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Abstract Urban gas pipelines pose significant risks to public safety and infrastructure integrity, necessitating thorough risk assessment methodologies to mitigate potential hazards. This study investigates the dynamics of population distribution, demographic characteristics, and building structures to assess the risk associated with gas pipelines. Using geospatial analysis techniques, we analyze population distribution patterns during both day and night periods. Additionally, we conduct an in-depth vulnerability assessment considering multiple criteria maps, highlighting areas of heightened vulnerability in proximity to gas pipelines and older buildings. This study incorporated the concept of individual risk and the intrinsic parameters of gas pipelines to develop a hazard map. Hazard analysis identifies areas with elevated risks, particularly around main pipeline intersections and high-pressure zones. Integrating hazard and vulnerability assessments, we generate risk maps for both day and night periods, providing valuable insights into spatial risk distribution dynamics. The findings underscore the importance of considering temporal variations in risk assessment and integrating demographic and structural factors into hazard analysis for informed decision-making in pipeline management and safety measures.

Abstract The challenge of making flexible, standard, and early medical diagnoses is significant. However, some limitations are not fully overcome. First, the diagnosis rules established by medical experts or learned from a trained dataset prove static and too general. It leads to decisions that lack adaptive flexibility when finding new circumstances. Secondly, medical terminological interoperability is highly critical. It increases realism and medical progress and avoids isolated systems and the difficulty of data exchange, analysis, and interpretation. Third, criteria for diagnosis are often heterogeneous and changeable. It includes symptoms, patient history, demographic, treatment, genetics, biochemistry, and imaging. Symptoms represent a high-impact indicator for early detection. It is important that we deal with these symptoms differently, which have a great relationship with semantics, vary widely, and have linguistic information. This negatively affects early diagnosis decision-making. Depending on the circumstances, the diagnosis is made solo on imaging and some medical tests. In this case, although the accuracy of the diagnosis is very high, can these decisions be considered an early diagnosis or prove the condition is deteriorating? Our contribution in this paper is to present a real medical diagnostic system based on semantics, fuzzy, and dynamic decision rules. We attempt to integrate ontology semantics reasoning and fuzzy inference. It promotes fuzzy reasoning and handles knowledge representation problems. In complications and symptoms, ontological semantic reasoning improves the process of evaluating rules in terms of interpretability, dynamism, and intelligence. A real-world case study, ADNI, is presented involving the field of Alzheimer’s disease (AD). The proposed system has indicated the possibility of the system to diagnose AD with an accuracy of 97.2%, 95.4%, 94.8%, 93.1%, and 96.3% for AD, LMCI, EMCI, SMC, and CN respectively.

Artificial intelligence (AI)-based diagnostic systems provide less error-prone and safer support to clinicians, enhancing the medical decision-making process. This study presents a smart and reliable healthcare framework for detecting Alzheimer's disease (AD) progression. Early detection of AD before the onset of clinical symptoms is the most crucial step in starting timely treatment. To predict the conversion of cognitively normal patients to those with AD, three-dimensional 3D magnetic resonance imaging (MRI) whole-brain neuroimaging methods have been extensively studied. However, depending on the 3D volume, this method is computationally expensive. To solve this problem, we used an approximate rank pooling method originally designed for video action recognition with a 3D MRI volume to obtain a compressed representation of multiple two-dimensional (2D) MRI slices. This study proposes a hybrid multimodal CNN-BiLSTM deep model for AD progression detection, in which the resulting dynamic 2D images are fused with cognitive features. Moreover, a novel explainable AI approach is proposed to provide visual explanations using the resulting longitudinal 2D dynamic images. Temporal explanations were provided by visualizing the affected brain regions captured using longitudinal 2D MRIs. By utilizing a sample of 1,692 subjects with multimodal data from the Alzheimer’s Disease Neuroimaging Initiative dataset, our method was assessed using a 10-fold cross-validation process. The model achieved an area under the receiver operating characteristics curve (AUC) of 94% using longitudinal 2D three-time-step dynamic image data. The fusion of 2D dynamic images with cognitive features enhanced the performance by 2% in terms of the AUC. Patients who gradually develop AD, show changes in various brain regions. For such patients, our system highlights the critical role of the hippocampus, medial amygdala, caudal hippocampus, and lateral amygdala at the initial time steps. In the late stages of AD, the system detects abnormalities in extra brain regions such as the medial temporal gyrus, superior temporal gyrus, fusiform gyrus, and caudal hippocampus; indicating that patients have completely progressed to AD.

