Data Augmentation Procedure Research Articles

Towards explainable evaluation: Explaining predicted performance using local performance regions

Identifying which instances in a learning problem are difficult to be predicted by a model is important to avoid critical errors at deployment time as well as to plan how to learn an improved model (e.g., by training data cleaning or augmentation). Previous works have been mainly devoted on measuring instance hardness or developing meta-learners (e.g., assessors) to predict a base model performance based on the instances’ features while neglecting interpretability. In this paper, we propose a method to explain the performance of learned models in a problem based on the induction of meta-rules. Each meta-rule identifies a local region of instances, called Local Performance Region (LPR), where the base model has a predictable performance. The meta-rules are induced using a reduced number of attributes, in such a way that each LPR can be more easily inspected (e.g., by an attribute plot). The proposed method combines assessors, data augmentation and rule induction procedures. Initially, given a dataset of interest and a base model, we build an assessor model, which will be able to predict the base model’s performance for new instances. The assessor is trained based on the test results obtained when the base model is evaluated, thus generalizing the observed errors across instances in the dataset. In our work, we built an assessor in a case study to predict the probability of incorrect classifications of a Random Forest (RF) base model, achieving a mean absolute error of 0.05 in a hold out experiment. Once learned, the assessor is used to predict the model’s errors for new instances in an augmented dataset, covering a variety of features. Finally, meta-rules are learned to approximate the assessor’s predictions in local regions of instances. Experiments show the usefulness of the proposal by finding 18 local regions of bad RF performance, demonstrating a special case of LPRs, called Local Hard Regions (LHRs). By explaining the (in)correctness of model predictions, LPRs constitute a novel application in explainable AI, but focusing on explaining model performance, which can be adopted to different ML contexts.

Deep learning based capsule networks for breast cancer classification using ultrasound images

Purposes: Breast cancer (BC) is a disease in which the breast cells multiply uncontrolled. Breast cancer is one of the most often diagnosed malignancies in women worldwide. Early identification of breast cancer is critical for limiting the impact on affected people's health conditions. The influence of technology and artificial intelligence approaches (AI) in the health industry is tremendous as technology advances. Deep learning (DL) techniques are used in this study to classify breast lumps. Materials and Methods: The study makes use of two distinct breast ultrasound images (BUSI) with binary and multiclass classification. To assist the models in understanding the data, the datasets are exposed to numerous preprocessing and hyperparameter approaches. With data imbalance being a key difficulty in health analysis, due to the likelihood of not having a condition exceeding that of having the disease, this study applies a cutoff stage to impact the decision threshold in the datasets data augmentation procedures. The capsule neural network (CapsNet), Gabor capsule network (GCN), and convolutional neural network (CNN) are the DL models used to train the various datasets. Results: The findings showed that the CapsNet earned the maximum accuracy value of 93.62% while training the multiclass data, while the GCN achieved the highest model accuracy of 97.08\% when training the binary data. The models were also evaluated using a variety of performance assessment parameters, which yielded consistent results across all datasets. Conclusion: The study provides a non-invasive approach to detect breast cancer; and enables stakeholders, medical practitioners, and health research enthusiasts a fresh view into the analysis of breast cancer detection with DL techniques to make educated judgements.

Remaining Useful Life prediction based on physics-informed data augmentation

Current approaches for monitoring machine health (SOH) and effective prognostics depend on the extensive use of complete degradation data trajectories, implying the reliance on data generation techniques that involve functional degradation of the real system until the failure state is reached. These commonly adopted approaches that depend on labeled target data remain operationally and economically nonviable for most industries and safety critical systems. This paper presents novel approaches that alleviate the existing dependence of most prognostics procedures on Remaining Useful Life (RUL) labeled data for training. To this end, firstly, a hybrid data augmentation procedure is proposed that enables the integration of system knowledge available a priori as well as physics of failure, within the training data. Secondly, an unsupervised Health Index (HI) extraction approach is developed, followed by a long-term prediction of this same HI, that leads to an efficient prediction of RUL without labeled data. Finally, a reliability-based assessment is performed to validate the proposed approach. This comprehensive approach (i.e. integrating all the various stages involved in achieving a RUL prediction based on unlabeled data) is tested on a real industrial aircraft system demonstrating the effectiveness of the proposed approach in real industrial context.

