Genus of numerical semigroups generated by three elements

In this paper we study numerical semigroups generated by three elements. We give a characterization of pseudo-symmetric numerical semigroups. Also, we will give a simple algorithm to get all the pseudo-symmetric numerical semigroups with give Frobenius number.Comment: 7 page

Nonequilibrium Green's Function Approach to Phonon Transport in Defective Carbon Nanotubes

We have developed a new theoretical formalism for phonon transport in nanostructures using the nonequilibrium phonon Green's function technique and have applied it to thermal conduction in defective carbon nanotubes. The universal quantization of low-temperature thermal conductance in carbon nanotubes can be observed even in the presence of local structural defects such as vacancies and Stone-Wales defects, since the long wavelength acoustic phonons are not scattered by local defects. At room temperature, however, thermal conductance is critically affected by defect scattering since incident phonons are scattered by localized phonons around the defects. We find a remarkable change from quantum to classical features for the thermal transport through defective CNTs with increasing temperature.Comment: 5 pages, 3 figures, accepted for publication in Phys. Rev. Let

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

Motion of the Tippe Top : Gyroscopic Balance Condition and Stability

We reexamine a very classical problem, the spinning behavior of the tippe top on a horizontal table. The analysis is made for an eccentric sphere version of the tippe top, assuming a modified Coulomb law for the sliding friction, which is a continuous function of the slip velocity $\vec v_P$ at the point of contact and vanishes at $\vec v_P=0$. We study the relevance of the gyroscopic balance condition (GBC), which was discovered to hold for a rapidly spinning hard-boiled egg by Moffatt and Shimomura, to the inversion phenomenon of the tippe top. We introduce a variable $\xi$ so that $\xi=0$ corresponds to the GBC and analyze the behavior of $\xi$. Contrary to the case of the spinning egg, the GBC for the tippe top is not fulfilled initially. But we find from simulation that for those tippe tops which will turn over, the GBC will soon be satisfied approximately. It is shown that the GBC and the geometry lead to the classification of tippe tops into three groups: The tippe tops of Group I never flip over however large a spin they are given. Those of Group II show a complete inversion and the tippe tops of Group III tend to turn over up to a certain inclination angle $\theta_f$ such that $\theta_f<\pi$, when they are spun sufficiently rapidly. There exist three steady states for the spinning motion of the tippe top. Giving a new criterion for stability, we examine the stability of these states in terms of the initial spin velocity $n_0$. And we obtain a critical value $n_c$ of the initial spin which is required for the tippe top of Group II to flip over up to the completely inverted position.Comment: 52 pages, 11 figures, to be published in SIAM Journal on Applied Dynamical Syste

Real Options and Signaling in Strategic Investment Games

A game in which an incumbent and an entrant decide the timings of entries into a new market is investigated. The profit flows involve two uncertain factors: (1) the basic level of the demand of the market observed only by the incumbent and (2) the fluctuation of the profit flow described by a geometric Brownian motion that is common to both firms. The optimal timing for the incumbent, who privately knows the high demand, is earlier than that for the low-demand incumbent. This earlier entrance, however, reveals the information of the high demand to the entrant, so that the entrant observing the timing of the incumbent would accelerate the its own timing of the investment that reduces the monopolistic profit of the incumbent. Therefore, the high-demand incumbent may delay the timing of the investment in order to hide the information strategically. The equilibria of this signaling game are characterized, and the conditions for the manipulative revelation are investigated. The values of both firms are compared with the case of complete information.Real Option, Investment Timing, Signaling, Asymmetric Information, Game Theory