Search results for: wavelet analysis

Authors: Anthony Spiteri Staines

Abstract:

This paper examines the modeling and analysis of a cruise control system using a Petri net based approach, task graphs, invariant analysis and behavioral properties. It shows how the structures used can be verified and optimized.

Keywords: Software Engineering, Real Time Analysis andDesign, Petri Nets, Task Graphs, Parallelism.

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Authors: Somnath Dey, Debasis Samanta

Abstract:

Iris-based biometric authentication is gaining importance in recent times. Iris biometric processing however, is a complex process and computationally very expensive. In the overall processing of iris biometric in an iris-based biometric authentication system, feature processing is an important task. In feature processing, we extract iris features, which are ultimately used in matching. Since there is a large number of iris features and computational time increases as the number of features increases, it is therefore a challenge to develop an iris processing system with as few as possible number of features and at the same time without compromising the correctness. In this paper, we address this issue and present an approach to feature extraction and feature matching process. We apply Daubechies D4 wavelet with 4 levels to extract features from iris images. These features are encoded with 2 bits by quantizing into 4 quantization levels. With our proposed approach it is possible to represent an iris template with only 304 bits, whereas existing approaches require as many as 1024 bits. In addition, we assign different weights to different iris region to compare two iris templates which significantly increases the accuracy. Further, we match the iris template based on a weighted similarity measure. Experimental results on several iris databases substantiate the efficacy of our approach.

Keywords: Iris recognition, biometric, feature processing, patternrecognition, pattern matching.

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Authors: M. Pollar, M. Jaroensutasinee, K. Jaroensutasinee

Abstract:

The population structure of the Tor tambroides was investigated with morphometric data (i.e. morphormetric measurement and truss measurement). A morphometric analysis was conducted to compare specimens from three waterfalls: Sunanta, Nan Chong Fa and Wang Muang waterfalls at Khao Nan National Park, Nakhon Si Thammarat, Southern Thailand. The results of stepwise discriminant analysis on seven morphometric variables and 21 truss variables per individual were the same as from a neural network. Fish from three waterfalls were separated into three groups based on their morphometric measurements. The morphometric data shows that the nerual network model performed better than the stepwise discriminant analysis.

Keywords: Morphometric, Tor tambroides, Stepwise Discriminant Analysis , Neural Network Analysis.

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Authors: Fadi Eleiwi, Taous Meriem Laleg-Kirati, Sofiane Khelladi, Farid Bakir

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This paper presents the use of a semi-classical signal analysis method that has been developed recently for the analysis of turbomachinery flow unsteadiness. We will focus on the correlation between theSemi-Classical Signal Analysis parameters and some physical parameters in relation with turbomachinery features. To demonstrate the potential of the proposed approach, a static pressure signal issued from a rotor/stator interaction of a centrifugal pump is studied. Several configurations of the pump are compared.

Keywords: Semi-classical signal analysis, turbomachines, newindices, physical parameters

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Authors: Zhu Jiaming, Yu Mengna

Abstract:

In this article, models based on quantitative analysis, physical geometry and regression analysis are established, by using analytic hierarchy process analysis, fuzzy cluster analysis, fuzzy photographic and data fitting. The reasons of various leaf shapes among different species and the differences between the leaf shapes on same tree have been solved by using software, such as Eviews, VB and Matlab. We also successfully estimate the leaf mass of a tree and the correlation with the tree profile.

Keywords: Leaf shape; Mass; Fuzzy cluster; Regression analysis; Eviews; Matlab

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Authors: L. Zehtaban, D. Roller

Abstract:

Apart from geometry, functionality is one of the most significant hallmarks of a product. The functionality of a product can be considered as the fundamental justification for a product existence. Therefore a functional analysis including a complete and reliable descriptor has a high potential to improve product development process in various fields especially in knowledge-based design. One of the important applications of the functional analysis and indexing is in retrieval and design reuse concept. More than 75% of design activity for a new product development contains reusing earlier and existing design know-how. Thus, analysis and categorization of product functions concluded by functional indexing, influences directly in design optimization. This paper elucidates and evaluates major classes for functional analysis by discussing their major methods. Moreover it is finalized by presenting a noble hybrid approach for functional analysis.

Keywords: Functional analysis, design reuse, functionalindexing and representation.

