Modification of a neuronal network direction using stepwise photo-thermal etching of an agarose architecture

Control over spatial distribution of individual neurons and the pattern of neural network provides an important tool for studying information processing pathways during neural network formation. Moreover, the knowledge of the direction of synaptic connections between cells in each neural network can provide detailed information on the relationship between the forward and feedback signaling. We have developed a method for topographical control of the direction of synaptic connections within a living neuronal network using a new type of individual-cell-based on-chip cell-cultivation system with an agarose microchamber array (AMCA). The advantages of this system include the possibility to control positions and number of cultured cells as well as flexible control of the direction of elongation of axons through stepwise melting of narrow grooves. Such micrometer-order microchannels are obtained by photo-thermal etching of agarose where a portion of the gel is melted with a 1064-nm infrared laser beam. Using this system, we created neural network from individual Rat hippocampal cells. We were able to control elongation of individual axons during cultivation (from cells contained within the AMCA) by non-destructive stepwise photo-thermal etching. We have demonstrated the potential of our on-chip AMCA cell cultivation system for the controlled development of individual cell-based neural networks

Crystalizing the Spinon Basis

The quasi-particle structure of the higher spin XXZ model is studied. We obtained a new description of crystals associated with the level $k$ integrable highest weight $U_q(\widehat{sl_2})$ modules in terms of the creation operators at $q=0$ (the crystaline spinon basis). The fermionic character formulas and the Yangian structure of those integrable modules naturally follow from this description. We have also derived the conjectural formulas for the multi quasi-particle states at $q=0$.Comment: 25 pages, late

Emotional Communication in Finger Braille

We describe analyses of the features of emotions (neutral, joy, sadness, and anger) expressed by Finger Braille interpreters and subsequently examine the effectiveness of emotional expression and emotional communication between people unskilled in Finger Braille. The goal is to develop a Finger Braille system to teach emotional expression and a system to recognize emotion. The results indicate the following features of emotional expression by interpreters. The durations of the code of joy were significantly shorter than the durations of the other emotions, the durations of the code of sadness were significantly longer, and the finger loads of anger were significantly larger. The features of emotional expression by unskilled subjects were very similar to those of the interpreters, and the coincidence ratio of emotional communication was 75.1%. Therefore, it was confirmed that people unskilled in Finger Braille can express and communicate emotions using this communication medium

Tau functions in combinatorial Bethe ansatz

We introduce ultradiscrete tau functions associated with rigged configurations for A^{(1)}_n. They satisfy an ultradiscrete version of the Hirota bilinear equation and play a role analogous to a corner transfer matrix for the box-ball system. As an application, we establish a piecewise linear formula for the Kerov-Kirillov-Reshetikhin bijection in the combinatorial Bethe ansatz. They also lead to general N-soliton solutions of the box-ball system.Comment: 52 page

Five-dimensional AGT Conjecture and the Deformed Virasoro Algebra

We study an analog of the AGT relation in five dimensions. We conjecture that the instanton partition function of 5D N=1 pure SU(2) gauge theory coincides with the inner product of the Gaiotto-like state in the deformed Virasoro algebra. In four dimensional case, a relation between the Gaiotto construction and the theory of Braverman and Etingof is also discussed.Comment: 12 pages, reference added, minor corrections (typos, notation changes, etc

Character Formulae of sl^n\hat{sl}_n-Modules and Inhomogeneous Paths

Let B_{(l)} be the perfect crystal for the l-symmetric tensor representation of the quantum affine algebra U'_q(\hat{sl(n)}). For a partition mu = (mu_1,...,mu_m), elements of the tensor product B_{(mu_1)} \otimes ... \otimes B_{(mu_m)} can be regarded as inhomogeneous paths. We establish a bijection between a certain large mu limit of this crystal and the crystal of an (generally reducible) integrable U_q(\hat{sl(n)})-module, which forms a large family depending on the inhomogeneity of mu kept in the limit. For the associated one dimensional sums, relations with the Kostka-Foulkes polynomials are clarified, and new fermionic formulae are presented. By combining their limits with the bijection, we prove or conjecture several formulae for the string functions, branching functions, coset branching functions and spinon character formula of both vertex and RSOS types.Comment: 42 pages, LaTeX2.0