Real-time motion artifact suppression using convolution neural networks with penalty in fNIRS.

Removing motion artifacts (MAs) from functional near-infrared spectroscopy (fNIRS) signals is crucial in practical applications, but a standard procedure is not available yet. Artificial neural networks have found applications in diverse domains, such as voice and image processing, while their utility in signal processing remains limited. In this work, we introduce an innovative neural network-based approach for online fNIRS signals processing, tailored to individual subjects and requiring minimal prior experimental data. Specifically, this approach employs one-dimensional convolutional neural networks with a penalty network (1DCNNwP), incorporating a moving window and an input data augmentation procedure. In the training process, the neural network is fed with simulated data derived from the balloon model for simulation validation and semi-simulated data for experimental validation, respectively. Visual validation underscores 1DCNNwP's capacity to effectively suppress MAs. Quantitative analysis reveals a remarkable improvement in signal-to-noise ratio by over 11.08 dB, surpassing the existing methods, including the spline-interpolation, wavelet-based, temporal derivative distribution repair with a 1 s moving window, and spline Savitzky-Goaly methods. Contrast-to-noise ratio (CNR) analysis further demonstrated 1DCNNwP's ability to restore or enhance CNRs for motionless signals. In the experiments of eight subjects, our method significantly outperformed the other approaches (except offline TDDR, t < -3.82, p < 0.01). With an average signal processing time of 0.53 ms per sample, 1DCNNwP exhibited strong potential for real-time fNIRS data processing. This novel univariate approach for fNIRS signal processing presents a promising avenue that requires minimal prior experimental data and adapts seamlessly to varying experimental paradigms.

A data augmentation procedure to improve detection of spike ripples in brain voltage recordings

Epilepsy is a major neurological disorder characterized by recurrent, spontaneous seizures. For patients with drug-resistant epilepsy, treatments include neurostimulation or surgical removal of the epileptogenic zone (EZ), the brain region responsible for seizure generation. Precise targeting of the EZ requires reliable biomarkers. Spike ripples - high-frequency oscillations that co-occur with large amplitude epileptic discharges - have gained prominence as a candidate biomarker. However, spike ripple detection remains a challenge. The gold-standard approach requires an expert manually visualize and interpret brain voltage recordings, which limits reproducibility and high-throughput analysis. Addressing these limitations requires more objective, efficient, and automated methods for spike ripple detection, including approaches that utilize deep neural networks. Despite advancements, dataset heterogeneity and scarcity severely limit machine learning performance. Our study explores long-short term memory (LSTM) neural network architectures for spike ripple detection, leveraging data augmentation to improve classifier performance. We highlight the potential of combining training on augmented and in vivo data for enhanced spike ripple detection and ultimately improving diagnostic accuracy in epilepsy treatment.

A Note on Ising Network Analysis with Missing Data.

The Ising model has become a popular psychometric model for analyzing item response data. The statistical inference of the Ising model is typically carried out via a pseudo-likelihood, as the standard likelihood approach suffers from a high computational cost when there are many variables (i.e., items). Unfortunately, the presence of missing values can hinder the use of pseudo-likelihood, and a listwise deletion approach for missing data treatment may introduce a substantial bias into the estimation and sometimes yield misleading interpretations. This paper proposes a conditional Bayesian framework for Ising network analysis with missing data, which integrates a pseudo-likelihood approach with iterative data imputation. An asymptotic theory is established for the method. Furthermore, a computationally efficient Pólya-Gamma data augmentation procedure is proposed to streamline the sampling of model parameters. The method's performance is shown through simulations and a real-world application to data on major depressive and generalized anxiety disorders from the National Epidemiological Survey on Alcohol and Related Conditions (NESARC).

