Statistics, Optimization & Information Computing

Evaluation of Transformer-Based Large Language Models for Email Spam Detection Using BERT, Phi, and Gemma

Thu, 26 Dec 2024 00:00:00 +0800

In this paper, we study how LLMs based on the transformer architecture work and the possibility of adjusting these models to use only the body of email messages to classify them as spam or ham. The models studied are BERT, Gemma, and Phi. All of them underwent quantization stages, fine-tuning with a real dataset, and evaluation with metrics commonly used in binary classification problems. The Gemma model achieves over 99% accuracy in detecting spam, standing out as the best among the compared models.

A phase-portrait stability analysis for a reaction wheel pendulum using a generalized backstepping control approach

Oscar Danilo Montoya Giraldo, Carlos Alberto Ramírez-Vanegas, Fernando MEsa — Sat, 31 Aug 2024 00:00:00 +0800

This research presents a stability analysis of a reaction wheel pendulum (RWP) using the phase-portrait method. To derive the general control law that stabilizes the RWP system in the upper vertical position, a comprehensive backstepping control design is provided. This control is formulated in a generalized manner for a two-dimensional dynamic system, with the key advantage of guaranteeing asymptotic stability via Lyapunov's stability theorem. In this approach, the upper vertical position transitions from an unstable saddle point in open loop to a stable node in closed loop. The backstepping control design, when applied to the RWP system, incorporates a polynomial-based controller combined with a trigonometric function. A qualitative comparison with existing literature, including passivity- and Lyapunov-based control designs, confirms the generalization capabilities of the proposed backstepping controller. The phase-portrait analysis was conducted using MATLAB version 2024$b$.

ChatGPT as an intelligent self-Continuous Professional Development tool for teachers

Wed, 02 Oct 2024 00:00:00 +0800

Artificial intelligence, with its vast capabilities, has permeated various sectors of society, including education. This technological revolution has brought significant changes to both teaching and learning processes. This study aims to assess teachers' motivation to utilize AI-based tools, specifically ChatGPT, as a means of self-professional development to aid in the preparation of their pedagogical tasks. To this end, an online training session on the use of ChatGPT-4 was conducted with 41 physics teachers in the Fez-Meknes region of Morocco. During this training, teachers prepared lessons using both traditional and AI-enhanced methods. To measure their motivation towards the intelligent method, the IMMS-ARCS survey -based on four factors (Attention, Relevance, Confidence, and Satisfaction)- was employed, a global Alpha Cronbach=0.901 indicates an excellent internal consistency between the 36 items. The results indicate that teachers generally exhibit a positive attitude towards using ChatGPT as an innovative tool that can assist and streamline their teaching tasks. Additionally, the findings reveal that the four motivational factors are positively correlated, with higher values of these predictors indicating greater overall teachers’ motivation to adopt ChatGPT-4 as an intelligent tool for self-development of a new skills to improve their competencies, ultimately, enhancing students’ outcomes.

Analyzing Smart Inventory Management System Performance Over Time with State-Based Markov Model and Reliability Approach, Enhanced by Blockchain Security and Transparency

NABIL CHBAIK, Azeddine KHIAT, Ayoub BAHNASSE, Hassan OUAJJI — Sun, 06 Oct 2024 00:00:00 +0800

In response to the evolving demands of modern inventory management, this paper introduces a quantitative mathematical model aimed at assessing the performance of a smart inventory management system, emphasizing the integration of blockchain technology to enhance security and transparency. By considering essential hardware components, including ESP32 module, HC-SR04 ultrasonic sensor, battery, and jumper wires, the model utilizes Markov modeling and a reliability-based approach. Its primary objective is to enable timely repair and maintenance activities, ensuring sustained system availability by identifying and addressing weak components. Efficient operation of all system parts is critical for the timely transmission of inventory data. Through the incorporation of blockchain technology, the study addresses security and transparency concerns, alongside evaluating key reliability metrics such as reliability, unreliability, and Mean Time to Failure (MTTF). Sensitivity analysis identifies critical components, highlighting the importance of maintenance for components like the switch and servo motor. The research underscores the role of blockchain technology in fortifying security and transparency in smart inventory management systems, alongside emphasizing the significance of reliability metrics in system performance optimization.

