A Method to Change Phase Transition Nature -- Toward Annealing Method --

In this paper, we review a way to change nature of phase transition with annealing methods in mind. Annealing methods are regarded as a general technique to solve optimization problems efficiently. In annealing methods, we introduce a controllable parameter which represents a kind of fluctuation and decrease the parameter gradually. Annealing methods face with a difficulty when a phase transition point exists during the protocol. Then, it is important to develop a method to avoid the phase transition by introducing a new type of fluctuation. By taking the Potts model for instance, we review a way to change the phase transition nature. Although the method described in this paper does not succeed to avoid the phase transition, we believe that the concept of the method will be useful for optimization problems.Comment: 27 pages, 3 figures, revised version will appear in proceedings of Kinki University Quantum Computing Series Vo.

A Theory of Multidimensional Information Disclosure

We study disclosure of information about the multidimensional state of the world when uninformed receivers' actions affect the sender's utility. Given a disclosure rule, the receivers form an expectation about the state following each message. Under the assumption that the senderfs expected utility is written as the expected value of a quadratic function of those conditional expectations, we identify conditions under which full and no disclosure is optimal for the sender and show that a linear transformation of the state is optimal if it is normally distributed. We apply our theory to advertising, political campaigning, and monetary policy.

Network-Growth Rule Dependence of Fractal Dimension of Percolation Cluster on Square Lattice

To investigate the network-growth rule dependence of certain geometric aspects of percolation clusters, we propose a generalized network-growth rule introducing a generalized parameter $q$ and we study the time evolution of the network. The rule we propose includes a rule in which elements are randomly connected step by step and the rule recently proposed by Achlioptas {\it et al.} [Science {\bf 323} (2009) 1453]. We consider the $q$-dependence of the dynamics of the number of elements in the largest cluster. As $q$ increases, the percolation step is delayed. Moreover, we also study the $q$-dependence of the roughness and the fractal dimension of the percolation cluster.Comment: 4 pages, 5 figures, accepted for publication in Journal of the Physical Society of Japa