Critical bending point in the Lyapunov localization spectra of many-particle systems

The localization spectra of Lyapunov vectors in many-particle systems at low density exhibit a characteristic bending behavior. It is shown that this behavior is due to a restriction on the maximum number of the most localized Lyapunov vectors determined by the system configuration and mutual orthogonality. For a quasi-one-dimensional system this leads to a predicted bending point at n_c \approx 0.432 N for an N particle system. Numerical evidence is presented that confirms this predicted bending point as a function of the number of particles N.Comment: 4 pages, 4 figure

Magnetization switching by microwaves initially rotating in opposite direction to precession

A common understanding of magnetization switching in microwave-assisted magnetization reversal is that the rotation direction of the microwaves should be the same with the precession direction of the magnetization. In this letter however, we show that microwaves initially rotating opposite to the magnetization precession destabilize the magnetization at an equilibrium and induces the switching more efficiently, when the microwave frequency depends on time. This argument is analytically deduced from energy balance equation. We also establish a model satisfying this condition, and confirm magnetization switching solely by microwaves by using numerical simulation.Comment: 5 pages, 4 figure

Deformation and α\alpha clustering in excited states of 42^{42}Ca

The coexistence of various low-lying deformed states in $^{42}$Ca and $\alpha$--$^{38}$Ar correlations in those deformed states have been investigated using deformed-basis antisymmetrized molecular dynamics. Wave functions of the low-lying states are obtained via parity and angular momentum projections and the generator coordinate method (GCM). Basis wave functions of the GCM calculation are obtained via energy variations with constraints on the quadrupole deformation parameter $\beta$ and the distance between $\alpha$ and $^{38}$Ar clusters. The rotational band built on the $J^\pi = 0_2^+$ (1.84 MeV) state as well as the $J^\pi = 0_3^+$ (3.30 MeV) state are both reproduced. The coexistence of two additional $K^\pi = 0^+$ rotational bands is predicted; one band is shown to be built on the $J^\pi = 0_3^+$ state. Members of the ground-state band and the rotational band built on the $J^\pi = 0_3^+$ state contain $\alpha$--$^{38}$Ar cluster structure components.Comment: 11 pages, 6 figure

A mean value theorem for the square of class number times regulator of quadratic extensions

Let $k$ be a number field. In this paper, we give a formula for the mean value of the square of class numbers times regulators for certain families of quadratic extensions of $k$ characterized by finitely many local conditions. We approach this by using the theory of the zeta function associated with the space of pair of quaternion algebras.Comment: 35 pages, AMS LaTeX; added a reference and rewrote Section

Online Spatial Concept and Lexical Acquisition with Simultaneous Localization and Mapping

In this paper, we propose an online learning algorithm based on a Rao-Blackwellized particle filter for spatial concept acquisition and mapping. We have proposed a nonparametric Bayesian spatial concept acquisition model (SpCoA). We propose a novel method (SpCoSLAM) integrating SpCoA and FastSLAM in the theoretical framework of the Bayesian generative model. The proposed method can simultaneously learn place categories and lexicons while incrementally generating an environmental map. Furthermore, the proposed method has scene image features and a language model added to SpCoA. In the experiments, we tested online learning of spatial concepts and environmental maps in a novel environment of which the robot did not have a map. Then, we evaluated the results of online learning of spatial concepts and lexical acquisition. The experimental results demonstrated that the robot was able to more accurately learn the relationships between words and the place in the environmental map incrementally by using the proposed method.Comment: This paper was accepted in the 2017 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2017