The main aim of this paper is to discuss the influence of fractal dimensions on the behavior of the solutions of the Grad-Shafranov equation. Our study is based on the product-like fractal measure ...approach constructed by Li and Ostoja-Starzewski in their attempt to explore anisotropic fractal continuum media. The fractal Grad-Shafranov equation gives the possibility to analyze, in a toroidal fusion reactor, the plasma equilibrium in fractal dimensions. Examples of the exact equilibrium solution are given for both the vacuum case outside the plasma and the toroidally shaped spheromak. Note: PACS numbers 05.45.Df: Fractals; 28.52.−s: Fusion reactors; 52.30.Cv: Magnetohydrodynamics; and 52.55.Ip: Spheromaks.
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This article presents and studies a two-level grad-div stabilized finite element discretization method for solving numerically the steady incompressible Navier–Stokes equations. The method consists ...of two steps. In the first step, we compute a rough solution by solving a nonlinear Navier–Stokes system on a coarse grid. And then, in the second step, we pass the coarse grid solution to a fine grid to linearize the nonlinear term, update the solution by solving a linearized problem based on Newton iterations. In both steps, a grad-div stabilization term is incorporated into the system to reduce the influence of pressure on the approximate velocity. We analyze stability and asymptotic convergence of the approximate solutions, derive explicit dependence of the solution errors on the grad-div stabilization parameter and viscosity. We perform also some numerical tests to validate the theoretical analysis and illustrate the efficiency of the proposed method. Compared with the standard two-level method without stabilizations, the grad-div stabilization term added in present method improves the accuracy of the approximate velocity, accelerates the convergence of the nonlinear iterations for the coarse mesh nonlinear system, and reduces the computational time.
•A two-level grad-div stabilized finite element discretization method for the incompressible Navier–Stokes equations is presented.•The method is easy to implement based on existing codes.•The method can yield much better solutions than the standard two-level discretization method with reduction in computational time when the viscosity is small.•Convergence results with respective to the mesh size, viscosity and stabilization parameter are derived.•Numerical results demonstrate the promise of the proposed method.
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In the recent pandemic, accurate and rapid testing of patients remained a critical task in the diagnosis and control of COVID-19 disease spread in the healthcare industry. Because of the sudden ...increase in cases, most countries have faced scarcity and a low rate of testing. Chest X-rays have been shown in the literature to be a potential source of testing for COVID-19 patients, but manually checking X-ray reports is time-consuming and error-prone. Considering these limitations and the advancements in data science, we proposed a Vision Transformer-based deep learning pipeline for COVID-19 detection from chest X-ray-based imaging. Due to the lack of large data sets, we collected data from three open-source data sets of chest X-ray images and aggregated them to form a 30 K image data set, which is the largest publicly available collection of chest X-ray images in this domain to our knowledge. Our proposed transformer model effectively differentiates COVID-19 from normal chest X-rays with an accuracy of 98% along with an AUC score of 99% in the binary classification task. It distinguishes COVID-19, normal, and pneumonia patient's X-rays with an accuracy of 92% and AUC score of 98% in the Multi-class classification task. For evaluation on our data set, we fine-tuned some of the widely used models in literature, namely, EfficientNetB0, InceptionV3, Resnet50, MobileNetV3, Xception, and DenseNet-121, as baselines. Our proposed transformer model outperformed them in terms of all metrics. In addition, a Grad-CAM based visualization is created which makes our approach interpretable by radiologists and can be used to monitor the progression of the disease in the affected lungs, assisting healthcare.
Myocardial infarction (MI) accounts for a high number of deaths globally. In acute MI, accurate electrocardiography (ECG) is important for timely diagnosis and intervention in the emergency setting. ...Machine learning is increasingly being explored for automated computer-aided ECG diagnosis of cardiovascular diseases. In this study, we have developed DenseNet and CNN models for the classification of healthy subjects and patients with ten classes of MI based on the location of myocardial involvement. ECG signals from the Physikalisch-Technische Bundesanstalt database were pre-processed, and the ECG beats were extracted using an R peak detection algorithm. The beats were then fed to the two models separately. While both models attained high classification accuracies (more than 95%), DenseNet is the preferred model for the classification task due to its low computational complexity and higher classification accuracy than the CNN model due to feature reusability. An enhanced class activation mapping (CAM) technique called Grad-CAM was subsequently applied to the outputs of both models to enable visualization of the specific ECG leads and portions of ECG waves that were most influential for the predictive decisions made by the models for the 11 classes. It was observed that Lead V4 was the most activated lead in both the DenseNet and CNN models. Furthermore, this study has also established the different leads and parts of the signal that get activated for each class. This is the first study to report features that influenced the classification decisions of deep models for multiclass classification of MI and healthy ECGs. Hence this study is crucial and contributes significantly to the medical field as with some level of visible explainability of the inner workings of the models, the developed DenseNet and CNN models may garner needed clinical acceptance and have the potential to be implemented for ECG triage of MI diagnosis in hospitals and remote out-of-hospital settings.
•This is the first study to explain the inner workings of the DenseNet and CNN models developed for MI detection.•DenseNet is a better model than CNN, for rapid classification of MI.•Model is developed with ten-fold cross-validation. Hence, it is robust and accurate.•Obtained high accuracy of 98.9% for the classification of ten MI classes with DenseNet model.