Model order reduction by convex displacement interpolation

We present a nonlinear interpolation technique for parametric fields that exploits optimal transportation of coherent structures of the solution to achieve accurate performance. The approach generalizes the nonlinear interpolation procedure introduced in [Iollo, Taddei, J. Comput. Phys., 2022] to multi-dimensional parameter domains and to datasets of several snapshots. Given a library of high-fidelity simulations, we rely on a scalar testing function and on a point set registration method to identify coherent structures of the solution field in the form of sorted point clouds. Given a new parameter value, we exploit a regression method to predict the new point cloud; then, we resort to a boundary-aware registration technique to define bijective mappings that deform the new point cloud into the point clouds of the neighboring elements of the dataset, while preserving the boundary of the domain; finally, we define the estimate as a weighted combination of modes obtained by composing the neighboring snapshots with the previously-built mappings. We present several numerical examples for compressible and incompressible, viscous and inviscid flows to demonstrate the accuracy of the method. Furthermore, we employ the nonlinear interpolation procedure to augment the dataset of simulations for linear-subspace projection-based model reduction: our data augmentation procedure is designed to reduce offline costs — which are dominated by snapshot generation — of model reduction techniques for nonlinear advection-dominated problems.

Soil nutrient prediction for paddy cultivation via soil fertility and pH trained hybrid architecture: Recommendations based on nutrient deficiency

Soil testing can assist in determining how much fertilizer is necessary, as it depends on the fertility and crop of the soil. Through soil fertility and pH-trained hybrid architecture, a new soil nutrient prediction model for paddy agriculture is proposed in this work. First, data acquisition takes place, which is the act of gathering soil data, and it is subsequently preprocessed using the Improved Normalization method. A soil information dataset is employed in this work to help with this. Subsequently, the preprocessed data undergoes data augmentation; the correlation method facilitates an enhanced data augmentation procedure. In this case, the data used for the correlation approach is min-max normalization data. The augmented data is used to extract soil properties such as pH level and soil fertility index. Additionally, a hybrid classifier strategy that combines RNN and Modified LSTM is suggested for nutrient prediction. Lastly, this article suggested some fertilizers for nutritional insufficiency based on the projection. The hybrid prediction classifiers that have been suggested perform better in experiments than the classic classifier models, which include LSTM, RNN, SVM, Bi-GRU, and DNN, in terms of sensitivity, accuracy, FPR, MCC, precision, and efficiency in predicting nutrients. Even though the CNN (0.075), Bi-GRU (0.080), LSTM (0.087), DBN (0.078), Enhanced-1DCNN DLM (0.080), RNN (0.085), and RFA (0.052) obtained maximal FPR ratings, the FPR of the Modified LSTM+RNN scheme is 0.052.

P‐58: Novel Defect Data Augmentation in Display Manufacturing Process

In this paper, we propose novel defect data augmentation procedure to overcome imbalanced class in development of machine learning models for display manufacturing process. As the amount of defective samples is extremely small compared to that of good samples, it causes severe overfitting and poor performance of models. In addition, numeric or tabular data augmentation is not suitable by GAN or VAE algorithms and its accuracy or similarity is lower than that of image augmentation. To settle this problem, we utilize both over and under sampling, and introduce anomaly score to figure out which process or equipment is in anomaly state. Kernel function or XAI algorithms are also utilized to discover effective features which differentiates defective samples and normal samples. After these process, we use to CT‐GAN to increase the number of defect datasets. In this way, we have demonstrated the enhanced the performance of GAN algorithm in tabular and numeric data.

Deep learning performance analysis for facial expression based autism spectrum disorder identification

The subject matter of this paper revolves around the utilization of Deep Learning techniques for the identification of Autism Spectrum Disorder (ASD) through facial expression analysis. The goal is to assess the performance of various Deep Learning architectures in this context, aiming to support the evaluation of AI-based ASD identification technologies within medical imaging standards. The tasks undertaken include conducting a comprehensive performance analysis of different Deep Learning models, emphasizing the significance of data augmentation techniques, and evaluating the convergence ability of these models. Methods employed involve a simulation setup for evaluating Deep Learning architectures using facial expression images of children with ASD. The research utilizes secondary data from open-source sharing platforms comprising 2,840 optical images. The evaluation is conducted with consideration of data ratio settings and data augmentation procedures. Results indicate that data augmentation significantly improves the recall performance, with ResNet-101 architecture demonstrating superior accuracy, precision, and convergence ability compared to ResNet-50 and VGG-16. Finally, the conclusion drawn from this analysis highlights the efficacy of ResNet-101 with augmented data. It stands out as the most suitable model for ASD identification based on facial expressions, emphasizing its potential for early intervention and increased awareness. the scientific novelty of the results obtained lies in its contribution to advancing the state of the art in AI-driven ASD identification, adhering to medical standards, enhancing model performance through data augmentation, and facilitating early intervention strategies for improved patient outcomes.

