This paper is concerned with the mathematical analysis of the stochastic infectious model under subclinical infections and vaccination. In the modern society with the advanced medical technology, we have still various kinds of the infectious disease threat including Coronavirus disease (COVID-19). Hence, the control and the analysis of infection diseases is one of major problems in epidemiology. In the control of the infectious diseases, vaccination plays an important role. In the realistic spread of the infectious disease, environmental change and individual difference cause some kinds of random fluctuations in the infection and the recovery rates. Moreover, noting that one of characteristics of COVID-19 is the existence of subclinical infections, we propose the stochastic infectious model under subclinical infections and vaccination with waning immunity. Since the stability analysis of the infectious model is effective in the control of the spread of the infectious disease, we analyze the stability of the stochastic infectious model. We derive the stability conditions for the proposed stochastic infectious model to be stable. By numerical simulations, we show the efficacy of the stability theorems derived in this paper.

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Past quantum state estimation is a controversial issue, and it has been studied from both theoretical curiosity and practical necessity. Some studies propose quantum state smoothing methods, yet it is still an open problem in what situations ensure the past quantum states. This paper discusses conditions that the past quantum observable estimation becomes a past quantum state estimation and proposes two recursive methods of quantum state smoother.

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Sequential Markov Chain Monte Carlo (SMCMC) methods can be applied in the Bayesian inference framework with the nonlinear non-Gaussian state space model. SMCMC can avoid the weight degeneracy which impact the performance of Sequential Monte Carlo (SMC) methods in the high-dimensional state space model. Recently, Discrete Bouncy Particle Sampler (DBPS) is proposed as the refinement step in the Composite Metropolis-Hasting (MH) Kernel of SMCMC framework. Traditional Bouncy Particle Sampler has the reducible problem. In this paper, we explore different velocity refresh method to avoid the reducible problem in the DBPS method and embed the velocity refresh step into the SMCMC framework. We perform experiments to evaluate the proposed methods and the state-of-the-art SMCMC methods.

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In this study, our proposed method, which estimates un-known parameter values of stochastic differential equation (SDE) models without explicit description of probability density function (PDF) data, is furtherly tested on a non-linear random vibration system. In our proposed method, it is assumed that a measured PDF is obtained from a random dynamical system whose structure is described by a known SDE model with unknown parameter values. With the help of Itô calculus, the Fokker–Planck equation (FPE) is derived from the SDE model. The measured PDF and candidate parameter values are substituted into the FPE to calculate a FPE residual. Our method is applied to a random Duffing–van der Pol (DVP) system. The resulting FPE residuals show that our method is capable of the unknown parameter estimation for the parameters having sufficient sensitivity of the FPE residuals.

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We claim the existence of a stochastic viscosity solution to obstacle stochastic partial differential equation associated with double barrier backward doubly stochastic differential equation, by using the Doss-Sussman transformation.

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In this paper, two methods for estimating unknown parameters involved in the SIR-based epidemic models are investigated via the pseudomeasurement approach.

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The optimal control problems are investigated for the vaccination of SIR-based epidemic models by introducing the exact linearization via sate feedback.

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In this paper, we attempt to obtain the statistical models between the number of coronavirus case confirmed and coronavirus fatalities in Japan, based on the data reported from Japan Broadcasting Corporation (NHK). Specially, we have been developing the method of obtaining the regressive models between the numbers of daily new coronavirus infection and daily new coronavirus fatalities, based on the maximum like-lyhood method (MLM) and Akaike’s Information Criteria (AIC). Finally, we present the regressive models of using NHK data; from January 29, 2020 to October 11, 2021.

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In this paper, we investigate the effect of norm selection in the scenario approach to robust feasibility problems. Robust feasibility problems can be converted into robust optimization problems by minimizing an objective function such as the norm of decision variables. In such cases, the choice of the norm may affect the robustness of the optimal solution in the scenario approach. The 2- and ∞-norms are compared by simulating two numerical examples, which represent two extremal situations for minimizing ∞-norm.

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In this paper, we use a scenario program to study the sparse robust control for uncertain linear discrete-time systems. For the robustness of designed sparse optimal control, we deal with the uncertainty set by sampling a finite number of randomly generated scenarios of the uncertain variable. Specifically, we present a sparse robust control design via scenario program, where we minimize the ℓ¹ norm of the control signal to promote the sparse inputs, while satisfying the constraint with a scenario counterpart so as to guarantee the probabilistic robustness. A numerical example is illustrated to show the the effectiveness of proposed approach.

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The fundamental topic addressed in this paper concerns stochastic optimization problems. More specifically, our problem of interest is the determination of a ground state of a Hamiltonian function of an Ising model through the application of a simulated annealing algorithm based on parallel dynamics. Some theoretical aspects which were already mathematically proven by the same authors are presented in order to justify the application of simulated annealing for a particular class of probabilistic cellular automata. After that, it is demonstrated via simulations that for some class of examples its performance is higher than the performance of a well-stablished simulated annealing algorithm based on a single spin-flip dynamics, the so-called Glauber dynamics. In the end, we propose a derivation of the method presented initially in this paper and show through simulations that its accuracy in obtaining ground states is significantly higher within all studied cases. The observations in this paper support the need of further investigations of simulated annealing based on parallel dynamics from a rigorous perspective aiming at determining the limitations of such methods and finding clear directions to solve real-world combinatorial problems in an optimal way.

