Cluster synchronization in an ensemble of neurons interacting through chemical synapses

In networks of periodically firing spiking neurons that are interconnected with chemical synapses, we analyze cluster state, where an ensemble of neurons are subdivided into a few clusters, in each of which neurons exhibit perfect synchronization. To clarify stability of cluster state, we decompose linear stability of the solution into two types of stabilities: stability of mean state and stabilities of clusters. Computing Floquet matrices for these stabilities, we clarify the total stability of cluster state for any types of neurons and any strength of interactions even if the size of networks is infinitely large. First, we apply this stability analysis to investigating synchronization in the large ensemble of integrate-and-fire (IF) neurons. In one-cluster state we find the change of stability of a cluster, which elucidates that in-phase synchronization of IF neurons occurs with only inhibitory synapses. Then, we investigate entrainment of two clusters of IF neurons with different excitability. IF neurons with fast decaying synapses show the low entrainment capability, which is explained by a pitchfork bifurcation appearing in two-cluster state with change of synapse decay time constant. Second, we analyze one-cluster state of Hodgkin-Huxley (HH) neurons and discuss the difference in synchronization properties between IF neurons and HH neurons.Comment: Notation for Jacobi matrix is changed. Accepted for publication in Phys. Rev.

Chaos synchronization in gap-junction-coupled neurons

Depending on temperature the modified Hodgkin-Huxley (MHH) equations exhibit a variety of dynamical behavior including intrinsic chaotic firing. We analyze synchronization in a large ensemble of MHH neurons that are interconnected with gap junctions. By evaluating tangential Lyapunov exponents we clarify whether synchronous state of neurons is chaotic or periodic. Then, we evaluate transversal Lyapunov exponents to elucidate if this synchronous state is stable against infinitesimal perturbations. Our analysis elucidates that with weak gap junctions, stability of synchronization of MHH neurons shows rather complicated change with temperature. We, however, find that with strong gap junctions, synchronous state is stable over the wide range of temperature irrespective of whether synchronous state is chaotic or periodic. It turns out that strong gap junctions realize the robust synchronization mechanism, which well explains synchronization in interneurons in the real nervous system.Comment: Accepted for publication in Phys. Rev.

The Mixed State of Charge-Density-Wave in a Ring-Shaped Single Crystals

Charge-density-wave (CDW) phase transition in a ring-shaped crystals, recently synthesized by Tanda et al. [Nature, 417, 397 (2002)], is studied based on a mean-field-approximation of Ginzburg-Landau free energy. It is shown that in a ring-shaped crystals CDW undergoes frustration due to the curvature (bending) of the ring (geometrical frustration) and, thus, forms a mixed state analogous to what a type-II superconductor forms under a magnetic field. We discuss the nature of the phase transition in the ring-CDW in relation to recent experiments.Comment: 6 pages, 4 figure

On the Canonical Formalism for a Higher-Curvature Gravity

Following the method of Buchbinder and Lyahovich, we carry out a canonical formalism for a higher-curvature gravity in which the Lagrangian density ${\cal L}$ is given in terms of a function of the salar curvature $R$ as ${\cal L}=\sqrt{-\det g_{\mu\nu}}f(R)$. The local Hamiltonian is obtained by a canonical transformation which interchanges a pair of the generalized coordinate and its canonical momentum coming from the higher derivative of the metric.Comment: 11 pages, no figures, Latex fil

Domain-wall structure of a classical Heisenberg ferromagnet on a Mobius strip

We study theoretically the structure of domain walls in ferromagnetic states on Mobius strips. A two-dimensional classical Heisenberg ferromagnet with single-site anisotropy is treated within a mean-field approximation by taking into account the boundary condition to realize the Mobius geometry. It is found that two types of domain walls can be formed, namely, parallel or perpendicular to the circumference, and that the relative stability of these domain walls is sensitive to the change in temperature and an applied magnetic field. The magnetization has a discontinuity as a function of temperature and the external field.Comment: 7 pages, 10 figures; published versio

Near-Infrared Coronagraphic Observations of the T Tauri Binary System UY Aur

We present a near-infrared image of UY Aur, a 0.9" separated binary system, using the Coronagraphic Imager with Adaptive Optics on the Subaru Telescope. Thanks to adaptive optics, the spatial resolution of our image was ~0.1" in the full width at half maximum of the point spread function, the highest achieved. By comparison with previous measurements, we estimated that the orbital period is ~1640 yrs and the total mass of the binary is ~1.73 solar mass. The observed H-band magnitude of the secondary varies by as much as 1.3 mag within a decade, while that of the primary is rather stable. This inconstancy may arise from photospheric variability caused by an uneven accretion rate or from the rotation of the secondary. We detected a half-ring shaped circumbinary disk around the binary with a bright southwest part but a barely detectable northeast portion. The brightness ratio is ~57. Its inner radius and inclination are about 520 AU and 42, respectively. The disk is not uniform but has remarkable features, including a clumpy structure along the disk, circumstellar material inside the inner cavity, and an extended armlike structure. The circumstellar material inside the cavity probably corresponds to a clump or material accreting from the disk onto the binary. The armlike structure is a part of the disk, created by the accretion from the outer region of the disk or encounters with other stellar systems.Comment: 16 pages, 6 figures; accepted for publication in A

Oscillator neural network model with distributed native frequencies

We study associative memory of an oscillator neural network with distributed native frequencies. The model is based on the use of the Hebb learning rule with random patterns ($\xi_i^{\mu}=\pm 1$), and the distribution function of native frequencies is assumed to be symmetric with respect to its average. Although the system with an extensive number of stored patterns is not allowed to get entirely synchronized, long time behaviors of the macroscopic order parameters describing partial synchronization phenomena can be obtained by discarding the contribution from the desynchronized part of the system. The oscillator network is shown to work as associative memory accompanied by synchronized oscillations. A phase diagram representing properties of memory retrieval is presented in terms of the parameters characterizing the native frequency distribution. Our analytical calculations based on the self-consistent signal-to-noise analysis are shown to be in excellent agreement with numerical simulations, confirming the validity of our theoretical treatment.Comment: 9 pages, revtex, 6 postscript figures, to be published in J. Phys.

