tree Regression (DTR), K-Nearest Neighbors (KNN), Naïve Bayes (NB), Random Forest (RF), Simple Linear Regression (SLR), Support Vector Machine (SVM) and Support Vector Regression (SVR) and optimal Multi-Criteria Decision Making (MCDM) methods including Best-Worst Method (BWM) and Fallback bargaining in the Cheshmeh-Kileh watershed, Iran. BFGP conditioning factors were selected for the Sub-Watershed (SW) and weighed using MCDM (BWM and Fallback bargaining algorithm) methods. BFGP maps of five classes were generated and analyzed. MCDM methods were also integrated with ML algorithms for optimum performance evaluation of the integrated unit. Based on the results, in the integrated model of BWM and Fallback bargaining algorithm with ML algorithms, SVR and RF algorithms was selected as the optimal model, respectively. In BWM in the Sehezar River, the upstream had the highest BFGP. The pattern of spatial changes based on the Fallback bargaining algorithm in the upstream of Sehezar River was similar to BWM. The combined approach of RF-GTA with the factors of minimum temperature (Tn), NDSI and elevation showed the highest correlation. It was observed that that the Fallback bargaining algorithm and BWM of the MCDM exhibited similarity in output of regarding the spatial change patterns of the BFGP. Also, Fallback bargaining exhibited a 67% similarity with the integrated RF-GTA in BFGP prioritization of the SWs, while BWM performed poorly. This suggests that the Fallback bargaining algorithm was more effective than BWM of the MCDM methods for SWs BFGP prioritization. The general summary indicated that the combined use of MCDM and MLAs were valuable tools in BF studies and helped in better understanding the complex hydrological processes. The findings of our research may be of help to Iran Water Resources Research Company using hydrological data arising from base flow studies to support their analysis. In conclusion, understanding the BF characteristics of SWs allows watershed managers to effectively prioritize conservation and restoration efforts aimed at protecting and enhancing the natural flow regime.

Optimization and Performance Evaluation of Deep Learning Algorithm in Medical Image Processing

In this paper, the optimization and performance evaluation of deep learning algorithm in medical image processing are studied. Firstly, the paper introduces the importance and challenges of medical image processing, and expounds the application prospect of deep learning in this field. Subsequently, this paper discusses the optimization methods of deep learning algorithm in detail, including model structure design, data preprocessing, super parameter adjustment and so on. In terms of performance evaluation, this study selected classic models such as U-Net, DeepLab and DenseNet, and compared them with ROC curve and AUC value to evaluate their predictive ability in medical image classification. The results show that the DenseNet model shows high performance in prediction accuracy, while the performance of U-Net and DeepLab models is slightly average. Finally, the advantages and disadvantages of each model are analyzed, and the future research direction is prospected. This study is of great significance to promote the development and application of medical image processing technology, and provides important theoretical and technical support for medical diagnosis and treatment.

Performance Evaluation of Congestion Control Algorithm in TCP/IP Differentiated Services During COVID-19 Pandemic Due to Heavy Surge in Real-Time Traffic

Numerous nations implemented countrywide lockdowns because of the COVID-19 epidemic, which forced almost all peoples to remain at home. The imposition of confinement restrictions led to an increase in residential users' Internet traffic demands, particularly for distant work, entertainment, commerce, and education. This resulted in changes to the traffic patterns within the Internet core. In this research, we investigate the impact of the countrywide lockdowns on internet traffic based on dscp values by collecting data from class-A, class-B and Class-C ISP.(Three Class-A ISP, Three Class-B ISP and Three Class-C ISP) which leads to heavy congestion in the network and finally the performance valuation is carried out. The overall rise is exponential in nature, we notice that the traffic volume climbed by 15-30% almost in a quarter, which is a significant gain in such a short amount of time. Direct examination of the traffic sources reveals that, although hypergiants continue to account for a sizeable portion of traffic, there has been a greater increase in non-hypergiant traffic as well as in traffic from home-use applications like Web conferencing, VPNs, and gaming. Academic networks show significant overall declines whereas many networks, particularly those serving residential users, pharmaceutical companies, online interaction platform increases in traffic demands. However, we can see significant gains in these networks when we look at applications related to lecturing and remote working. The changes in the nature of use by customers show that there is a sharp difference in application pertaining to usage. Previous to this period, most usage is on YouTube, Facebook and google search. However, after this period most traffic diverted to online platforms such as zoom, google meet, Teams, and others as well as OTT platform comes into the picture. Over the past two decades, there has been a notable shift in user profiles. In the early 2010s, we saw most traffic was inclined on stored video and audio data in continuation with conventional traffic [23, 49, 66], which was followed by content delivery and streaming applications [7, 24, 35, 37, 52], and mobile applications [32, 67] in the 2010s. Even though user profile modifications are a moving target, they usually take years to complete. So, it was possible to stay current, for example, by measurements. The impact of this pandemic created chaotic conditions as most traffic migrated to real time surge data. Thus, the congestion management becomes more complicated as of previous challenges. The ISP forced to provide more bandwidth to real-time traffic which leads to overprovisioning. Thus, an efficient algorithm is required for managing such surge traffic which may especially meet real time traffic as required by most customers. This paper thus focuses on impact of after corona-19 pandemic effect, the shift of traffic by various users and applications the behavior of some existing algorithms in terms of congestion management and finally suggested a balanced method for managing congestion in such heavy surge traffic.

