Spontaneous structure formation in a network of chaotic units with variable connection strengths

As a model of temporally evolving networks, we consider a globally coupled logistic map with variable connection weights. The model exhibits self-organization of network structure, reflected by the collective behavior of units. Structural order emerges even without any inter-unit synchronization of dynamics. Within this structure, units spontaneously separate into two groups whose distinguishing feature is that the first group possesses many outwardly-directed connections to the second group, while the second group possesses only few outwardly-directed connections to the first. The relevance of the results to structure formation in neural networks is briefly discussed.Comment: 4 pages, 3 figures, REVTe

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

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

Homogeneous Connectivity of Potential Energy Network in a Solidlike State of Water Cluster

A novel route to the exponential trapping-time distribution within a solidlike state in water clusters is described. We propose a simple homogeneous network (SHN) model to investigate dynamics on the potential energy networks of water clusters. In this model, it is shown that the trapping-time distribution in a solidlike state follows the exponential distribution, whereas the trapping-time distribution in local potential minima within the solidlike state is not exponential. To confirm the exponential trapping-time distribution in a solidlike state, we investigate water clusters, $($H${}_2$O$)_6$ and $($H${}_2$O$)_{12}$, by molecular dynamics simulations. These clusters change dynamically from solidlike to liquidlike state and vice versa. We find that the probability density functions of trapping times in a solidlike state are described by the exponential distribution whereas those of interevent times of large fluctuations in potential energy within the solidlike state follow the Weibull distributions. The results provide a clear evidence that transition dynamics between solidlike and liquidlike states in water clusters are well described by the SHN model, suggesting that the exponential trapping-time distribution within a solidlike state originates from the homogeneous connectivity in the potential energy network.Comment: 9 pages, 8 figure

Predictive flavour symmetries of the neutrino mass matrix

Here we propose an $A_4$ flavour symmetry model which implies a lower bound on the neutrinoless double beta decay rate, corresponding to an effective mass parameter M_{ee} \gsim 0.03 eV, and a direct correlation between the expected magnitude of CP violation in neutrino oscillations and the value of $\sin^2\theta_{13}$, as well as a nearly maximal CP phase $\delta$.Comment: 4 pages, 4 figure

Quaternion Family Symmetry of Quarks and Leptons

To a first approximation, the quark mixing matrix has $\theta^q_{13} = \theta^q_{23} = 0$, whereas the lepton mixing matrix has $\theta^l_{23} = \pi/4$. We show how this structure may be understood if the family symmetry is $Q_8$, the quaternion group of eight elements. We find three viable scenarios for the Majorana neutrino mass matrix, each depending on 4 parameters and predicting a specific mass spectrum. The phenomenology of the two Higgs doublets which generate the Yukawa sector is analyzed and testable predictions are derived. We discuss also the closely related model based on $D_4$, the symmetry group of the square.Comment: latex, 10 pages, 2 eps figures, notations revised, classification of $D_4$ models correcte

Aquarium

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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

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