Mixed Emotion Recognition Through Facial Expression using Transformer-Based Model

Limas Jaya Akeh, Gede Putra Kusuma — Wed, 02 Oct 2024 00:00:00 +0800

Basic facial expressions such as Angry, Disgust, Surprised, Happy, Scared, and Sadness can express emotions. However, in conversations, compound emotions can form Mixed Facial emotions, a combination of basic emotions that is much more complex Mixed emotion recognition is a recent study that has not been researched enough, even though datasets already contain mixed emotions This research aims to implement and fine-tune Transformer-based models such as Vision Transformer, Swin Transformer v2, and ConvNet-based model such as ConvNeXt architecture to identify and recognize mixed emotions through human faces using the IMED Dataset Various configurations with fine-tuned hyperparameters are tested and vary between each model The result shows that Vision Transformer architecture outperform other models in Mixed Emotion Recognition from Facial expressions and reach up to 79.37% Testing accuracy compared to Swin Transformer v2 model with 65.36% Testing accuracy and ConvNext with 74.77% Testing accuracy.

Synergistic Approaches for Accurate Arrhythmia Prediction: A Hybrid AI Model Integrating Higuchi Dimensional Fractal, RR-intervals and Attention-based Convolutional Neural Network in ECG Signal Analysis

Nadia Berrahou, Abdelmajid El Alami, Rachid El Alami, Hassan Qjidaa — Sun, 22 Sep 2024 00:00:00 +0800

In recent years, numerous methods for detecting arrhythmias using a 12-lead ECG have emerged, with deep learning approaches notably demonstrating effectiveness and gaining widespread adoption. However, the classification of inter-patient ECG data for arrhythmia detection remains a significant challenge. Despite the increased utilization of deep learning methodologies, a noticeable gap persists in achieving optimal performance in inter-patient ECG classification. In this paper, we introduce a new method based on a 1D deep learning model that incorporates an attention mechanism into convolutional neural networks for arrhythmia detection. 1D-CNN layers automatically extract morphological characteristics from ECG data, providing an accurate technique for spatial feature extraction. Simultaneously, the attention mechanism enables the model to focus on crucial segments of a signal. To enhance temporal context, four RR-interval features are included, and the potential of the Higuchi Dimensional Fractal is explored as a method for extracting additional features from ECG signals. Consequently, the classification layers benefit from the combination of both temporal and deep features, contributing to the final arrhythmia classification. We validated the proposed method using the MIT-BIH arrhythmia dataset, employing an inter-patient paradigm for model training and validation. Additionally, to assess its generalization ability, we tested it on the INCART dataset. The proposed method attained an average accuracy of 98.75\% for three classes and 97.96\% for four classes on the MIT-BIH arrhythmia dataset. On the INCART dataset, it achieves an average accuracy of 98.12\% for three classes. The experimental results indicate the superiority of this method in comparison to existing methods for recognizing arrhythmias. Thus, our method demonstrates enhanced generalization and potential effectiveness in identifying arrhythmias in real-world datasets characterized by class imbalances, showcasing its practical applicability.

Garduino: Sustainable Indoor Gardening Developed with Mobile Interface

Mon, 26 Aug 2024 00:00:00 +0800

Smart gardening is more than just a laboratory experiment in today's world. The system enables water conservation and energy efficiency. Furthermore, it also improves plant health and increases production rate. Traditional methods involved a constant need to attend to the garden physically to water the plants. This task effectively gets easier with preinstalled water channels and mobile interfaces. The Internet of Things (IoT) can be a game-changer for the entire gardening experience. The challenges to implementing the system include understanding the plant's needs, and knowing how to operate the app interface. IoT can play a huge role in monitoring our garden remotely. This research proposes the idea of going a step ahead in terms of using automation for gardening experience. With the signature autopilot mode, the user app can control the automation, and the user does not need to turn on the water pump even from the app interface. Under certain set conditions, sensors will auto-detect garden status and start or stop machines based on pre-defined conditions. Through proper mathematical analysis and algorithmic approach, this work presents a great option for elderly people who find it difficult to water plants physically.