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Authors: Sepehr Damavandinejadmonfared, Ali Khalili Mobarakeh, Mohsen Pashna, , Jiangping Gou Sayedmehran Mirsafaie Rizi, Saba Nazari, Shadi Mahmoodi Khaniabadi, Mohamad Ali Bagheri

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In this paper a novel algorithm is proposed to merit the accuracy of finger vein recognition. The performances of Principal Component Analysis (PCA), Kernel Principal Component Analysis (KPCA), and Kernel Entropy Component Analysis (KECA) in this algorithm are validated and compared with each other in order to determine which one is the most appropriate one in terms of finger vein recognition.

Keywords: Biometrics, finger vein recognition, PrincipalComponent Analysis (PCA), Kernel Principal Component Analysis(KPCA), Kernel Entropy Component Analysis (KPCA).

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Authors: Sadi Vural, Hiromi Tomii, Hironori Yamauchi

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With the advent of digital cinema and digital broadcasting, copyright protection of video data has been one of the most important issues. We present a novel method of watermarking for video image data based on the hardware and digital wavelet transform techniques and name it as “traceable watermarking" because the watermarked data is constructed before the transmission process and traced after it has been received by an authorized user. In our method, we embed the watermark to the lowest part of each image frame in decoded video by using a hardware LSI. Digital Cinema is an important application for traceable watermarking since digital cinema system makes use of watermarking technology during content encoding, encryption, transmission, decoding and all the intermediate process to be done in digital cinema systems. The watermark is embedded into the randomly selected movie frames using hash functions. Embedded watermark information can be extracted from the decoded video data. For that, there is no need to access original movie data. Our experimental results show that proposed traceable watermarking method for digital cinema system is much better than the convenient watermarking techniques in terms of robustness, image quality, speed, simplicity and robust structure.

Keywords: Decoder, Digital content, JPEG2000 Frame, System-On-Chip, traceable watermark, Hash Function, CRC-32.

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Authors: Proud Arunrangsiwed

Abstract:

The part of “future direction” in the findings of meta-analysis could provide the great direction to conduct the future studies. This study, “The Documentary Analysis of Meta-Analysis Research in Violence of Media” would conclude “future directions” out of 10 meta-analysis papers. The purposes of this research are to find an appropriate research design or an appropriate methodology for the future research related to the topic, “violence of media”. Further research needs to explore by longitudinal and experimental design, and also needs to have a careful consideration about age effects, time spent effects, enjoyment effects and ordinary lifestyle of each media consumer.

Keywords: Aggressive, future direction, meta-analysis, media, violence.

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Authors: Omid Mirmotahari, Yngvar Berg

Abstract:

In this paper we promote the Ultra Low Voltage (ULV) NAND gate to replace either partly or entirely the encryption block of a design to withstand power analysis attack.

Keywords: Differential Power Analysis (DPA), Low Voltage (LV), Ultra Low Voltage (ULV), Floating-Gate (FG), supply current analysis.

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Authors: Pingping Lin, Xudong Luo

Abstract:

Natural language often conveys emotions of speakers. Therefore, sentiment analysis on what people say is prevalent in the field of natural language process and has great application value in many practical problems. Thus, to help people understand its application value, in this paper, we survey various applications of sentiment analysis, including the ones in online business and offline business as well as other types of its applications. In particular, we give some application examples in intelligent customer service systems in China. Besides, we compare the applications of sentiment analysis on Twitter, Weibo, Taobao and Facebook, and discuss some challenges. Finally, we point out the challenges faced in the applications of sentiment analysis and the work that is worth being studied in the future.

Keywords: Natural language processing, sentiment analysis, application, online comments.

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Authors: Jie Liu, Xudong Luo, Pingping Lin, Yifan Fan

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Facebook, Twitter, Weibo, and other social media and significant e-commerce sites generate a massive amount of online texts, which can be used to analyse people’s opinions or sentiments for better decision-making. So, sentiment analysis, especially the fine-grained sentiment analysis, is a very active research topic. In this paper, we survey various methods for fine-grained sentiment analysis, including traditional sentiment lexicon-based methods, ma-chine learning-based methods, and deep learning-based methods in aspect/target/attribute-based sentiment analysis tasks. Besides, we discuss their advantages and problems worthy of careful studies in the future.

