A Note on the Profit Distribution among a Manufacturer and its Retailers

Examining two polar forms of restricted franchise contract, Nariu (2004) studied the pricing behavior of manufacturers and retailers and the market outcomes. This note provides a concise justification for his assumptions on contractual restraints. Introducing some fixed amount that a manufacturer must invest to build up its production facility, we show that a bargaining solution to distribute the total net profit among a manufacturer and its exclusive retailers assigns zero franchise fee payment to any retailers, if the investment is not large.bargaining solution

Energy landscape analysis of neuroimaging data

Computational neuroscience models have been used for understanding neural dynamics in the brain and how they may be altered when physiological or other conditions change. We review and develop a data-driven approach to neuroimaging data called the energy landscape analysis. The methods are rooted in statistical physics theory, in particular the Ising model, also known as the (pairwise) maximum entropy model and Boltzmann machine. The methods have been applied to fitting electrophysiological data in neuroscience for a decade, but their use in neuroimaging data is still in its infancy. We first review the methods and discuss some algorithms and technical aspects. Then, we apply the methods to functional magnetic resonance imaging data recorded from healthy individuals to inspect the relationship between the accuracy of fitting, the size of the brain system to be analyzed, and the data length.Comment: 22 pages, 4 figures, 1 tabl

Upper Bound of Real Log Canonical Threshold of Tensor Decomposition and its Application to Bayesian Inference

Tensor decomposition is now being used for data analysis, information compression, and knowledge recovery. However, the mathematical property of tensor decomposition is not yet fully clarified because it is one of singular learning machines. In this paper, we give the upper bound of its real log canonical threshold (RLCT) of the tensor decomposition by using an algebraic geometrical method and derive its Bayesian generalization error theoretically. We also give considerations about its mathematical property through numerical experiments

Behavior of Hydroxyl Radicals on Water Ice at Low Temperatures

Because chemical reactions on/in cosmic ice dust grains covered by amorphous solid water (ASW) play important roles in generating a variety of molecules, many experimental and theoretical studies have focused on the chemical processes occurring on the ASW surface. In laboratory experiments, conventional spectroscopic and mass-spectrometric detection of stable products is generally employed to deduce reaction channels and mechanisms. However, despite their importance, the details of chemical reactions involving reactive species (i.e., free radicals) have not been clarified because of the absence of experimental methods for in situ detection of radicals. Because OH radicals can be easily produced in interstellar conditions by not only the photolysis and/or ion bombardments of H2O but also the reaction of H and O atoms, they are thought to be one of the most abundant radicals on ice dust. In this context, the development of a close monitoring method of OH radicals on the ASW surface may help to elucidate the chemical reactions occurring on the ASW surface.Comment: 25 pages, 9 figures; Accepted for publication in Acc. Chem. Re

An experimental study on learning about voting powers

We investigate experimentally whether subjects can learn, from their limited experiences, about relationships between the distribution of votes in a group and associated voting powers in weighted majority voting systems (WMV). Subjects are asked to play two-stage games repeatedly. In the second stage of the game, a group of four subjects bargains over how to divide fixed amount of resources among themselves through the WMV determined in the first stage. In the first stage, two out of four subjects in the group, independently and simultaneously, choose from two options that jointly determine the distribution of a given number of votes among four members. These two subjects face a 2 ~ 2 matrix that shows the distribution of votes, but not associated voting powers, among four members for each outcome. Therefore, to obtain higher rewards, subjects need to learn about the latter by actually playing the second stage. The matrix subjects face in the first stage changes during the experiment to test subjects' understanding of relationships between distribution of votes and voting power. The results of our experiments suggest that although (a) many subjects learn to choose, in the votes apportionment stage, the option associated with a higher voting power, (b) it is not easy for them to learn the underlying relationships between the two and correctly anticipate their voting powers when they face a new distribution of votes.

Efficient method for simulating quantum electron dynamics under the time dependent Kohn-Sham equation

A numerical scheme for solving the time-evolution of wave functions under the time dependent Kohn-Sham equation has been developed. Since the effective Hamiltonian depends on the wave functions, the wave functions and the effective Hamiltonian should evolve consistently with each other. For this purpose, a self-consistent loop is required at every time-step for solving the time-evolution numerically, which is computationally expensive. However, in this paper, we develop a different approach expressing a formal solution of the TD-KS equation, and prove that it is possible to solve the TD-KS equation efficiently and accurately by means of a simple numerical scheme without the use of any self-consistent loops.Comment: 5 pages, 3 figures. Physical Review E, 2002, in pres