Parkinson’s disease ranks as the second most prevalent neurological disorder after Alzheimer’s disease. Convolutional neural networks (CNNs) have been extensively employed in Parkinson’s disease (PD) detection using MR images. However, CNN models generally focus on local features while prone to capture global representations. On the other hand, the vision transformer (ViT) excels at capturing global features through its self-attention mechanism, but it compromises local feature representations. Additionally, the varying magnitude of MR data poses a challenge for ViT, potentially leading to the gradient vanishing problem. To address these limitations, this paper proposed a novel framework that combines the Swin-Transformer and CNN to capture both local and global features effectively. To mitigate the gradient vanishing issue in ViT, we used skipped connections and cosine attention mechanism in VIT that preserves the output distribution regardless of input magnitude variations. The proposed model comprises three primary blocks: Transformer-block, convolutional block, and dense-block. The input image is processed concurrently by the cosine transformer and convolutional block. Subsequently, the extracted features from both blocks are concatenated and fed to the dense block for decision-making. The proposed model achieved promesing results of 96%, 97%, 95%, and 95% in terms of accuracy, sensitivity, specificity, and area under the curve, respectively.

Epidemic spreading on networks becomes a hot issue of nonlinear systems, which has attracted many researchers’ attention in recent years. A novel epidemic spreading model with variant factors in complex networks is proposed and investigated in this paper. One main feature of this model is that virus variation is investigated in the process of epidemic dynamical spreading. The global dynamics of this model involving an endemic equilibrium and a disease-free equilibrium are, respectively, discussed. Some sufficient conditions are given for the existence of the endemic equilibrium. In addition, the global asymptotic stability problems of the disease-free equilibrium and the endemic equilibrium are also investigated by the Routh-Hurwitz stability criterion and Lyapunov stability criterion. And the uniform persistence condition of the new system is studied. Finally, numerical simulations are provided to illustrate obtained theoretical results.

Parkinson’s disease (PD) is a chronic and progressive neurological disease that mostly shakes and compromises the motor system of the human brain. Patients with PD can face resting tremors, loss of balance, bradykinesia, and rigidity problems. Complex patterns of PD, i.e., with relevance to other neurological diseases and minor changes in brain structure, make the diagnosis of this disease a challenge and cause inaccuracy of about 25% in the diagnostics. The research community utilizes different machine learning techniques for diagnosis using handcrafted features. This paper proposes a computer-aided diagnostic system using a convolutional neural network (CNN) to diagnose PD. CNN is one of the most suitable models to extract and learn the essential features of a problem. The dataset is obtained from Parkinson’s Progression Markers Initiative (PPMI), which provides different datasets (benchmarks), such as T2-weighted MRI for PD and other healthy controls (HC). The mid slices are collected from each MRI. Further, these slices are registered for alignment. Since the PD can be found in substantia nigra (i.e., the midbrain), the midbrain region of the registered T2-weighted MRI slice is selected using the freehand region of interest technique with a 33 × 33 sized window. Several experiments have been carried out to ensure the validity of the CNN. The standard measures, such as accuracy, sensitivity, specificity, and area under the curve, are used to evaluate the proposed system. The evaluation results show that CNN provides better accuracy than machine learning techniques, such as naive Bayes, decision tree, support vector machine, and artificial neural network.

This article addresses a consensus problem of second-order discrete-time agents in general directed networks with nonuniform position constraints, switching topologies, and communication delays. A projection operation is performed to ensure the agents stay in some given convex sets, and a distributed algorithm is employed for the consensus achievement of all agents. The analysis approach is to use a linear transformation to convert the original system into an equivalent system and then merge the nonlinear error term into the convex null of the agents’ states so as to prove the consensus convergence of the system based on the properties of the non-negative matrices. It is shown that all agents finally converge to a consensus point while their positions stay in the corresponding constraint sets as long as the union of the communication graphs among each certain time interval is strongly connected even when the communication delays are considered. Finally, numerical simulation examples are given to show the theoretical results.