Keywords: sentiment analysis, fine-grained, machine learning, deep learning

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Authors: Pingping Lin, Xudong Luo, Yifan Fan

Abstract:

Sentiment analysis is a very active research topic. Every day, Facebook, Twitter, Weibo, and other social media, as well as significant e-commerce websites, generate a massive amount of comments, which can be used to analyse peoples opinions or emotions. The existing methods for sentiment analysis are based mainly on sentiment dictionaries, machine learning, and deep learning. The first two kinds of methods rely on heavily sentiment dictionaries or large amounts of labelled data. The third one overcomes these two problems. So, in this paper, we focus on the third one. Specifically, we survey various sentiment analysis methods based on convolutional neural network, recurrent neural network, long short-term memory, deep neural network, deep belief network, and memory network. We compare their futures, advantages, and disadvantages. Also, we point out the main problems of these methods, which may be worthy of careful studies in the future. Finally, we also examine the application of deep learning in multimodal sentiment analysis and aspect-level sentiment analysis.

Keywords: Natural language processing, sentiment analysis, document analysis, multimodal sentiment analysis, deep learning.

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Authors: Cristina G. Dascâlu, Corina Dima Cozma, Elena Carmen Cotrutz

Abstract:

The medical data statistical analysis often requires the using of some special techniques, because of the particularities of these data. The principal components analysis and the data clustering are two statistical methods for data mining very useful in the medical field, the first one as a method to decrease the number of studied parameters, and the second one as a method to analyze the connections between diagnosis and the data about the patient-s condition. In this paper we investigate the implications obtained from a specific data analysis technique: the data clustering preceded by a selection of the most relevant parameters, made using the principal components analysis. Our assumption was that, using the principal components analysis before data clustering - in order to select and to classify only the most relevant parameters – the accuracy of clustering is improved, but the practical results showed the opposite fact: the clustering accuracy decreases, with a percentage approximately equal with the percentage of information loss reported by the principal components analysis.

Keywords: Data clustering, medical data, principal components analysis.

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Authors: Cameron Hamilton, Walter Potter, Gerrit Hoogenboom, Ronald McClendon, Will Hobbs

Abstract:

A model was constructed to predict the amount of solar radiation that will make contact with the surface of the earth in a given location an hour into the future. This project was supported by the Southern Company to determine at what specific times during a given day of the year solar panels could be relied upon to produce energy in sufficient quantities. Due to their ability as universal function approximators, an artificial neural network was used to estimate the nonlinear pattern of solar radiation, which utilized measurements of weather conditions collected at the Griffin, Georgia weather station as inputs. A number of network configurations and training strategies were utilized, though a multilayer perceptron with a variety of hidden nodes trained with the resilient propagation algorithm consistently yielded the most accurate predictions. In addition, a modeled direct normal irradiance field and adjacent weather station data were used to bolster prediction accuracy. In later trials, the solar radiation field was preprocessed with a discrete wavelet transform with the aim of removing noise from the measurements. The current model provides predictions of solar radiation with a mean square error of 0.0042, though ongoing efforts are being made to further improve the model’s accuracy.

Keywords: Artificial Neural Networks, Resilient Propagation, Solar Radiation, Time Series Forecasting.

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Authors: Chothmal, Basant Agarwal

Abstract:

Sentiment analysis means to classify a given review document into positive or negative polar document. Sentiment analysis research has been increased tremendously in recent times due to its large number of applications in the industry and academia. Sentiment analysis models can be used to determine the opinion of the user towards any entity or product. E-commerce companies can use sentiment analysis model to improve their products on the basis of users’ opinion. In this paper, we propose a new One-class Support Vector Machine (One-class SVM) based sentiment analysis model for movie review documents. In the proposed approach, we initially extract features from one class of documents, and further test the given documents with the one-class SVM model if a given new test document lies in the model or it is an outlier. Experimental results show the effectiveness of the proposed sentiment analysis model.

Keywords: Feature selection methods, Machine learning, NB, One-class SVM, Sentiment Analysis, Support Vector Machine.

