A Monte Carlo model for networks between professionals and society

We propose a network model with a fixed number of nodes and links and with a dynamic which favors links between nodes differing in connectivity. We observe a phase transition and parameter regimes with degree distributions following power laws, P(k)∼k^-γ$P(k)\sim k^{-\gamma }$, with γ$\gamma$ ranging from 0.2$0.2$ to 0.5$0.5$, small-world properties, with a network diameter following D(N)∼logN$D(N)\sim \log N$ and relative high clustering, following C(N)∼1/N$C(N)\sim 1/N$ and C(k)∼k^-α$C(k)\sim k^{-\alpha }$, with α$\alpha$ close to 3. We compare our results with data from real-world protein interaction networks.     

Exploring self-similarity of complex cellular networks: The edge-covering method with simulated annealing and log-periodic sampling

Song et al. [Self-similarity of complex networks, Nature 433 (2005) 392–395] have recently used a version of the box-counting method, called the node-covering method, to quantify the self-similar properties of 43 cellular networks: the minimal number _NV$N_V$ of boxes of size ?$?$ needed to cover all the nodes of a cellular network was found to scale as the power-law _NV∼(?+1)^-_DV$N_V\sim (?+1{)}^{-D_V}$ with a fractal dimension _DV=3.53±0.26$D_V=3.53\pm 0.26$. We implement an alternative box-counting method in terms of the minimum number _NE$N_E$ of edge-covering boxes which is well-suited to cellular networks, where the search over different covering sets is performed with the simulated annealing algorithm. The method also takes into account a possible discrete scale symmetry to optimize the sampling rate and minimize possible biases in the estimation of the fractal dimension. With this methodology, we find that _NE$N_E$ scales with respect to ?$?$ as a power-law _NE∼?^-_DE$N_E\sim {?}^{-D_E}$ with _DE=2.67±0.15$D_E=2.67\pm 0.15$ for the 43 cellular networks previously analyzed by Song et al. [Self-similarity of complex networks, Nature 433 (2005) 392–395]. Bootstrap tests suggest that the analyzed cellular networks may have a significant log-periodicity qualifying a discrete hierarchy with a scaling ratio close to 2.     

Heavy neutral gauge bosons at the LHC in an extended MSSM

Searching for heavy neutral gauge bosons Z^′$Z^{\prime }$, predicted in extensions of the Standard Model based on a U(1)^′$\mathrm{U}{(1)}^{\prime }$ gauge symmetry, is one of the challenging objectives of the experiments carried out at the Large Hadron Collider. In this paper, we study Z^′$Z^{\prime }$ phenomenology at hadron colliders according to several U(1)^′$\mathrm{U}{(1)}^{\prime }$-based models and in the Sequential Standard Model. In particular, possible Z^′$Z^{\prime }$ decays into supersymmetric particles are included, in addition to the Standard Model modes so far investigated. We point out the impact of the U(1)^′$\mathrm{U}{(1)}^{\prime }$ group on the MSSM spectrum and, for a better understanding, we consider a few benchmarks points in the parameter space. We account for the D-term contribution, due to the breaking of U(1)^′$\mathrm{U}{(1)}^{\prime }$, to slepton and squark masses and investigate its effect on Z^′$Z^{\prime }$ decays into sfermions. Results on branching ratios and cross sections are presented, as a function of the MSSM and U(1)^′$\mathrm{U}{(1)}^{\prime }$ parameters, which are varied within suitable ranges. We pay special attention to final states with leptons and missing energy and make predictions on the number of events with sparticle production in Z^′$Z^{\prime }$ decays, for a few values of integrated luminosity and centre-of-mass energy of the LHC.     