CNN Based Face Emotion Recognition System for Healthcare Application

INTRODUCTION: Because it has various benefits in areas such psychology, human-computer interaction, and marketing, the recognition of facial expressions has gained a lot of attention lately.&#x0D; OBJECTIVES: Convolutional neural networks (CNNs) have shown enormous potential for enhancing the accuracy of facial emotion identification systems. In this study, a CNN-based approach for recognizing facial expressions is provided. METHODS: To boost the model's generalizability, transfer learning and data augmentation procedures are applied. The recommended strategy defeated the existing state- of-the-art models when examined on multiple benchmark datasets, including the FER-2013, CK+, and JAFFE databases. &#x0D; RESULTS: The results suggest that the CNN-based approach is fairly excellent at properly recognizing face emotions and has a lot of potential for usage in detecting facial emotions in practical scenarios.&#x0D; CONCLUSION: Several diverse forms of information, including oral, textual, and visual, maybe applied to comprehend emotions. In order to increase prediction accuracy and decrease loss, this research recommended a deep CNN model for emotion prediction from facial expression.

Deep learning and data augmentation for partial discharge detection in electrical machines

Fault testing in the production line of automotive traction machines is essential to ensure the desired lifetime. Since repetitive partial discharges (PDs) caused by anomalies in the insulation system lead to premature breakdowns of electrical machines, a reliable PD detection is of great importance. This paper proposes deep learning (DL) methods to improve the discrimination of PD from background noise in comparison with the state-of-the-art amplitude based PD detection in the production line. First, a systematic data extraction and labeling procedure is introduced to obtain correctly labeled datasets from arbitrary PD measurements. In addition, datasets are enhanced with low signal-to-noise ratio PD pulses by applying a special data augmentation approach. 13 different convolutional, recurrent and fully connected neural networks are compared for various time-frequency representations of the input signals. Hyperparameters for input transform, network topology and solver are optimized for all 13 combinations to ensure a fair case study. As a result, the two-dimensional convolutional neural network with continuous wavelet transform achieves the best accuracy of around 99.76% on a test dataset of PD signals originating from previously not utilized test objects. All DL models considered in this comparison outperform the state-of-the-art threshold-based PD classification. Even for PD events with an amplitude close to the noise level, the detection rate is still around 95% for the best network. Furthermore, without applying the proposed data augmentation procedure, the DL models investigated are not able to distinguish small PD pulses from noise.

Rapid BRIR generation approach using Variational Auto-Encoders and LSTM neural networks

This article proposes a rapid binaural room impulse response (BRIR) generation for real-time auralization with a moving receiver inside a room and a fixed sound source. The proposed method uses generative models, such as variational auto-encoders and long short-term memory neural networks. First, a number of static receivers are modeled within a given room, covering a representative area where listeners can typically be found. Then, a BRIR is simulated in each receiver, and from them, more BRIRs uniformly distributed in the scenario are synthesized through a data augmentation procedure. In the sequel, by applying an unsupervised model to cluster the receivers positionally, the BRIRs are organized into groups. Furthermore, variational autoencoder training is performed to reduce computational complexity. The results when comparing the reconstructed BRIRs with the original ones show that the error is within the just noticeable difference threshold. A computational cost analysis in terms of the total number of operations is carried out, achieving a computational gain of over 75%, and a storage reduction of more than 99% with respect to classic BRIR generation techniques. This opens the possibility of obtaining a reliable real-time auralization with a moving receiver inside the room.

Wireless water consumption sensing system for building energy efficiency: A visual-based approach with self-powered operation