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Authors: Maria C. Proença, Marco Aniceto, Pedro N. Santos, José C. Freitas

Abstract:

A methodology based on wavelets is proposed for the automatic location and delimitation of defects in limestone plates. Natural defects include dark colored spots, crystal zones trapped in the stone, areas of abnormal contrast colors, cracks or fracture lines, and fossil patterns. Although some of these may or may not be considered as defects according to the intended use of the plate, the goal is to pair each stone with a map of defects that can be overlaid on a computer display. These layers of defects constitute a database that will allow the preliminary selection of matching tiles of a particular variety, with specific dimensions, for a requirement of N square meters, to be done on a desktop computer rather than by a two-hour search in the storage park, with human operators manipulating stone plates as large as 3 m x 2 m, weighing about one ton. Accident risks and work times are reduced, with a consequent increase in productivity. The base for the algorithm is wavelet decomposition executed in two instances of the original image, to detect both hypotheses – dark and clear defects. The existence and/or size of these defects are the gauge to classify the quality grade of the stone products. The tuning of parameters that are possible in the framework of the wavelets corresponds to different levels of accuracy in the drawing of the contours and selection of the defects size, which allows for the use of the map of defects to cut a selected stone into tiles with minimum waste, according the dimension of defects allowed.

Keywords: Automatic detection, wavelets, defects, fracture lines.

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Authors: Mingxin Zhang, Zhaogan Lu, Junyi Shen

Abstract:

In current common research reports, salient regions are usually defined as those regions that could present the main meaningful or semantic contents. However, there are no uniform saliency metrics that could describe the saliency of implicit image regions. Most common metrics take those regions as salient regions, which have many abrupt changes or some unpredictable characteristics. But, this metric will fail to detect those salient useful regions with flat textures. In fact, according to human semantic perceptions, color and texture distinctions are the main characteristics that could distinct different regions. Thus, we present a novel saliency metric coupled with color and texture features, and its corresponding salient region extraction methods. In order to evaluate the corresponding saliency values of implicit regions in one image, three main colors and multi-resolution Gabor features are respectively used for color and texture features. For each region, its saliency value is actually to evaluate the total sum of its Euclidean distances for other regions in the color and texture spaces. A special synthesized image and several practical images with main salient regions are used to evaluate the performance of the proposed saliency metric and other several common metrics, i.e., scale saliency, wavelet transform modulus maxima point density, and important index based metrics. Experiment results verified that the proposed saliency metric could achieve more robust performance than those common saliency metrics.

Keywords: salient regions, color and texture features, image segmentation, saliency metric

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Authors: A.R Alesaadi, M. Nafar, A.H. Gheisari

Abstract:

In this paper sensitivity analysis is performed for reliability evaluation of power systems. When examining the reliability of a system, it is useful to recognize how results change as component parameters are varied. This knowledge helps engineers to understand the impact of poor data, and gives insight on how reliability can be improved. For these reasons, a sensitivity analysis can be performed. Finally, a real network was used for testing the presented method.

Keywords: sensitivity analysis, reliability evaluation, powersystems.

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Authors: Kyekyung Kim, Sangseung Kang, Suyoung Chi, Jaehong Kim

Abstract:

In recent years, IT convergence technology has been developed to get creative solution by combining robotics or sports science technology. Object detection and recognition have mainly applied to sports science field that has processed by recognizing face and by tracking human body. But object detection and recognition using vision sensor is challenge task in real world because of illumination. In this paper, object detection and recognition using vision sensor applied to sports simulator has been introduced. Face recognition has been processed to identify user and to update automatically a person athletic recording. Human body has tracked to offer a most accurate way of riding horse simulator. Combined image processing has been processed to reduce illumination adverse affect because illumination has caused low performance in detection and recognition in real world application filed. Face has recognized using standard face graph and human body has tracked using pose model, which has composed of feature nodes generated diverse face and pose images. Face recognition using Gabor wavelet and pose recognition using pose graph is robust to real application. We have simulated using ETRI database, which has constructed on horse riding simulator.

Keywords: Horse riding simulator, Object detection, Object recognition, User identification, Pose recognition.

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Authors: Alexiou Dimitra, Fragkaki Maria

Abstract:

The objective of the paper is the study of geographic, economic and educational variables and their contribution to determine the position of each member-state among the EU-28 countries based on the values of seven variables as given by Eurostat. The Data Analysis methods of Multiple Factorial Correspondence Analysis (MFCA) Principal Component Analysis and Factor Analysis have been used. The cross tabulation tables of data consist of the values of seven variables for the 28 countries for 2014. The data are manipulated using the CHIC Analysis V 1.1 software package. The results of this program using MFCA and Ascending Hierarchical Classification are given in arithmetic and graphical form. For comparison reasons with the same data the Factor procedure of Statistical package IBM SPSS 20 has been used. The numerical and graphical results presented with tables and graphs, demonstrate the agreement between the two methods. The most important result is the study of the relation between the 28 countries and the position of each country in groups or clouds, which are formed according to the values of the corresponding variables.

