Classification of scale-free networks

While the emergence of a power law degree distribution in complex networks is intriguing, the degree exponent is not universal. Here we show that the betweenness centrality displays a power-law distribution with an exponent \eta which is robust and use it to classify the scale-free networks. We have observed two universality classes with \eta \approx 2.2(1) and 2.0, respectively. Real world networks for the former are the protein interaction networks, the metabolic networks for eukaryotes and bacteria, and the co-authorship network, and those for the latter one are the Internet, the world-wide web, and the metabolic networks for archaea. Distinct features of the mass-distance relation, generic topology of geodesics and resilience under attack of the two classes are identified. Various model networks also belong to either of the two classes while their degree exponents are tunable.Comment: 6 Pages, 6 Figures, 1 tabl

The Impact of Line Misidentification on Cosmological Constraints from Euclid and other Spectroscopic Galaxy Surveys

We perform forecasts for how baryon acoustic oscillation (BAO) scale and redshift-space distortion (RSD) measurements from future spectroscopic emission line galaxy (ELG) surveys such as Euclid are degraded in the presence of spectral line misidentification. Using analytic calculations verified with mock galaxy catalogs from log-normal simulations we find that constraints are degraded in two ways, even when the interloper power spectrum is modeled correctly in the likelihood. Firstly, there is a loss of signal-to-noise ratio for the power spectrum of the target galaxies, which propagates to all cosmological constraints and increases with contamination fraction, $f_c$. Secondly, degeneracies can open up between $f_c$ and cosmological parameters. In our calculations this typically increases BAO scale uncertainties at the 10-20% level when marginalizing over parameters determining the broadband power spectrum shape. External constraints on $f_c$, or parameters determining the shape of the power spectrum, for example from cosmic microwave background (CMB) measurements, can remove this effect. There is a near-perfect degeneracy between $f_c$ and the power spectrum amplitude for low $f_c$ values, where $f_c$ is not well determined from the contaminated sample alone. This has the potential to strongly degrade RSD constraints. The degeneracy can be broken with an external constraint on $f_c$, for example from cross-correlation with a separate galaxy sample containing the misidentified line, or deeper sub-surveys.Comment: 18 pages, 7 figures, updated to match version accepted by ApJ (extra paragraph added at the end of Section 4.3, minor text edits

Probing Cosmic Strings with Satellite CMB measurements

We study the problem of searching for cosmic string signal patterns in the present high resolution and high sensitivity observations of the Cosmic Microwave Background (CMB). This article discusses a technique capable of recognizing Kaiser-Stebbins effect signatures in total intensity anisotropy maps, and shows that the biggest factor that produces confusion is represented by the acoustic oscillation features of the scale comparable to the size of horizon at recombination. Simulations show that the distribution of null signals for pure Gaussian maps converges to a $\chi^2$ distribution, with detectability threshold corresponding to a string induced step signal with an amplitude of about 100 \muK which corresponds to a limit of roughly $G\mu < 1.5\times 10^{-6}$. We study the statistics of spurious detections caused by extra-Galactic and Galactic foregrounds. For diffuse Galactic foregrounds, which represents the dominant source of contamination, we derive sky masks outlining the available region of the sky where the Galactic confusion is sub-dominant, specializing our analysis to the case represented by the frequency coverage and nominal sensitivity and resolution of the Planck experiment.Comment: 14 pages, 3 figures, to be published in JCA

Holomorphic selection rules, the origin of the mu term, and thermal inflation

When an abelian gauge theory with integer charges is spontaneously broken by the expectation value of a charge Q field, there remains a Z_Q discrete symmetry. In a supersymmetric theory, holomorphy adds additional constraints on the operators that can appear in the effective superpotential. As a result, operators with the same mass dimension but opposite sign charges can have very different coupling strengths. In the present work we characterize the operator hierarchies in the effective theory due to holomorphy, and show that there exist simple relationships between the size of an operator and its mass dimension and charge. Using such holomorphy-induced operator hierarchies, we construct a simple model with a naturally small supersymmetric mu term. This model also provides a concrete realization of late-time thermal inflation, which has the ability to solve the gravitino and moduli problems of weak-scale supersymmetry.Comment: 18 pages, 1 figur