Background: Depression is a pervasive mental health condition, particularly affecting older adults, where early detection and intervention are essential to mitigate its impact. This study presents an explainable multi-layer dynamic ensemble framework designed to detect depression and assess its severity, aiming to improve diagnostic precision and provide insights into contributing health factors. Methods: Using data from the National Social Life, Health, and Aging Project (NSHAP), this framework combines classical machine learning models, static ensemble methods, and dynamic ensemble selection (DES) approaches across two stages: detection and severity prediction. The depression detection stage classifies individuals as normal or depressed, while the severity prediction stage further classifies depressed cases as mild or moderate-severe. Finally, a confirmation depression scale prediction model estimates depression severity scores to support the two stages. Explainable AI (XAI) techniques are applied to improve model interpretability, making the framework more suitable for clinical applications. Results: The framework’s FIRE-KNOP DES algorithm demonstrated high efficacy, achieving 88.33% accuracy in depression detection and 83.68% in severity prediction. XAI analysis identified mental and non-mental health indicators as significant factors in the framework’s performance, emphasizing the value of these features for accurate depression assessment. Conclusions: This study emphasizes the potential of dynamic ensemble learning in mental health assessments, particularly in detecting and evaluating depression severity. The findings provide a strong foundation for future use of dynamic ensemble frameworks in mental health assessments, demonstrating their potential for practical clinical applications.

Abstract Alzheimer’s disease (AD) is the most common form of dementia. Early and accurate detection of AD is crucial to plan for disease modifying therapies that could prevent or delay the conversion to sever stages of the disease. As a chronic disease, patient’s multivariate time series data including neuroimaging, genetics, cognitive scores, and neuropsychological battery provides a complete profile about patient’s status. This data has been used to build machine learning and deep learning (DL) models for the early detection of the disease. However, these models still have limited performance and are not stable enough to be trusted in real medical settings. Literature shows that DL models outperform classical machine learning models, but ensemble learning has proven to achieve better results than standalone models. This study proposes a novel deep stacking framework which combines multiple DL models to accurately predict AD at an early stage. The study uses long short-term memory (LSTM) models as base models over patient’s multivariate time series data to learn the deep longitudinal features. Each base LSTM classifier has been optimized using the Bayesian optimizer using different feature sets. As a result, the final optimized ensembled model employed heterogeneous base models that are trained on heterogeneous data. The performance of the resulting ensemble model has been explored using a cohort of 685 patients from the University of Washington's National Alzheimer’s Coordinating Center dataset. Compared to the classical machine learning models and base LSTM classifiers, the proposed ensemble model achieves the highest testing results (i.e., 82.02, 82.25, 82.02, and 82.12 for accuracy, precision, recall, and F1-score, respectively). The resulting model enhances the performance of the state-of-the-art literature, and it could be used to build an accurate clinical decision support tool that can assist domain experts for AD progression detection.

ABSTRACTMost countries and territories worldwide are affected by coronavirus disease 2019 (COVID-19), and some cities have become known as epicenters owing to high outbreaks. Because of the changeable and unknown nature of the virus, managers of different cities could learn from the experiences of cities that have been successful in controlling COVID-19 instead of wasting time exploring different methods. It would be even more beneficial if they analyzed the experiences of similar cities. The similarity of such cities could be examined within a geographic information system based on various criteria. This study investigated the similarities among eight cities – Wuhan, Tehran, Bergamo, Madrid, Paris, Daegu, New York, and Berlin – in terms of the COVID-19 situation (target) in these locations based on proximity factors, weather, and demographic criteria. First, the factor and target layers were prepared, and then similar cities were identified using a similarity model and different distance metrics. The results were aggregated using the Copeland method because of the different outcomes for each metric. The most similar city was identified for each selected city, and its similarity level was determined based on these criteria. The results suggested the following pairs of similar cities: Wuhan–Berlin, Tehran–Berlin, Daegu–Wuhan, Bergamo–Madrid, Paris–Madrid, and New York–Paris based on COVID-19 related data up to 15 April 2020 (target T1), and Daegu–Wuhan, Tehran–Madrid, Bergamo–Paris, Berlin–Paris, and New York–Madrid up to 8 December 2021 (target T2) with a minimum and maximum similarity rate of 82.85% and 92.36%, respectively. For similar cities, the most similar factors among the proximity criteria are the distance from bus and metro stations; among weather, the criteria are humidity and pressure; and among demographics, the criteria are male and female population ratios, literacy ratio, and death ratio from asthma and cancer, with a minimum and maximum difference of 0% and 64.94%, respectively. In addition, according to the random forests ranking results (with root mean squared error = 0.23), temperature, distance from the bank, and gender were the most important criteria for the eight studied cities. Identifying these important factors helps to determine hotspots or places of future outbreaks to choose control strategies according to the cultural and ecological conditions of each city.