Levinson parallel algorithm: A Finite-Dimensional Approach with an Infinite-Dimensional Perspective

Marcano José, Infante Saba, Sánchez Luis — Mon, 25 Nov 2024 00:00:00 +0800

A normalization of the generators of the defect spaces of an isometry is obtained, a version of the Levinson algorithm for Toeplitz block matrices in the infinite-dimensional case is built. Additionally, a factorization of the inverse of the Toeplitz matrix by blocks is obtained. Under this methodology, the obtained recurrences in the infinite dimensional case coincide with the case of the finite dimension, and an autoregressive linear filter to estimate stationary second-order stochastic processes is obtained, usually, the area extension in statistics, applications to spectral estimation, analysis of functional data and prediction problems among other applications is required. The parallelized algorithm for computing multiplications and inverses of block matrices is developed using the Pthreads POSIX library. Two real examples of the literature is illustrated, the parameters of a VAR$(1)$ model and an autoregressive process of order $5$ (AR $(5)$) are estimated. The predicted values in each case are obtained. The estimated quality of the parallelized algorithm is validated, the $T^{RC}$ test as a measure of goodness of fit is used, negligible estimation errors are shown. The performance of the parallel algorithm by the acceleration and efficiency factors is measured, an increase of $8\%$ in speed with respect to the sequential version and the most efficient for $P = 2$ threads are shown.

Geometric weighted least squares estimation

Reinhard Oldenburg — Thu, 19 Dec 2024 00:00:00 +0800

Optimal efficiency of least squares (LS) estimation requires that the error variables (residuals) have equal variance (homoscedasticity). In LS applications with multiple output variables, heteroscedasticity can even cause bias. In weighted LS, weights are chosen to compensate for differences in variance. The selection of these weights can be challenging, depending on the specific application. This paper introduces a general method, Geometric Weighted Least Squares (GWLS) estimation, which estimates weights using the inequality between the geometric and arithmetic means. A simulation study explores the performance of the method.

A Structural Equation Modeling of Teachers’ Job Satisfaction: An Application in Saudi Arabia-TALIS 2018

Bothinah Altaf — Sun, 06 Oct 2024 00:00:00 +0800

Structural equation modeling (SEM) is one of the indispensable multivariate statistical techniques for analyzing
complex relationships in many fields. The education field has emerged as an active area of SEM applications due to the inherent nature of its interacting variables. This research applies SEM to provide an in-depth analysis of the factors influencing teachers’ job satisfaction in Saudi Arabia. The study draws upon data collected from Saudi teachers who participated for the first time in the Teaching and Learning International Survey (TALIS-2018). For this purpose, 2744 teachers and 192 principals from the secondary school level were selected using a stratified sampling strategy. The results indicated school climate, professional practices, motivation and participation, and student-teacher interaction significantly impacted teacher job satisfaction (β=0.35,0.12,0.17 and 0.21) respectively p-value=0.000. Not surprisingly, the stress construct negatively impacted job satisfaction with (β=-0.30) with p-value=0.000. Based on the results, teacher satisfaction can be enhanced by focusing on variables that have a significant influence and avoiding stress causes.