A family of functions for mass and energy flux splitting of the Euler equations

Flux vector splitting algorithms for the Euler equations are based on dividing the mass, momentum and energy fluxes into a “forward directed flux” F⁺$F^{+}$ and a “backward directed flux” F^-$F^{-}$ (with F^-=0$F^{-}=0$ for Mach numbers M>1$M>1$ and F⁺=0$F^{+}=0$ for M<-1$M<-1$). van Leer (1979, 1982) 4 and 5 proposed using polynomials of the Mach number for computing F⁺$F^{+}$ and F^-$F^{-}$ in the subsonic regime, and derived the lowest order polynomials that satisfy a set of chosen criteria. In this paper, we explore the possibility of increasing the order of these polynomials, with the purpose of reducing the diffusion across slow moving contact discontinuities of the flux vector splitting algorithm. We find that a moderate reduction of the diffusion, resulting in sharper shocks and contact discontinuities, can indeed be obtained with the higher order polynomials for the split fluxes.     

Scattering rates for leptogenesis: Damping of lepton flavour coherence and production of singlet neutrinos

Using the Closed Time Path (CTP) approach, we perform a systematic leading order calculation of the relaxation rate of flavour correlations of left-handed Standard Model leptons. This quantity is of pivotal relevance for flavoured leptogenesis in the Early Universe, and we find it to be 5.19×10⁻³T$5.19\times {10}^{-3}T$ at T=10⁷ GeV$T={10}^7\text{GeV}$ and 4.83×10⁻³T$4.83\times {10}^{-3}T$ at T=10¹³ GeV$T={10}^{13}\text{GeV}$, in substantial agreement with estimates used in previous phenomenological analyses. These values apply to the Standard Model with a Higgs-boson mass of 125 GeV$125\text{GeV}$. The dependence of the numerical coefficient on the temperature T is due to the renormalisation group running. The leading linear and logarithmic dependencies of the flavour relaxation rate on the gauge and top-quark couplings are extracted, such that the results presented in this work can readily be applied to extensions of the Standard Model. We also derive the production rate of light (compared to the temperature) sterile right-handed neutrinos, a calculation that relies on the same methods. We confirm most details of earlier results, but find a substantially larger contribution from the t-channel exchange of fermions.     

Analysis of cascading failure in complex power networks under the load local preferential redistribution rule

In recent years several global blackouts have drawn a lot of attention to security problems in electric power transmission systems. Here we analyze the cascading failure in complex power networks based on the local preferential redistribution rule of the broken node’s load, where the weight of a node is correlated with its link degree k$k$ as k^β$k^{\beta }$. It is found that there exists a threshold α^∗${\alpha }^{\ast }$ such that cascading failure is induced and enhanced when the value of tolerance parameter is smaller than the threshold. It is also found that the larger β$\beta$ is the more robust the power network is.     

Localization of disordered bosons and magnets in random fields

We study localization properties of disordered bosons and spins in random fields at zero temperature. We focus on two representatives of different symmetry classes, hard-core bosons (XY magnets) and Ising magnets in random transverse fields, and contrast their physical properties. We describe localization properties using a locator expansion on general lattices. For 1d Ising chains, we find non-analytic behavior of the localization length as a function of energy at ω=0$\omega =0$, ξ⁻¹(ω)=ξ⁻¹(0)+A|ω|^α${\xi }^{-1}\left(\omega \right)={\xi }^{-1}\left(0\right)+A{\left|\omega \right|}^{\alpha }$, with α$\alpha$ vanishing at criticality. This contrasts with the much smoother behavior predicted for XY magnets. We use these results to approach the ordering transition on Bethe lattices of large connectivity K$K$, which mimic the limit of high dimensionality. In both models, in the paramagnetic phase with uniform disorder, the localization length is found to have a local maximum at ω=0$\omega =0$. For the Ising model, we find activated scaling at the phase transition, in agreement with infinite randomness studies. In the Ising model long range order is found to arise due to a delocalization and condensation initiated at ω=0$\omega =0$, without a closing mobility gap. We find that Ising systems establish order on much sparser (fractal) subgraphs than XY models. Possible implications of these results for finite-dimensional systems are discussed.     

