Hybrid Convolutional Neural Network Research Articles

Uncertainty Quantification with Mixed Data by Hybrid Convolutional Neural Network for Additive Manufacturing

Uncertainty Quantification with Mixed Data by Hybrid Convolutional Neural Network for Additive Manufacturing

A novel hybrid deep CNN model for breast cancer classification using Lipschitz-based image augmentation and recursive feature elimination

Breast cancer is the leading cause of death for women worldwide. Despite its difficulties, the histopathological diagnosis must be used because modern imaging techniques cannot differentiate between benign and malignant tumors. This article introduces a hybrid deep learning method with recursive feature elimination for categorizing histopathology images of breast lesions as benign or malignant, using standard datasets, to increase diagnostic accuracy. The proposed four-stage model includes several novel techniques. First, a modified Lipschitz-based image augmentation technique is utilized to ensure a proportionate representation of various sample classes. K-fold cross-validation is employed to mitigate the bias that emerges from the selection of training and testing datasets. Then, for efficient feature extraction, a hybrid convolutional neural network (CNN) approach is used by integrating three CNNs (PResNet-34, FE-VGG-16, and M-AlexNet). With the proposed universum twin support vector machine-based recursive feature elimination technique, the initial 1,000 features extracted by each deep model are further reduced to 100. Finally, the deep features are subsequently combined into a set of 300 features, which are then fed into machine learning classifiers such as decision tree, k-nearest neighborhood, linear discriminant analysis, linear regression, and support vector machine. The results demonstrate that the proposed hybrid CNN model outperforms state-of-the-art techniques in accurately classifying breast lesions as benign or malignant, with an accuracy of 99.99 %, sensitivity of 99.56 %, specificity of 99.53 %, precision of 99.55 %, and F1 score of 99.77 %.

Learning-Based Approach for Automated Surface Inspection with Industrial Tomography Imaging

Abstract In recent years, advanced deep learning techniques have emerged as pivotal tools in enabling the development of robust vision-based solutions for steel surface inspection. This resulted in enhanced inspection accuracy, all while significantly reducing costs in the manufacturing industry. However, the lack of actual steel surface defects datasets currently places a certain constraint on further research into classifying those anomalies. As a consequence, the Convolutional Neural Network (CNN) technique, known for its prowess in image-related tasks, faces certain challenges especially in classifying less common defects. This work proposes a novel hybrid CNN model with an SVM classifier at the output layer for surface defects classification. The features extracted from the pre-trained ResNet152 and EfficientB0 CNN algorithms are concatenated and fed to the SVM layer for classification. Extensive experiments on a merged dataset consisting of the publicly available Northeastern University (NEU) dataset and Xsteel surface defect dataset (X-SDD) are carried out and the accuracy and F1 scores are calculated for performance evaluation. The merged dataset contains eleven typical defect types with a total of 2660 defect images. Then, the adopted algorithm is compared with ten fine-tuned deep learning models to evaluate the performance of transfer learning for steel defect detection and identification. The evaluation results show that the deep feature extraction and SVM classification produced better results than the transfer learning. Finally, the proposed classifier model is validated on a new collected dataset from a Computed Tomography scanner with an accuracy reaching over 96%.

Profitability trend prediction in crypto financial markets using Fibonacci technical indicator and hybrid CNN model

Cryptocurrency has become a popular trading asset due to its security, anonymity, and decentralization. However, predicting the direction of the financial market can be challenging, leading to difficult financial decisions and potential losses. The purpose of this study is to gain insights into the impact of Fibonacci technical indicator (TI) and multi-class classification based on trend direction and price-strength (trend-strength) to improve the performance and profitability of artificial intelligence (AI) models, particularly hybrid convolutional neural network (CNN) incorporating long short-term memory (LSTM), and to modify it to reduce its complexity. The main contribution of this paper lies in its introduction of Fibonacci TI, demonstrating its impact on financial prediction, and incorporation of a multi-classification technique focusing on trend strength, thereby enhancing the depth and accuracy of predictions. Lastly, profitability analysis sheds light on the tangible benefits of utilizing Fibonacci and multi-classification. The research methodology employed to carry out profitability analysis is based on a hybrid investment strategy—direction and strength by employing a six-stage predictive system: data collection, preprocessing, sampling, training and prediction, investment simulation, and evaluation. Empirical findings show that the Fibonacci TI has improved its performance (44% configurations) and profitability (68% configurations) of AI models. Hybrid CNNs showed most performance improvements particularly the C-LSTM model for trend (binary-0.0023) and trend-strength (4 class-0.0020) and 6 class-0.0099). Hybrid CNNs showed improved profitability, particularly in CLSTM, and performance in CLSTM mod. Trend-strength prediction showed max improvements in long strategy ROI (6.89%) and average ROIs for long-short strategy. Regarding the choice between hybrid CNNs, the C-LSTM mod is a viable option for trend-strength prediction at 4-class and 6-class due to better performance and profitability.