On a two-parameter weighted geometric distribution: properties, computation and applications

Mohammed Shakhatreh, Hazem Al-Mofleh — Sun, 25 Aug 2024 00:00:00 +0800

In this article, we introduce a flexible two-parameter weighted geometric distribution characterized by its appealing properties. A key feature of this distribution is its ability to accommodate a wide range of skewness, making it particularly suitable for modeling right-skewed data. The distribution also exhibits a unimodal shape and an increasing failure rate. Several statistical measures are derived, and the distribution parameters are estimated using the method of maximum likelihood. The accuracy of these estimates is evaluated through a Monte Carlo simulation study. To demonstrate the flexibility, versatility, and practical importance of the proposed model, we analyze three real count data sets, showing its superiority over several existing models.

Kumaraswamy Alpha Power Lomax Distribution: Properties and Applications in Actuarial Sciences

Wondimu Fikre, Harmanpreet S. Kapoor, Kanchan Jain — Fri, 27 Sep 2024 00:00:00 +0800

The Kumaraswamy alpha power Lomax model, a five-parameter sub-model of the Kumaraswamy alpha power transformed family, is explored in detail. It is of particular interest because there are a variety of possible symmetrical and asymmetrical forms for the density function of this distribution. The proposed distribution is loaded with several features. Maximum likelihood, least squares, weighted least squares, and Cramer-von Mises are the four techniques used to estimate the parameters of the new model. A simulation study has been conducted to assess its effectiveness. Actuarial measures like value at risk and tail value at risk are also derived. Compared to other recently introduced heavy-tailed distributions, the tail of the proposed distribution is heavier. Moreover, the model's usefulness is investigated using four real data sets from the fields of insurance, finance, and reliability. Compared to other well-known Lomax-based and competing distributions, the results demonstrate that the proposed distribution can fit the data better.

Estimating the Parameters of the Odd Lomax Exponential Distribution

Ali Salman Habeeb — Sat, 16 Nov 2024 00:00:00 +0800

In this study, we introduce two methods for estimation of the unknown parameters of the Odd Lomax Exponential $(OLE)$ distribution are Least Squares Estimation $(LSE)$ and Maximum Likelihood Estimation $(MLE)$. Some statistical functions and mathematical properties were derived for which investigated from distribution’s flexibility . Through Monte Carlo simulations we investigated the performance of the estimate for these parameters, and us comparison these estimations in terms of bias and mean squared error $(MSE)$ for various sample sizes and four different scenarios of initial parameter values for two methods. Our analysis revealed that least square estimation consistently outperformed on $MLE$, yielding lower MSE values. Additionally, both two methods demonstrated decreasing in criteria values with increasing sample size, indicating improved accuracy for larger datasets. To evaluate the applicability of the $OLE$ distribution, we applied it to two types of dataset in the reliability engineering field. All computational and graphics in this work were performed in a Matlab, 23b code.

A new power xgamma distribution: statistical properties, estimation methods and application

Khawla Boudjerda — Tue, 24 Sep 2024 00:00:00 +0800

This paper introduces a novel probability distribution called the power xgamma distribution. We investigate several statistical properties essential for its characterization, including moments, moment generating function, quantile function, and order statistics. Estimation methods are explored to determine the parameters and characteristic functions of this distribution through a comprehensive simulation study. To illustrate its practical applicability, a real-world data example is provided, which demonstrates the effectiveness and relevance of the proposed model in empirical contexts.

Comparison between the FUZZY-ARFIMA model and the Hybrid ARFIMA -FUZZY model with application to agricultural data in the city of Mosul

Rehab Talal Ahmed, Omar salim Ibrahim — Tue, 24 Sep 2024 00:00:00 +0800

In this research, we studied forecasting based on time series data for red onion prices in Nineveh Governorate using model ARFIMA Autoregressive fractionally integrated moving average. A ARFIMA-FUZZY (FTS) hybrid model was proposed This model has the advantage and strength of the ARFIMA partial autoregressive integral in addition to the FUZZY-ARFIMA model and compared them with each other using evaluation criteria (BIC). For prediction, which is calculated using the statistical program R. The results showed that the ARFIMA-FUZZY (FTS) hybrid model is the best because it has the lowest (BIC) values. It is also the highest in forecast efficiency because it has the lowest values of forecast accuracy metrics (MSE, RMSE, MAE) and was chosen as the best forecast model.