Constraints on sub-GeV hidden sector gauge bosons from a search for heavy neutrino decays

Several models of dark matter motivate the concept of hidden sectors consisting of SU_(3)C×SU_(2)L×U_(1)Y$\mathit{SU}{(3)}_C\times \mathit{SU}{(2)}_L\times U{(1)}_Y$ singlet fields. The interaction between our and hidden matter could be transmitted by new abelian U^′(1)$U^{\prime }(1)$ gauge bosons A^′$A^{\prime }$ mixing with ordinary photons. If such A^′$A^{\prime }$?s with the mass in the sub-GeV range exist, they would be produced through mixing with photons emitted in decays of η   and η^′${\eta }^{\prime }$ neutral mesons generated by the high energy proton beam in a neutrino target. The A^′$A^{\prime }$?s would then penetrate the downstream shielding and be observed in a neutrino detector via their A^′→e⁺e⁻$A^{\prime }\to e^{+}{e}^{-}$ decays. Using bounds from the CHARM neutrino experiment at CERN that searched for an excess of e⁺e⁻$e^{+}{e}^{-}$ pairs from heavy neutrino decays, the area excluding the γ−A^′$\gamma -A^{\prime }$ mixing range 10⁻⁷???10⁻⁴${10}^{-7}???{10}^{-4}$ for the A^′$A^{\prime }$ mass region 1?_MA′?500 MeV$1?M_{A^{\prime }}?500\text{MeV}$ is derived. The obtained results are also used to constrain models, where a new gauge boson X   interacts with quarks and leptons. New upper limits on the branching ratio as small as Br(η→γX)?10⁻¹⁴$\mathrm{Br}(\eta \to \gamma X)?{10}^{-14}$ and Br(η^′→γX)?10⁻¹²$\mathrm{Br}({\eta }^{\prime }\to \gamma X)?{10}^{-12}$ are obtained, which are several orders of magnitude more restrictive than the previous bounds from the Crystal Barrel experiment.     

Global supersymmetry on curved spaces in various dimensions

We propose methods towards a systematic determination of d  -dimensional curved spaces where Euclidean field theories with rigid supersymmetry can be defined. The analysis is carried out from a group theory as well as from a supergravity point of view. In particular, by using appropriate gauged supergravities in various dimensions we show that supersymmetry can be defined in conformally flat spaces, such as non-compact hyperboloids Hⁿ⁺¹${\mathbb{H}}^{n+1}$ and compact spheres Sⁿ${\mathbb{S}}^n$ or – by turning on appropriate Wilson lines corresponding to R-symmetry vector fields – on S¹×Sⁿ${\mathbb{S}}^1\times {\mathbb{S}}^n$, with n<6$n<6$. By group theory arguments we show that Euclidean field theories with rigid supersymmetry cannot be consistently defined on round spheres S^d${\mathbb{S}}^d$ if d>5$d>5$ (despite the existence of Killing spinors). We also show that distorted spheres and certain orbifolds are also allowed by the group theory classification.     

Minimal hypersurfaces in a nearly Kaehler 6-sphere

In this paper we show that for a compact minimal hypersurface M$M$ of constant scalar curvature in the unit sphere S⁶$S^6$ with the shape operator A$A$ satisfying ‖A‖²>5${\Vert A\Vert }^2>5$, there exists an eigenvalue λ>10$\lambda >10$ of the Laplace operator of the hypersurface M$M$ such that ‖A‖²=λ−5${\Vert A\Vert }^2=\lambda -5$. This gives the next discrete value of ‖A‖²${\Vert A\Vert }^2$ greater than 0 and 5.     

Percolation theory and fragmentation measures in social networks

We study the statistical properties of a recently proposed social networks measure of fragmentation F after removal of a fraction q of nodes or links from the network. The measure F   is defined as the ratio of the number of pairs of nodes that are not connected in the fragmented network to the total number of pairs in the original fully connected network. We compare this measure with the one traditionally used in percolation theory, _P∞$P_{\infty }$, the fraction of nodes in the largest cluster relative to the total number of nodes. Using both analytical and numerical methods, we study Erd?s–Rényi (ER) and scale-free (SF) networks under various node removal strategies. We find that for a network obtained after removal of a fraction q   of nodes above criticality, _P∞≈(1-F)^1/2$P_{\infty }\approx (1-F{)}^{1/2}$. For fixed _P∞$P_{\infty }$ and close to criticality, we show that 1-F$1-F$ better reflects the actual fragmentation. For a given _P∞$P_{\infty }$, 1-F$1-F$ has a broad distribution and thus one can improve significantly the fragmentation of the network. We also study and compare the fragmentation measure F   and the percolation measure _P∞$P_{\infty }$ for a real national social network of workplaces linked by the households of the employees and find similar results.     

