The purpose of this paper is to propose the stochastic infectious model with time delay and to study the stability of the disease-free steady state. In the prevalence of infectious diseases, environmental change and individual difference cause some kinds of random fluctuations in the infection rate, immune effect, etc. Hence, the stochastic infectious model plays an important role in the analysis of the infectious disease. Moreover, in the vector-borne diseases such as malaria and dengue fever, there exists time delay caused by an incubation period in the virus development in the vectors on the transmission of disease. Taking these facts into consideration, we propose a stochastic susceptible-infected-recovered model with time delay. We analyze stability of the disease-free steady state using the stochastic Lyapunov function, and study the influence of time delay and the random noise on the stability by numerical simulations.

In this paper, we develop data visualization methods which consider interlayer correlations in deep neural networks (DNN). In general, DNN naturally acquires multiple feature representations corresponding to their intermediate layers through their learning process. In order to understand relationships of those intermediate features which are strongly correlated with each other, we utilize canonical correlation analysis (CCA) to visualize the data distributions of different feature layers in a common subspace. Our method can grasp movement of samples between consecutive layers in DNN. By using standard benchmark data sets, we show that our visualization results contain much information that typical visualization methods (such as principal component analysis) usually do not represent.

The shepherding problem is to guide or control a number of sheep by means of a small number of shepherds, which has useful applications outside the original sheep setting, such as to robotics and crowd control. Many simulations have been conducted to investigate the motion of a group, whereas less research has focused on controlling a group. Therefore, the present paper aims to clarify effective group control through the shepherding problem. Specifically, we focus on a simple algorithm called V-formation control and execute computer simulations.

Multi-agent systems over noisy networks with linear symmetric agents are considered. The topology of the network which defines the availability of communication among the agents is assumed to be a directed, weakly connected and balanced graph or an undirected and connected one. Furthermore, the communication graph is allowed to be time varying. The aim of this study is to establish a stochastic averaging consensus algorithm under a noisy environment for each time-varying network. The convergence analysis of the proposed algorithms reveals an explicit relation between the number of iterations and the closeness of the agreement, which gives a stopping rule for the consensus algorithm. The results are illustrated through numerical examples.