The use of smart wireless remote water meters has become popular due to their efficiency in avoiding manual labor and automate meter reading. The current implementation of these measurement instruments often requires expensive external power sources and separate data aggregators, posing challenges for circuit safety and the goal of reducing carbon emissions in aging communities. In response, a novel wireless system has been developed to accurately measure water consumption in buildings. This system incorporates advanced machine learning techniques and utilizes the potential of water-based energy in a seamless manner. This novel methodology utilizes optical sensors to acquire visual data of water gauges and exploits machine learning techniques, specifically the AVSM model also called Advanced Visual Sensing Model (AVSM). This methodology employs a rigorous approach to achieve accurate metric determinations, thereby eliminating the necessity for additional hardware or excessive power configurations. Moreover, an integrated micro water generator has been seamlessly implemented, demonstrating the capability to effectively transfer energy to a lithium battery for the purpose of storage. This implementation guarantees consistent functionality and a significant decrease in reliance on external power supplies. The data augmentation procedure involves the stochastic manipulation of image luminance, resulting in encouraging results when used in conjunction with the AVSM model. Significantly, the dimensions of the model have been significantly decreased, while maintaining a commendable mean average precision (mAP). By leveraging this method and visual-based features, the system can contribute to overall building energy efficiency and reduce the burdens of manual meter reading while supporting CO2 emissions reduction as a feasible and cost-effective solution for building management, promoting sustainability, and advancing energy-efficient practices in old communities. This new wireless system for measuring water usage provides a practical and affordable way to enhance energy efficiency in buildings, lessen the workload of manual meter reading, and help meet carbon emissions reduction goals. As well as optimizing resource and energy use, this method also aligns with eco-friendly solutions to combat global warming and climate change.

Robust night flow analysis in water distribution networks: A BiLSTM deep autoencoder approach

Night flow analysis is predominantly used to identify incipient (gradual) leakages in real-life Water Distribution Networks (WDNs). However, due to extreme stochastic demand especially in residentially dominated district metering areas (DMAs) and the emergence of sleepless cities, traditional night flow analysis methods have become inefficient. This study proposes a semi-supervised sequence-to-sequence Bidirectional Long Short-Term Memory (BiLSTM) deep Auto Encoder (AE) method for night flow analysis in WDNs. To enhance the generalisation power of the deep AE, a vigorous data augmentation procedure based engineering domain knowledge and inherent properties of DMA is presented. The proposed method learns the underlying benign patterns in night flow (2:00 am to 4:00 am) and identifies significant deviations that represent the development of incipient leakages. The method was validated on residential, commercial, and industrial DMAs in a real-life WDN in the Ålesund Municipality of Norway. The results from the study showed that the proposed method is a robust and superior alternative to traditional night flow under extreme stochastic consumer demand. The proposed BiLSTM deep AE method was able to identify unreported leakages in the DMAs within 1 day or at most 4 days compared with at least 15 days identification time by traditional minimum night flow (MNF) and average night flow (ANF) analyses. Additionally, traditional minimum night flow analysis also produced more false positives compared with the proposed method. The results also revealed the usage of point estimates to represent night flow as done in MNF and ANF analyses fail to capture all salient information regarding night flow compared to the BiLSTM deep AE.

DR-NASNet: Automated System to Detect and Classify Diabetic Retinopathy Severity Using Improved Pretrained NASNet Model.

Diabetes is a widely spread disease that significantly affects people's lives. The leading cause is uncontrolled levels of blood glucose, which develop eye defects over time, including Diabetic Retinopathy (DR), which results in severe visual loss. The primary factor causing blindness is considered to be DR in diabetic patients. DR treatment tries to control the disease's severity, as it is irreversible. The primary goal of this effort is to create a reliable method for automatically detecting the severity of DR. This paper proposes a new automated system (DR-NASNet) to detect and classify DR severity using an improved pretrained NASNet Model. To develop the DR-NASNet system, we first utilized a preprocessing technique that takes advantage of Ben Graham and CLAHE to lessen noise, emphasize lesions, and ultimately improve DR classification performance. Taking into account the imbalance between classes in the dataset, data augmentation procedures were conducted to control overfitting. Next, we have integrated dense blocks into the NASNet architecture to improve the effectiveness of classification results for five severity levels of DR. In practice, the DR-NASNet model achieves state-of-the-art results with a smaller model size and lower complexity. To test the performance of the DR-NASNet system, a combination of various datasets is used in this paper. To learn effective features from DR images, we used a pretrained model on the dataset. The last step is to put the image into one of five categories: No DR, Mild, Moderate, Proliferate, or Severe. To carry this out, the classifier layer of a linear SVM with a linear activation function must be added. The DR-NASNet system was tested using six different experiments. The system achieves 96.05% accuracy with the challenging DR dataset. The results and comparisons demonstrate that the DR-NASNet system improves a model's performance and learning ability. As a result, the DR-NASNet system provides assistance to ophthalmologists by describing an effective system for classifying early-stage levels of DR.