Optimization and Performance Evaluation of Artificial Intelligence Algorithms in Game Design

This article aims to optimize artificial intelligence algorithms in game design to enhance game performance and player experience. Therefore, an innovative method called Dynamic Game AI Fitness Optimization Algorithm (DGAFOA) was proposed in the article, and its effectiveness was verified through experiments. In the experimental section, this article applies the DGAFOA algorithm to a typical role-playing game and compares it with traditional fixed parameter AI algorithms. The experimental results show that the DGAFOA algorithm exhibits significant advantages in key indicators such as game task completion rate and player satisfaction. Specifically, game AI using the DGAFOA algorithm can respond more quickly and accurately to player behavior, improving the overall smoothness and fun of the game. In addition, the DGAFOA algorithm also introduces ε- The greedy strategy balances exploration and utilization, effectively avoiding the problem of AI getting stuck in local optima. This enables game AI to maintain stable performance while still possessing the ability to explore new strategies, bringing players more surprises and challenges.

Implementation of K-means Clustering Algorithm for the Indonesian Stock Exchange

In the dynamic field of financial markets, effective analysis and understanding of stock market behavior are very crucial for investors, analysts, and policymakers. This study investigates the implementation of the K-means algorithm for clustering stocks listed on the Indonesian Stock Exchange (IDX). The main objectives of this research include exploring IDX's clustering patterns, identifying groups based on their trading characteristics, and evaluating algorithm performance. Some challenging parts have been addressed, such as data quality, feature selection, determining the optimal number of clusters, scalability, interpretability, and evaluation. Precise data preprocessing, feature engineering, and algorithm optimization provide insight into the clustering structure of the Indonesian stock market, helping investors in portfolio diversification, risk management, and strategic decision-making. The results show the potential of the K-means algorithm in thoroughly uncovering important patterns on the IDX, thereby contributing to the advancement of market analysis methodologies adapted to the Indonesian financial environment.

Performance evaluation of pair selection algorithms in device-to-device communication using relay-assisted techniques

Communication services that are dependable are crucial, particularly during emergencies when the regular infrastructure for communication may be disrupted or nonexistent. In such situations, device-to-device (D2D) communication can be a helpful choice since it allows user equipment (UE) that is close to one another to connect directly, bypassing the cellular network infrastructure. The primary focus of this thesis is the application of D2D communication in a decentralized emergency scenario with a damaged eNodeB. The main objective is to find an appropriate strategy for finding and selecting D2D couples by simulating several methods in MATLAB. This study compares three D2D pair selection algorithms: distance-based, Signal-to-Interference and Noise Ratio (SINR)-based, and data rate-based distance-based. The simulation results show that the data rate-based strategy is the most effective method for selecting D2D couples in emergency scenarios. In contrast to algorithms that rely on distance and SINR, this one reduces the chance of an outage by 20%. Bit error rate (BER), capacity, spectral efficiency, and energy efficiency are the three types of links that are assessed: direct links, relay links, and UE relay links. The results show that, with the lowest BER and maximum data throughput, the direct link is the most reliable and efficient communication option. However, the relay connection and the UE relay link show better overall spectral efficiency in comparison to the direct link, indicating their ability to transport more data per unit of bandwidth. The option that consumes the least energy among the three is the direct link. The study demonstrates the great potential of D2D communication in emergency scenarios where conventional communication infrastructure may not be available. The direct link is the most dependable and effective alternative for communication, according to the data, although the UE link can still function effectively in the event that the direct link is compromised. The data rate-based method is a useful strategy for finding and choosing D2D partners. The results of this study can direct the development of D2D emergency communication solutions in 5G networks.

