Discontinuous phase transitions of conserved threshold transfer process with deterministic hopping.

The deterministic conserved threshold transfer process, which is a variant of the conserved threshold transfer process modified in a way as that hopping of a particle is to be deterministic, is proposed. The critical behavior of the model is investigated in one, two, and four dimensions. It is found that the order parameter yields a discontinuous transition; i.e., the transition appears to be first ordered in all dimensions considered. The origin of such a discontinuous transition is investigated, considering clustering of active sites and accumulation of critical sites just before the steady state is reached.

Validity of scaling relations in absorbing phase transitions with a conserved field.

The two scaling relations in absorbing phase transitions, nu_||=beta/theta and z=nu_||/nu_(perpendicular), are studied for a conserved lattice gas model. The critical indices calculated elaborately from the all-sample average density of active particles appear to satisfy both relations. However, the exponent nu_(perpendicular) calculated from the surviving samples does not appear to be consistent with the value in the thermodynamic limit. This is in contrast with earlier observations [M. Rossi, Phys. Rev. Lett. 85, 1803 (2000); S. Lübeck and P. C. Heger, Phys. Rev. E. 68, 056102 (2003)], in that the former scaling relation was claimed to be violated.

Universality split in absorbing phase transition with conserved field on fractal lattices.

The universality split in absorbing phase transition between the conserved lattice gas (CLG) model and the conserved threshold transfer process (CTTP) is investigated on a checkerboard fractal and on a Sierpinski gasket. The critical exponents theta, beta, nu||, and z, which are associated with, respectively, the density of active particles in time, the order parameter, the temporal correlation length, and the dynamics of active particles, are elaborately measured for two models on selected fractal lattices. The exponents for the CLG model are found to be distinctly different from those of the CTTP model on a checkerboard fractal, whereas the two models exhibit the same critical behavior on a Sierpinski gasket, indicating that the universality split between the two models occurs only on a checkerboard fractal. Such a universality split is attributed from the dominant hopping mechanisms caused by the intrinsic properties of the underlying fractal lattice.

Absorbing phase transition in a conserved lattice gas model in one dimension.

We investigated the nonequilibrium phase transition of the conserved lattice gas model in one dimension using two update methods: i.e., the sequential update and the parallel update. We measured the critical indices of theta, beta, nu(parallel), and nu(perpendicular), and found that, for a parallel update, the exponents were delicately influenced by the hopping rule of active particles. When the hopping rule was designed to be symmetric, the results were found to be consistent with those of the sequential update. The exponents we obtained were precisely the same as the corresponding results of a recently presented lattice model of two species of particles with a conserved field in one dimension, in contrast with the authors' claim. We also found that one of the scaling relations known for absorbing phase transition is violated.

Phase-model analysis of coupled neuronal oscillators with multiple connections.

Synchronization of the coupled neuronal oscillators with multiple connections of different coupling nature is analyzed using the phase-model reduction method. Each coupling connection contributes to the dynamic behavior of the system in a complex nonlinear fashion. In the phase-model scheme, the contribution of the individual connections can be separated in terms of the effective coupling functions associated with each connection and a linear superposition of them provides the total effective coupling of the coupled system. The case of multiple connections with various conduction time delays is also examined, which is shown to be capable of promoting synchronization over an ensemble of spatially distributed neuronal oscillators in an efficient way.

Bifurcation analysis of mode-locking structure in a Hodgkin-Huxley neuron under sinusoidal current.

Nervous systems under periodic stimuli display rich dynamical states including mode-locking and chaotic responses, which have been a subject of intense studies in neurodynamics. The bifurcation structure of the Hodgkin-Huxley neuron under sinusoidal stimulus is studied in detail. The mechanisms of the firing onset and rich firing dynamics are studied with the help of the codimension-2 bifurcations, which play the role of the organizing center for myriads of saddle-node, period-doubling, and inverse-flip bifurcations forming the boundaries of the complex mode-locking structure. This study provides a useful insight into the organization of similar bifurcation structures in excitable systems such as neurons under periodic forcing.

Bona fide stochastic resonance and multimodality in the stochastic Hodgkin-Huxley neuron.

The phenomena of stochastic resonance (SR) has attracted much attention in the studies of the excitable systems, in particular, the nervous systems under noise. Recently, an alternative SR condition, called the bona fide SR, was proposed for the bistable system under noise, based on the notion of the residence time distribution. As the forcing frequency increases, there exists an optimal resonant frequency. We study the SR in a stochastic Hodgkin-Huxley neuron, which has an inherent natural frequency in addition to the stochastic time scale. We have observed two resonant conditions; one between periodic forcing and natural frequencies, and the other between the periodic forcing and the stochastic frequencies. These resonance conditions show the bona fide stochastic resonance with multimodality. For comparison, we have studied the bona fide SR in the stochastic FitzHugh-Nagumo neuron, where, the multimodality is not observed. The differences in the resonance structure of two neuron models are understood in terms of differences in the phase portraits.

Optimization of methanol biosynthesis from methane using Methylosinus trichosporium OB3b.

Methylosinus trichosporium OB3b oxidized methane to methanol in the presence of a high concentration of Cu2+. Further oxidation of methanol to formaldehyde was prevented by adding 200 mM NaCl which acted as a methanol dehydrogenase H inhibitor. The bacterium, 0.6 mg dry cell ml(-1), in methane/air (1:4, v/v) at 25 degrees C in 12.9 mM phosphate buffer (pH 7) containing 20 mM sodium formate and 200 mM NaCl accumulated 7.7 mM methanol over 36 h.

Orientation tuning and synchronization in the hypercolumn model.

The orientation selectivity in the firing rate of neurons is one of the most well-known properties of neurons in the primary visual cortex. To understand the dynamical mechanism of the orientation tuning, we introduce a biologically plausible network for a hypercolumn and investigate dynamical responses of its columnar activities. Numerical simulations show that the spike activities between excitatory cells in the same column exhibit strong synchronization and sharp orientation selectivity. The tuning curves for the synchronized activities also show orientation selectivity similar to those for the firing rate. The comparison between the two tuning curves for the firing rate and the synchronized activities suggests that the orientation selectivity is strongly correlated with the synchronized activities. We find from the analysis of columnar activities that the orientation selectivity depends strongly upon the inhibitory coupling strength and the synchronization upon the excitatory coupling strength. In particular, we find that at appropriate coupling parameters both sharp orientation selectivity and maximal synchronization can be achieved. This suggests the importance of the balance between the excitatory coupling and the inhibitory coupling in the primary visual cortex for visual information processing.