Representational and sequential feature learning model for fault classification in power system

ABSTRACT The classification of three-phase faults in electrical power systems is essential. The vast majority of fault classification techniques are focused on machine learning framework that requires pre-processing algorithms and rely highly on feature engineering. In this paper, a hybrid Convolutional Neural Network and Long Short Term Memory (CNN-LSTM) deep learning model is designed and employed for fault classification. With this combination, both representational and sequential features are automatically extracted and effectively learned using lesser trainable parameters from the raw temporal data. The raw three-phase current and voltage data are used as input for the proposed model. The performance of the proposed model is tested using a 10-fold cross-validation technique on large simulated data produced from a standard IEEE 30-bus system. The efficacy of the proposed model is confirmed by comparing it with different standards and existing models from the literature. The impact of noisy data and load variation conditions are also studied and analysed on the model’s performance.

Detection of Deepfake Media Using a Hybrid CNN–RNN Model and Particle Swarm Optimization (PSO) Algorithm

Deepfakes are digital audio, video, or images manipulated using machine learning algorithms. These manipulated media files can convincingly depict individuals doing or saying things they never actually did. Deepfakes pose significant risks to our lives, including national security, financial markets, and personal privacy. The ability to create convincing deep fakes can also harm individuals’ reputations and can be used to spread disinformation and fake news. As such, there is a growing need for reliable and accurate methods to detect deep fakes and prevent their harmful effects. In this paper, a hybrid convolutional neural network (CNN) and recurrent neural network (RNN) with a particle swarm optimization (PSO) algorithm is utilized to demonstrate a deep learning strategy for detecting deepfake videos. High accuracy, sensitivity, specificity, and F1 score were attained by the proposed approach when tested on two publicly available datasets: Celeb-DF and the Deepfake Detection Challenge Dataset (DFDC). Specifically, the proposed method achieved an average accuracy of 97.26% on Celeb-DF and an average accuracy of 94.2% on DFDC. The results were compared to other state-of-the-art methods and showed that the proposed method outperformed many. The proposed method can effectively detect deepfake videos, which is essential for identifying and preventing the spread of manipulated content online.

A hybrid convolutional neural network-transformer method for received signal strength indicator fingerprinting localization in Long Range Wide Area Network

In recent years, low-power wide area networks (LPWANs), particularly Long-Range Wide Area Network (LoRaWAN) technology, are increasingly being adopted into large-scale Internet of Things (IoT) applications thanks to having the ability to offer cost-effective long-range wireless communication at low-power. The need to provide location-stamped communications to IoT applications for meaningful interpretation of physical measurements from IoT devices has increased demand to incorporate location estimation capabilities into LoRaWAN networks. Fingerprint-based localization methods are increasingly becoming popular in LoRaWAN networks because of their relatively high accuracy compared to range-based localization methods. This work proposes hybrid convolutional neural networks (CNNs)-transformer fingerprinting method to localize a node in a LoRaWAN network. CNNs are adopted to complement the strengths of the Transformer by adding the ability to capture local features from input data and consequently allow the Transformer, through the attention mechanism, to effectively learn global dependencies from the input data. Specifically, the proposed method works by first learning the local location features from the input data using the CNNs and passing the resulting information to the transformer encoder to learn global features from the input data. The output of the transformer encoder is then concatenated with information learned at the local level and then passed through the regressor for the final location estimation. With a localization performance of 290.71 m mean error achieved, the proposed method outperformed similar state-of-the-art works in the literature evaluated on the same publicly available LoRaWAN dataset.

