STUDIES OF THE MECHANISM OF ACTION OF COBAMIDE COENZYMES

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/73404/1/j.1749-6632.1964.tb45046.x.pd

Dynamical mean-filed approximation to small-world networks of spiking neurons: From local to global, and/or from regular to random couplings

By extending a dynamical mean-field approximation (DMA) previously proposed by the author [H. Hasegawa, Phys. Rev. E {\bf 67}, 41903 (2003)], we have developed a semianalytical theory which takes into account a wide range of couplings in a small-world network. Our network consists of noisy $N$-unit FitzHugh-Nagumo (FN) neurons with couplings whose average coordination number $Z$ may change from local ($Z \ll N$) to global couplings ($Z=N-1$) and/or whose concentration of random couplings $p$ is allowed to vary from regular ($p=0$) to completely random (p=1). We have taken into account three kinds of spatial correlations: the on-site correlation, the correlation for a coupled pair and that for a pair without direct couplings. The original $2 N$-dimensional {\it stochastic} differential equations are transformed to 13-dimensional {\it deterministic} differential equations expressed in terms of means, variances and covariances of state variables. The synchronization ratio and the firing-time precision for an applied single spike have been discussed as functions of $Z$ and $p$. Our calculations have shown that with increasing $p$, the synchronization is {\it worse} because of increased heterogeneous couplings, although the average network distance becomes shorter. Results calculated by out theory are in good agreement with those by direct simulations.Comment: 19 pages, 2 figures: accepted in Phys. Rev. E with minor change

Nonlocal mechanism for cluster synchronization in neural circuits

The interplay between the topology of cortical circuits and synchronized activity modes in distinct cortical areas is a key enigma in neuroscience. We present a new nonlocal mechanism governing the periodic activity mode: the greatest common divisor (GCD) of network loops. For a stimulus to one node, the network splits into GCD-clusters in which cluster neurons are in zero-lag synchronization. For complex external stimuli, the number of clusters can be any common divisor. The synchronized mode and the transients to synchronization pinpoint the type of external stimuli. The findings, supported by an information mixing argument and simulations of Hodgkin Huxley population dynamic networks with unidirectional connectivity and synaptic noise, call for reexamining sources of correlated activity in cortex and shorter information processing time scales.Comment: 8 pges, 6 figure

Theory of Interaction of Memory Patterns in Layered Associative Networks

A synfire chain is a network that can generate repeated spike patterns with millisecond precision. Although synfire chains with only one activity propagation mode have been intensively analyzed with several neuron models, those with several stable propagation modes have not been thoroughly investigated. By using the leaky integrate-and-fire neuron model, we constructed a layered associative network embedded with memory patterns. We analyzed the network dynamics with the Fokker-Planck equation. First, we addressed the stability of one memory pattern as a propagating spike volley. We showed that memory patterns propagate as pulse packets. Second, we investigated the activity when we activated two different memory patterns. Simultaneous activation of two memory patterns with the same strength led the propagating pattern to a mixed state. In contrast, when the activations had different strengths, the pulse packet converged to a two-peak state. Finally, we studied the effect of the preceding pulse packet on the following pulse packet. The following pulse packet was modified from its original activated memory pattern, and it converged to a two-peak state, mixed state or non-spike state depending on the time interval

Exact solution of a linear molecular motor model driven by two-step fluctuations and subject to protein friction

We investigate by analytical means the stochastic equations of motion of a linear molecular motor model based on the concept of protein friction. Solving the coupled Langevin equations originally proposed by Mogilner et al. (A. Mogilner et al., Phys. Lett. {\bf 237}, 297 (1998)), and averaging over both the two-step internal conformational fluctuations and the thermal noise, we present explicit, analytical expressions for the average motion and the velocity-force relationship. Our results allow for a direct interpretation of details of this motor model which are not readily accessible from numerical solutions. In particular, we find that the model is able to predict physiologically reasonable values for the load-free motor velocity and the motor mobility.Comment: 12 pages revtex, 6 eps-figure

Supermode suppression to below-130 dBc/Hz in a 10 GHz harmonically mode-locked external sigma cavity semiconductor laser

We demonstrate supermode suppression to levels below - 125 dBc/Hz and - 132 dBc/Hz using Fabry-Perot etalons with finesse values of 180 and 650, respectively, for a 10 GHz harmonically mode-locked external sigma cavity semiconductor laser. The laser was hybridly mode-locked using direct electrical modulation in a compact package without the need for an external modulator

Sparse and Dense Encoding in Layered Associative Network of Spiking Neurons

A synfire chain is a simple neural network model which can propagate stable synchronous spikes called a pulse packet and widely researched. However how synfire chains coexist in one network remains to be elucidated. We have studied the activity of a layered associative network of Leaky Integrate-and-Fire neurons in which connection we embed memory patterns by the Hebbian Learning. We analyzed their activity by the Fokker-Planck method. In our previous report, when a half of neurons belongs to each memory pattern (memory pattern rate $F=0.5$), the temporal profiles of the network activity is split into temporally clustered groups called sublattices under certain input conditions. In this study, we show that when the network is sparsely connected ($F<0.5$), synchronous firings of the memory pattern are promoted. On the contrary, the densely connected network ($F>0.5$) inhibit synchronous firings. The sparseness and denseness also effect the basin of attraction and the storage capacity of the embedded memory patterns. We show that the sparsely(densely) connected networks enlarge(shrink) the basion of attraction and increase(decrease) the storage capacity

Nonlinear Impurity Modes in Homogeneous and Periodic Media

We analyze the existence and stability of nonlinear localized waves described by the Kronig-Penney model with a nonlinear impurity. We study the properties of such waves in a homogeneous medium, and then analyze new effects introduced by periodicity of the medium parameters. In particular, we demonstrate the existence of a novel type of stable nonlinear band-gap localized states, and also reveal an important physical mechanism of the oscillatory wave instabilities associated with the band-gap wave resonances.Comment: 11 pages, 3 figures; To be published in: Proceedings of the NATO Advanced Research Workshop "Nonlinearity and Disorder: Theory and Applications" (Tashkent, 2-6 Oct, 2000) Editors: P.L. Christiansen and F.K. Abdullaev (Kluwer, 2001