PODB: A learning-based polarimetric object detection benchmark for road scenes in adverse weather conditions

Due to its insensitivity to light intensity and the capability to capture multidimensional information, polarimetric imaging technology has been proven to have advantages over traditional intensity-based imaging techniques for object detection tasks in adverse environmental conditions, particularly in road traffic scenarios. Recently, with the rapid development of artificial intelligence technology, deep learning (DL)-powered object detection techniques can further enhance recognition accuracy and algorithm robustness. This improvement is made possible by the ability of DL technology to leverage large datasets and extract deeper levels of target-specific features. However, constructing large-scale polarimetric datasets poses challenges as obtaining polarimetric information requires multiple captures of intensity images. In other words, the workload is several times higher compared to traditional imaging techniques. To address the current scarcity of polarimetric datasets and evaluate the practical performance of various algorithms on polarimetric datasets, this paper proposes a Polarimetric Object Detection Benchmark (PODB) dataset. The PODB provides an integrated quality evaluation framework for DL-based object detection algorithms in complex road scenes by incorporating polarimetric imaging. Besides, we conducted extensive object detection experiments using the PODB, which allowed for a comprehensive validation and performance evaluation of effective benchmark algorithms. Furthermore, a physics-based multi-scale image fusion cascaded object detection neural network model is proposed. By combining the multidimensional information provided by polarized images with an adaptive learning multi-decision object detection neural network model, the recognition accuracy of complex road scenes in adverse weather conditions has been improved by approximately 10%. Additionally, we anticipate that PODB will serve as an effective platform for evaluating and comparing the performance of object detection algorithms, as well as providing researchers with a baseline for future studies in developing new DL-based methods.

Performance Analysis and Evaluation of Clustering Algorithms using WEKA

Clustering, an unsupervised learning technique, to find inherent groupings in un-labelled data. It seems to be referring to a study or research paper that examines and uses a number of clustering algorithms, including the canopy method, k-Means clustering, hierarchical clustering, density-based clustering, and EM algorithm. WEKA, a clustering program, is used for the examination of these techniques. and the effectiveness of these algorithms is evaluated through experiments using social network Ads datasets. The goal of this research paper or study seems to be to assess how well these clustering algorithms perform in grouping data within social network Ads datasets. Such analyses can help identify the most suitable algorithm for a specific type of data or problem domain and may lead to insights into the underlying structure of the data.

Comprehensive evaluation measures of nonlinear estimation algorithm performance

Although many scholars say that their algorithms are better than others in the state estimation problem, only a fewer convincing algorithms were applied to engineering practices. The reason is that their algorithms outperform others only in some aspects such as the estimation accuracy or the computation load. To solve the problem of performance evaluation of state estimation algorithms, in this paper, the comprehensive evaluation measures (CEM) for evaluating the nonlinear estimation algorithm (NEA) is proposed, which can comprehensively reflect the performance of the NEAs. First, we introduce three types of the NEAs. Second, the CEM combining the flatness, estimation accuracy and computation time of the NEAs, is designed to evaluate the above NEAs. Finally, the superiority of the CEM is verified by a numerical example, which helps decision makers of nonlinear estimation algorithms theoretically and technically.

Manual evaluation of record linkage algorithm performance in four real-world datasets.

Patient data is fragmented across multiple repositories, yielding suboptimal and costly care. Record linkage algorithms are widely accepted solutions for improving completeness of patient records. However, studies often fail to fully describe their linkage techniques. Further, while many frameworks evaluate record linkage methods, few focus on producing gold standard datasets. This highlights a need to assess these frameworks and their real-world performance. We use real-world datasets and expand upon previous frameworks to evaluate a consistent approach to the manual review of gold standard datasets and measure its impact on algorithm performance. We applied the framework, which includes elements for data description, reviewer training and adjudication, and software and reviewer descriptions, to four datasets. Record-pairs were formed and 15,000 records were randomly sampled from these pairs. After training, two reviewers determined match status for each record-pair. If reviewers disagreed, a third reviewer was used for final adjudication. Between the four datasets, the percent discordant rate ranged from 1.8-13.6%. While reviewers' discordance rate typically ranged between 1% and 5%, one exhibited a 59% discordance rate, showing the importance of the third reviewer. The original analysis was compared to three sensitivity analyses. The original analysis most often exhibited the highest predictive values compared to the sensitivity analyses. Reviewers vary in their assessment of a gold standard, which can lead to variances in estimates for matching performance. Our analysis demonstrates how a multi-reviewer process can be applied to create gold standards, identify reviewer discrepancies, and evaluate algorithm performance.