Developing a hybrid convolutional neural network for automatic aphid counting in sugar beet fields

Aphids can cause direct damage and indirect virus transmission to crops. Timely monitoring and control of their populations are thus critical. However, the manual counting of aphids, which is the most common practice, is labor-intensive and time-consuming. Additionally, two of the biggest challenges in aphid counting are that aphids are small objects and their density distributions are varied in different areas of the field. To address these challenges, we proposed a hybrid automatic aphid counting network architecture which integrates the detection network and the density map estimation network. When the distribution density of aphids is low, it utilizes an improved Yolov5 to count aphids. Conversely, when the distribution density of aphids is high, it switches to CSRNet to count aphids. To the best of our knowledge, this is the first framework integrating the detection network and the density map estimation network for counting tasks. Through comparison experiments of counting aphids, it verified that our proposed approach outperforms all other methods in counting aphids. It achieved the lowest MAE and RMSE values for both the standard and high-density aphid datasets: 2.93 and 4.01 (standard), and 34.19 and 38.66 (high-density), respectively. Moreover, the AP of the improved Yolov5 is 5 % higher than that of the original Yolov5. Especially for extremely small aphids and densely distributed aphids, the detection performance of the improved Yolov5 is significantly better than the original Yolov5. This work provides an effective early warning caused by aphids in sugar beet fields, offering protection for sugar beet growth and ensuring sugar beet yield. The datasets and project code are released at: https://github.com/JunfengGaolab/Counting-Aphids.

Enhancing Urban Traffic Management Through Hybrid Convolutional and Graph Neural Network Integration

Traffic congestion has made city planning and citizen well-being difficult due to fast city growth and the increasing number of vehicles. Traditional traffic management fails to solve urban transportation's ever-changing issues. Traffic prediction and control systems are vital for enhancing Traffic Flow (TF) and minimizing congestion. Smart cities need advanced prediction models to regulate urban TF as traffic management becomes more complex. This paper introduces a hybrid Convolutional Neural Networks (CNN) and Graph Neural Networks (GNN) model for better real-time traffic management. The hybrid model combines CNNs' spatial feature extraction with GNNs' structural and relational data processing to analyze and predict traffic conditions. Traffic camera images are pre-processed to extract spatial characteristics. Traffic network graph construction is used for structural research. The model accurately captures traffic topology and space. The proposed method sequentially processes spatial data with CNNs and integrates them with GNNs. The final hybrid model is trained on one year of traffic data from diverse circumstances and events. The hybrid model is compared to CNN, GNN, and traditional Traffic Prediction Models (TPM) like ARIMA and SVM utilizing MAE, RMSE, and MAPE. The hybrid GNN+CNN model outperforms benchmark models with lower MAE, RMSE, and MAPE across several prediction intervals.

Hybrid HAR-CNN Model: A Hybrid Convolutional Neural Network Model for Predicting and Recognizing the Human Activity Recognition

Human activity recognition (HAR) is an active research area in computer vision from past several years and research is still continuing in this field due to the unavailability of perfect recognition system. The human activity recognition system it covers e-health, patient monitoring, assistive daily living activities, video surveillance, security and behaviour analysis, and sports analysis. Many researchers have suggested techniques that use visual perception to detect human activities. Researchers will need to address problems including light variations in human activity detection, interclass similarity between scenes, the surroundings and recording setting, and temporal variation in order to construct an efficient vision-based human activity recognition system. However, a significant drawback of many deep learning models is their inability to achieve satisfactory results in real-world scenarios due to the conflicts mentioned above. To address this challenge, we developed a hybrid HAR-CNN classifier aimed at enhancing the learning outcomes of Deep CNNs by combining two models: Improved CNN and VGG-19. Using the KTH dataset, we collected 6,000 images for training, validation, and testing of our proposed technique. Our research findings indicate that the Hybrid HAR-CNN model, which combines Improved CNN with VGG-19 Net, outperforms individual deep learning models such as Improved CNN and VGG-19 Net.

