Possibility of Direct Measurement of the Acceleration of the Universe Using 0.1 Hz Band Laser Interferometer Gravitational Wave Antenna in Space

It may be possible to construct a laser interferometer gravitational wave antenna in space with $h_{rms}\sim 10^{-27}$ at $f\sim 0.1{\rm Hz}$ in this century. We show possible specification of this antenna which we call DECIGO. Using this antenna we show that 1) typically $10^5$ ($10^4\sim 10^6$) chirp signals of coalescing binary neutron stars per year may be detected with S/N $\sim 10^4$. 2) We can directly measure the acceleration of the universe by ten years observation of binary neutron stars. 3) The stochastic gravitational waves of \Omega_{GW}\gsim 10^{-20} predicted by the inflation may be detected by correlation analysis for which effects of the recent cosmic acceleration would become highly important. Our formula for phase shift due to accelerating motion might be also applied for binary sources of LISA.Comment: 5 pages, 1 figure, revised version, Phys.Rev.Lett in pres

Analysis of relative influence of nodes in directed networks

Many complex networks are described by directed links; in such networks, a link represents, for example, the control of one node over the other node or unidirectional information flows. Some centrality measures are used to determine the relative importance of nodes specifically in directed networks. We analyze such a centrality measure called the influence. The influence represents the importance of nodes in various dynamics such as synchronization, evolutionary dynamics, random walk, and social dynamics. We analytically calculate the influence in various networks, including directed multipartite networks and a directed version of the Watts-Strogatz small-world network. The global properties of networks such as hierarchy and position of shortcuts, rather than local properties of the nodes, such as the degree, are shown to be the chief determinants of the influence of nodes in many cases. The developed method is also applicable to the calculation of the PageRank. We also numerically show that in a coupled oscillator system, the threshold for entrainment by a pacemaker is low when the pacemaker is placed on influential nodes. For a type of random network, the analytically derived threshold is approximately equal to the inverse of the influence. We numerically show that this relationship also holds true in a random scale-free network and a neural network.Comment: 9 figure

Non-Gaussianity test for discriminating gravitational wave backgrounds around 0.1-1Hz

We propose a non-Gaussianity test for gravitational wave backgrounds by combining data streams of multiple detectors. This simple method allows us to check whether a detected background is "smooth" enough to be consistent with an inflation-type background, or is contaminated by individually undetectable weak burst signals. The proposed test would be quite useful for the Big Bang Observer or DECIGO whose primary target is a background from inflation at 0.1-1Hz where gravitational wave bursts from supernovae of population III stars might become a troublesome foreground.Comment: 5 pages, to appear in ApJ

Oberlin partial ulnar nerve transfer for restoration in obstetric brachial plexus palsy of a newborn: case report

An 8 month old male infant with Erb's birth palsy was treated with two peripheral nerve transfers. Except for rapid motor reinnervations, elbow flexion was obtained by an Oberlin's partial ulnar nerve transfer, while shoulder abduction was restored by an accessory-to-suprascapular nerve transfer. The initial contraction of the biceps muscle occurred two months after surgery. Forty months after surgery, elbow flexion reached M5 without functional loss of the ulnar nerve. This case demonstrates an excellent result of an Oberlin's nerve transfer for restoration of flexion of the elbow joint in Erb's birth palsy. However, at this time partial ulnar nerve transfer for Erb's birth palsy is an optional procedure; a larger number of cases will need to be studied for it to be widely accepted as a standard procedure for Erb's palsy at birth

Collective fluctuations in networks of noisy components

Collective dynamics result from interactions among noisy dynamical components. Examples include heartbeats, circadian rhythms, and various pattern formations. Because of noise in each component, collective dynamics inevitably involve fluctuations, which may crucially affect functioning of the system. However, the relation between the fluctuations in isolated individual components and those in collective dynamics is unclear. Here we study a linear dynamical system of networked components subjected to independent Gaussian noise and analytically show that the connectivity of networks determines the intensity of fluctuations in the collective dynamics. Remarkably, in general directed networks including scale-free networks, the fluctuations decrease more slowly with the system size than the standard law stated by the central limit theorem. They even remain finite for a large system size when global directionality of the network exists. Moreover, such nontrivial behavior appears even in undirected networks when nonlinear dynamical systems are considered. We demonstrate it with a coupled oscillator system.Comment: 5 figure

Update of HΦ\mathcal{H}\Phi: Newly added functions and methods in versions 2 and 3

$\mathcal{H}\Phi$ [$aitch$-$phi$] is an open-source software package of numerically exact and stochastic calculations for a wide range of quantum many-body systems. In this paper, we present the newly added functions and the implemented methods in vers. 2 and 3. In ver. 2, we implement spectrum calculations by the shifted Krylov method, and low-energy excited state calculations by the locally optimal blocking preconditioned conjugate gradient (LOBPCG) method. In ver. 3, we implement the full diagonalization method using ScaLAPACK and GPGPU computing via MAGMA. We also implement a real-time evolution method and the canonical thermal pure quantum (cTPQ) state method for finite-temperature calculations. The Wannier90 format for specifying the Hamiltonians is also implemented. Using the Wannier90 format, it is possible to perform the calculations for the $ab$ $initio$ low-energy effective Hamiltonians of solids obtained by the open-source software RESPACK. We also update Standard mode \unicode{x2014}simplified input format in $\mathcal{H}\Phi$\unicode{x2014} to use these functions and methods. We explain the basics of the implemented methods and how to use them.Comment: 21 pages, 10 figures, 2 table

Kω — Open-source library for the shifted Krylov subspace method of the form (zI−H)x=b

We develop Kω, an open-source linear algebra library for the shifted Krylov subspace methods. The methods solve a set of shifted linear equations (zkI−H)x(k)=b(k=0,1,2,…) for a given matrix H and a vector b, simultaneously. The leading order of the operational cost is the same as that for a single equation. The shift invariance of the Krylov subspace is the mathematical foundation of the shifted Krylov subspace methods. Applications in materials science are presented to demonstrate the advantages of the algorithm over the standard Krylov subspace methods such as the Lanczos method. We introduce benchmark calculations of (i) an excited (optical) spectrum and (ii) intermediate eigenvalues by the contour integral on the complex plane. In combination with the quantum lattice solver HΦ, Kω can realize parallel computation of excitation spectra and intermediate eigenvalues for various quantum lattice models