General Connectivity Distribution Functions for Growing Networks with Preferential Attachment of Fractional Power

We study the general connectivity distribution functions for growing networks with preferential attachment of fractional power, $\Pi_{i} \propto k^{\alpha}$, using the Simon's method. We first show that the heart of the previously known methods of the rate equations for the connectivity distribution functions is nothing but the Simon's method for word problem. Secondly, we show that the case of fractional $\alpha$ the $Z$-transformation of the rate equation provides a fractional differential equation of new type, which coincides with that for PA with linear power, when $\alpha = 1$. We show that to solve such a fractional differential equation we need define a transidental function $\Upsilon (a,s,c;z)$ that we call {\it upsilon function}. Most of all previously known results are obtained consistently in the frame work of a unified theory.Comment: 10 page

Spin-orbital gap of multiorbital antiferromagnet

In order to discuss the spin-gap formation in a multiorbital system, we analyze an e_g-orbital Hubbard model on a geometrically frustrated zigzag chain by using a density-matrix renormalization group method. Due to the appearance of a ferro-orbital arrangement, the system is regarded as a one-orbital system, while the degree of spin frustration is controlled by the spatial anisotropy of the orbital. In the region of strong spin frustration, we observe a finite energy gap between ground and first-excited states, which should be called a spin-orbital gap. The physical meaning is clarified by an effective Heisenberg spin model including correctly the effect of the orbital arrangement influenced by the spin excitation.Comment: 8 pages, 6 figures, extended versio

Universal Irreversibility of Normal Quantum Diffusion

Time-reversibility measured by the deviation of the perturbed time-reversed motion from the unperturbed one is examined for normal quantum diffusion exhibited by four classes of quantum maps with contrastive physical nature. Irrespective of the systems, there exist a universal minimal quantum threshold above which the system completely loses the past memory, and the time-reversed dynamics as well as the time-reversal characteristics asymptotically trace universal curves independent of the details of the systems.Comment: 4 pages, 4 figure

Fundamental relation between longitudinal and transverse conductivities in the quantum Hall system

We investigate the relation between the diagonal ($\sigma_{xx}$) and off-diagonal ($\sigma_{xy}$) components of the conductivity tensor in the quantum Hall system. We calculate the conductivity components for a short-range impurity potential using the linear response theory, employing an approximation that simply replaces the self-energy by a constant value $-i \hbar /(2 \tau)$ with $\tau$ the scattering time. The approximation is equivalent to assuming that the broadening of a Landau level due to disorder is represented by a Lorentzian with the width $\Gamma = \hbar /(2 \tau)$. Analytic formulas are obtained for both $\sigma_{xx}$ and $\sigma_{xy}$ within the framework of this simple approximation at low temperatures. By examining the leading terms in $\sigma_{xx}$ and $\sigma_{xy}$, we find a proportional relation between $\mathrm{d}\sigma_{xy}/\mathrm{d}B$ and $B \sigma_{xx}^2$. The relation, after slight modification to account for the long-range nature of the impurity potential, is shown to be in quantitative agreement with experimental results obtained in the GaAs/AlGaAs two-dimensional electron system at the low magnetic-field regime where spin splitting is negligibly small.Comment: 21 pages, 8 figures, accepted for publication in J. Phys.: Condens. Matte

Molecular Clouds as Cosmic Ray Laboratories

We will here discuss how the gamma-ray emission from molecular clouds can be used to probe the cosmic ray flux in distant regions of the Galaxy and to constrain the highly unknown cosmic ray diffusion coefficient. In particular we will discuss the GeV to TeV emission from runaway cosmic rays penetrating molecular clouds close to young and old supernova remnants and in molecular clouds illuminated by the background cosmic ray flux.Comment: to appear on Proceedings of 25th Texas Symposium on Relativistic Astrophysic

Foreshadowing of Performance Accuracy by Event-Related Potentials: Evidence from a Minimal-Conflict Task

