Dementia is a degenerative disease that is increasingly prevalent in an aging society. Alzheimer’s disease (AD), the most common type of dementia, is best mitigated via early detection and management. Deep learning is an artificial intelligence technique that has been used to diagnose and predict diseases by extracting meaningful features from medical images. The convolutional neural network (CNN) is a representative application of deep learning, serving as a powerful tool for the diagnosis of AD. Recently, vision transformers (ViT) have yielded classification performance exceeding that of CNN in some diagnostic image classifications. Because the brain is a very complex network with interrelated regions, ViT, which captures direct relationships between images, may be more effective for brain image analysis than CNN. Therefore, we propose a method for classifying dementia images by applying 18F-Florbetaben positron emission tomography (PET) images to ViT. Data were evaluated via binary (normal control and abnormal) and ternary (healthy control, mild cognitive impairment, and AD) classification. In a performance comparison with the CNN, VGG19 was selected as the comparison model. Consequently, ViT yielded more effective performance than VGG19 in binary classification. However, in ternary classification, the performance of ViT cannot be considered excellent. These results show that it is hard to argue that the ViT model is better at AD classification than the CNN model.

In the present work we establish for the first time a class of $(P,\mathrm{m})$ -superquadratic functions and look into its features. Using them, we come up with the Jensen and Hermite–Hadamard inequalities, as well as the fractional versions of Hermite–Hadamard inequalities with respect to Riemann–Liouville fractional integral operators. The findings are confirmed by certain numerical calculations and graphical depictions that take a few appropriate examples into account. The study is enhanced by the addition of applications of special means, moments of random variables, and modified Bessel functions of the first kind. This is achieved by considering new functions pertaining to the uniform probability density function and taking the modified Bessel functions of the first kind into consideration. The new results clearly provide extensions and improvements of the work given in the literature.

In this paper, we investigate the generalized Milne-type integral inequalities via the framework of generalized $m$ -convex mappings on fractal sets. To accomplish this, we propose a new generalized integral identity that involves differentiable generalized $m$ -convex mappings. Based on the latest identity we drive a number of the latest fractal Milne-type integral inequalities. Also, we provide fractal Milne-type inequalities for bounded mappings. Some illustrative examples and applications to additional inequalities for the generalized special means and various error estimates for the generalized Milne-type quadrature formula are obtained to further support our results. The findings presented in this research offer important generalizations and extensions of previous work in the field.