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In this paper, we proposed a dynamic optimization problem involving a two-stage fractional system subjected to both a terminal state inequality constraint and continuous state inequality constraints in a microbial batch process. The objective function was the productivity of 1,3-propanediol at the terminal time, while the decision variables were the initial concentrations of biomass and glycerol, and the terminal time of the batch process. We first equivalently transformed the problem with free terminal time into one with fixed terminal time in a new time horizon by applying a proposed time-scaling transformation. We then converted the equivalent problem into an optimization problem with only box constraints by using an exact penalty function method. A novel third-order numerical scheme was presented for solving the two-stage fractional system. On this basis, we developed an improved particle swarm optimization algorithm to solve the resulting optimization problem. Finally, numerical results showed that a significant increase in the productivity of 1,3-propanediol at the terminal time was obtained compared with the previously reported results.

In this paper, we developed a novel numerical method for solving general nonlinear fractional ordinary differential equations (FODEs). First, we transformed the nonlinear FODEs into the equivalent Volterra integral equations. We then developed a time-stepping algorithm for the numerical solution of the Volterra integral equations based on the third-order Taylor expansion for approximating the integrands in the Volterra integral equations on a chosen mesh with the mesh parameter $ h $. This approximation led to implicit nonlinear algebraic equations in the unknowns at each given mesh point, and an iterative algorithm based on Newton's method was developed to solve the resulting implicit equations. A convergence analysis of this numerical scheme showed that the error between the exact solution and numerical solution at each mesh point is $ \mathcal{O}(h^{3}) $, independent of the fractional order. Finally, four numerical examples were solved to verify the theoretical results and demonstrate the effectiveness of the proposed method.

Abstract The combination of the time-scaling transformation and control parameterization has proven to be an effective approach in addressing optimal control problems involving switching systems with predefined subsystem sequences. However, this approach has certain limitations. First, the number of control switchings is required to be no less than the number of subsystem switchings. Second, the switching of the subsystem must be accompanied by the switching of the control. Third, this scheme introduces many hyperparameters, leading to combinatorial explosion. To address these drawbacks, we introduce a novel computational approach such that the control switching can be independent of subsystem switching. The superiority of this novel approach can be clearly observed from the solutions obtained using the proposed method for solving two illustrative examples.

Abstract Issue COVID-19 has resulted in mortality worldwide and exposed vulnerabilities in public health systems. Although countries have since transitioned to the endemic phase, it is nonetheless important to identify inequities within populations to improve public health strategies in light of another health crisis. Purpose This study aims to offer deeper insights into the sex and age differentials in COVID-19 fatality across different states in Malaysia, from the pandemic’s start to the country’s transition to the endemic phase. Methodology Analyses utilized data on the number of COVID-19 cases and deaths in Malaysia from January 2020 until April 2022. Case fatality rate (CFR) was computed for each state based on sex and age groups, for four periods (January–December 2020, January–June 2021, July–December 2021, and January–April 2022). Principal component analysis (PCA) uncovered patterns in the data and produced a multivariate visualization of the COVID-19 fatality within Malaysia. Findings Findings revealed heterogeneity in fatality and identified several vulnerable states, notably in the northern region (Kelantan, Perlis) and on the East Coast (Sabah, Sarawak). A sex disparity was apparent in Kelantan as the CFR among older females was higher than their male counterparts. Sabah exhibited relatively higher CFR among the child population from 2020 to 2021. Implication The findings deepened our understanding of COVID-19 fatality complexity, providing recommendations for Malaysia’s government in preparing for future health crises. Malaysia’s case study offers lessons on the need to address regional disparities and implement targeted strategies to protect vulnerable subgroups.

