Despite the advanced medical technology, infectious diseases remain a continuing threat to mankind. Hence, a prevention of prevalence of infectious diseases is one of important problems in epidemiology. In the past, the public health system has prepared for some strategies such as antibiotics and vaccines to control the infectious disease development. In order to build up more effective strategies, we need a precise theoretical analysis of infectious diseases. From a theoretical viewpoint, the mathematical model which describes the spread of the infectious disease has a very important role. In this paper, we study the stochastic modeling of the infectious disease in populations consisting of four groups: susceptible, infected, recovered and vaccinated. We consider the optimal vaccination strategy under the framework of the stochastic optimal control problem. Applying the stochastic maximum principle and the four-step scheme to the considered stochastic optimal control problem, we construct a feasible optimal vaccination system.
For computing a Nash (saddle point) solution to a zero-sum differential game for a general nonlinear system, Mukai et al. presented an iterative Sequential Quadratic-Quadratic Method (SQQM) as follows. Given a solution estimate, they defined a subproblem which approximates the original problem up to the second order around the solution estimate. They proposed to replace the subproblem with another subproblem in order to obtain a game problem with only a linear dynamics by removing the quadratic terms in the system dynamics and adding them to the payoff function as in Lagrangian function. We can now solve this subproblem conveniently by a Riccati equation method. We then update the solution estimate by adding its Nash solution to the current solution estimate for the original game. Through our extensive experiments, we observed not only local convergence of the SQQM but also much faster convergence of the SQQM than the iterative methods based on lower order approximations such as the Sequential Linear-Quadratic Method (SLQM). In this paper we will establish local convergence of the SQQM.
A stochastic-computational scheme is presented for generating as-is graph structure spanning complex local geographics. In this schematics, GPS tracks uploaded by a multitude of probe vehicles are exploited to expand a network of feasible roadway patterns. By associating the GPS tracks with a multitude of Brownian motions conditioned by landmark allocation, the graph structure is successively augmented in terms of feasible roadway segments. In reference to the augmented information, symbolic design of over-the-horizon maneuvering process can be interactively substantiated into a chain of topological minors grounded on the local geographics.
In this paper, we consider an optimization problem for observations of stationary LQG stochastic control systems which employ the stationary Kalman filter. The performance of the Kalman filter and that of the LQG stochastic optimal control are both dependent on the gain matrix in the linear observation. One of the authors has already developed methods of optimizing this gain matrix based on the estimation or control individual performance under a quadratic performance criterion. This paper discusses a hybrid problem by taking into account of both estimator and regulator performances. By introducing the eigenvalues-eigenvectors representation of a nonnegative definite symmetric matrix, the condition of optimality is derived. Also, numerical calculations are easily carried out by introducing multi-dimensional polar coordinates systems.
We analytically solved the equations for Brillouin optical time domain reflectometry (BOTDR), which is a distributed strain/temperature sensing system that uses a property where the scattering spectrum shifts in proportion to the change of the strain/temperature. Although the equations include both spontaneous and stimulated Brillouin scattering terms, we show that the largest part of the measured spectrum arises from spontaneous scattering in usual BOTDR conditions. This indicates that the term related to stimulated scattering in the equations for BOTDR can be ignored and we show that the observed spectrum is analytically represented in that case.
In this paper, the author investigates a class of fuzzy random sets as the vague perception of a crisp phenomenon or a crisp random phenomenon. First, considering that the vague perception of a crisp phenomenon fluctuates slightly but randomly due to the state of a capricious person’s mind, a new class of fuzzy random set is introduced. Secondly, the proposed fuzzy random set is generalized as the vague perception of a crisp random phenomenon. The expectations of the introduced fuzzy random sets are investigated from the viewpoint of the multivalued logic proposed by Kwakernaak.