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The purpose of this paper is to present a recursive algorithm and its implementation in Maple and Mathematica for the computation of joint moments and cumulants of Hawkes processes with exponential kernels. Numerical results and computation times are also discussed. Obtaining closed form expressions can be computationally intensive, as joint fifth cumulant and moment formulas can be respectively expanded into up to 3,288 and 27,116 summands.

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This paper investigates the numerical procedure for solving the continuous-time portfolio optimization under a no-short selling constraint and a leverage constraint. The optimal investment strategy is designed for achieving the pre-determined target wealth. The performance criterion is defined by a suitable function of the difference between the investor’s wealth and the target wealth. However, the explicit boundary condition is no longer available in this situation. To improve the accuracy decreasing by the lack of the boundary conditions, we use the twice integrated radial basis function in the kernel-based collocation method. The obtained investment strategy is evaluated by the Monte-Carlo simulations based on empirical data.

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Value at Risk (VaR) is one of well employed risk measures in quantitative risk management in finance and insurance. In this paper, we deal with the estimate of VaR for the portfolio problem. The portfolio we consider consists of two risk variables, which are assumed not necessarily to be independent but possibly nonlinearly related; the relation is described by a copula function. As well known, copula provides a flexible tool to treating a nonlinear dependence among random variables. We are thus concerned with the estimate of copula-based VaR. A determination formula for this copula-based VaR is derived, which does not involve the copula density and is ready to be computed. Empirical study shows that the established formula works fairly well.

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In this paper, we give some numerical results related to Hata and Yasuda [1] that constructed an optimal investment and reinsurance strategies of maximizing the expected power utility maximization problem for an insurer. In our numerical experiments, we use pathwise analysis and the Monte-Carlo simulation, and compare four cases which have or do not have investment and reinsurance. And as performance criteria, we adopt return, risk, Sharp ratio, terminal wealth, utility values and their ranking.

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In this paper, we improve the building extraction from scenery images in terms of computational time and energy consumption without decreasing extraction accuracy. The improved method, which is based on the clustering method, also employs GrabCut, which is segmentation algorithm based on graph theory. For acceleration, the image, resolution of which is decreased, is used to drive GrabCut. Our experiment, which employed 106 scenery images, demonstrated that the improved method significantly decreased the computational time by 1.10 s or more compared with the comparative methods. In addition, the energy consumption, which is important to implement the building extraction on devices with limited computational resources, was significantly decreased by 1.18 mWh or more. Furthermore, the improved method did not decrease the extraction accuracy.

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Students often raise their hands in school classes, and the teacher calls on a student among those who raise their hands. However, when many people raise their hands, counting the number of raised hands takes time. Moreover, there is also the problem of missing some people and being confused about whom to call on. This paper uses YOLO to detect people who raise their hands and identify individuals using a face recognition system. Here we use the zoom function of the PTZ camera to perform face recognition in a wide-area. In addition, we construct a prototype system to automatically calls on a person among those who raised their hands on Jetson AGX Xavier.

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We have been developing the PPP algorithms based on our GR (GNSS Regresion) models with applying CLAS (Centimeter Level Augmentation Service) data from Japan Quasi-Zenith-Satellite-System (QZSS)[1]-[7]. In this paper, we examine the accuracy and convergence of positioning estimators applying the fixed-point Kalman smoother. Throughout the numerical experiments the total 3D-RMS error by applying CLAS and fixed-point Kalman smoother is approximately 0.15 [m].

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The stochastic process models are treated to estimate reliability assessments for degradation phenomena. In particular, the geometric Brownian motion and the gamma process models are handled, and the Bayesian procedures are applied to the models with the Markov chain Monte Carlo method. In addition, the estimation methods based on the empirical Bayesian, the maximum likelihood, and the generalized moment are also appropriated to the models. The information criterion EIC is used to select a fitted model among the stochastic models with the estimation procedures. The marginal likelihood with the Laplace’s method plays important roles in the methodologies proposed in this paper. In this paper, the Bayesian method with prior distributions is emphasized to apply expert opinions based on engineers for the reliability analysis. It is proposed that an expert opinion adopted to the analyzed phenomenon is chosen by using the information criterion EIC.

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This research proposes a pseudo-measurement approach to construct a Kalman filter for a liquid level control system model of a separator in an Ocean Thermal Energy Conversion (OTEC) experimental plant with Uehara cycle. Pseudo-measurement is recognized as an estimation method for a system dynamics including unknown parameters. After constructing the system involving pseudo-measurement, the Kalman filter and the feedback controller are derived. The behavior of the system is evaluated through numerical simulation.

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