Mathematical Biosciences and Engineering最新文献

Glaucoma is a chronic neurodegenerative disease that can result in irreversible vision loss if not treated in its early stages. The cup-to-disc ratio is a key criterion for glaucoma screening and diagnosis, and it is determined by dividing the area of the optic cup (OC) by that of the optic disc (OD) in fundus images. Consequently, the automatic and accurate segmentation of the OC and OD is a pivotal step in glaucoma detection. In recent years, numerous methods have resulted in great success on this task. However, most existing methods either have unsatisfactory segmentation accuracy or high time costs. In this paper, we propose a lightweight deep-learning architecture for the simultaneous segmentation of the OC and OD, where we have adopted fuzzy learning and a multi-layer perceptron to simplify the learning complexity and improve segmentation accuracy. Experimental results demonstrate the superiority of our proposed method as compared to most state-of-the-art approaches in terms of both training time and segmentation accuracy.

In this paper, in order to realize the predefined-time control of n-dimensional chaotic systems with disturbance and uncertainty, a disturbance observer and sliding mode control method were presented. A sliding manifold was designed for ensuring that when the error system runs on it, the tracking error was stable within a predefined time. A sliding mode controller was developed which enabled the dynamical system to reach the sliding surface within a predefined time. The total expected convergence time can be acquired through presetting two predefined-time parameters. The results demonstrated the feasibility of the proposed control method.

Sparse-view computed tomography (CT) is an important way to reduce the negative effect of radiation exposure in medical imaging by skipping some X-ray projections. However, due to violating the Nyquist/Shannon sampling criterion, there are severe streaking artifacts in the reconstructed CT images that could mislead diagnosis. Noting the ill-posedness nature of the corresponding inverse problem in a sparse-view CT, minimizing an energy functional composed by an image fidelity term together with properly chosen regularization terms is widely used to reconstruct a medical meaningful attenuation image. In this paper, we propose a regularization, called the box-constrained nonlinear weighted anisotropic total variation (box-constrained NWATV), and minimize the regularization term accompanying the least square fitting using an alternative direction method of multipliers (ADMM) type method. The proposed method is validated through the Shepp-Logan phantom model, alongisde the actual walnut X-ray projections provided by Finnish Inverse Problems Society and the human lung images. The experimental results show that the reconstruction speed of the proposed method is significantly accelerated compared to the existing $ L_1/L_2 $ regularization method. Precisely, the central processing unit (CPU) time is reduced more than 8 times.

Due to irregular sampling or device failure, the data collected from sensor network has missing value, that is, missing time-series data occurs. To address this issue, many methods have been proposed to impute random or non-random missing data. However, the imputation accuracy of these methods are not accurate enough to be applied, especially in the case of complete data missing (CDM). Thus, we propose a cross-modal method to impute time-series missing data by dense spatio-temporal transformer nets (DSTTN). This model embeds spatial modal data into time-series data by stacked spatio-temporal transformer blocks and deployment of dense connections. It adopts cross-modal constraints, a graph Laplacian regularization term, to optimize model parameters. When the model is trained, it recovers missing data finally by an end-to-end imputation pipeline. Various baseline models are compared by sufficient experiments. Based on the experimental results, it is verified that DSTTN achieves state-of-the-art imputation performance in the cases of random and non-random missing. Especially, the proposed method provides a new solution to the CDM problem.

Bearings are critical components of industrial equipment and have a significant impact on the safety of industrial physical systems. Their failure may lead to equipment shutdown and accidents, posing a significant risk to production safety. However, it is difficult to obtain a large amount of bearing fault data in practice, which makes the problem of small sample size a major challenge for bearing fault detection. In addition, some methods may overlook important features in bearing vibration signals, leading to insufficient detection capabilities. To address the challenges in bearing fault detection, this paper proposed a few sample learning methods based on the multidimensional convolution and attention mechanism. First, a multichannel preprocessing method was designed to more effectively utilize the information in the bearing vibration signal. Second, by extracting multidimensional features and enhancing the attention to important features through multidimensional convolution operations and attention mechanisms, the feature extraction ability of the network was improved. Furthermore, nonlinear mapping of feature vectors into the metric space to calculate distance can better measure the similarity between samples, thereby improving the accuracy of bearing fault detection and providing important guarantees for the safe operation of industrial systems. Extensive experiments have shown that the proposed method has good fault detection performance under small sample conditions, which is beneficial for reducing machine downtime and economic losses.

The leader-following consensus (LFC) issue is investigated in this paper for multi-agent systems (MASs) subject to actuator saturation with semi-Markov switching topologies (SMST). A new consensus protocol is proposed by using a semi-Markov process to model the switching of network topologies. Compared to the traditional Markov switching topologies, the SMST is more general and practical because the transition rates are time-varying. By using the local sector conditions and a suitable Lyapunov-Krasovskii functional, some sufficient conditions are proposed such that the leaderfollowing mean-square consensus is locally achieved. Based on the derived sufficient conditions, an optimization problem is analyzed to determine the consensus feedback gains and to find a maximal estimate of the domain of consensus attraction (DOCA) of a closed-loop model. At the end, a numerical case is presented to verify the performance of the design method.