A comparative study of ensemble learning algorithms for high-frequency trading

High-Frequency Trading utilizes powerful mathematical algorithms to execute transactions at an extremely rapid pace, which makes the use of machine learning techniques for prediction necessary. This paper evaluates the effectiveness of various ensemble learning algorithms, including Boosting (Adaboost and XGBoost), Bagging (Random Forest and Bagging-LSVM), and Stacking, in predicting stock prices using High-Frequency Trading (HFT) data from the Casablanca Stock Exchange. The data contains 311.812 transactions at the millisecond precision level and was obtained under a non-disclosure agreement. Three performance metrics are used: Root Mean Squared Error (RMSE), Mean Absolute Error (MAE) and Mean of the Squared Errors (MSE) and accuracy of predictions is assessed daily, monthly and annually. The study shows that the Stacking Model outperforms other algorithms in forecasting prices across different periods due to its ability to generate profit from multiple learners and construct a robust model. These results provide valuable insights for improving High-Frequency Trading (HFT) strategies, including the accuracy and robustness of the algorithms in predicting stock prices, which are crucial for effective HFT strategies. The findings highlight how each algorithm characteristics and performance metrics can enhance decision-making in HFT. The novelty of this study lies in its unique combination of a focus on an emerging market, the application of advanced ensemble learning algorithms to high-frequency data, and its comprehensive approach to evaluating algorithm performance. Also, this paper is the first study that focuses on applying ensemble learning algorithms to high-frequency data in Casablanca Stock Exchange and one of the rare that focuses on African stock markets. Thus, this study is pioneering in its comparative analysis of machine learning techniques for HFT in Morocco, introducing sophisticated and more accurate tools for analyzing and predicting Casablanca Stock Exchange trends.

Performance evaluation of machine learning algorithms and impact of activation functions in artificial neural network classifier for bearing fault diagnosis

Machine learning algorithms are used to identify the bearing condition. In this work, different machine learning techniques such as decision tree, logistic regression, support vector machine (SVM), and artificial neural network (ANN) are used and compared to find healthy and faulty conditions of the bearing. The identification of the condition of the bearing is based on vibrations recorded using Fast Fourier Transform Analyzer. The vibration data recorded for the bearings have been used to categorize the condition of the bearing as healthy or faulty by applying machine learning techniques. The dataset of healthy and faulty bearings is collected using a four-channel Fast Fourier Transform Analyzer (FFT) analyzer. However, the statistical feature extraction technique has been used to evaluate the accuracy and performance of artificial neural network, support vector machine, logistic regression, and decision tree algorithms based on their classification accuracy and total costs. The result of the work reveals that the performance of the activation function based artificial neural network (ANN-AF) and SVM algorithm is better than logistic regression and decision tree models. However, it is observed that the use of appropriate activation functions within the ANN-AF technique improves the accuracy of the machine learning model.

Hippopotamus optimization algorithm: a novel nature-inspired optimization algorithm

The novelty of this article lies in introducing a novel stochastic technique named the Hippopotamus Optimization (HO) algorithm. The HO is conceived by drawing inspiration from the inherent behaviors observed in hippopotamuses, showcasing an innovative approach in metaheuristic methodology. The HO is conceptually defined using a trinary-phase model that incorporates their position updating in rivers or ponds, defensive strategies against predators, and evasion methods, which are mathematically formulated. It attained the top rank in 115 out of 161 benchmark functions in finding optimal value, encompassing unimodal and high-dimensional multimodal functions, fixed-dimensional multimodal functions, as well as the CEC 2019 test suite and CEC 2014 test suite dimensions of 10, 30, 50, and 100 and Zigzag Pattern benchmark functions, this suggests that the HO demonstrates a noteworthy proficiency in both exploitation and exploration. Moreover, it effectively balances exploration and exploitation, supporting the search process. In light of the results from addressing four distinct engineering design challenges, the HO has effectively achieved the most efficient resolution while concurrently upholding adherence to the designated constraints. The performance evaluation of the HO algorithm encompasses various aspects, including a comparison with WOA, GWO, SSA, PSO, SCA, FA, GOA, TLBO, MFO, and IWO recognized as the most extensively researched metaheuristics, AOA as recently developed algorithms, and CMA-ES as high-performance optimizers acknowledged for their success in the IEEE CEC competition. According to the statistical post hoc analysis, the HO algorithm is determined to be significantly superior to the investigated algorithms. The source codes of the HO algorithm are publicly available at https://www.mathworks.com/matlabcentral/fileexchange/160088-hippopotamus-optimization-algorithm-ho.