Leveraging spatial transcriptomics data to recover cell locations in single-cell RNA-seq with CeLEry

Single-cell RNA sequencing (scRNA-seq) has revolutionized our understanding of cellular heterogeneity in health and disease. However, the lack of physical relationships among dissociated cells has limited its applications. To address this issue, we present CeLEry (Cell Location recovEry), a supervised deep learning algorithm that leverages gene expression and spatial location relationships learned from spatial transcriptomics to recover the spatial origins of cells in scRNA-seq. CeLEry has an optional data augmentation procedure via a variational autoencoder, which improves the method’s robustness and allows it to overcome noise in scRNA-seq data. We show that CeLEry can infer the spatial origins of cells in scRNA-seq at multiple levels, including 2D location and spatial domain of a cell, while also providing uncertainty estimates for the recovered locations. Our comprehensive benchmarking evaluations on multiple datasets generated from brain and cancer tissues using Visium, MERSCOPE, MERFISH, and Xenium demonstrate that CeLEry can reliably recover the spatial location information for cells using scRNA-seq data.

DAmcqrnn: An approach to censored monotone composite quantile regression neural network estimation

Quantile regression neural network (QRNN) model has recently become popular in solving complex nonlinear problems, but the quantile curves achieved by QRNN model may cross each other, leading to unreliable results. To remedy this defect, monotone composite quantile regression neural network (MCQRNN) model is more attractive with non-crossing quantile predictions. However, few works have been involved in the literature to apply MCQRNN model for censoring issues. Based on the data augmentation algorithm, this study presents an iterative estimation method, which is a three-step alternating process, for censored MCQRNN model. Step 1 imputes the censored data through a data augmentation procedure. Step 2 updates the MCQRNN model with the imputed data. Step 3 makes predictions by the updated MCQRNN model. Simulation studies and real data application demonstrate that our proposed method is not only superior to the available censored methods with respect to quantile loss and C-index, but also yields very close prediction results to those obtained by full uncensored data. Avoiding the quantile crossing problem, the proposed method is more flexible to cope with different types of censoring, overcoming the limitation that the existing censored methods only work for single censoring type with unbelievable predictions caused by the crossing phenomenon.

A DEEP LEARNING FRAMEWORK TO LOCALIZE THE EPILEPTOGENIC ZONE FROM DYNAMIC FUNCTIONAL CONNECTIVITY USING A COMBINED GRAPH CONVOLUTIONAL AND TRANSFORMER NETWORK.

Localizing the epileptogenic zone (EZ) is a critical step in the treatment of medically refractory epilepsy. Resting-state fMRI (rs-fMRI) offers a new window into this task by capturing dynamically evolving co-activation patterns, also known as connectivity, in the brain. In this work, we present the first automated framework that uses dynamic functional connectivity from rs-fMRI to localize the EZ across a heterogeneous epilepsy cohort. Our framework uses a graph convolutional network for feature extraction, followed by a transformer network, whose attention mechanism learns which time points of the rs-fMRI scan are important for EZ localization. We train our framework on augmented data derived from the Human Connectome Project and evaluate it on a clinical epilepsy dataset. Our results demonstrate the clear advantages of our convolutional + transformer combination and data augmentation procedure over ablated and comparison models.

Cardiac LGE MRI Segmentation With Cross-Modality Image Augmentation and Improved U-Net.

Image segmentation is a challenging problem in imaging informatics, which stems from the intersection of imaging techniques, computer science and biomedicine. In particular, accurate segmentation of cardiac structures in late gadolinium enhancement (LGE) cardiac magnetic resonance (CMR) is of great clinical importance for cardiac function assessment and myocardial disease diagnosis. However, it is a well-known challenge due to its special imaging modality and the lack of labeled LGE samples. In this paper, we propose an unsupervised ventricular segmentation algorithm that can perform biventricular segmentation of LGE images in the absence of labeled LGE data. There are two primary modules, the data augmentation procedure and the segmentation network. The easily available annotated balanced-Steady State Free Precession (bSSFP) images are employed for cross-modal data augmentation by image translation, where a single bSSFP image is converted into multiple synthetic LGE images while preserving the original morphological structure. Then, the proposed segmentation network is trained with the synthetic LGE images and used for segmenting real LGE images. Validation experiments demonstrated the effectiveness and advantages of the proposed algorithm.