Two Circular-Rotational Eigenmodes in Vortex Gyrotropic Motions in Soft Magnetic Nanodots

We found, by micromagnetic numerical and analytical calculations, that the clockwise (CW) and counterclockwise (CCW) circular-rotational motions of a magnetic vortex core in a soft magnetic circular nanodot are the elementary eigenmodes existing in the gyrotropic motion with respect to the corresponding CW and CCW circular-rotational-field eigenbasis. Any steady-state vortex gyrotropic motions driven by a linearly polarized oscillating in-plane magnetic field in the linear regime can be perfectly understood according to the superposition of the two circular eigenmodes, which show asymmetric resonance characteristics reflecting the vortex polarization. The relative magnitudes in the amplitude and phase between the CCW and CW eigenmodes determine the elongation and orientation of the orbital trajectories of the vortex core motions, respectively, which trajectories vary with the polarization and chirality of the given vortex as well as the field frequency across the resonance frequency.Comment: 30 pages, 7 figure

Map equation for link community

Community structure exists in many real-world networks and has been reported being related to several functional properties of the networks. The conventional approach was partitioning nodes into communities, while some recent studies start partitioning links instead of nodes to find overlapping communities of nodes efficiently. We extended the map equation method, which was originally developed for node communities, to find link communities in networks. This method is tested on various kinds of networks and compared with the metadata of the networks, and the results show that our method can identify the overlapping role of nodes effectively. The advantage of this method is that the node community scheme and link community scheme can be compared quantitatively by measuring the unknown information left in the networks besides the community structure. It can be used to decide quantitatively whether or not the link community scheme should be used instead of the node community scheme. Furthermore, this method can be easily extended to the directed and weighted networks since it is based on the random walk.Comment: 9 pages,5 figure

Schwinger Boson Formulation and Solution of the Crow-Kimura and Eigen Models of Quasispecies Theory

We express the Crow-Kimura and Eigen models of quasispecies theory in a functional integral representation. We formulate the spin coherent state functional integrals using the Schwinger Boson method. In this formulation, we are able to deduce the long-time behavior of these models for arbitrary replication and degradation functions. We discuss the phase transitions that occur in these models as a function of mutation rate. We derive for these models the leading order corrections to the infinite genome length limit.Comment: 37 pages; 4 figures; to appear in J. Stat. Phy

Monogamy and polygamy for multi-qubit entanglement using R\'enyi entropy

Using R\'enyi-$\alpha$ entropy to quantify bipartite entanglement, we prove monogamy of entanglement in multi-qubit systems for $\alpha \geq 2$. We also conjecture a polygamy inequality of multi-qubit entanglement with strong numerical evidence for $0.83-\epsilon \leq \alpha \leq 1.43+\epsilon$ with $0<\epsilon<0.01$.Comment: 19 pages, 2 figure

Preheating and Affleck-Dine leptogenesis after thermal inflation

Previously, we proposed a model of low energy Affleck-Dine leptogenesis in the context of thermal inflation. The lepton asymmetry is generated at the end of thermal inflation, which occurs at a relatively low energy scale with the Hubble parameter somewhere in the range 1 \keV \lesssim H \lesssim 1 \MeV. Thus Hubble damping will be ineffective in bringing the Affleck-Dine field into the lepton conserving region near the origin, leaving the possibility that the lepton number could be washed out. Previously, we suggested that preheating could damp the amplitude of the Affleck-Dine field allowing conservation of the lepton number. In this paper, we demonstrate numerically that preheating does efficiently damp the amplitude of the Affleck-Dine field and that the lepton number is conserved as the result. In addition to demonstrating a crucial aspect of our model, it also opens the more general possibility of low energy Affleck-Dine baryogenesis.Comment: 38 pages, 17 figure