Kazuo Sakai

Perspective reversal caused by chaotic switching in PDP schema model

A new dynamics of chaotic switching is proposed based on a particular type of network, i.e., the PDP (parallel distributed processing) scheme model. By applying a mean-field approximation, a one-dimensional map is derived, by which a variety of dynamics in the PDP schema model are reproduced. Introducing a dynamics of relative biases, successive chaotic switchings are realized. This new dynamics is applied to a well-known cognitive phenomenon of perspective reversal for ambiguous patterns such as a Necker cube. The chaotic states of network activations are interpreted as wondering states to search a new percept. New experimental results are given, which are categorized into three states: (1) one percept with confidence, (2) alternative percept, and (3) uncertain percept without confidence. The frequencies of persistent times in the three states are compared with simulations by logistic maps. It is shown that the chaotic theory could give new insights to cognitive science.<<ETX>>

Analysis of Magneto-Oscillatory Spectra in Cuprous Oxide, with Classical “Quasi-Closed" Unstable Trajectories

A quantum manifestation of classical non-integrability is found and analyzed in solid state spectroscopy. Magneto-oscillatory spectra in cuprous oxide are observed and attributed to classical unstable trajectories of the system of magnetized hydrogen-type atom which has long been a prototype of non-integrable system. Classical trajectories are numerically calculated with various initial conditions, and it is found that quasi-closed trajectories contribute to the spectrum. The resultant trajectories are sorted in three groups according to their recurrence frequencies (quasi-period). The three quasi-periods are shown to be corresponding to the characteristic three peaks of the auto-correlation function of photon absorbed excitonic state. This novel method for assignment using quasi-closed unstable trajectories has implications on complex spectrum remained unclear. We attempt to investigate how the classical non-integrability is reflected in spectroscopic properties in solid state.For this purpose, magneto-oscillatory spectra in Cu2O are observed and analyzed with the classical Hamiltonian of a magnetized hydrogen-type atom.In our previous work, 1) main modulation in the spectra was assigned to the shortest quasi-period of an electron.We can connect absorption spectra σ(ω) with corresponding non-integrable classical system as follows: firstly, we adopt the Heller’s formula, 2)

ASSIGNMENT OF QUASI-LANDAU LEVELS IN MAGNETO-OSCILLATORY SPECTRA IN CUPROUS OXIDE TO CLASSICAL UNSTABLE TRAJECTORIES OF HYDROGEN TYPE ATOMS

Abstract It is found, for the first time in the field of solid state spectroscopy, that quasi-Landau levels in magneto-oscillatory spectra in cuprous oxide reflect “classical non-integrability.” Cuprous oxide is well known to exhibit excitonic absorption spectra of typical wannier type near the absorption edge in yellow spectral region. Magneto-oscillatory spectra are observed in the region above the limiting energy of the exciton series in magnetic fields. The spectra are measured at liquid helium temperature with right and left circularly polarized light in magnetic fields up to 4.5xa0T generated by a superconducting magnet. The observed spectra look like “Landau levels” corresponding to the optical transitions between states of the hole in a valence band and those of the electron in a conduction band without Coulomb attraction between them qualitatively, but never coincide with the Landau levels quantitatively. By calculating inverse Fourier transform of the observed spectra (IFFT spectra), three peaks are found in the auto-correlation function of the excited excitonic state. These spectra are interpreted as those of a hydrogen type atom with the effective masses of the electron–hole pair in homogeneous magnetic field, which is known to be a typical non-integrable system in classical mechanics. Instead of obtaining the quantum mechanical motions of wave packet, the classical trajectories are numerically calculated. First peak of the IFFT spectra is assigned to the trajectories on which the wave packet circulates and returns to approximately to the starting point after the duration corresponding to the first peak. Immediately after that, the trajectories are rapidly apart from the starting point on account of their instability, which reflects the classical non-integrability of the system.

Interpretation of magneto-oscillatory spectra in cuprous oxide as quantum manifestation of classical non-integrability

Abstract The magneto-oscillatory spectra in cuprous oxide (Cu 2 O) are observed to have multi-oscillatory structure, and this structure is successfully interpreted as a consequence of classical non-integrability of the Hamiltonian of an electron–hole (e–h) pair generated in the sample in magnetic fields. The spectra are analyzed with use of the Heller formula which connects absorption cross section with overlap integral of the photon-absorbed wave function (PAWF) as a function of time. The overlap integral in our spectra are experimentally obtained by inverse Fourier transform of the spectra, and three characteristic times are observed as the peak times of the overlap integral. Then, the overlap integral is numerically estimated by calculating recurrence times of the trajectories of a classical hydrogen atom in magnetic fields. The characteristic times and the recurrence times coincide with each other well.

An agent oriented environment for collaborative learning: lessons learned through vocational training on Software Design with UML

With the increasing popularity of e-learning, much attention has been focused not only on individualized learning but also on collaborative learning in where several learners participate. In this research, a system designed to actualize collaborative learning is developed. The contents of collaborative learning to run on the system are prepared and subsequently validation experiments have been conducted. This paper describes the agent-oriented collaborative learning system and the contents of the collaborative learning exercise, and reports the results of the validation experiment that is conducted.

Fluctuation of capillary pulse as an index for driver's internal states

In this paper, fluctuations of capillary pulses are discussed under different internal state conditions, especially different emotional states. Capillary pulses of finger were measured under various situations such as watching video movies, answering quizzes and so on. It is found that fluctuations of finger capillary pulses can be used for estimating the drivers internal states. Suitable indices for the fluctuation are moment and density of its return-map.<<ETX>>

Chaos Causes Perspective Reversals for Ambiguious Patterns

A new chaotic mechanism is found to cause perspective reversal for ambiguious patterns. And the new senario to cause perspective reversal is proposed with use of chaos, by reexamining the psychological parameters of schema. The psychological parameters are incorporated into a PDP schema model proposed by Rumelhart et al., and a simple one-dimensional map is derived in a mean-field approximation. The numerical experiments for a one-dimensional logistic map are performed, and the results are compared with new psychological experiments of perspective reversals for a Necker cube by 96 students. It is shown that these are qualitatively good agreement with each other. This gives a concrete example of the role of chaos in cognitive science.