Abstract:
It is widely thought that resting state functional connectivity likely reflects functional interaction among brain areas and that different functional areas interact with different sets of brain areas. A method for mapping areal boundaries has been formulated based on the large-scale spatial characteristics of regional interaction revealed by resting state functional connectivity. In the present study, we present a novel analysis for areal boundary mapping that requires only the signal timecourses within a region of interest, without reference to the information from outside the region. The areal boundaries were generated by the novel analysis and were compared with those generated by the previously-established standard analysis. The boundaries were robust and reproducible across the two analyses, in two regions of interest tested. These results suggest that the information for areal boundaries is readily available inside the region of interest.

Abstract:
This note aims to achieve a parsimonious fractionally-integrated autoregressive and moving average (ARFIMA) model for recent time series data of Japan's unemployment rate. A brief review of the ARFIMA model is provided, leading to econometric modeling of the data in the ARFIMA framework. It is demonstrated that the preferred ARFIMA model is a satisfactory representation of the data and is useful as a forecasting device.

Abstract:
We discuss Green's-function solutions of the equation for a geometrically thin, axisymmetric Keplerian accretion disc with a viscosity prescription "\nu ~ R^n". The mathematical problem was solved by Lynden-Bell & Pringle (1974) for the special cases with boundary conditions of zero viscous torque and zero mass flow at the disc center. While it has been widely established that the observational appearance of astrophysical discs depend on the physical size of the central object(s), exact time-dependent solutions with boundary conditions imposed at finite radius have not been published for a general value of the power-law index "n". We derive exact Green's-function solutions that satisfy either a zero-torque or a zero-flux condition at a nonzero inner boundary R_{in}>0, for an arbitrary initial surface density profile. Whereas the viscously dissipated power diverges at the disc center for the previously known solutions with R_{in}=0, the new solutions with R_{in}>0 have finite expressions for the disc luminosity that agree, in the limit t=>infinity, with standard expressions for steady-state disc luminosities. The new solutions are applicable to the evolution of the innermost regions of thin accretion discs.

Abstract:
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.

Abstract:
The Laser Interferometer Space Antenna (LISA) will detect gravitational wave signals from coalescing pairs of massive black holes in the total mass range (10^5 - 10^7)/Msol out to cosmological distances. Identifying and monitoring the electromagnetic counterparts of these events would enable cosmological studies and offer new probes of gas physics around well-characterized massive black holes. Milosavljevic & Phinney (2005) proposed that a circumbinary disk around a binary of mass ~10^6 Msol will emit an accretion-powered X-ray afterglow approximately one decade after the gravitational wave event. We revisit this scenario by using Green's function solutions to calculate the temporal viscous evolution and the corresponding electromagnetic signature of the circumbinary disk. Our calculations suggest that an electromagnetic counterpart may become observable as a rapidly brightening source soon after the merger, i.e. several years earlier than previously thought. The afterglow can reach super-Eddington luminosities without violating the local Eddington flux limit. It is emitted in the soft X-ray by the innermost circumbinary disk, but it may be partially reprocessed at optical and infrared frequencies. We also find that the spreading disk becomes increasingly geometrically thick close to the central object as it evolves, indicating that the innermost flow could become advective and radiatively inefficient, and generate a powerful outflow. We conclude that the mergers of massive black holes detected by LISA offer unique opportunities for monitoring on humanly tractable timescales the viscous evolution of accretion flows and the emergence of outflows around massive black holes with precisely known masses, spins and orientations.

Abstract:
Dynamics on networks are often characterized by the second smallest eigenvalue of the Laplacian matrix of the network, which is called the spectral gap. Examples include the threshold coupling strength for synchronization and the relaxation time of a random walk. A large spectral gap is usually associated with high network performance, such as facilitated synchronization and rapid convergence. In this study, we seek to enhance the spectral gap of undirected and unweighted networks by removing nodes because, practically, the removal of nodes often costs less than the addition of nodes, addition of links, and rewiring of links. In particular, we develop a perturbative method to achieve this goal. The proposed method realizes better performance than other heuristic methods on various model and real networks. The spectral gap increases as we remove up to half the nodes in most of these networks.

Abstract:
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.

Abstract:
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.

Abstract:
CPUs and operating systems are moving from 32 to 64 bits, and hence it is important to have good pseudorandom number generators designed to fully exploit these word lengths. However, existing 64-bit very long period generators based on linear recurrences modulo 2 are not completely optimized in terms of the equidistribution properties. Here we develop 64-bit maximally equidistributed pseudorandom number generators that are optimal in this respect and have speeds equivalent to 64-bit Mersenne Twisters. We provide a table of specific parameters with period lengths from $2^{607}-1$ to $2^{44497}-1$. Further, we focus on the SIMD-oriented Fast Mersenne Twister generator SFMT19937, and point out that the use of 64-bit output sequences deteriorates its equidistribution properties compared with 32-bit output sequences. We also show that this SFMT generator fails a standard empirical statistical test.