Abstract This paper considers an optimal control problem of nonlinear Markov jump systems with continuous state inequality constraints. Due to the presence of continuous‐time Markov chain, no existing computation method is available to solve such an optimal control problem. In this paper, a derandomisation technique is introduced to transform the nonlinear Markov jump system into a deterministic system, which simultaneously gives rise to an equivalent deterministic dynamic optimisation problem. The control parametrisation technique is then used to partition the time horizon into a sequence of subintervals such that the control function is approximated by a piecewise constant function consistent with the partition. The heights of the piecewise constant function on the corresponding subintervals are taken as decision variables to be optimised. In this way, the approximate dynamic optimisation problem is an optimal parameter selection problem, which can be viewed as a finite dimensional optimisation problem. To solve it using a gradient‐based optimisation method, the gradient formulas of the cost function and the constraint functions are derived. Finally, a real‐world practical problem involving a bioreactor tank model is solved using the method proposed.

Abstract 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%.

In this paper, a financial risk model, which is formulated from the risk management process of financial markets, is studied. By considering the presence of Gaussian white noise, the financial risk model is reformulated as a stochastic optimal control problem. On this basis, two efficient computational approaches for state estimation, which are the extended Kalman filter (EKF) and unscented Kalman filter (UKF) approaches, are applied. Later, based on the state estimate given by the EKF and UKF approaches, a linear feedback control policy is designed from the stationary condition. For illustration, some parameter values and the initial conditions of the financial risk model are used for the simulation of the stochastic optimal control problem. From the results, it is noticed that the UKF algorithm provides a better state estimate with a smaller value of the sum of squared errors (SSE) as compared to the SSE given by the EKF algorithm. Thus, the estimated output trajectory has a high accuracy that is close to the real output. Moreover, the control effort assists in estimating the state dynamics at the minimum cost. In conclusion, the efficiency of the computational approaches for optimal control of the financial risk model has been well presented.

An unmanned surface vehicles (USV) set point tracking problem is investigated in this paper. The stochastic model predictive control (SMPC) scheme is utilized to design the controller in order to reject the environment disturbances and meet the physical constraints. The design problem is formulated as a chance-constrained stochastic optimization problem, which is non-convex. Thus, the problem is computationally prohibitive. For this, the convex conditional value at risk (CVaR) approximation is introduced to convert the chance constraints into deterministic convex constraints. The converted constraints are then further transformed into the second order cone (SOC) constraints. Therefore, the proposed method is computationally tractable and hence can be implemented online. A numerical example is provided to illustrate the effectiveness of the proposed method.

BackgroundThe 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.MethodsThis 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.ResultsConfirmed 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.ConclusionVisualization 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.

In this paper, we construct a regional logistics model from a macroperspective. First, based on the gravity model, the index of logistics attraction between cities is established as the weight of the model, and hence the regional logistics weighted model is constructed. Next, we use the social network analysis method to analyze its structure and make specific recommendations for the construction of logistics networks. Finally, we analyze the model’s response to random attacks and deliberate attacks. From our study, it is found that when the failure nodes or edges reach a certain percentage, the regional logistics network will collapse on a large scale. Therefore, it is important to optimization the threshold of the regional logistics network. This clearly provides a new perspective for the study of the regional logistics networks.

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.

This paper is concerned with the boundedness and attractiveness of nonlinear switched delay systems whose subsystems have different equilibria. Some sufficient conditions which can guarantee the system’s boundedness are obtained. In addition, we work out the region where the solution will remain and furthermore the relationship between the initial function and the bounded region. Based on the new concept of attractor with switching laws, we show that the nonlinear switched delay system is attractive and then obtain the attractive region.

We introduce and study a new class of auxiliary problems for solving the equilibrium problem in Banach spaces. Not only the existence of approximate solutions of the equilibrium problem is proven, but also the strong convergence of approximate solutions to an exact solution of the equilibrium problem is shown. Furthermore, we give some iterative schemes for solving some generalized mixed variational-like inequalities to illuminate our results.

Envelope constrained filter design is concerned with the time domain synthesis of a filter whose response to a specified input signal stays within prescribed upper and lower bounds and in addition has minimal noise enhancement. In many practical applications, a ``soft`` approach, such as least mean square, is not the most suitable and it becomes necessary to use ``hard`` constraints such as the ones considered in the paper. We present an overview of key ideas related to robust continuous time envelope constrained filter design.