Performance evaluation of individual tree detection and segmentation algorithms using ALS data in Chir Pine (Pinus roxburghii) forest

The application of individual tree detection algorithms for assessing forest inventories and aiding decision-making in forestry has been a subject of research for more than two decades. Nevertheless, there is a notable research gap in the development of robust algorithms capable of automatically detecting trees of different species, ages, and varied crown sizes in dense forest environments. In this study, we conducted a comprehensive evaluation of six different individual tree detection (ITD) algorithms using airborne LiDAR data in Chir Pine (Pinus roxburghii) forests. This research represents one of the pioneering efforts in applying ITD algorithms to Chir Pine forests using ALS data. We categorized ITD routines into two groups: those reliant on local maxima as treetops and initial seeds for crown delineation, and those that do not require explicit treetop identification. To assess accuracy, we developed a special Individual Tree Matching (ITM) algorithm, enabling the matching of LiDAR-detected trees with 284 reference trees measured in the field. Our analysis involved various combinations of filtering fixed window sizes and adaptive window sizes applied to the point cloud, unsmoothed, and smoothed canopy height model (CHM). Our results highlighted the effectiveness of the 3 × 3m fixed window size method on unsmoothed CHM, achieving an overall F-score of 0.65 and a tree detection rate of 86%. Additionally, the Dalponte 2016 method proved superior for crown segmentation using identified treetops, consistently measuring mean crown radii within 0.5 m of reference field trees. Among the methods not relying on treetops, the adaptive mean shift algorithm (AMS3D) delivered strong performance, boasting an overall F-score of 0.67 and mean crown radii within 0.1 m. Our study revealed a high correlation between LiDAR-detected tree heights and field-measured tree heights across all evaluated methods. Overall, our findings underscore the potential of ITD algorithms in enhancing forest attribute measurement accuracy and facilitating climate-responsive forest management strategies.

Credit Fraud Recognition Based on Performance Evaluation of Deep Learning Algorithm

Over time, the growth of credit cards and the financial data need credit models to support banks in making financial decisions. So, to avoid fraud in internet transactions which increased with the growth of technology it is crucial to develop an efficient fraud detection system. Deep Learning techniques are superior to other Machine Learning techniques in predicting the customer behavior of credit cards depending on the missed payments probability of customers. The BiLSTM model proposed to train on Taiwanese non-transactional dataset for bank credit cards to decrease the losses of banks. The Bidirectional LSTM reached 98% accuracy in fraud credit detection compared with other Machine Learning techniques.

Performance evaluation of deep learning image reconstruction algorithm for dual-energy spectral CT imaging: A phantom study.

To evaluate the performance of deep learning image reconstruction (DLIR) algorithm in dual-energy spectral CT (DEsCT) as a function of radiation dose and image energy level, in comparison with filtered-back-projection (FBP) and adaptive statistical iterative reconstruction-V (ASIR-V) algorithms. An ACR464 phantom was scanned with DEsCT at four dose levels (3.5 mGy, 5 mGy, 7.5 mGy, and 10 mGy). Virtual monochromatic images were reconstructed at five energy levels (40 keV, 50 keV, 68 keV, 74 keV, and 140 keV) using FBP, 50% and 100% ASIR-V, DLIR at low (DLIR-L), medium (DLIR-M), and high (DLIR-H) settings. The noise power spectrum (NPS), task-based transfer function (TTF) and detectability index (d') were computed and compared among reconstructions. NPS area and noise increased as keV decreased, with DLIR having slower increase than FBP and ASIR-V, and DLIR-H having the lowest values. DLIR had the best 40 keV/140 keV noise ratio at various energy levels, DLIR showed higher TTF (50%) than ASIR-V for all materials, especially for the soft tissue-like polystyrene insert, and DLIR-M and DLIR-H provided higher d' than DLIR-L, ASIR-V and FBP in all dose and energy levels. As keV increases, d' increased for acrylic insert, and d' of the 50 keV DLIR-M and DLIR-H images at 3.5 mGy (7.39 and 8.79, respectively) were higher than that (7.20) of the 50 keV ASIR-V50% images at 10 mGy. DLIR provides better noise containment for low keV images in DEsCT and higher TTF(50%) for the polystyrene insert over ASIR-V. DLIR-H has the lowest image noise and highest detectability in all dose and energy levels. DEsCT 50 keV images with DLIR-M and DLIR-H show potential for 65% dose reduction over ASIR-V50% withhigher d'.

