The sixth Painleve equation arising from D_4^{(1)} hierarchy

The sixth Painleve equation arises from a Drinfel'd-Sokolov hierarchy associated with the affine Lie algebra of type D_4 by similarity reduction.Comment: 14 page

Statistical learning in songbirds:From self-tutoring to song culture

At the onset of vocal development, both songbirds and humans produce variable vocal babbling with broadly distributed acoustic features. Over development, these vocalizations differentiate into the well-defined, categorical signals that characterize adult vocal behaviour. A broadly distributed signal is ideal for vocal exploration, that is, for matching vocal production to the statistics of the sensory input. The developmental transition to categorical signals is a gradual process during which the vocal output becomes differentiated and stable. But does it require categorical input? We trained juvenile zebra finches with playbacks of their own developing song, produced just a few moments earlier, updated continuously over development. Although the vocalizations of these self-tutored (ST) birds were initially broadly distributed, birds quickly developed categorical signals, as fast as birds that were trained with a categorical, adult song template. By contrast, siblings of those birds that received no training (isolates) developed phonological categories much more slowly and never reached the same level of category differentiation as their ST brothers. Therefore, instead of simply mirroring the statistical properties of their sensory input, songbirds actively transform it into distinct categories. We suggest that the early self-generation of phonological categories facilitates the establishment of vocal culture by making the song easier to transmit at the micro level, while promoting stability of shared vocabulary at the group level over generations

Complex sequencing rules of birdsong can be explained by simple hidden Markov processes

Complex sequencing rules observed in birdsongs provide an opportunity to investigate the neural mechanism for generating complex sequential behaviors. To relate the findings from studying birdsongs to other sequential behaviors, it is crucial to characterize the statistical properties of the sequencing rules in birdsongs. However, the properties of the sequencing rules in birdsongs have not yet been fully addressed. In this study, we investigate the statistical propertiesof the complex birdsong of the Bengalese finch (Lonchura striata var. domestica). Based on manual-annotated syllable sequences, we first show that there are significant higher-order context dependencies in Bengalese finch songs, that is, which syllable appears next depends on more than one previous syllable. This property is shared with other complex sequential behaviors. We then analyze acoustic features of the song and show that higher-order context dependencies can be explained using first-order hidden state transition dynamics with redundant hidden states. This model corresponds to hidden Markov models (HMMs), well known statistical models with a large range of application for time series modeling. The song annotation with these models with first-order hidden state dynamics agreed well with manual annotation, the score was comparable to that of a second-order HMM, and surpassed the zeroth-order model (the Gaussian mixture model (GMM)), which does not use context information. Our results imply that the hierarchical representation with hidden state dynamics may underlie the neural implementation for generating complex sequences with higher-order dependencies

Devil's staircase transition of the electronic structures in CeSb

Solids with competing interactions often undergo complex phase transitions with a variety of long-periodic modulations. Among such transition, devil's staircase is the most complex phenomenon, and for it, CeSb is the most famous material, where a number of the distinct phases with long-periodic magnetostructures sequentially appear below the Neel temperature. An evolution of the low-energy electronic structure going through the devil's staircase is of special interest, which has, however, been elusive so far despite the 40-years of intense researches. Here we use bulk-sensitive angle-resolved photoemission spectroscopy and reveal the devil's staircase transition of the electronic structures. The magnetic reconstruction dramatically alters the band dispersions at each transition. We moreover find that the well-defined band picture largely collapses around the Fermi energy under the long-periodic modulation of the transitional phase, while it recovers at the transition into the lowest-temperature ground state. Our data provide the first direct evidence for a significant reorganization of the electronic structures and spectral functions occurring during the devil's staircase.Comment: 22 pages, 5 figure

Dynamic Expression of Cadherins Regulates Vocal Development in a Songbird

BACKGROUND: Since, similarly to humans, songbirds learn their vocalization through imitation during their juvenile stage, they have often been used as model animals to study the mechanisms of human verbal learning. Numerous anatomical and physiological studies have suggested that songbirds have a neural network called 'song system' specialized for vocal learning and production in their brain. However, it still remains unknown what molecular mechanisms regulate their vocal development. It has been suggested that type-II cadherins are involved in synapse formation and function. Previously, we found that type-II cadherin expressions are switched in the robust nucleus of arcopallium from cadherin-7-positive to cadherin-6B-positive during the phase from sensory to sensorimotor learning stage in a songbird, the Bengalese finch. Furthermore, in vitro analysis using cultured rat hippocampal neurons revealed that cadherin-6B enhanced and cadherin-7 suppressed the frequency of miniature excitatory postsynaptic currents via regulating dendritic spine morphology. METHODOLOGY/PRINCIPAL FINDINGS: To explore the role of cadherins in vocal development, we performed an in vivo behavioral analysis of cadherin function with lentiviral vectors. Overexpression of cadherin-7 in the juvenile and the adult stages resulted in severe defects in vocal production. In both cases, harmonic sounds typically seen in the adult Bengalese finch songs were particularly affected. CONCLUSIONS/SIGNIFICANCE: Our results suggest that cadherins control vocal production, particularly harmonic sounds, probably by modulating neuronal morphology of the RA nucleus. It appears that the switching of cadherin expressions from sensory to sensorimotor learning stage enhances vocal production ability to make various types of vocalization that is essential for sensorimotor learning in a trial and error manner