Estimation of extreme quantiles of confirmed COVID-19 cases using South African data

Claris Shoko, Caston Sigauke — Fri, 04 Oct 2024 00:00:00 +0800

Background: Forecasting is important in any scientific field, including COVID-19 epidemiology. Daily confirmed COVID-19 cases are in different phases that are characterised by peaks.
Probabilistic forecasting is ideal in modelling time series data as it helps quantify uncertainties surrounding forecasts using data from South Africa. In this paper, we develop models that can be used to capture uncertainties of forecasts associated with the COVID-19 pandemic. Method: A three-stage approach to probabilistic forecasting is used in this study. The stochastic gradient boosting, generalised additive model, additive quantile regression and the nonlinear quantile regression are used to predict extremely high quantiles, i.e. 0.95-, 0.99- and 0.995-quantiles. The second stage combines each model’s predicted extremely high quantiles using the weighted mean and median methods. The pinball loss and coverage probabilities are used to evaluate the accuracy of the predictions in the third stage. Results: For all the extreme quantiles, i.e. the 0.95-, 0.99- and 0.995-quantiles, the cubic spline regression method gives the best predictions regarding the lowest pinball losses, which are 171.41, 563.49 and 115.28, respectively. The weighted mean average model dominated by the mean is the second best regarding the pinball losses but the best regarding the coverage probability. Conclusion: This study provides insights into the strengths and weaknesses of different models for short-term extreme quantile prediction of COVID-19. Estimating extreme quantiles of daily COVID-19 using models with high predictive capabilities, such as the weighted mean-median model dominated by the mean, is important to public health officials and policymakers for planning and preparing for potential surges in CoVID-19 cases and similar pandemics in the future.

Improving representativeness in big data analysis through weighted machine learning methods: A case study on the logistic regression model

Lamyae Benhlima, Mohammed El Haj Tirari — Sat, 28 Sep 2024 00:00:00 +0800

In the presence of Big Data, it is essential to recognize that despite the abundance of data, these often do not faithfully represent the target populations. Therefore, analyzing these vast datasets does not guarantee representativeness, as they are collected without proper sampling design. Integrating survey weights and auxiliary information into machine learning algorithms constitutes a major challenge in making the samples more representative of the overall population. Moreover, only a few statistical learning software packages offer options to include these weights in their estimation process. In this paper, we introduce a novel weighted configuration of the logistic regression algorithm and employ a bootstrap method to compare its performance against non-weighted models. Our contributions demonstrate the importance and relevance of incorporating different weights for instances and provide a practical approach for analysts in settings where traditional statistical learning tools fall short. This work bridges a critical gap in statistical learning, ensuring that conclusions drawn from large datasets are robust and generalizable.

A Note on Prior Selection in Bayesian Estimation

Muhammad M. Seliem, Amr R. Kamel, Ibrahim M. Taha, Mona Mahmoud Abu El-Nasr — Sat, 12 Oct 2024 00:00:00 +0800

The parameter according to the Bayesian approach is handled as a variable that is random and with a probability distribution, rather than an unknown and fixed number. Statistical inference is dependent on the posterior distribution of the parameter rather than only the likelihood function. Choosing the prior distribution is a fundamental step in determining the posterior distribution, and it can be done objectively or subjectively. When the subjective technique is utilized, the prior distribution reflects the prior information the researcher had before coming into contact with the data. When utilizing the objective method, the prior distribution can be chosen in such a way that it has the least influence on the prior distribution. In this paper, a new way of selecting the prior distribution in Bayesian analysis was proposed. According to this strategy, for a given distribution, the prior distribution should be comparable to or the same as the data distributed. The performance of this method was compared to other estimation methods and found to have significantly better performance compared to other estimators. This result was confirmed though a Monte Carlo simulation experiments, with some selected performance criteria mainly, the root mean squared error (RMSE) and the Bias.