Dilepton excess from local parity breaking in baryon matter

We propose that local parity breaking induced by a large-scale fluctuation of topological charge at large temperatures and/or condensation of pseudoscalar mesons in the isotriplet channel for large baryon densities may be responsible for the substantial dilepton excess that is found for low invariant masses and moderate values of _pT$p_T$ in central heavy ions collisions. This insofar unexplained enhancement could be understood by a combination of two effects leading to an excess of both e⁺e⁻$e^{+}{e}^{-}$ and μ⁺μ⁻${\mu }^{+}{\mu }^{-}$ pairs with respect to theoretical predictions based on conventional hadronic processes: (a) a modification of the dispersion relation of photons and vector mesons propagating in such a nuclear medium due to local parity breaking; (b) the appearance of new decay channels, forbidden by parity conservation in QCD in the usual vacuum. Possible signatures of this effect and perspectives for its detection are discussed.     

Electromagnetic and microwave absorption properties of Alnico powder composites

A novel application of Alnico powder as a thinner microwave absorbing material was investigated. The flake-like Alnico fine powder was found to have excellent complex permeability μ=μ^′-jμ^″$\mu ={\mu }^{\prime }-j{\mu }^{″}$ and permittivity ε=ε^′-jε^″$\epsilon ={\epsilon }^{\prime }-j{\epsilon }^{″}$ in the frequency range of 2–18 GHz. The powder was made from extremely brittle ribbons which were produced using a single roller melt spinning technique. The dependences of the absorption characteristics on the frequency, thickness, and both the dielectric permittivity and magnetic permeability were obtained based on a model in which an electromagnetic wave is incident normal to the surface of the absorbing material backed by a perfect conductor. The samples have the largest values of μ^′${\mu }^{\prime }$ and μ^″${\mu }^{″}$ at 2 GHz. A minimum reflection loss of −11.4 dB is obtained at 2 GHz for composite with volume fraction 60% of Alnico powder and absorber thickness of 1.8 mm. The results show that flake-like Alnico powder composites can be applied as thinner microwave absorbers in S-band (2–4 GHz).     

Dark matter annihilation in the Galactic Center as seen by the Fermi Gamma Ray Space Telescope

We analyze the first two years of data from the Fermi Gamma Ray Space Telescope from the direction of the inner 10° around the Galactic Center with the intention of constraining, or finding evidence of, annihilating dark matter. We find that the morphology and spectrum of the emission between 1.25° and 10° from the Galactic Center is well described by the processes of decaying pions produced in cosmic ray collisions with gas, and the inverse Compton scattering of cosmic ray electrons in both the disk and bulge of the Inner Galaxy, along with gamma rays from known points sources in the region. The observed spectrum and morphology of the emission within approximately 1.25° (∼175 parsecs) of the Galactic Center, in contrast, departs from the expectations for by these processes. Instead, we find an additional component of gamma ray emission that is highly concentrated around the Galactic Center. The observed morphology of this component is consistent with that predicted from annihilating dark matter with a cusped (and possibly adiabatically contracted) halo distribution (ρ∝r−γ$\rho \propto r^{-\gamma }$, with γ=1.18$\gamma =1.18$ to 1.33). The observed spectrum of this component, which peaks at energies between 1–4 GeV (in E²$E^2$ units), can be well fit by a 7–10 GeV dark matter particle annihilating primarily to tau leptons with a cross section in the range of 〈σv〉=4.6×¹⁰⁻²⁷$〈\sigma v〉=4.6\times {10}^{-27}$ to 5.3×¹⁰⁻²⁶ cm³/s$5.3\times {10}^{-26}{\text{cm}}^3/\text{s}$, depending on how the dark matter distribution is normalized. We also discuss other sources for this emission, including the possibility that much of it originates from the Milky Way?s supermassive black hole.