Abstract Automated multi-organ segmentation plays an essential part in the computer-aided diagnostic (CAD) of chest X-ray fluoroscopy. However, developing a CAD system for the anatomical structure segmentation remains challenging due to several indistinct structures, variations in the anatomical structure shape among different individuals, the presence of medical tools, such as pacemakers and catheters, and various artifacts in the chest radiographic images. In this paper, we propose a robust deep learning segmentation framework for the anatomical structure in chest radiographs that utilizes a dual encoder–decoder convolutional neural network (CNN). The first network in the dual encoder–decoder structure effectively utilizes a pre-trained VGG19 as an encoder for the segmentation task. The pre-trained encoder output is fed into the squeeze-and-excitation (SE) to boost the network’s representation power, which enables it to perform dynamic channel-wise feature calibrations. The calibrated features are efficiently passed into the first decoder to generate the mask. We integrated the generated mask with the input image and passed it through a second encoder–decoder network with the recurrent residual blocks and an attention the gate module to capture the additional contextual features and improve the segmentation of the smaller regions. Three public chest X-ray datasets are used to evaluate the proposed method for multi-organs segmentation, such as the heart, lungs, and clavicles, and single-organ segmentation, which include only lungs. The results from the experiment show that our proposed technique outperformed the existing multi-class and single-class segmentation methods.

In this work, a machine learning (ML) model was created to predict intrinsic hardness of various compounds using their crystal chemistry. For this purpose, an initial dataset, containing the hardness values of 270 compounds and counterpart applied loads, was employed in the learning process. Based on various features generated using crystal information, an ML model, with a high accuracy (R2 = 0.942), was built using extreme gradient boosting (XGB) algorithm. Experimental validations conducted by hardness measurements of various compounds, including MSi2 (M = Nb, Ce, V, and Ta), Al2O3, and FeB4, showed that the XGB model was able to reproduce load-dependent hardness behaviors of these compounds. In addition, this model was also used to predict the behavior based on prototype crystal structures that are randomly substituted with elements.

In today’s world, technology has assumed an indispensable role in everyday life. However, though developments in the Internet of Things (IoT) have laid a foundation for achieving different educational purposes, IoT is not being employed to its full potential. A separate issue is that the topic of geometry has been neglected or received only limited attention in schools, particularly in the early years. Moreover, as geometry is of paramount importance, the idea of teaching geometry in early childhood should be investigated. This paper proposes an IoT-based approach for teaching basic geometric shapes to children aged 5 to 6. Specifically, five nodes were designed to act as the vertices of shapes. In addition, educational videos comprising three sections —identification, recognition, and recollection — were provided. Using a sample of 35 boys the proposed solution was assessed in terms of its effect on learning outcomes and the learning process using pre-test, simultaneous test, and post-tests. The findings revealed a noticeable improvement in learning outcomes. Furthermore, the proposed approach made learning enjoyable, which, compared to the traditional approach toward learning geometric shapes, is considered an improvement.

This study aims to predict head trauma outcome for Neurosurgical patients in children, adults, and elderly people. As Machine Learning (ML) algorithms are helpful in healthcare field, a comparative study of various ML techniques is developed. Several algorithms are utilized such as k-nearest neighbor, Random Forest (RF), C4.5, Artificial Neural Network, and Support Vector Machine (SVM). Their performance is assessed using anonymous patients' data. Then, a proposed double classifier based on Henry Gas Solubility Optimization (HGSO) is developed with Aquila optimizer (AQO). It is implemented for feature selection to classify patients' outcome status into four states. Those are mortality, morbidity, improved, or the same. The double classifiers are evaluated via various performance metrics including recall, precision, F-measure, accuracy, and sensitivity. Another contribution of this research is the original use of hybrid technique based on RF-SVM and HGSO to predict patient outcome status with high accuracy. It determines outcome status relationship with age and mode of trauma. The algorithm is tested on more than 1000 anonymous patients' data taken from a Neurosurgical unit of Mansoura International Hospital, Egypt. Experimental results show that the proposed method has the highest accuracy of 99.2% (with population size = 30) compared with other classifiers.

