A PBN is well known as a mathematical model of complex network systems such as gene regulatory networks. In Boolean networks, interactions between nodes (e.g., genes) are modeled by Boolean functions. In PBNs, Boolean functions are switched probabilistically. In this paper, for a PBN, a simplified representation that is effective in analysis and control is proposed. First, after a polynomial representation of a PBN is briefly explained, a simplified representation is derived. Here, the steady-state value of the expected value of the state is focused, and is characterized by a minimum feedback vertex set of an interaction graph expressing interactions between nodes. Next, using this representation, input selection and stabilization are discussed. Finally, the proposed method is demonstrated by a biological example.

We propose a method for reducing the size of a share in visual secret sharing schemes. The proposed method does not cause the leakage and the loss of the original image. The quality of the recovered image is almost same as that of previous schemes.

In this paper, a method is proposed to construct an n-out-of-n visual secret sharing scheme for gray-scale images, for short an (n,n)-VSS-GS scheme, which is optimal in the sense of contrast and pixel expansion, i.e., resolution. It is shown that any (n,n)-VSS-GS scheme can be constructed based on the so-called polynomial representation of basis matrices treated in [15],[16]. Furthermore, it is proved that such construction can attain the optimal (n,n)-VSS-GS scheme.

A visual secret sharing scheme (VSSS) is one of secret sharing schemes for images. Droste showed the method for constructing VSSS based on basis matrices whose contrast was high. Koga, Iwamoto, and Yamamoto also proposed the method for constructing a lattice-based VSSS and its polynomial representation. It is known that many good VSSSs are not in the class of lattice-based VSSSs. In this paper, we show the well-defined polynomial representation of a VSSS based on permuting different matrices for black-white images. The necessary and sufficient condition of the existence of a VSSS based on permuting different matrices can be obtained from the proposed polynomial representation. This condition is useful for constructing a good VSSS. We also point out that without additional data, it is possible to achieve member verification by using a VSSS. Using the proposed polynomial representation, the probability of detecting a cheater is analyzed.