Hybrid CNN Approach for Unknown Attack Detection in Edge-Based IoT Networks

INTRODUCTION: In the constantly growing Internet of Things (IoT), device security is crucial. As IoT gadgets pervade our lives, detecting unforeseen assaults is crucial to protecting them. Behavioral analysis, machine learning, and collaborative intelligence may be needed to protect against new dangers. This short discusses the need of detecting unexpected IoT attacks and essential security strategies for these interconnected environments.OBJECTIVES: This research uses the BoT-IoT dataset to create an enhanced IoT intrusion detection system. The goals are to optimize a CNN architecture for effective pattern recognition, address imbalanced data, and evaluate model performance using precision, recall, F1-score, and AUC-ROC measures. Improving IoT ecosystem reliability and security against unknown assaults is the ultimate goal.METHODS: The proposed methods use the BoT-IoT dataset to create a comprehensive IoT intrusion detection system. This involves tuning a Convolutional Neural Network (CNN) architecture to improve pattern recognition. Oversampling and class weighting address imbalanced data issues. RESULTS: The comprehensive evaluation of our innovative unknown attack detection method shows promise, suggesting it may be better than existing methods. A high accuracy, precision, recall, and f-measure of 98.23% were attained using an advanced model and feature selection methods. This achievement was achieved by using features designed to identify unknown attacks in the dataset, proving the proposed methodology works.CONCLUSION: This research presents an improved IoT Intrusion Detection System using the BoT-IoT dataset. The optimised Convolutional Neural Network architecture and imbalanced data handling approaches achieved 98.23% accuracy.

Advanced Heart Disease Prediction: Deep Learning-Enhanced Convolutional Neural Network in the Internet of Medical Things Environment

Using the large dataset from the UCI Machine Learning Repository, this study presents a state-of-the-art Hybrid Convolutional Neural Network (HCNN) for predicting heart disease. The HCNN design has convolutional layers, leftover blocks, and attention methods. These help pull more features from cardiovascular health data, even when the patterns are very complex. Utilizing these deep learning parts, the HCNN shows better prediction skills, getting higher accuracy, strong classification (AUC), and a fair F1 Score. Because the model can change to find complicated connections in the information, it could be used to make medical diagnosis better.  The HCNN is unique because it can instantly learn hierarchical structures from raw data. This lets it find hidden features that are important for accurately predicting heart disease. The convolutional layers help the model find local patterns, and the residue blocks stop problems with disappearing gradients, which makes training for deep designs more efficient. Attention processes make the network even more focused on important traits, which adds to its amazing ability to tell them apart. This work opens the door for researchers, doctors, and data scientists to use deep learning, and especially HCNN, to improve cardiovascular health analytics. This study takes a big step toward more accurate and efficient heart disease prognosis by giving a complete overview of the model's architecture and performance metrics. This opens the door for more research and use of advanced neural networks in the field of predictive medical diagnostics.

Customized Mechanism for Diabetic Risk Prediction: A Hybrid CNN–Autoencoder Approach with Emphasis on Retinal Imaging in the Elderly

Diabetes Mellitus presents a substantial health obstacle on a global scale, with a particular impact on the elderly demographic. Prompt identification is vital for efficient control and avoidance of complications. This study introduces a new Hybrid Convolutional Neural Network (CNN) and Autoencoder model specifically developed for accurately predicting the risk of diabetes at an early stage. The model is specifically designed to analyze retinal images in older individuals. The introduction of this paper presents a comprehensive analysis of the increasing incidence of diabetes in the elderly population and underscores the significance of early identification. Conventional approaches frequently encounter constraints in terms of precision and specificity, which has led to the investigation of sophisticated machine learning models. The Hybrid CNN–Autoencoder model combines the advantageous characteristics of both architectures, utilizing the CNN proficiency in extracting spatial features and the Autoencoder's capability for unsupervised feature learning.  The approach we use consists of training and validating the model using a comprehensive dataset of retinal images from elderly individuals. The model attains a remarkable accuracy of 90.92%, outperforming the typical deep learning and machine learning models frequently employed in predicting diabetic risk. The experimental results demonstrate the superior performance of the Hybrid CNN–Autoencoder model in terms of accuracy, sensitivity, and specificity. Comparative analysis shows that it is highly effective in identifying subtle patterns that indicate early signs of diabetes, surpassing traditional models and other modern deep learning methods. The research findings presented in this study make a valuable contribution to the expanding knowledge base on diabetes detection, specifically within the elderly population. The proven precision of the suggested model highlights its capacity as a dependable and tailored instrument for early forecasting, thus enabling prompt interventions and individualized healthcare strategies for individuals susceptible to diabetes.

