Communicability Angles Reveal Critical Edges for Network Consensus Dynamics

We consider the question of determining how the topological structure influences a consensus dynamical process taking place on a network. By considering a large dataset of real-world networks we first determine that the removal of edges according to their communicability angle -an angle between position vectors of the nodes in an Euclidean communicability space- increases the average time of consensus by a factor of 5.68 in real-world networks. The edge betweenness centrality also identifies -in a smaller proportion- those critical edges for the consensus dynamics, i.e., its removal increases the time of consensus by a factor of 3.70. We justify theoretically these findings on the basis of the role played by the algebraic connectivity and the isoperimetric number of networks on the dynamical process studied, and their connections with the properties mentioned before. Finally, we study the role played by global topological parameters of networks on the consensus dynamics. We determine that the network density and the average distance-sum -an analogous of the node degree for shortest-path distances, account for more than 80% of the variance of the average time of consensus in the real-world networks studied.Comment: 15 pages, 2 figure

Oscillations in the G-type Giants

The precise radial-velocity measurements of 4 G-type giants, 11Com, $\zeta$ Hya, $\epsilon$ Tau, and $\eta$ Her were carried out. The short-term variations with amplitudes, 1-7m/s and periods, 3-10 hours were detected. A period analysis shows that the individual power distribution is in a Gaussian shape and their peak frequencies ($\nu_{max}$) are in a good agreement with the prediction by the scaling law. With using a pre-whitening procedure, significant frequency peaks more than 3 $\sigma$ are extracted for these giants. From these peaks, we determined the large frequency separation by constructing highest peak distribution of collapsed power spectrum, which is also in good agreement with what the scaling law for the large separation predicts. Echelle diagrams of oscillation frequency were created based on the extracted large separations, which is very useful to clarify the properties of oscillation modes. In these echelle diagrams, odd-even mode sequences are clearly seen. Therefore, it is certain that in these G-type giants, non-radial modes are detected in addition to radial mode. As a consequence, these properties of oscillation modes are shown to follow what Dzymbowski et al.(2001) and Dupret et al.(2009) theoretically predicted. Damping times for these giants were estimated with the same method as that developed by Stello et al.(2004). The relation of Q value (ratio of damping time to period) to the period was discussed by adding the data of the other stars ranging from dwarfs to giants.Comment: 28 pages, 16 figures, accepted for publication in PASJ 62, No.4, 201

Decentralized Algorithms for Consensus-Based Power Packet Distribution

Power packets are proposed as a transmission unit that can deliver power and information simultaneously. They are transferred using the store-and-forward method of power routers. A system that achieves power supply/demand in this manner is called a power packet network (PPN). A PPN is expected to enhance structural robustness and operational reliability in an energy storage system (ESS) with recent diverse distributed sources. However, this technology is still in its early stage, and faces numerous challenges, such as high cost of implementation and complicated energy management. In this paper, we propose a novel power control based on decentralized algorithms for a PPN. Specifically, the power supply is triggered and managed by communications between power routers. We also discuss the mechanism of the decentralized algorithm for the operation of power packets and reveal the feasibility of the given control method and application by forming biased power flows on the consensus-based distribution.Comment: This paper was submitted to Nonlinear Theory and Its Applications, IEICE on October 29, 202

Beryllium Abundances of Solar-Analog Stars

An extensive beryllium abundance analysis was conducted for 118 solar analogs (along with 87 FGK standard stars) by applying the spectrum synthesis technique to the near-UV region comprising the Be II line at 3131.066 A, in an attempt to investigate whether Be suffers any depletion such as the case of Li showing a large diversity. We found that, while most of these Sun-like stars are superficially similar in terms of their A(Be) (Be abundances) around the solar value within ~ +/- 0.2dex, 4 out of 118 samples turned out strikingly Be-deficient (by more than ~2 dex) and these 4 stars belong to the group of lowest v_e sin i (projected rotation velocity). Moreover, even for the other majority showing an apparent similarity in Be, we can recognize a tendency that A(Be) gradually increases with an increase in v_e sin i. These observational facts suggest that any solar analog star (including the Sun) generally suffers some kind of Be depletion during their lives, where the rotational velocity (or the angular momentum) plays an important role in the sense that depletion tends to be enhanced by slower rotation. Hence, our findings require that the occasionally stated view "G-type dwarfs with T_eff ~< 6000 K are essentially homogeneous in Be with their original composition retained" should be revised. Also, our analysis indicates that the difference of ~0.2 dex in A(Be) between the solar photosphere and the meteorite really exists, implying that "UV missing opacity" is irrelevant at least for this Be II line.Comment: 18 pages, 12 figures, 3 tables and 3 electronic tables (included as ancillary files), accepted for publication in Publ. Astron. Soc. Japan (2011, Vol. 63, No. 4

A Linear Inverse Model for Colored-Gaussian Noise

We propose a novel data-driven linear inverse model, called Colored-LIM, to extract the linear dynamics and diffusion matrix that define a linear stochastic process driven by an Ornstein-Uhlenbeck colored-noise. The Colored-LIM is a new variant of the classical linear inverse model (LIM) which relies on the white noise assumption. Similar to LIM, the Colored-LIM approximates the linear dynamics from a finite realization of a stochastic process and then solves the diffusion matrix based on, for instance, a generalized fluctuation-dissipation relation, which can be done by solving a system of linear equations. The main difficulty is that in practice, the colored-noise process can be hardly observed while it is correlated to the stochastic process of interest. Nevertheless, we show that the local behavior of the correlation function of the observable encodes the dynamics of the stochastic process and the diffusive behavior of the colored-noise. In this article, we review the classical LIM and develop Colored-LIM with a mathematical background and rigorous derivations. In the numerical experiments, we examine the performance of both LIM and Colored-LIM. Finally, we discuss some false attempts to build a linear inverse model for colored-noise driven processes, and investigate the potential misuse and its consequence of LIM in the appendices.Comment: 23 pages, 3 figure

State Concentration Exponent as a Measure of Quickness in Kauffman-type Networks

We study the dynamics of randomly connected networks composed of binary Boolean elements and those composed of binary majority vote elements. We elucidate their differences in both sparsely and densely connected cases. The quickness of large network dynamics is usually quantified by the length of transient paths, an analytically intractable measure. For discrete-time dynamics of networks of binary elements, we address this dilemma with an alternative unified framework by using a concept termed state concentration, defined as the exponent of the average number of t-step ancestors in state transition graphs. The state transition graph is defined by nodes corresponding to network states and directed links corresponding to transitions. Using this exponent, we interrogate the dynamics of random Boolean and majority vote networks. We find that extremely sparse Boolean networks and majority vote networks with arbitrary density achieve quickness, owing in part to long-tailed in-degree distributions. As a corollary, only relatively dense majority vote networks can achieve both quickness and robustness.Comment: 6 figure