Neural networks decide or predict something by learning examples. Recently, improving equips and enlarging data enable the deep learning to perform complex decision. However, some objects require a lot of learning time to improve the precision.In this study, we investigate the number of required epochs for neural networks to study three-input Boolean functions. Then, we find that the number of required epochs depends on each of Boolean functions. Thus, by focusing on the structure of Boolean functions, we find that we can estimate the minimum number of required epochs according to the property of disjunctive normal form of the Boolean function.

In recent years, mobile terminals come to be used to assist works. However, we can not say that they are enough suitable to assist works either that occupy hands or that are accomplished in environment with water or fire, which cause troubles with electronic devices. In this study, in order to solve this problem, we propose an assist system using projection mapping and NUI. Note that our system is not an application program, but replaces the former UI simply. Our system consists of a depth camera, an RGB camera, and a projector. It causes a click event by detecting whether a user touches the screen. By replacing the click operation with the touching on the projected screen, it can utilize various existing applications and contents.

Java8 introduced the notion of streams that is a new data structure and supports multi-core processors. When the sum method is called for a stream of floating-point numbers, the summation is calculated at high-speed by applying MapReduce, which distributes computations to cores. However, since floating-point calculation causes an error, simple adaptation of this method can not determine the result uniquely. Then, in this study, we develop a summation program that can be applied to a stream with MapReduce. Our method can calculate at high-speed with keeping correctly rounded.

In order to communicate in cipher over IP multi-cast, each of joining and leaving participants causes renewing keys. Moreover, the number of renewed keys depends on the key management system. LKH, one of the key management systems, uses a tree structure to manage keys to share with participants. Every node of the tree is given a key, and each leaf of the tree is corresponding to a participant. If all members are handled equally, by using a balanced binary tree, the average number of renewed keys per join and leave is estimated at ⌈log2n ⌉, where n denotes the number of participants. In this study, we introduce a scenario that the key management system can distinguish between inconstant members and stable members, instead of handling members equally. Under this scenario, our system improves the number of renewing keys efficiently by considering another tree structure against the balanced binary tree structure.

This paper studies the "usefulness" of initial conditions for distributed algorithms on anonymous networks. In the literature, several initial conditions such as making one vertex a leader, giving the number of vertex to each vertices, and so on, have been considered. In this paper, we study a relation between the initial condition by considering transformation algorithm from one initial condition to another. For such transformation algorithms, we consider in this paper, both deterministic and randomized distributed algorithms. For each deterministic and randomized transformation type, we show that the relation induces an infinite lattice structure among equivalence classes of initial conditions.