No abstract

No abstract

We propose a system of equations with nonlocal flux in two space dimensions which is closely modeled after the 2D Boussinesq equations in a hyperbolic flow scenario. Our equations involve a simplified vorticity stretching term and Biot-Savart law and provide insight into the underlying intrinsic mechanisms of singularity formation. We prove stable, controlled finite time blowup involving upper and lower bounds on the vorticity up to the time of blowup for a wide class of initial data.

Melanoma, one of the most dangerous types of skin cancer, results in a very high mortality rate. Early detection and resection are two key points for a successful cure. Recent researches have used artificial intelligence to classify melanoma and nevus and to compare the assessment of these algorithms to that of dermatologists. However, training neural networks on an imbalanced dataset leads to imbalanced performance, the specificity is very high but the sensitivity is very low. This study proposes a method for improving melanoma prediction on an imbalanced dataset by reconstructed appropriate CNN architecture and optimized algorithms. The contributions involve three key features as custom loss function, custom mini-batch logic, and reformed fully connected layers. In the experiment, the training dataset is kept up to date including 17,302 images of melanoma and nevus which is the largest dataset by far. The model performance is compared to that of 157 dermatologists from 12 university hospitals in Germany based on the same dataset. The experimental results prove that our proposed approach outperforms all 157 dermatologists and achieves higher performance than the state-of-the-art approach with area under the curve of 94.4%, sensitivity of 85.0%, and specificity of 95.0%. Moreover, using the best threshold shows the most balanced measure compare to other researches, and is promisingly application to medical diagnosis, with sensitivity of 90.0% and specificity of 93.8%. To foster further research and allow for replicability, we made the source code and data splits of all our experiments publicly available.

No abstract