Rich-club network topology to minimize synchronization cost due to phase difference among frequency-synchronized oscillators

Functions of some networks, such as power grids and large-scale brain networks, rely on not only frequency synchronization, but also phase synchronization. Nevertheless, even after the oscillators reach to frequency-synchronized status, phase difference among oscillators often shows non-zero constant values. Such phase difference potentially results in inefficient transfer of power or information among oscillators, and avoid proper and efficient functioning of the network. In the present study, we newly define synchronization cost by the phase difference among the frequency-synchronized oscillators, and investigate the optimal network structure with the minimum synchronization cost through rewiring-based optimization. By using the Kuramoto model, we demonstrate that the cost is minimized in a network topology with rich-club organization, which comprises the densely-connected center nodes and peripheral nodes connecting with the center module. We also show that the network topology is characterized by its bimodal degree distribution, which is quantified by Wolfson's polarization index. Furthermore, we provide analytical interpretation on why the rich-club network topology is related to the small amount of synchronization cost.Comment: 4 figures + one appendix figur

Driving the Growth of the Earliest Supermassive Black Holes with Major Mergers of Host Galaxies

The formation mechanism of supermassive black holes (SMBHs) in general, and of $\sim 10^9\,{\rm M}_{\odot}$ SMBHs observed as luminous quasars at redshifts $z> 6$ in particular, remains an open fundamental question. The presence of such massive BHs at such early times, when the Universe was less than a billion years old, implies that they grew via either super-Eddington accretion, or nearly uninterrupted gas accretion near the Eddington limit; the latter, at first glance, is at odds with empirical trends at lower redshifts, where quasar episodes associated with rapid BH growth are rare and brief. In this work, I examine whether and to what extent the growth of the $z> 6$ quasar SMBHs can be explained within the standard quasar paradigm, in which major mergers of host galaxies trigger episodes of rapid gas accretion below or near the Eddington limit. Using a suite of Monte Carlo merger tree simulations of the assembly histories of the likely hosts of the $z> 6$ quasars, I investigate (i) their growth and major merger rates out to $z\sim 40$, and (ii) how long the feeding episodes induced by host mergers must last in order to explain the observed $z> 6$ quasar population without super-Eddington accretion. The halo major merger rate scales roughly as $\propto (1+z)^{5/2}$, with quasar hosts typically experiencing $> 10$ major mergers between $15> z > 6$ ($\approx 650\,{\rm Myr}$), compared to $\sim 1$ for typical massive galaxies at $3>z > 0$ ($\approx 11 \,{\rm Gyr}$). An example of a viable sub-Eddington SMBH growth model is one where a host merger triggers feeding for a duration comparable to the halo dynamical time. These findings suggest that the growth mechanisms of the earliest quasar SMBHs need not have been drastically different from their counterparts at lower redshifts.Comment: 24 pages, 5 figures, invited submission to a focus issue on galactic centers in Classical and Quantum Gravit

Recurring flares from supermassive black hole binaries: implications for tidal disruption candidates and OJ 287

I discuss the possibility that accreting supermassive black hole (SMBH) binaries with sub-parsec separations produce periodically recurring luminous outbursts that interrupt periods of relative quiescence. This hypothesis is motivated by two characteristics found generically in simulations of binaries embedded in prograde accretion discs: (i) the formation of a central, low-density cavity around the binary, and (ii) the leakage of gas into this cavity, occurring once per orbit via discrete streams on nearly radial trajectories. The first feature would reduce the emergent optical/UV flux of the system relative to active galactic nuclei powered by single SMBHs, while the second can trigger quasiperiodic fluctuations in luminosity. I argue that the quasiperiodic accretion signature may be much more dramatic than previously thought, because the infalling gas streams can strongly shock-heat via self-collision and tidal compression, thereby enhancing viscous accretion. Any optically thick gas that is circularized about either SMBH can accrete before the next pair of streams is deposited, fueling transient, luminous flares that recur every orbit. Due to the diminished flux in between accretion episodes, such cavity-accretion flares could plausibly be mistaken for the tidal disruptions of stars in quiescent nuclei. The flares could be distinguished from tidal disruption events if their quasiperiodic recurrence is observed, or if they are produced by very massive SMBHs that cannot disrupt solar-type stars. They may be discovered serendipitously in surveys such as LSST or eROSITA. I present a heuristic toy model as a proof of concept for the production of cavity-accretion flares, and generate mock light curves and specta. I also apply the model to the active galaxy OJ 287, whose production of quasiperiodic pairs of optical flares has long fueled speculation that it hosts a SMBH binary.Comment: 15 pages, 5 figures. Accepted for publication in MNRA

A note on testing parameter constancy in cointegrated vector autoregression: the case of near I(2) processes

This note investigates the behaviour of a parameter-constancy test statistic when near I(2) (integrated of order 2) variables are incorporated in a cointegrated vector autoregressive system. Simulation studies indicate that the presence of such variables has a significant impact on size properties of the constancy test.Parameter Constancy, Cointegraed Vector Autoregression, Near I(2) Variable.

A note on small-sample correction for hypothesis testing on cointegrating vectors: recursive Monte Carlo analysis

This note conducts recursive Monte Carlo experiments on the Bartlett correction for a likelihood-based test on cointegrating vectors. The experiments show that the correction can reduce size distortions even in situations where regularity conditions for I(1) cointegration analysis are satisfied only marginally.Cointegrating Vector, Small Sample, Bartlett Correction, Recursive Monte Carlo Experiment.

Investigating time series properties of a dynamic system for Japan's import demand

This note aims to investigate time series properties of a dynamic system for Japan's aggregate import demand. A multivariate cointegration analysis of Japanese data reveals a stable economic linkage interpretable as a long-run import demand function. A vector equilibrium correction system is then estimated, which exhibits short-run and long-run interdependent relationships between aggregate import demand and the ratio of import price to domestic price level.Aggregate Import Demand, Cointegration, Vector Equilibrium Correction System.