State Differentiation by Transient Truncation in Coupled Threshold Dynamics

Dynamics with a threshold input--output relation commonly exist in gene, signal-transduction, and neural networks. Coupled dynamical systems of such threshold elements are investigated, in an effort to find differentiation of elements induced by the interaction. Through global diffusive coupling, novel states are found to be generated that are not the original attractor of single-element threshold dynamics, but are sustained through the interaction with the elements located at the original attractor. This stabilization of the novel state(s) is not related to symmetry breaking, but is explained as the truncation of transient trajectories to the original attractor due to the coupling. Single-element dynamics with winding transient trajectories located at a low-dimensional manifold and having turning points are shown to be essential to the generation of such novel state(s) in a coupled system. Universality of this mechanism for the novel state generation and its relevance to biological cell differentiation are briefly discussed.Comment: 8 pages. Phys. Rev. E. in pres

Long transients and cluster size in globally coupled maps

We analyze the asymptotic states in the partially ordered phase of a system of globally coupled logistic maps. We confirm that, regardless of initial conditions, these states consist of a few clusters, and they properly belong in the ordered phase of these systems. The transient times necessary to reach the asymptotic states can be very long, especially very near the transition line separating the ordered and the coherent phases. We find that, where two clusters form, the distribution of their sizes corresponds to windows of regular or narrow-band chaotic behavior in the bifurcation diagram of a system of two degrees of freedom that describes the motion of two clusters, where the size of one cluster acts as a bifurcation parameter.Comment: To appear in Europhysics Letter

Dynamics of Coupling Functions in Globally Coupled Maps: Size, Periodicity and Stability of Clusters

It is shown how different globally coupled map systems can be analyzed under a common framework by focusing on the dynamics of their respective global coupling functions. We investigate how the functional form of the coupling determines the formation of clusters in a globally coupled map system and the resulting periodicity of the global interaction. The allowed distributions of elements among periodic clusters is also found to depend on the functional form of the coupling. Through the analogy between globally coupled maps and a single driven map, the clustering behavior of the former systems can be characterized. By using this analogy, the dynamics of periodic clusters in systems displaying a constant global coupling are predicted; and for a particular family of coupling functions, it is shown that the stability condition of these clustered states can straightforwardly be derived.Comment: 12 pp, 5 figs, to appear in PR

Periodicity Manifestations in the Turbulent Regime of Globally Coupled Map Lattice

We revisit the globally coupled map lattice (GCML). We show that in the so called turbulent regime various periodic cluster attractor states are formed even though the coupling between the maps are very small relative to the non-linearity in the element maps. Most outstanding is a maximally symmetric three cluster attractor in period three motion (MSCA) due to the foliation of the period three window of the element logistic maps. An analytic approach is proposed which explains successfully the systematics of various periodicity manifestations in the turbulent regime. The linear stability of the period three cluster attractors is investigated.Comment: 34 pages, 8 Postscript figures, all in GCML-MSCA.Zi

Molecular Discreteness in Reaction-Diffusion Systems Yields Steady States Not Seen in the Continuum Limit

We investigate the effects of spatial discreteness of molecules in reaction-diffusion systems. It is found that discreteness within the so called Kuramoto length can lead to a localization of molecules, resulting in novel steady states that do not exist in the continuous case. These novel states are analyzed theoretically as the fixed points of accelerated localized reactions, an approach that was verified to be in good agreement with stochastic particle simulations. The relevance of this discreteness-induced state to biological intracellular processes is discussed.Comment: 5 pages, 3 figures, revtex

Collective motions in globally coupled tent maps with stochastic updating

We study a generalization of globally coupled maps, where the elements are updated with probability $p$. When $p$ is below a threshold $p_c$, the collective motion vanishes and the system is the stationary state in the large size limit. We present the linear stability analysis.Comment: 6 pages including 5 figure

Overlap/Domain-wall reweighting

We investigate the eigenvalues of nearly chiral lattice Dirac operators constructed with five-dimensional implementations. Allowing small violation of the Ginsparg-Wilson relation, the HMC simulation is made much faster while the eigenvalues are not significantly affected. We discuss the possibility of reweighting the gauge configurations generated with domain-wall fermions to those of exactly chiral lattice fermions.Comment: 7 pages, 3 figures, presented at the 31st International Symposium on Lattice Field Theory (Lattice 2013), 29 July-3 August 2013, Mainz, German

WZWZ Production at eγe\gamma Colliders and Anomalous Quartic WWZγWWZ\gamma Coupling

We investigate the constraints on the anomalous quartic $W^{+}W^{-}Z\gamma$ gauge boson coupling through the process $e^{-}\gamma\to \nu_{e}W^{-}Z$. Considering incoming beam polarizations and the longitudinal and transverse polarization states of the final W and Z boson we find 95% confidence level limits on the anomalous coupling parameter $a_{n}$ with an integrated luminosity of 500 $fb^{-1}$ and $\sqrt{s}$=0.5, 1 TeV energies. We show that initial beam and final state polarizations improve the sensitivity to the anomalous coupling by up to factors of 2 - 3.5 depending on the energy.Comment: published versio