Recent studies employing stimulus-response compatibility tasks suggest that an increase in the amplitude of the positive deflection of the response-locked event-related potential (ERP) foreshadows errors on forthcoming trials. However, no studies have tested the generalizability of error-foreshadowing positivity to tasks without stimulus-response interference.The present study adopted an alternating-response task, in which the participants responded to the pointing direction of an arrowhead (up or down). Although the arrowhead direction alternated for the majority of trials (95%), occasionally this pattern was broken by a repeated stimulus, termed a lure trial. We compared the matched-reaction-time correct-preceding ERP with the error-preceding ERP on lure-preceding trials. There was no evidence that errors are foreshadowed by the increase of a positive electroencephalogram (EEG) deflection. To the contrary, analyses of ERPs time-locked to electromyogram (EMG) onset on the five consecutive lure-preceding trials showed larger positive deflections on correct-preceding than error-preceding trials. The post-response negativity did not differ between correct-preceding and error-preceding trials.These results suggest that in minimal conflict tasks a decreased positivity may foreshadow incorrect performance several trials prior to the error, possibly reflecting the waning of task-related efforts. Therefore, error-foreshadowing brain signals may be task-specific

Pan-Arctic Sea Ice Prediction System with the MIROC Climate Model

第6回極域科学シンポジウム分野横断セッション：[IA] 急変する北極気候システム及びその全球的な影響の総合的解明―GRENE北極気候変動研究事業研究成果報告2015―11月19日（木）　国立極地研究所１階交流アトリウ

Macdonald operators and homological invariants of the colored Hopf link

Using a power sum (boson) realization for the Macdonald operators, we investigate the Gukov, Iqbal, Kozcaz and Vafa (GIKV) proposal for the homological invariants of the colored Hopf link, which include Khovanov-Rozansky homology as a special case. We prove the polynomiality of the invariants obtained by GIKV's proposal for arbitrary representations. We derive a closed formula of the invariants of the colored Hopf link for antisymmetric representations. We argue that a little amendment of GIKV's proposal is required to make all the coefficients of the polynomial non-negative integers.Comment: 31 pages. Published version with an additional appendi

Evaluation of measurement accuracies of the Higgs boson branching fractions in the International Linear Collider

Precise measurement of Higgs boson couplings is an important task for International Linear Collider (ILC) experiments and will facilitate the understanding of the particle mass generation mechanism. In this study, the measurement accuracies of the Higgs boson branching fractions to the $b$ and $c$ quarks and gluons, $\Delta Br(H\to b\bar{b},\sim c\bar{c},\sim gg)/Br$, were evaluated with the full International Large Detector model (\texttt{ILD\_00}) for the Higgs mass of 120 GeV at the center-of-mass (CM) energies of 250 and 350 GeV using neutrino, hadronic and leptonic channels and assuming an integrated luminosity of $250 {\rm fb^{-1}}$, and an electron (positron) beam polarization of -80% (+30%). We obtained the following measurement accuracies of the Higgs cross section times branching fraction ($\Delta (\sigma \cdot Br)/\sigma \cdot Br$) for decay of the Higgs into $b\bar{b}$, $c\bar{c}$, and $gg$; as 1.0%, 6.9%, and 8.5% at a CM energy of 250 GeV and 1.0%, 6.2%, and 7.3% at 350 GeV, respectively. After the measurement accuracy of the cross section ($\Delta\sigma/\sigma$) was corrected using the results of studies at 250 GeV and their extrapolation to 350 GeV, the derived measurement accuracies of the branching fractions ($\Delta Br/Br$) to $b\bar{b}$, $c\bar{c}$, and gg were 2.7%, 7.3%, and 8.9% at a CM energy of 250 GeV and 3.6%, 7.2%, and 8.1% at 350 GeV, respectively.Comment: 15 pages, 6 figure

Unified force law for granular impact cratering

Experiments on the low-speed impact of solid objects into granular media have been used both to mimic geophysical events and to probe the unusual nature of the granular state of matter. Observations have been interpreted in terms of conflicting stopping forces: product of powers of projectile depth and speed; linear in speed; constant, proportional to the initial impact speed; and proportional to depth. This is reminiscent of high-speed ballistics impact in the 19th and 20th centuries, when a plethora of empirical rules were proposed. To make progress, we developed a means to measure projectile dynamics with 100 nm and 20 us precision. For a 1-inch diameter steel sphere dropped from a wide range of heights into non-cohesive glass beads, we reproduce prior observations either as reasonable approximations or as limiting behaviours. Furthermore, we demonstrate that the interaction between projectile and medium can be decomposed into the sum of velocity-dependent inertial drag plus depth-dependent friction. Thus we achieve a unified description of low-speed impact phenomena and show that the complex response of granular materials to impact, while fundamentally different from that of liquids and solids, can be simply understood