Synchronizations in small-world networks of spiking neurons: Diffusive versus sigmoid couplings

By using a semi-analytical dynamical mean-field approximation previously proposed by the author [H. Hasegawa, Phys. Rev. E, {\bf 70}, 066107 (2004)], we have studied the synchronization of stochastic, small-world (SW) networks of FitzHugh-Nagumo neurons with diffusive couplings. The difference and similarity between results for {\it diffusive} and {\it sigmoid} couplings have been discussed. It has been shown that with introducing the weak heterogeneity to regular networks, the synchronization may be slightly increased for diffusive couplings, while it is decreased for sigmoid couplings. This increase in the synchronization for diffusive couplings is shown to be due to their local, negative feedback contributions, but not due to the shorten average distance in SW networks. Synchronization of SW networks depends not only on their structure but also on the type of couplings.Comment: 17 pages, 8 figures, accepted in Phys. Rev. E with some change

Relevant gluonic energy scale of spontaneous chiral symmetry breaking from lattice QCD

We analyze which momentum component of the gluon field induces spontaneous chiral symmetry breaking in lattice QCD. After removing the high-momentum or low-momentum component of the gluon field, we calculate the chiral condensate and observe the roles of these momentum components. The chiral condensate is found to be drastically reduced by removing the zero-momentum gluon. The reduction is about 40% of the total in our calculation condition. The nonzero-momentum infrared gluon also has a sizable contribution to the chiral condensate. From the Banks-Casher relation, this result reflects the nontrivial relation between the infrared gluon and the zero-mode quark

Thermodynamic black di-rings

Previously the five dimensional $S^1$-rotating black rings have been superposed in a concentric way by some solitonic methods, and regular systems of two $S^1$-rotating black rings were constructed by the authors and then Evslin and Krishnan (we called these solutions "black di-rings"). In this place we show some characteristics of the solutions of five dimensional black di-rings, especially in thermodynamic equilibrium. After the summary of the di-ring expressions and their physical quantities, first we comment on the equivalence of the two different solution sets of the black di-rings. Then the existence of thermodynamic black di-rings is shown, in which both isothermality and isorotation between the inner black ring and the outer black ring are realized. We also give detailed analysis of peculiar properties of the thermodynamic black di-ring including discussion about a certain kind of thermodynamic stability (instability) of the system.Comment: 26 pages,10 figures; references added, typos corredte

Classical small systems coupled to finite baths

We have studied the properties of a classical $N_S$-body system coupled to a bath containing $N_B$-body harmonic oscillators, employing an $(N_S+N_B)$ model which is different from most of the existing models with $N_S=1$. We have performed simulations for $N_S$-oscillator systems, solving $2(N_S+N_B)$ first-order differential equations with $N_S \simeq 1 - 10$ and $N_B \simeq 10 - 1000$, in order to calculate the time-dependent energy exchange between the system and the bath. The calculated energy in the system rapidly changes while its envelope has a much slower time dependence. Detailed calculations of the stationary energy distribution of the system $f_S(u)$ ($u$: an energy per particle in the system) have shown that its properties are mainly determined by $N_S$ but weakly depend on $N_B$. The calculated $f_S(u)$ is analyzed with the use of the $\Gamma$ and $q$-$\Gamma$ distributions: the latter is derived with the superstatistical approach (SSA) and microcanonical approach (MCA) to the nonextensive statistics, where $q$ stands for the entropic index. Based on analyses of our simulation results, a critical comparison is made between the SSA and MCA. Simulations have been performed also for the $N_S$-body ideal-gas system. The effect of the coupling between oscillators in the bath has been examined by additional ($N_S+N_B$) models which include baths consisting of coupled linear chains with periodic and fixed-end boundary conditions.Comment: 30 pages, 16 figures; the final version accepted in Phys. Rev.

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

Feedback cooling of atomic motion in cavity QED

We consider the problem of controlling the motion of an atom trapped in an optical cavity using continuous feedback. In order to realize such a scheme experimentally, one must be able to perform state estimation of the atomic motion in real time. While in theory this estimate may be provided by a stochastic master equation describing the full dynamics of the observed system, integrating this equation in real time is impractical. Here we derive an approximate estimation equation for this purpose, and use it as a drive in a feedback algorithm designed to cool the motion of the atom. We examine the effectiveness of such a procedure using full simulations of the cavity QED system, including the quantized motion of the atom in one dimension.Comment: 22 pages, 17 figure

LaCo2B2: A Co-based layered superconductor with a ThCr2Si2-type structure

LaCo2B2 with a ThCr2Si2-type structure composed of alternately stacked La and CoB layers exhibits metallic electrical conductivity and Pauli paramagnetic behavior down to 2K. Bulk superconductivity with a Tc of ~4K emerges upon substitution with dopant elements; i.e., isovalent substitution to form (La1-xYx)Co2B2, or aliovalent substitution to form La(Co1-xFex)2B2. Highly covalent bonding between Co 3d and B 2p levels in the CoB layers, which is caused by the B 2p level being shallower than the Fermi level, removes magnetic ordering from Co 3d electrons even in the undoped samples.Comment: 3 figure

Quantum feedback control of atomic motion in an optical cavity

We study quantum feedback cooling of atomic motion in an optical cavity. We design a feedback algorithm that can cool the atom to the ground state of the optical potential with high efficiency despite the nonlinear nature of this problem. An important ingredient is a simplified state-estimation algorithm, necessary for a real-time implementation of the feedback loop. We also describe the critical role of parity dynamics in the cooling process and present a simple theory that predicts the achievable steady-state atomic energies