Performance evaluation of an occupant metabolic rate estimation algorithm using activity classification and object detection models

To create a comfortable indoor environment, the metabolic rate (MET), which affects the thermal sensation of occupants, needs to be reflected in real-time. Recently, methods employing computer vision techniques classify activities based on the pose of the body in images. However, these methods face challenges in determining the MET depending on the objects used, even with the same pose. Therefore, the objective of this study is to develop a MET estimation algorithm that can estimate various METs by integrating a pose-based activity classification model and an object detection model. To achieve this, an object detection model capable of detecting and classifying six regularly used objects indoors was developed, and a performance evaluation was conducted. The MET estimation algorithm was assessed through the implementation of a thermal control system, validating its applicability in experimental settings. As a result, the object detection model exhibited a real-time classification accuracy of 89%. Additionally, when evaluating the mode value over 15-s intervals, it demonstrated a classification accuracy of 100%. The algorithm exhibited a real-time estimation accuracy of 83% for the six METs and examining the mode value for 15-s intervals, it demonstrated a classification accuracy of 99%. This study thus confirmed the control capability of the proposed MET estimation algorithm and its potential for the estimation of various METs. The developed method can be used for the real-time estimation of occupant thermal comfort in indoor comfort-based control systems, contributing to the realization of a comfortable environment for occupants that protects their well-being.

Parallel implementation of Wiener's attack on RSA: Algorithm design and performance evaluation

The robustness of the RSA cryptosystem is intrinsically tied to the choice of public and private keys. As pinpointed by M. Wiener, should the private decryption exponent, d, be improperly chosen-either disproportionately large or unduly small in relation to the public key n-an adversary could feasibly deduce the private keys within a practical time span. In this paper, the algorithm invented by Wiener is revisited and find a way to parallelize the attacking algorithm by using OpenMP. The algorithm is based on the proof made in Wieners article, that if d<1/3 n^(1/4), then the private key d is the denominator of one of the convergent of CF(e/n). Using a constant set of private keys (e,n), an extensive series of simulated attacks employing Wieners method was conducted on a laptop to determine the optimal thread count for executing the parallel algorithm. The results indicate that the algorithms execution speed can be enhanced by a factor of 1.5607 (rounded to five significant figures). Specifically, while the sequential version of the algorithm averaged a runtime of 3518939.04 nanoseconds, its parallel counterpart averaged 2240493.28 nanoseconds.

A Performance Evaluation of Repetitive and Iterative Learning Algorithms for Periodic Tracking Control of Functional Electrical Stimulation System

Functional electrical stimulation (FES) is a medical device that delivers electrical pulses to the muscle, allowing patients with spinal cord injuries to perform activities such as walking, cycling, and grasping. It is critical for the FES to generate stimuli with the appropriate controller so that the desired movements can be precisely tracked. By considering the repetitive nature of the movements, the learning-based control algorithms are utilized for regulating the FES. Iterative learning control (ILC) and repetitive control (RC) are two learning algorithms that can be used to accomplish accurate repetitive motions. This study investigates a variety of ILC and RC designs with distinct learning functions; this constitutes our contribution to the field. The FES model of ankle angle, which is in a class of discrete-time linear systems is considered in this study. Two learning functions, i.e., proportional, and zero-phase learning functions, are simulated for the second-order FES model running at a sampling time of 0.1 s. The results indicate the superior performance of the ILC and RC in terms of convergence rate using the zero-phase learning function. ILC and RC with a zero-phase learning function can reach a zero root-mean-square error in two iterations if the model of the plant is correct. This is faster than proportional-based ILC and RC, which takes about 40 iterations. This indicates that the zero-phase learning function requires two iterations to ensure that the patient's ankle angle precisely tracks the intended trajectory. However, the tracking performance is degraded for both control methods, especially when the model is subject to uncertainties. This specific problem can lead to future research directions.