In demanding application scenarios such as clinical psychotherapy and criminal interrogation, the accurate recognition of micro-expressions is of utmost importance but poses significant challenges. One of the main difficulties lies in effectively capturing weak and fleeting facial features and improving recognition performance. To address this fundamental issue, this paper proposed a novel architecture based on a multi-scale 3D residual convolutional neural network. The algorithm leveraged a deep 3D-ResNet50 as the skeleton model and utilized the micro-expression optical flow feature map as the input for the network model. Drawing upon the complex spatial and temporal features inherent in micro-expressions, the network incorporated multi-scale convolutional modules of varying sizes to integrate both global and local information. Furthermore, an attention mechanism feature fusion module was introduced to enhance the model's contextual awareness. Finally, to optimize the model's prediction of the optimal solution, a discriminative network structure with multiple output channels was constructed. The algorithm's performance was evaluated using the public datasets SMIC, SAMM, and CASME Ⅱ. The experimental results demonstrated that the proposed algorithm achieves recognition accuracies of 74.6, 84.77 and 91.35% on these datasets, respectively. This substantial improvement in efficiency compared to existing mainstream methods for extracting micro-expression subtle features effectively enhanced micro-expression recognition performance and increased the accuracy of high-precision micro-expression recognition. Consequently, this paper served as an important reference for researchers working on high-precision micro-expression recognition.

This study developed a deterministic transmission model for the coronavirus disease of 2019 (COVID-19), considering various factors such as vaccination, awareness, quarantine, and treatment resource limitations for infected individuals in quarantine facilities. The proposed model comprised five compartments: susceptible, vaccinated, quarantined, infected, and recovery. It also considered awareness and limited resources by using a saturated function. Dynamic analyses, including equilibrium points, control reproduction numbers, and bifurcation analyses, were conducted in this research, employing analytics to derive insights. Our results indicated the possibility of an endemic equilibrium even if the reproduction number for control was less than one. Using incidence data from West Java, Indonesia, we estimated our model parameter values to calibrate them with the real situation in the field. Elasticity analysis highlighted the crucial role of contact restrictions in reducing the spread of COVID-19, especially when combined with community awareness. This emphasized the analytics-driven nature of our approach. We transformed our model into an optimal control framework due to budget constraints. Leveraging Pontriagin's maximum principle, we meticulously formulated and solved our optimal control problem using the forward-backward sweep method. Our experiments underscored the pivotal role of vaccination in infection containment. Vaccination effectively reduces the risk of infection among vaccinated individuals, leading to a lower overall infection rate. However, combining vaccination and quarantine measures yields even more promising results than vaccination alone. A second crucial finding emphasized the need for early intervention during outbreaks rather than delayed responses. Early interventions significantly reduce the number of preventable infections, underscoring their importance.

With the consideration of the complexity of the transmission of Cholera, a partially degenerated reaction-diffusion model with multiple transmission pathways, incorporating the spatial heterogeneity, general incidence, incomplete immunity, and Holling type Ⅱ treatment was proposed. First, the existence, boundedness, uniqueness, and global attractiveness of solutions for this model were investigated. Second, one obtained the threshold condition $ mathcal{R}_{0} $ and gave its expression, which described global asymptotic stability of disease-free steady state when $ mathcal{R}_{0} < 1 $, as well as the maximum treatment rate as zero. Further, we obtained the disease was uniformly persistent when $ mathcal{R}_{0} > 1 $. Moreover, one used the mortality due to disease as a branching parameter for the steady state, and the results showed that the model undergoes a forward bifurcation at $ mathcal{R}_{0} $ and completely excludes the presence of endemic steady state when $ mathcal{R}_{0} < 1 $. Finally, the theoretical results were explained through examples of numerical simulations.

Dempster-Shafer evidence theory, as a generalization of probability theory, is a powerful tool for dealing with a variety of uncertainties, such as incompleteness, ambiguity, and conflict. Because of its advantages in information fusion compared with traditional probability theory, it is widely used in various fields. However, the classic Dempster's combination rule assumes that evidences are independent of each other, which is difficult to satisfy in real life. Ignoring the dependence among the evidences will lead to unreasonable fusion results, and even wrong conclusions. Considering the limitations of D-S evidence theory, this paper proposed a new evidence fusion model based on principal component analysis (PCA) to deal with the dependence among evidences. First, the approximate independent principal components of each information source were obtained based on principal component analysis. Second, the principal component data set was used as a new information source for evidence theory. Third, the basic belief assignments (BBAs) were constructed. As the fundamental construct of evidence theory, a BBA is a probabilistic function corresponding to each hypothesis, quantifying the belief assigned based on the evidence at hand. This function facilitates the synthesis of disparate evidence sources into a mathematically coherent and unified belief structure. After constructing the BBAs, the BBAs were fused and a conclusion was drawn. The case study verified that the proposed method is more robust than several traditional methods and can deal with redundant information effectively to obtain more stable results.