Data-Driven Techniques for Short-Term Electricity Price Forecasting through Novel Deep Learning Approaches with Attention Mechanisms

The electricity market is constantly evolving, being driven by factors such as market liberalization, the increasing use of renewable energy sources (RESs), and various economic and political influences. These dynamics make it challenging to predict wholesale electricity prices. Accurate short-term forecasting is crucial to maintaining system balance and addressing anomalies such as negative prices and deviations from predictions. This paper investigates short-term electricity price forecasting using historical time series data and employs advanced deep learning algorithms. First, four deep learning models are implemented and proposed, which are a convolutional neural network (CNN) with an integrated attention mechanism, a hybrid CNN followed by a gated recurrent unit model (CNN-GRU) with an attention mechanism, and two ensemble learning models, which are a soft voting ensemble and a stacking ensemble model. Also, the optimized version of a transformer model, the Multi-Head Attention model, is introduced. Finally, the perceptron model is used as a benchmark for comparison. Our results show excellent prediction accuracy, particularly in the hybrid CNN-GRU model with attention, thereby achieving a mean absolute percentage error (MAPE) of 6.333%. The soft voting ensemble model and the Multi-Head Attention model also performed well, with MAPEs of 6.125% and 6.889%, respectively. These findings are significant, as previous studies have not shown high performance with transformer models and attention mechanisms. The presented results offer promising insights for future research in this field.

A Novel Transformer Network with a CNN-Enhanced Cross-Attention Mechanism for Hyperspectral Image Classification

Recently, with the remarkable advancements of deep learning in the field of image processing, convolutional neural networks (CNNs) have garnered widespread attention from researchers in the domain of hyperspectral image (HSI) classification. Moreover, due to the high performance demonstrated by the transformer architecture in classification tasks, there has been a proliferation of neural networks combining CNNs and transformers for HSI classification. However, the majority of the current methods focus on extracting spatial–spectral features from the HSI data of a single size for a pixel, overlooking the rich multi-scale feature information inherent to the data. To address this problem, we designed a novel transformer network with a CNN-enhanced cross-attention (TNCCA) mechanism for HSI classification. It is a dual-branch network that utilizes different scales of HSI input data to extract shallow spatial–spectral features using a multi-scale 3D and 2D hybrid convolutional neural network. After converting the feature maps into tokens, a series of 2D convolutions and dilated convolutions are employed to generate two sets of Q (queries), K (keys), and V (values) at different scales in a cross-attention module. This transformer with CNN-enhanced cross-attention explores multi-scale CNN-enhanced features and fuses them from both branches. Experimental evaluations conducted on three widely used hyperspectral image (HSI) datasets, under the constraint of limited sample size, demonstrate excellent classification performance of the proposed network.

SwinUNeLCsT: Global–local spatial representation learning with hybrid CNN–transformer for efficient tuberculosis lung cavity weakly supervised semantic segmentation

Radiological diagnosis of lung cavities (LCs) is the key to identifying tuberculosis (TB). Conventional deep learning methods rely on a large amount of accurate pixel-level data to segment LCs. This process is time-consuming and laborious, especially for those subtle LCs. To address such challenges, firstly, we introduce a novel 3D TB LCs imaging convolutional neural network (CNN)-transformer hybrid model (SwinUNeLCsT). The core idea of SwinUNeLCsT is to combine local details and global dependencies for TB CT scan image feature representation to effectively improve the recognition ability of LCs. Secondly, to reduce the dependence on accurate pixel-level annotations, we design an end-to-end LCs weakly supervised semantic segmentation (WSSS) framework. Through this framework, radiologists need only to classify the number and the approximate location (e.g., left lung, right lung, or both) of LCs in the CT scan to achieve efficient segmentation of the LCs. This process eliminates the need for meticulously drawing boundaries, greatly reducing the cost of annotation. Extensive experimental results show that SwinUNeLCsT outperforms currently popular medical 3D segmentation methods in the supervised semantic segmentation paradigm. Meanwhile, our WSSS framework based on SwinUNeLCsT also performs best among the existing state-of-the-art medical 3D WSSS methods.