Least squares estimation for reflected Ornstein-Uhlenbeck processes with one and two sided barriers

Fateh Merahi, Abdelouahab Bibi — Thu, 12 Sep 2024 00:00:00 +0800

Diffusion processes for modelling, among others, dataset for instance, (macro-) econometrics, mathematical finance, biology, queueing, and electrical engineering often involve reflecting one or two barriers. In this paper, we investigate the least squares estimation $\left(LSE\right)$ for a one dimensional continuous-time ergodic reflected Ornstein-Uhlenbeck $(ROU)$ processes that returns continuously and immediately to the interior of the state space when it attains one and/or two-sided barriers. Both the estimates based on continuously observed processes and discretely observed processes are considered. So, we derive explicit formulas for the estimates, and then we establish their consistency and asymptotic normality ($CAN$). We also illustrate the $CAN$ properties of the estimates through a Monte Carlo simulation and comparing with respect to maximum likelihood estimation ($LME$) as benchmark method showing the performance of the proposed estimators with
moderate sample sizes. The method is valid irrespective of the length of the time intervals between consecutive observations.

On Rainbow Vertex Antimagic Coloring of Related Prism Graphs and Its Operations

Sat, 07 Sep 2024 00:00:00 +0800

Let $G=(V,E)$ be a simple, connected and un-directed graph, for $f:E(G)\rightarrow\{1,2,\dots, |E(G)|\}$, the weight of a vertex $v\in V(G)$ under $f$ is $w_f(v)=\Sigma_{e \in E(v)} f(e)$, where $E(v)$ is the set of vertices incident to $v$. The function $f$ is called vertex antimagic edge labeling if every vertex has distinct weight. While, rainbow vertex coloring is a coloring of graph vertices where each vertex on the graph is connected by a path that all internal vertices on the $u-v$ path have different colors. We introduce a new notion, namely a rainbow vertex antimagic coloring, which is a combination of antimagic labeling and rainbow vertex coloring. The rainbow vertex antimagic connection number of $G$, denoted by $rvac(G)$, is the smallest number of colors taken over all rainbow colorings induced by rainbow vertex antimagic labelings of $G$. In this paper we aim to discover some new lemmas or theorems regarding to $rvac(G)$.

Optimizing Asset Management by using Double Declining Balance and The KNN Algorithm

Khaera Tunnisa, Wahyuni Ekasasmita, Egi Fahrezi Iswan — Wed, 28 Aug 2024 00:00:00 +0800

Satker PTN is a ministry work unit whose entire income goes into the state account and is not given ownership of its assets. One of the Satker PTN in Indonesia is the Bacharuddin Jusuf Habibie Institute of Technology (ITH). ITH's operational procedures follow the rules of Satker PTN: not given asset ownership rights. The management of BMN ITH assets has not been optimal due to limited human resources which cause difficulties in the maintenance process, checking asset conditions and procurement of goods so that digitalization tools are needed that can be used to increase the efficiency of decision making and asset data analysis. This study optimizes asset management at ITH by using the depreciation method, namely the Double Declining Balance Method to determine asset depreciation. The Multilabel Classification Method uses the K-Nearest Neighbor Algorithm to classify good asset conditions, checking needs improvement. This study evaluates the depreciation of Chromebook, HDMI Cable, Electronic Plug, LCD Projector and Microphone assets over a 5-year period. Based on the results of the study, the DDB method produces a lower Final Book Value with a faster depreciation rate. The DDB method is effective in accelerating the depreciation of high-tech assets that tend to have shorter economic lives. The kNN algorithm classifies asset conditions based on historical asset lending data that includes features related to asset depreciation and usage. The results of the comparison of the kNN and Random Forest models in asset data classification are evaluated in Cross Validation, Confusion Matrix and ROC Analysis. Evaluation of the kNN Cross Validation Model with a value of k = 27 with 5 and 10 folds with an AUC value of 0.982, accuracy of 0.981, F1 score of 0.980, precision of 0.984, recall of 0.981, and MCC of 0.871. Evaluation of the Random Forest Cross Validation Model using 50 decision trees and 5 folds with an Auc value of 0.979, accuracy, F1 score, precision, recall and MCC are the same as the kNN model. The results of the kNN and Random Forest Confusion Matrices provide similar results and are a more detailed picture of prediction errors, including false positives and false negatives, which helps in understanding and improving the model. The results of the ROC Analysis evaluation show the Threshold values of the Checking, Good, Repair categories, namely 0.794, 0.259, 0.083 for kNN and 0.692, 0.247, 0.102 for Random Forest. Based on the evaluation results, this study shows that the kNN model is able to distinguish asset categories, is accurate in predicting asset status and can reduce false positives so that only assets that really need attention can be followed up. This study combines the DDB and KNN methods can be easily implemented, accelerate asset depreciation, classify asset conditions effectively, reduce repair operational costs and can optimize asset management by implementing models in asset applications.