The Discovery of a Very Narrow-Line Star Forming Obat a Redshift of 5.66ject

We report on the discovery of a very narrow-line star forming object beyond redshift of 5. Using the prime-focus camera, Suprime-Cam, on the 8.2 m Subaru telescope together with a narrow-passband filter centered at $\lambda_{\rm c}$ = 8150 \AA with passband of $\Delta\lambda$ = 120 \AA, we have obtained a very deep image of the field surrounding the quasar SDSSp J104433.04$-$012502.2 at a redshift of 5.74. Comparing this image with optical broad-band images, we have found an object with a very strong emission line. Our follow-up optical spectroscopy has revealed that this source is at a redshift of $z=5.655\pm0.002$, forming stars at a rate $\sim 13 ~ h_{0.7}^{-2} ~ M_\odot$ yr$^{-1}$. Remarkably, the velocity dispersion of Ly$\alpha$-emitting gas is only 22 km s$^{-1}$. Since a blue half of the Ly$\alpha$ emission could be absorbed by neutral hydrogen gas, perhaps in the system, a modest estimate of the velocity dispersion may be $\gtrsim$ 44 km s$^{-1}$. Together with a linear size of 7.7 $h_{0.7}^{-1}$ kpc, we estimate a lower limit of the dynamical mass of this object to be $\sim 2 \times 10^9 M_\odot$. It is thus suggested that LAE J1044$-$0123 is a star-forming dwarf galaxy (i.e., a subgalactic object or a building block) beyond redshift 5 although we cannot exclude a possibility that most Ly$\alpha$ emission is absorbed by the red damping wing of neutral intergalactic matter.Comment: 6 pages, 2 figures. ApJ Letters, in pres

Interface superconductivity in the eutectic Sr2RuO4-Ru: 3-K phase of Sr2RuO4

The eutectic system Sr2RuO4-Ru is referred to as the 3-K phase of the spin-triplet supeconductor Sr2RuO4 because of its enhanced superconducting transition temperature Tc of ~3 K. We have investigated the field-temperature (H-T) phase diagram of the 3-K phase for fields parallel and perpendicular to the ab-plane of Sr2RuO4, using out-of-plane resistivity measurements. We have found an upturn curvature in the Hc2(T) curve for H // c, and a rather gradual temperature dependence of Hc2 close to Tc for both H // ab and H // c. We have also investigated the dependence of Hc2 on the angle between the field and the ab-plane at several temperatures. Fitting the Ginzburg-Landau effective-mass model apparently fails to reproduce the angle dependence, particularly near H // c and at low temperatures. We propose that all of these charecteric features can be explained, at least in a qualitative fashion, on the basis of a theory by Sigrist and Monien that assumes surface superconductivity with a two-component order parameter occurring at the interface between Sr2RuO4 and Ru inclusions. This provides evidence of the chiral state postulated for the 1.5-K phase by several experiments.Comment: 7 pages and 5 figs; accepted for publication in Phys. Rev.

Comprehensive analysis of liver and blood miRNA in precancerous conditions

Streptozotocin administration to mice (STZ-mice) induces type I diabetes and hepatocellular carcinoma (HCC). We attempted to elucidate the carcinogenic mechanism and the miRNA expression status in the liver and blood during the precancerous state. Serum and liver tissues were collected from STZ-mice and non-treated mice (CTL-mice) at 6, 10, and 12 W. The exosome enriched fraction extracted from serum was used. Hepatic histological examination and hepatic and exosomal miRNA expression analysis were serially performed using next-generation sequencing (NGS). Human miRNA expression analysis of chronic hepatitis liver tissue and exosomes, which were collected before starting the antiviral treatment, were also performed. No inflammation or fibrosis was found in the liver of CTL-mice during the observation period. In STZ-mice, regeneration and inflammation of hepatocytes was found at 6 W and nodules of atypical hepatocytes were found at 10 and 12 W. In the liver tissue, during 6–12 W, the expression levels of let-7f-5p, miR-143-3p, 148a-3p, 191-5p, 192-5p, 21a-5p, 22-3p, 26a-5p, and 92a-3p was significantly increased in STZ-mice, and anti-oncogenes of their target gene candidates were down-regulated. miR-122-5p was also significantly down-regulated in STZ-mice. Fifteen exosomal miRNAs were upregulated in STZ-mice. Six miRNAs (let-7f-5p, miR-10b-5p, 143-3p, 191-5p, 21a-5p, and 26a-5p) were upregulated, similarly to human HCC cases. From the precancerous state, aberrant expression of hepatic miRNAs has already occurred, and then, it can promote carcinogenesis. In exosomes, the expression pattern of common miRNAs between mice and humans before carcinogenesis was observed and can be expected to be developed as a cancer predictive marker