The digitalization of music has led to increased availability of music globally, and this spread has further raised the possibility of plagiarism. Numerous methods have been proposed to analyze the similarity between two pieces of music. However, these traditional methods are either focused on good processing speed at the expense of accuracy or they are not able to properly identify the correct features and the related feature weights needed for achieving accurate comparison results. Therefore, to overcome these issues, we introduce a novel model for detecting plagiarism between two given pieces of music. The model does this with a focus on the accuracy of the similarity comparison. In this paper, we make the following three contributions. First, we propose the use of provenance data along with musical data to improve the accuracy of the model’s similarity comparison results. Second, we propose a deep learning-based method to classify the similarity level of a given pair of songs. Finally, using linear regression, we find the optimized weights of extracted features following the ground truth data provided by music experts. We used the main dataset, containing 3800 pieces of music, to evaluate the proposed method’s accuracy; we also developed several additional datasets with their own established ground truths. The experimental results show that our method, which we call ‘TruMuzic’, improves the overall accuracy of music similarity comparison by 10% compared to the other state-of-the-art methods from recent literature.

Cutaneous leishmaniasis is a complex infection that is caused by different species of Leishmania and affects more than 2 million people in 88 countries. Identifying the environmental factors affecting the occurrence of cutaneous leishmaniasis and preparing a risk map is one of the basic tools to control and manage this disease. The aim of this study was a spatial prediction of cutaneous leishmaniasis in Isfahan province, Iran using three machine learning algorithms (decision tree (DT), support vector regression (SVR), and linear regression (LR)). The spatial database was created using data collected on the number of diseases in Isfahan province from 2011 to 2018, as well as ten environmental parameters (temperature, humidity, rainfall, altitude, slope, wind speed, normalized difference vegetation index (NDVI), number of sunny days, number of frosty days, and distance to stream) that affect the incidence of leishmaniasis. Furthermore, the fuzzy method was employed in this study to reduce uncertainty and evaluate the effect of environmental factors on disease prevalence. Using the holdout method and 70:30 ratios, the data were used to model and prepare a leishmaniasis prediction map and evaluate the results, respectively. The accuracy of the maps satisfied with the DT, SVR, and LR algorithms was 0.951, 0.934, and 0.914, respectively, according to the receiver operating characteristic (ROC) curve and area under the curve (AUC). Furthermore, the eastern and southern parts of the province have the lowest risk of leishmaniasis. The result of this issue is the identification of high-risk areas of the disease and increase life and peace for people in the community.

Multi-label classification (MLC) is considered an essential research subject in the computer vision field, principally in medical image analysis. For this merit, we derive benefits from MLC to diagnose multiple grades of diabetic retinopathy (DR) from various colored fundus images, especially from multi-label (ML) datasets. Therefore, ophthalmologists can detect early signs of DR as well as various grades to initiate appropriate treatment and avoid DR complications. In this paper, we propose a comprehensive ML computer-aided diagnosis (CAD) system based on deep learning technique. The proposed system's main contribution is to detect and analyze various pathological changes accompanying DR development in the retina without injecting the patient with dye or making expensive scans. The proposed ML-CAD system visualizes the different pathological changes and diagnoses the DR grades for the ophthalmologists. First, we eliminate noise, enhance quality, and standardize the sizes of the retinal images. Second, we differentiated between the healthy and DR cases by calculating the gray level run length matrix average in four different directions. The system automatically extracts the four changes: exudates, microaneurysms, hemorrhages, and blood vessels by utilizing a deep learning technique (U-Net). Next, we extract six features, which are the gray level co-occurrence matrix, areas of the four segmenting pathology variations, and the bifurcation points count of the blood vessels. Finally, the resulting features were afforded to an ML support vector machine (SVM) based on a classifier chain to differentiate the various DR grades. We utilized eight benchmark datasets (four of them are considered ML) and six different performance evaluation metrics to evaluate the proposed system's performance. It achieved 95.1%, 91.9%, 86.1%, 86.8%, 84.7%, 86.2% for accuracy, area under the curve, sensitivity, specificity, positive predictive value, and dice similarity coefficient, respectively. The experiments show encouraging results as compared with other systems.