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Introduction: Brain tumors are abnormal cell growths in the brain, posing significant treatment challenges. Accurate early detection using non-invasive methods is crucial for effective treatment. ...This research focuses on improving the early detection of brain tumors in MRI images through advanced deep-learning techniques. The primary goal is to identify the most effective deep-learning model for classifying brain tumors from MRI data, enhancing diagnostic accuracy and reliability. Methods: The proposed method for brain tumor classification integrates segmentation using K-means++, feature extraction from the Spatial Gray Level Dependence Matrix (SGLDM), and classification with ResNet50, along with synthetic data augmentation to enhance model robustness. Segmentation isolates tumor regions, while SGLDM captures critical texture information. The ResNet50 model then classifies the tumors accurately. To further improve the interpretability of the classification results, Grad-CAM is employed, providing visual explanations by highlighting influential regions in the MRI images. Result: In terms of accuracy, sensitivity, and specificity, the evaluation on the Br35H::BrainTumorDetection2020 dataset showed superior performance of the suggested method compared to existing state-of-the-art approaches. This indicates its effectiveness in achieving higher precision in identifying and classifying brain tumors from MRI data, showcasing advancements in diagnostic reliability and efficacy. Discussion: The superior performance of the suggested method indicates its robustness in accurately classifying brain tumors from MRI images, achieving higher accuracy, sensitivity, and specificity compared to existing methods. The method's enhanced sensitivity ensures a greater detection rate of true positive cases, while its improved specificity reduces false positives, thereby optimizing clinical decision-making and patient care in neuro-oncology.
This work studies a parallel grad-div stabilized finite element algorithm for the damped Stokes equations. In this algorithm, in the light of a fully overlapping domain decomposition technique, we ...solve a global grad-div stabilized problem to compute a local solution in an intersecting subdomain on a global composite mesh, which is fine in the subdomain and rough elsewhere, making the proposed algorithm easy to implement based on an available sequential solver. We derive error bounds of the approximate solutions from our presented algorithm by the theoretical tool of local a priori estimate for the grad-div stabilized finite element solution. Numerical results verify the validity of the theoretical analysis and demonstrate the benefits of the proposed algorithm. On the one hand, compared with the counterpart one excluding grad-div stabilization, this algorithm can reduce significantly the effect of pressure on the approximate velocities, and hence, yields much better approximate velocities in the case of small viscosities. On the other hand, it takes much less computational time in getting approximate solutions with a comparable accuracy than the standard grad-div stabilization method.
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We present Mars Atmosphere and Volatile EvolutioN (MAVEN) observations of a giant magnetic flux rope in the Martian dayside ionosphere. The flux rope was observed at an altitude of <300 km, ...downstream from strong subsolar crustal magnetic fields. The peak field amplitude was ∼200 nT, resulting in the largest difference between the observed magnetic field strength and a model for crustal magnetic fields of the entire MAVEN primary science phase. MAVEN detected planetary ions, including H+, O+, and
O2+, across the structure. The axial orientation estimated for the flux rope indicates that it likely formed as a result of interactions between the local crustal and overlaid draped interplanetary magnetic fields. Pitch angle distributions of ionospheric photoelectrons imply that this structure is connected to the Martian upper atmosphere. However, the flux rope is not present in observations at the next commensurable orbit crossing (approximately two Martian days later), implying that it eventually detaches from the atmosphere and is carried downstream. The flux rope observations occurred during an interplanetary coronal mass ejection event at Mars, suggesting that the disturbed upstream state played a role in allowing the interplanetary magnetic field to penetrate deeper into the Martian ionosphere than is typical, allowing the formation of the flux rope.
Key Points
MAVEN observed a giant flux rope near the subsolar point of the Martian ionosphere, downstream from the strong crustal fields
The observed giant ionospheric flux rope was formed via interactions between the local crustal and overlaid draped magnetic fields
The event was observed during the ICME passage by Mars, indicating that the ICME played a role in forming the observed giant flux rope
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Automatic accent classification is an active research field concerning speech processing. It can be useful to identify a speaker's region of origin, which can be applied in police investigations ...carried out by Law Enforcement Agencies, as well as for the improvement of current speech recognition systems. This paper presents a novel descriptor called Grad-Transfer, extracted using the Gradient-weighted Class Activation Mapping (Grad-CAM) method based on convolutional neural network (CNN) interpretability. Additionally, we propose a methodology for accent classification that implements Grad-Transfer, which is based on transferring the knowledge acquired by a CNN to a classical machine learning algorithm. The paper works on two hypotheses: the coarse localization maps produced by Grad-CAM on spectrograms are able to highlight the regions of the spectrograms that are important for predicting accents, and Grad-Transfer descriptors computed from audios represent distinctive descriptions of the target accents. These hypotheses were demonstrated experimentally, clustering the generated Grad-Transfer descriptors according to the original accent of the audios using Birch and <inline-formula><tex-math notation="LaTeX">k</tex-math></inline-formula>-means algorithms. We carried out experiments on the Voice Cloning Toolkit dataset, seeing an increase of macro average accuracy, and unweighted average recall in the results obtained by a Gaussian Naive Bayes classifier up to <inline-formula><tex-math notation="LaTeX">23.00\%</tex-math></inline-formula>, and <inline-formula><tex-math notation="LaTeX">23.58\%</tex-math></inline-formula>, respectively, compared to a model trained with spectrograms. This demonstrates that Grad-Transfer is able to improve the performance of accent classification models and opens the door to new implementations in similar tasks.
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