Multi-Objective Design Optimization of Planar Spiral Inductors Using Enhanced Metaheuristic Techniques

Hamid Bouali, Soufiane Abi, Bachir Benhala, Mohammed Guerbaoui — Fri, 13 Sep 2024 00:00:00 +0800

The study presented in this paper improves the Multi-Objective Artificial Bee Colony (MOABC) method. It evaluates its performance using Generational Distance (GD), Spread (SP), and Hypervolume (HV) metrics on the Zitzler-Deb-Thiele (ZDT) benchmark functions. Subsequently, the improved MOABC method, along with Multi-Objective Particle Swarm Optimization (MOPSO) and the Non-Dominated Sorting Genetic Algorithm II (NSGA-II), is applied to optimize the design of a square planar spiral inductor. The objectives are to maximize the quality factor ($Q$) and minimize the inductor area ($A$) simultaneously while maintaining a necessary inductance of $4\, \text{nH}$ at a $2.4\, \text{GHz}$ operating frequency, utilizing $0.13\, \mu \text{m}$ CMOS technology. The optimization findings are verified and confirmed using Advanced Design System (ADS) Momentum, demonstrating the feasibility of multi-objective optimization for integrated inductor design.

Some directs numerical methods for solving the nonlinear optimal control problem practical in aeronautic

Mohamed Aliane, Nacima Moussouni — Sat, 07 Sep 2024 00:00:00 +0800

In this study, we have implemented direct numerical methods to convert the continuous optimal control problem into a nonlinear optimization problem. We used three discretization techniques: the Euler method, the second-order Runge-Kutta method, and the fourth-order Runge-Kutta method. Subsequently, the resulting non-linear optimization problem was solved using MATLAB's fmincon function. To evaluate the efficiency and accuracy of the proposed approach, we modeled a nonlinear optimal control problem relevant to aeronautics. Our objective was to minimize the travel time of a rocket from an initial point to a final point at a specified altitude, considering aerodynamic forces and gravity, with the control variable being the rocket's heel angle. To compare the different methods, we developed a MATLAB implementation and showcased various simulation results.

A New Estimator for Shannon Entropy

Hadi Alizadeh Noughabi, Mohammad Shafaei Noughabi — Tue, 07 Jan 2025 00:00:00 +0800

In this paper we propose a new estimator of the entropy of a continuous random variable. The estimator is obtained by modifying the estimator proposed by Vasicek (1976). Consistency of the proposed estimator is proved, and comparisons are made with Vasicek’s estimator (1976), Ebrahimi et al.’s estimator (1994) and Correa’s estimator (1995). The results indicate that the proposed estimator has smaller mean squared error than considered alternative estimators. The proposed estimator is applied to a real data set for illustration.