The super packed functionalities and artificial intelligence (AI)-powered applications have made the Android operating system a big player in the market. Android smartphones have become an integral part of life and users are reliant on their smart devices for making calls, sending text messages, navigation, games, and financial transactions to name a few. This evolution of the smartphone community has opened new horizons for malware developers. As malware variants are growing at a tremendous rate every year, there is an urgent need to combat against stealth malware techniques. This paper proposes a visualization and machine learning-based framework for classifying Android malware. Android malware applications from the DREBIN dataset were converted into grayscale images. In the first phase of the experiment, the proposed framework transforms Android malware into fifteen different image sections and identifies malware files by exploiting handcrafted features associated with Android malware images. The algorithms such as Gray Level Co-occurrence Matrix-based (GLCM), Global Image deScripTors (GIST), and Local Binary Pattern (LBP) are used to extract the handcrafted features from the image sections. The extracted features were further classified using machine learning algorithms like K-Nearest Neighbors, Support Vector Machines, and Random Forests. In the second phase of the experiment, handcrafted features were fused with CNN features to form the feature fusion strategy. The classification performance was evaluated against every malware image file section. The results obtained using the Feature Fusion strategy are compared with handcrafted features results. The experiment results conclude to the fact that Feature Fusion-SVM model is most suited for the identification and classification of Android malware using the certificate and Android Manifest (CR + AM) malware images. It attained an high accuracy of 93.24%.

The intensive care unit (ICU) admits the most seriously ill patients requiring extensive monitoring. Early ICU mortality prediction is crucial for identifying patients who are at great risk of dying and for providing suitable interventions to save their lives. Accordingly, early prediction of patients at high mortality risk will enable their provision of appropriate and timely medical services. Although various severity scores and machine-learning models have recently been developed for early mortality prediction, such prediction remains challenging. This paper proposes a novel stacking ensemble approach to predict the mortality of ICU patients. Our approach is more accurate and medically intuitive compared to the literature work. Data were prepared and feature selection was processed under the supervision of the ICU domain expert. The data were split into six modalities based on the expert's decisions. For the prediction process, a separate classifier was selected for each modality based on the performance of the classifiers. We utilized the most popular and diverse classifiers in the literature, including linear discriminant analysis, decision tree (DT), multilayer perceptron, k-nearest neighbor, and logistic regression (LR). Then, a stacking ensemble classifier was constructed and optimized based on the fusion of these five classifier decisions. The framework was evaluated using 10,664 patients from the medical information mart for intensive care (MIMIC III) benchmark dataset. To predict patient mortality, extensive experiments were conducted using the patients' time series data of different lengths. For each patient, the first 6, 12, and 24 hours of the first stay were tested. The results indicate that our model outperformed the state-of-the-art approaches in terms of accuracy (94.4%), F1 score (93.7%), precision (96.4%), recall (91.1%), and area under the receiver operator characteristic (ROC) curve (93.3%). These results demonstrate the ability and efficiency of our approach to predict ICU mortality.

In this study, isothermal compression tests of highly ductile AZ31-0.5Ca Mg alloys were conducted at different strain rates (0.001–0.1 s−1) and temperatures (423–523 K) along with extruded direction. The flow stress characteristics were evaluated at elevated temperatures. In addition, a strain-dependent constitutive model based on the Arrhenius equation and machine learning (ML) were constructed to evaluate the stress–strain flow behavior. To build the ML model, experimental data containing temperature, strain, and strain rate were used to train various ML algorithms. The results show that under lower temperatures and higher strain rates, the curves exhibited strain hardening, which is due to the higher activation energy, while when increasing the temperature at a fixed strain rate, the strain hardening decreased and curves were divided into two regimes. In the first regime, a slight increase in strain hardening occurred, while in the second regime, dynamic recrystallization and dynamic recovery controlled the deformation mechanism. Our ML results demonstrate that the ML model outperformed the strain-dependent constitutive model.

