Asymptotic Learning Curve and Renormalizable Condition in Statistical Learning Theory

Bayes statistics and statistical physics have the common mathematical structure, where the log likelihood function corresponds to the random Hamiltonian. Recently, it was discovered that the asymptotic learning curves in Bayes estimation are subject to a universal law, even if the log likelihood function can not be approximated by any quadratic form. However, it is left unknown what mathematical property ensures such a universal law. In this paper, we define a renormalizable condition of the statistical estimation problem, and show that, under such a condition, the asymptotic learning curves are ensured to be subject to the universal law, even if the true distribution is unrealizable and singular for a statistical model. Also we study a nonrenormalizable case, in which the learning curves have the different asymptotic behaviors from the universal law

Emotional Empathy as a Mechanism of Synchronisation in Child-Robot Interaction

Simulating emotional experience, emotional empathy is the fundamental ingredient of interpersonal communication. In the speaker-listener scenario, the speaker is always a child, the listener is a human or a toy robot. Two groups of neurotypical children aged 6 years on average composed the population: one Japanese (n = 20) and one French (n = 20). Revealing potential similarities in communicative exchanges in both groups when in contact with a human or a toy robot, the results might signify that emotional empathy requires the implication of an automatic identification. In this sense, emotional empathy might be considered a broad idiosyncrasy, a kind of synchronisation, offering the mind a peculiar form of communication. Our findings seem to be consistent with the assumption that children’s brains would be constructed to simulate the feelings of others in order to ensure interpersonal synchronisation

Absence of the impurity-induced magnetic order in the electron-doped high-T_c_ cuprates Pr_0.86_LaCe_0.14_Cu_1-y_(Zn, Ni)_y_O_4_

Zero-field muon-spin-relaxation measurements have been carried out in order to investigate the Zn- and Ni-substitution effects on the Cu-spin dynamics in the electron-doped Pr_0.86_LaCe_0.14_Cu_1-y_(Zn, Ni)_y_O_4+\alpa-\delta_ with y = 0, 0.01, 0.02, 0.05 and different values of the reduced oxygen content \delta(\delta \le 0.09). For the samples with y = 0 and very small \delta values of \delta < 0.01, a muon-spin precession due to the formation of a long-range antiferromagnetic order has been observed at low temperatures below \~ 5 K. For the moderately oxygen-reduced samples of 0.01 \le \delta \le 0.09, on the contrary, no muon-spin precession has been observed and the temperature dependence of the spectra is similar to one another regardless of the y value. That is, no impurity-induced slowing down of the Cu-spin fluctuations has been detected, which is very different from the results of the hole-doped high-T_c_ cuprates. The reason is discussed.Comment: 13 pages, 2 figures, Proceedings of ISS2004 (to be published in Physica C

In-plane anisotropy on the transport properties in the modulated Bi_2O_2-based conductors Bi-2212 and Bi-Sr-Co-O

We investigated the in-plane anisotropy on the resistivity and thermopower of the Bi_2Sr_2CaCu_2O_{8+\delta} (Bi-2212) and Bi-Sr-Co-O (BiCo) single crystals. In Bi-2212, the b-axis resistivity is higher than the a-axis resistivity, and is expressed as a sum of the a-axis resistivity and an additional residual resistivity. A downward deviation due to pseudogap is observed below a characteristic temperature T^*, which is isotropic in the form of conductivity. These results suggest that the modulation structure along the b-axis works as an anisotropic scattering center, but does not affect the pseudogap formation. On the other hand, the anisotropy of the resistivity and the thermopower in Pb-doped BiCo is substantial, probably owing to the misfit structure between the hexagonal CoO_2 layer and the rock salt Bi_2O_2 layer. However, the anisotropy in the resistivity in Pb-free BiCo is very small, suggesting that the in-plane anisotropy is averaged by the modulation structure, whose direction is tilted by 45 deg from the a- and b-axes.Comment: 4pages 5 figures, Proceedings of ISS2001, Physica C (in press

Development of Cu-spin correlation in Bi_1.74_Pb_0.38_Sr_1.88_Cu_1-y_Zn_y_O_6+d_ high-temperature superconductors observed by muon spin relaxation

A systematic muon-spin-relaxation study in Bi-2201 high-Tc cuprates has revealed for the first time that the Cu-spin correlation (CSC) is developed at low temperatures below 2 K in a wide range of hole concentration where superconductivity appears. The CSC tends to become weak gradually with increasing hole-concentration. Moreover, CSC has been enhanced through the 3% substitution of Zn for Cu. These results are quite similar to those observed in La-214 high-Tc cuprates. Accordingly, it has been suggested that the intimate relation between the so-called spin-charge stripe correlations and superconductivity is a universal feature in hole-doped high-Tc cuprates. Furthermore, apparent development of CSC, which is suppressed through the Zn substitution oppositely, has been observed in non-superconducting heavily overdoped samples, being argued in the context of a recently proposed ferromagnetic state in heavily overdoped cuprates.Comment: 6 pages, 5 figure