Using a Hybrid Convolutional Neural Network with a Transformer Model for Tomato Leaf Disease Detection

Diseases of tomato leaves can seriously damage crop yield and financial rewards. The timely and accurate detection of tomato diseases is a major challenge in agriculture. Hence, the early and accurate diagnosis of tomato diseases is crucial. The emergence of deep learning has dramatically helped in plant disease detection. However, the accuracy of deep learning models largely depends on the quantity and quality of training data. To solve the inter-class imbalance problem and improve the generalization ability of the classification model, this paper proposes a cycle-consistent generative-adversarial-network-based Transformer model to generate diseased tomato leaf images for data augmentation. In addition, this paper uses a Transformer model and densely connected CNN architecture to extract multilevel local features. The Transformer module is utilized to capture global dependencies and contextual information accurately to expand the sensory field of the model. Experiments show that the proposed model achieved 99.45% accuracy on the PlantVillage dataset. The 2018 Artificial Intelligence Challenger dataset and the private dataset attained accuracies of 98.30% and 95.4%, and the proposed classification model achieved a higher accuracy and smaller model size compared to previous deep learning models. The classification model is generalizable and robust and can provide a stable theoretical framework for crop disease prevention and control.

EEG channel selection using Gramian Angular Fields and spectrograms for energy data visualization

Electroencephalography (EEG)-based brain-computer interfaces (BCIs) have a wide range of applications in affect recognition. The usage of irrelevant information channels when decoding brain activity from different regions can negatively impact the task at hand. Therefore, further research is needed to determine the ideal channels for detecting superior performances. In this study, deep learning models and 2-D image representations are used to assess the efficacy of EEG channels for subjective valence responses to energy data visualizations. The EEG signals are converted into spectrograms and Gramian Angular Field (GAF) images. A hybrid Convolution Neural Network (CNN)-Long-Short Term Memory (LSTM) model and LSTM network are used to extract feature sets from the converted images. These feature sets, after reducing their dimensionality using a principal component analysis (PCA) method, are fed into a boosting classifier (AdaBoost). The performance metrics of both models and 2-D representations are compared. The LSTM and CNN-LSTM models with GAFs and spectrograms achieve state-of-the-art accuracies. The CNN-LSTM model achieves the highest performance when using spectrograms for the F8 channel, while the GAF method performs relatively lower for the F3 channel. The CNN-LSTM model with the spectrogram method produces reliable results, and hence, this method is used for further analysis of the remaining channel pairs. This study suggests that using a single EEG channel is more effective than using multiple channels for recognizing emotions in energy data visualizations. The proposed methodology is an efficient way to select channels for this purpose.

Adaptive Deep Learning with Optimization Hybrid Convolutional Neural Network and Recurrent Neural Network for Prediction Lemon Fruit Ripeness

Adaptive Deep Learning with Optimization Hybrid Convolutional Neural Network and Recurrent Neural Network for Prediction Lemon Fruit Ripeness

Novel cloud-AIoT fault diagnosis for industrial diesel generators based hybrid deep learning CNN-BGRU algorithm

The industrial diesel generator is essential to provide electric power during emergencies and requires accurate failure diagnosis in preventative maintenance services. This research presents a novel AIoT system-based hybrid deep learning algorithm for online monitoring of the anomaly conditions of 125 kW/250 kW industrial generators. Firstly, the IoT modules with different precise sensors are developed to be installed on 125 kW and 250 kW industrial generators to simulate other faults conditions in the laboratory. Then, the supervised learning operations are deployed to train deep learning algorithms with collected labeled data. The proposed algorithm, a hybrid convolution neural network bidirectional gate recurrent unit (CNN-BGRU), is deployed to extract deep features from long sequential historical signals and classify the anomaly conditions. The experiments in different 10 s, 20 s, and 30 s sampling frequencies are performed to evaluate and analyze with various benchmarks, which demonstrate efficiencies of the proposed CNN-BGRU method with other traditional deep learning algorithms, including RNN, CNN, GRU, LSTM, BRNN, and BGRU methods. The proposed hybrid method accomplishes the supreme augmentation of 29.43 % loss, 36.55 % validating loss, 25.86 % MAE, 27.00 % validating MAE, 16.78 % MSE, 20.64 % validating MSE, 6.36 % Pre, 25.34 % validating Pre, 17.30 % Rec, and 26.91 % validating Rec compared with state-of-the-art approaches. The AIoT system-based hybrid CNN-BGRU algorithm provides better improvement and higher accuracy in fault diagnosis of firefighting pumps for maintenance service in Industry 4.0.