This paper proposes a novel variant of the Grey Wolf Optimization (GWO) algorithm, named Velocity-Aided Grey Wolf Optimizer (VAGWO). The original GWO lacks a velocity term in its position-updating procedure, and this is the main factor weakening the exploration capability of this algorithm. In VAGWO, this term is carefully set and incorporated into the updating formula of the GWO. Furthermore, both the exploration and exploitation capabilities of the GWO are enhanced in VAGWO via stressing the enlargement of steps that each leading wolf takes towards the others in the early iterations while stressing the reduction in these steps when approaching the later iterations. The VAGWO is compared with a set of popular and newly proposed meta-heuristic optimization algorithms through its implementation on a set of 13 high-dimensional shifted standard benchmark functions as well as 10 complex composition functions derived from the CEC2017 test suite and three engineering problems. The complexity of the proposed algorithm is also evaluated against the original GWO. The results indicate that the VAGWO is a computationally efficient algorithm, generating highly accurate results when employed to optimize high-dimensional and complex problems.

Since December 2019, the global health population has faced the rapid spreading of coronavirus disease (COVID-19). With the incremental acceleration of the number of infected cases, the World Health Organization (WHO) has reported COVID-19 as an epidemic that puts a heavy burden on healthcare sectors in almost every country. The potential of artificial intelligence (AI) in this context is difficult to ignore. AI companies have been racing to develop innovative tools that contribute to arm the world against this pandemic and minimize the disruption that it may cause. The main objective of this study is to survey the decisive role of AI as a technology used to fight against the COVID-19 pandemic. Five significant applications of AI for COVID-19 were found, including (1) COVID-19 diagnosis using various data types (e.g., images, sound, and text); (2) estimation of the possible future spread of the disease based on the current confirmed cases; (3) association between COVID-19 infection and patient characteristics; (4) vaccine development and drug interaction; and (5) development of supporting applications. This study also introduces a comparison between current COVID-19 datasets. Based on the limitations of the current literature, this review highlights the open research challenges that could inspire the future application of AI in COVID-19.

The volume of adult content on the world wide web is increasing rapidly. This makes an automatic detection of adult content a more challenging task, when eliminating access to ill-suited websites. Most pornographic webpage-filtering systems are based on n-gram, naïve Bayes, K-nearest neighbor, and keyword-matching mechanisms, which do not provide perfect extraction of useful data from unstructured web content. These systems have no reasoning capability to intelligently filter web content to classify medical webpages from adult content webpages. In addition, it is easy for children to access pornographic webpages due to the freely available adult content on the Internet. It creates a problem for parents wishing to protect their children from such unsuitable content. To solve these problems, this paper presents a support vector machine (SVM) and fuzzy ontology-based semantic knowledge system to systematically filter web content and to identify and block access to pornography. The proposed system classifies URLs into adult URLs and medical URLs by using a blacklist of censored webpages to provide accuracy and speed. The proposed fuzzy ontology then extracts web content to find website type (adult content, normal, and medical) and block pornographic content. In order to examine the efficiency of the proposed system, fuzzy ontology, and intelligent tools are developed using Protégé 5.1 and Java, respectively. Experimental analysis shows that the performance of the proposed system is efficient for automatically detecting and blocking adult content.

Spatial modulation (SM) is a multiple-input multiple-output (MIMO) technique that achieves a MIMO capacity by conveying information through antenna indices, while keeping the transmitter as simple as that of a single-input system. Quadrature SM (QSM) expands the spatial dimension of the SM into in-phase and quadrature dimensions, which are used to transmit the real and imaginary parts of a signal symbol, respectively. A parallel QSM (PQSM) was recently proposed to achieve more gain in the spectral efficiency. In PQSM, transmit antennas are split into parallel groups, where QSM is performed independently in each group using the same signal symbol. In this paper, we analytically model the asymptotic pairwise error probability of the PQSM. Accordingly, the constellation design for the PQSM is formulated as an optimization problem of the sum of multivariate functions. We provide the proposed constellations for several values of constellation size, number of transmit antennas, and number of receive antennas. The simulation results show that the proposed constellation outperforms the phase-shift keying (PSK) constellation by more than 10 dB and outperforms the quadrature-amplitude modulation (QAM) schemes by approximately 5 dB for large constellations and number of transmit antennas.