Iterative Chebyshev approximation method for optimal control problems.

We present a novel numerical approach for solving nonlinear constrained optimal control problems (NCOCPs). Instead of directly solving the NCOCPs, we start by linearizing the constraints and dynamic system, which results in a sequence of sub-problems. For each sub-problem, we use finite number of Chebyshev polynomials to estimate the control and state vectors. To eliminate the errors at non-collocation points caused by conventional collocation methods, we additionally estimate the coefficient functions involved in the linear constraints and dynamic system by Chebyshev polynomials. By leveraging the characteristics of Chebyshev polynomials, the approximate sub-problem is changed into an equivalent nonlinear optimization problem with linear equality constraints. Consequently, any feasible point of the approximate sub-problem will satisfy the constraints and dynamic system throughout the entire time scale. To validate the efficacy of the new method, we solve three examples and assess the accuracy of the method through the computation of its approximation error. Numerical results obtained show that our approach achieves lower approximation error when compared to the Chebyshev pseudo-spectral method. The proposed method is particularly suitable for scenarios that require high-precision approximation, such as aerospace and precision instrument production.

MACTFusion: Lightweight Cross Transformer for Adaptive Multimodal Medical Image Fusion.

Multimodal medical image fusion aims to integrate complementary information from different modalities of medical images. Deep learning methods, especially recent vision Transformers, have effectively improved image fusion performance. However, there are limitations for Transformers in image fusion, such as lacks of local feature extraction and cross-modal feature interaction, resulting in insufficient multimodal feature extraction and integration. In addition, the computational cost of Transformers is higher. To address these challenges, in this work, we develop an adaptive cross-modal fusion strategy for unsupervised multimodal medical image fusion. Specifically, we propose a novel lightweight cross Transformer based on cross multi-axis attention mechanism. It includes cross-window attention and cross-grid attention to mine and integrate both local and global interactions of multimodal features. The cross Transformer is further guided by a spatial adaptation fusion module, which allows the model to focus on the most relevant information. Moreover, we design a special feature extraction module that combines multiple gradient residual dense convolutional and Transformer layers to obtain local features from coarse to fine and capture global features. The proposed strategy significantly boosts the fusion performance while minimizing computational costs. Extensive experiments, including clinical brain tumor image fusion, have shown that our model can achieve clearer texture details and better visual quality than other state-of-the-art fusion methods.

Multi-objective two-stage emergent blood transshipment-allocation in COVID-19 epidemic.

The problem of blood transshipment and allocation in the context of the COVID-19 epidemic has many new characteristics, such as two-stage, trans-regional, and multi-modal transportation. Considering these new characteristics, we propose a novel multi-objective optimization model for the two-stage emergent blood transshipment-allocation. The objectives considered are to optimize the quality of transshipped blood, the satisfaction of blood demand, and the overall cost including shortage penalty. An improved integer encoded hybrid multi-objective whale optimization algorithm (MOWOA) with greedy rules is then designed to solve the model. Numerical experiments demonstrate that our two-stage model is superior to one-stage optimization methods on all objectives. The degree of improvement ranges from 0.69 to 66.26%.

Insights into Controlling the Spread of COVID-19: A Study Inspired by Seven of the Earliest Vaccinated Countries.

Background: The aim of the study is to derive deeper insights into the control of the spread of COVID-19 during the second half of 2021, from seven countries that are among the earliest to have accelerated the deployment of COVID-19 vaccines. Methodology. This study used data from the Global COVID-19 Index and Google COVID-19 Community Mobility Reports. Data was extracted on the 5th of each month from July to December 2021. Seven countries were selected-United Kingdom, United States of America, Israel, Canada, France, Italy, and Austria. The sample comprised number of new cases, hospitalisations, ICU admissions and deaths due to COVID-19, government stringency measures, partial and full vaccination coverage, and changes in human mobility. Principal component analysis was conducted, and the results were interpreted and visualized through 2-dimensional and 3-dimensional plots to reveal the systematic patterns of the data. Results: The first three principal components captured around 77.3% of variance in the data. The first component was driven by the spread of COVID-19 (31.6%), the second by mobility activities (transit, retail, and recreational) (24.3%), whereas the third by vaccination coverage, workplace-related mobility, and government stringency measures (21.4%). Visualizations showed lower or moderate levels of severity in COVID-19 during this period for most countries. By contrast, the surge in the USA was more severe especially in September 2021. Human mobility activities peaked in September for most countries and then receded in the following months as more stringent government measures were imposed, and countries began to grapple with a surge in COVID-19 cases. Conclusion: This study delineated the spread of COVID-19, human mobility patterns, widespread vaccination coverage, and government stringency measures on the overall control of COVID-19. While at least moderate levels of stringency measures are needed, high vaccine coverage is particularly important in curbing the spread of this disease.

Multivariate visualization of the global COVID-19 pandemic: A comparison of 161 countries.