Keywords: Multiple factorial correspondence analysis, principal component analysis, factor analysis, E.U.-28 countries, statistical package IBM SPSS 20, CHIC Analysis V 1.1 Software, Eurostat.eu statistics.

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Authors: J. R. Wang, W. Y. Cheng, J. S. Yeh, S. W. Chen, Y. M. Ferng, J. H. Yang, W. S. Hsu, C. Shih

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To understand the risk for dry storage concrete casks in the cask loading, transfer, and storage phase, the purpose of this research is to establish the probabilistic risk assessment (PRA) analysis methodology for dry storage concrete casks by using SAPHIRE 8 code. This analysis methodology is used to perform the study of Taiwan nuclear power plants (NPPs) dry storage system. The process of research has three steps. First, the data of the concrete casks and Taiwan NPPs are collected. Second, the PRA analysis methodology is developed by using SAPHIRE 8. Third, the PRA analysis is performed by using this methodology. According to the analysis results, the maximum risk is the multipurpose canister (MPC) drop case.

Keywords: PRA, Dry storage, concrete cask, SAPHIRE.

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Authors: Wang Chengcheng, Li Chuanri, Xu Fei, Guo Ying

Abstract:

Aiming at most of the aviation products are facing the problem of fatigue fracture in vibration environment, we makes use of the testing result of a bracket, analysis for the structure with ANSYS-Workbench, predict the life of the bracket by different ways, and compared with the testing result. With the research on analysis methods, make an organic combination of simulation analysis and testing, Not only ensure the accuracy of simulation analysis and life predict, but also make a dynamic supervision of product life process, promote the application of finite element simulation analysis in engineering practice.

Keywords: Random vibration, finite element simulation, fatigue, frequency domain.

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Authors: Dong Hoon Lim

Abstract:

A series of microarray experiments produces observations of differential expression for thousands of genes across multiple conditions. Principal component analysis(PCA) has been widely used in multivariate data analysis to reduce the dimensionality of the data in order to simplify subsequent analysis and allow for summarization of the data in a parsimonious manner. PCA, which can be implemented via a singular value decomposition(SVD), is useful for analysis of microarray data. For application of PCA using SVD we use the DNA microarray data for the small round blue cell tumors(SRBCT) of childhood by Khan et al.(2001). To decide the number of components which account for sufficient amount of information we draw scree plot. Biplot, a graphic display associated with PCA, reveals important features that exhibit relationship between variables and also the relationship of variables with observations.

Keywords: Principal component analysis, singular value decomposition, microarray data, SRBCT

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Authors: Liton Jude Rozario, Mohammad Reduanul Haque, Md. Ziarul Islam, Mohammad Shorif Uddin

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Face recognition is a technique to automatically identify or verify individuals. It receives great attention in identification, authentication, security and many more applications. Diverse methods had been proposed for this purpose and also a lot of comparative studies were performed. However, researchers could not reach unified conclusion. In this paper, we are reporting an extensive quantitative accuracy analysis of four most widely used face recognition algorithms: Principal Component Analysis (PCA), Independent Component Analysis (ICA), Linear Discriminant Analysis (LDA) and Support Vector Machine (SVM) using AT&T, Sheffield and Bangladeshi people face databases under diverse situations such as illumination, alignment and pose variations.

Keywords: PCA, ICA, LDA, SVM, face recognition, noise.

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Authors: Dong Wook Lee, Adrian Mistreanu

Abstract:

The authors have studied a method for analyzing containment and penetration using an explicit nonlinear Finite Element Analysis. This method may be used in the stage of concept design for the protection of external configurations or components of aircraft engines and nuclear power plant structures. This paper consists of the modeling method, the results obtained from the method and the comparison of the results with those calculated from simple analytical method. It shows that the containment capability obtained by proposed method matches well with analytically calculated containment capability.

Keywords: Computer Aided Engineering, CAE, containment analysis, Finite Element Analysis, FEA, impact analysis, penetration analysis.

