Extension of Information Geometry to Non-statistical Systems: Some Examples

Our goal is to extend information geometry to situations where statistical modeling is not obvious. The setting is that of modeling experimental data. Quite often the data are not of a statistical nature. Sometimes also the model is not a statistical manifold. An example of the former is the description of the Bose gas in the grand canonical ensemble. An example of the latter is the modeling of quantum systems with density matrices. Conditional expectations in the quantum context are reviewed. The border problem is discussed: through conditioning the model point shifts to the border of the differentiable manifold.Comment: 8 pages, to be published in the proceedings of GSI2015, Lecture Notes in Computer Science, Springe

Morphological Changes in the Vestibular Epithelia and Ganglion Induced by Ototoxic Drug

The morphological changes of the vestibular sensory epithelia and the vestibular ganglions induced by Gentamicin (GM) were investigated using scanning electron microscope, transmission electron microscope and light microscope. The guinea pigs were injected with a single application of 4 mg (0.1ml) of GM into the middle ear through the tympanic membrane. The vestibular organs and the ganglions were observed up to 6 months after the treatment. Four days after the injection, fused, ballooned and missing cilia were observed in the vestibular sensory epithelia. These changes progressed and extended toward the periphery of the crista and the macula. The changes of the vestibular ganglions were first observed one month after the treatment. The degenerative process started from destruction of the mitochondrial cristae and vacuolization of the cytoplasm in the Schwann cell. The next step of the change was dissociation of the myelin sheath around the ganglion cell. The cytoplasmic organelles in the ganglion cell gradually deteriorated. At the later stage, the myelin sheath around the ganglion cell disappeared and the number of the cell reduced. Furthermore, the myelin sheath of the nerve fiber was dissociated. In this study the signs of the vestibular ganglion damage were later than that of the vestibular organ. However, we thought the changes in the ganglion are probably due to direct influence of GM, since the degeneration was found to develop in a relatively short period

Semiclassical properties and chaos degree for the quantum baker's map

We study the chaotic behaviour and the quantum-classical correspondence for the baker's map. Correspondence between quantum and classical expectation values is investigated and it is numerically shown that it is lost at the logarithmic timescale. The quantum chaos degree is computed and it is demonstrated that it describes the chaotic features of the model. The correspondence between classical and quantum chaos degrees is considered.Comment: 30 pages, 4 figures, accepted for publication in J. Math. Phy