BACKGROUND: The aim of the study was to visualize the global spread of the COVID-19 pandemic over the first 90 days, through the principal component analysis approach of dimensionality reduction. METHODS: This study used data from the Global COVID-19 Index provided by PEMANDU Associates. The sample, representing 161 countries, comprised the number of confirmed cases, deaths, stringency indices, population density and GNI per capita (USD). Correlation matrices were computed to reveal the association between the variables at three time points: day-30, day-60 and day-90. Three separate principal component analyses were computed for similar time points, and several standardized plots were produced. RESULTS: Confirmed cases and deaths due to COVID-19 showed positive but weak correlation with stringency and GNI per capita. Through principal component analysis, the first two principal components captured close to 70% of the variance of the data. The first component can be viewed as the severity of the COVID-19 surge in countries, whereas the second component largely corresponded to population density, followed by GNI per capita of countries. Multivariate visualization of the two dominating principal components provided a standardized comparison of the situation in the161 countries, performed on day-30, day-60 and day-90 since the first confirmed cases in countries worldwide. CONCLUSION: Visualization of the global spread of COVID-19 showed the unequal severity of the pandemic across continents and over time. Distinct patterns in clusters of countries, which separated many European countries from those in Africa, suggested a contrast in terms of stringency measures and wealth of a country. The African continent appeared to fare better in terms of the COVID-19 pandemic and the burden of mortality in the first 90 days. A noticeable worsening trend was observed in several countries in the same relative time frame of the disease's first 90 days, especially in the United States of America.

Suppressing the Spikes in Electroencephalogram via an Iterative Joint Singular Spectrum Analysis and Low-Rank Decomposition Approach.

The novelty and the contribution of this paper consists of applying an iterative joint singular spectrum analysis and low-rank decomposition approach for suppressing the spikes in an electroencephalogram. First, an electroencephalogram is filtered by an ideal lowpass filter via removing its discrete Fourier transform coefficients outside the wave band, the wave band, the wave band, the wave band and the wave band. Second, the singular spectrum analysis is performed on the filtered electroencephalogram to obtain the singular spectrum analysis components. The singular spectrum analysis components are sorted according to the magnitudes of their corresponding eigenvalues. The singular spectrum analysis components are sequentially added together starting from the last singular spectrum analysis component. If the variance of the summed singular spectrum analysis component under the unit energy normalization is larger than a threshold value, then the summation is terminated. The summed singular spectrum analysis component forms the first scale of the electroencephalogram. The rest singular spectrum analysis components are also summed up together separately to form the residue of the electroencephalogram. Next, the low-rank decomposition is performed on the residue of the electroencephalogram to obtain both the low-rank component and the sparse component. The low-rank component is added to the previous scale of the electroencephalogram to obtain the next scale of the electroencephalogram. Finally, the above procedures are repeated on the sparse component until the variance of the current scale of the electroencephalogram under the unit energy normalization is larger than another threshold value. The computer numerical simulation results show that the spike suppression performance based on our proposed method outperforms that based on the state-of-the-art methods.

Robust Filtering for Nonlinear Nonhomogeneous Markov Jump Systems by Fuzzy Approximation Approach.

This paper addresses the problem of robust fuzzy L2-L∞ filtering for a class of uncertain nonlinear discrete-time Markov jump systems (MJSs) with nonhomogeneous jump processes. The Takagi-Sugeno fuzzy model is employed to represent such nonlinear nonhomogeneous MJS with norm-bounded parameter uncertainties. In order to decrease conservation, a polytope Lyapunov function which evolves as a convex function is employed, and then, under the designed mode-dependent and variation-dependent fuzzy filter which includes the membership functions, a sufficient condition is presented to ensure that the filtering error dynamic system is stochastically stable and that it has a prescribed L2-L∞ performance index. Two simulated examples are given to demonstrate the effectiveness and advantages of the proposed techniques.

Analysis of schizophrenia data using a nonlinear threshold index logistic model.

Genetic information, such as single nucleotide polymorphism (SNP) data, has been widely recognized as useful in prediction of disease risk. However, how to model the genetic data that is often categorical in disease class prediction is complex and challenging. In this paper, we propose a novel class of nonlinear threshold index logistic models to deal with the complex, nonlinear effects of categorical/discrete SNP covariates for Schizophrenia class prediction. A maximum likelihood methodology is suggested to estimate the unknown parameters in the models. Simulation studies demonstrate that the proposed methodology works viably well for moderate-size samples. The suggested approach is therefore applied to the analysis of the Schizophrenia classification by using a real set of SNP data from Western Australian Family Study of Schizophrenia (WAFSS). Our empirical findings provide evidence that the proposed nonlinear models well outperform the widely used linear and tree based logistic regression models in class prediction of schizophrenia risk with SNP data in terms of both Types I/II error rates and ROC curves.

Robust stability analysis of guaranteed cost control for impulsive switched systems.

This correspondence is concerned with the robust stability for a class of impulsive switched systems under the LQ guaranteed cost control. Some results on robust stability for this class of impulsive switched systems are obtained. Sufficient conditions for the existence of a guaranteed cost control law are also given. Subject to these sufficient conditions, the closed-loop uncertain impulsive switched system under the guaranteed cost control law is robustly stable with a guaranteed cost value.

Exponential stability of impulsive high-order Hopfield-type neural networks with time-varying delays.

This paper considers the problems of global exponential stability and exponential convergence rate for impulsive high-order Hopfield-type neural networks with time-varying delays. By using the method of Lyapunov functions, some sufficient conditions for ensuring global exponential stability of these networks are derived, and the estimated exponential convergence rate is also obtained. As an illustration, an numerical example is worked out using the results obtained.