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Authors: J. R. Wang, H. C. Chen, C. Shih, S. W. Chen, J. H. Yang, Y. Chiang

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In this study, we focus on the establishment of the analysis model for Maanshan PWR nuclear power plant (NPP) by using RADTRAD and SNAP codes with the FSAR, manuals, and other data. In order to evaluate the cumulative dose at the Exclusion Area Boundary (EAB) and Low Population Zone (LPZ) outer boundary, Maanshan NPP RADTRAD/SNAP model was used to perform the analysis of the DBA LOCA case. The analysis results of RADTRAD were similar to FSAR data. These analysis results were lower than the failure criteria of 10 CFR 100.11 (a total radiation dose to the whole body, 250 mSv; a total radiation dose to the thyroid from iodine exposure, 3000 mSv).

Keywords: RADionuclide, transport, removal, and dose estimation, RADTRAD, symbolic nuclear analysis package, SNAP, dose, PWR.

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Authors: Tawakal Hasnain Baluch, Adnan Masood, Javaid Iqbal, Umer Izhar, Umar Shahbaz Khan

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This paper will provide the kinematic and dynamic analysis of a lower limb exoskeleton. The forward and inverse kinematics of proposed exoskeleton is performed using Denevit and Hartenberg method. The torques required for the actuators will be calculated using Lagrangian formulation technique. This research can be used to design the control of the proposed exoskeleton.

Keywords: Dynamic Analysis, Exoskeleton, Kinematic Analysis, Lower Limb, Rehabilitation Robotics

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Authors: Sule Yucelbas, Gulay Tezel, Cuneyt Yucelbas, Seral Ozsen

Abstract:

In this study, it was tried to identify some heart rhythm disorders by electrocardiography (ECG) data that is taken from MIT-BIH arrhythmia database by subtracting the required features, presenting to artificial neural networks (ANN), artificial immune systems (AIS), artificial neural network based on artificial immune system (AIS-ANN) and particle swarm optimization based artificial neural network (PSO-NN) classifier systems. The main purpose of this study is to evaluate the performance of hybrid AIS-ANN and PSO-ANN classifiers with regard to the ANN and AIS. For this purpose, the normal sinus rhythm (NSR), atrial premature contraction (APC), sinus arrhythmia (SA), ventricular trigeminy (VTI), ventricular tachycardia (VTK) and atrial fibrillation (AF) data for each of the RR intervals were found. Then these data in the form of pairs (NSR-APC, NSR-SA, NSR-VTI, NSR-VTK and NSR-AF) is created by combining discrete wavelet transform which is applied to each of these two groups of data and two different data sets with 9 and 27 features were obtained from each of them after data reduction. Afterwards, the data randomly was firstly mixed within themselves, and then 4-fold cross validation method was applied to create the training and testing data. The training and testing accuracy rates and training time are compared with each other.

As a result, performances of the hybrid classification systems, AIS-ANN and PSO-ANN were seen to be close to the performance of the ANN system. Also, the results of the hybrid systems were much better than AIS, too. However, ANN had much shorter period of training time than other systems. In terms of training times, ANN was followed by PSO-ANN, AIS-ANN and AIS systems respectively. Also, the features that extracted from the data affected the classification results significantly.

Keywords: AIS, ANN, ECG, hybrid classifiers, PSO.

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Authors: K. Paisal

Abstract:

The purposes of this research were (1) to create a learning activity for constructivism, (2) study the Mathematical Analysis courses learning achievement, and (3) study students’ attitude toward the learning activity for constructivism. The samples in this study were divided into 2 parts including 3 Mathematical Analysis courses instructors of Suan Sunandha Rajabhat University who provided basic information and attended the seminar and 17 Mathematical Analysis courses students who were studying in the academic and engaging in the learning activity for constructivism. The research instruments were lesson plans constructivism, subjective Mathematical Analysis courses achievement test with reliability index of 0.8119, and an attitude test concerning the students’ attitude toward the Mathematical Analysis courses learning activity for constructivism. The result of the research show that the efficiency of the Mathematical Analysis courses learning activity for constructivism is 73.05/72.16, which is more than expected criteria of 70/70. The research additionally find that the average score of learning achievement of students who engaged in the learning activities for constructivism are equal to 70% and the students’ attitude toward the learning activity for constructivism are at the medium level.

Keywords: Constructivism, learning management, Mathematical Analysis courses.

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