Detecting communities in clustered networks based on group action on set

In this paper, we propose a well targeted algorithm (GAS algorithm) for detecting communities in high clustered networks by presenting group action technology on community division. During the processing of this algorithm, the underlying community structure of a clustered network emerges simultaneously as the corresponding partition of orbits by the permutation groups acting on the node set are achieved. As the derivation of the orbit partition, an algebraic structure r-cycle can be considered as the origin of the community. To be a priori estimation for the community structure of the algorithm, the community separability is introduced to indicate whether a network has distinct community structure. By executing the algorithm on several typical networks and the LFR benchmark, it shows that this GAS algorithm can detect communities accurately and effectively in high clustered networks. Furthermore, we compare the GAS algorithm and the clique percolation algorithm on the LFR benchmark. It is shown that the GAS algorithm is more accurate at detecting non-overlapping communities in clustered networks. It is suggested that algebraic techniques can uncover fresh light on detecting communities in complex networks.     

Spectral weights of the 2-dimensional t-J-type models: Wave function study

We examine the distribution of spectral weights (SWs) of the 2-dimensional t-t^′-t^″-J model describing cuprate superconductors in terms of the Gutzwiller projected Fermi liquid, as the possible normal state, and d-wave (superconducting) resonating valence bond state. Treat exactly strong correlation between electrons by numerical approach, we calculate SWs for removing an electron which can be compared with the observation made by the future angle-resolved photoemission spectroscopy experiment.     

An extended clique degree distribution and its heterogeneity in cooperation-competition networks

After Xiao et al. [W.-K. Xiao, J. Ren, F. Qi, Z.W. Song, M.X. Zhu, H.F. Yang, H.Y. Jin, B.-H. Wang, Tao Zhou, Empirical study on clique-degree distribution of networks, Phys. Rev. E 76 (2007) 037102], in this article we present an investigation on so-called k-cliques, which are defined as complete subgraphs of k (k>1) nodes, in the cooperation-competition networks described by bipartite graphs. In the networks, the nodes named actors are taking part in events, organizations or activities, named acts. We mainly examine a property of a k-clique called “k-clique act degree”, q, defined as the number of acts, in which the k-clique takes part. Our analytic treatment on a cooperation-competition network evolution model demonstrates that the distribution of k-clique act degrees obeys Mandelbrot distribution, P(q)∝(q+α)^−γ. To validate the analytical model, we have further studied 13 different empirical cooperation-competition networks with the clique numbers k=2 and k=3. Empirical investigation results show an agreement with the analytic derivations. We propose a new “heterogeneity index”, H, to describe the heterogeneous degree distributions of k-clique and heuristically derive the correlation between H and α and γ. We argue that the cliques, which take part in the largest number of acts, are the most important subgraphs, which can provide a new criterion to distinguish important cliques in the real world networks.     

Pricing European options with a log Student’s t-distribution: A Gosset formula

The distributions of returns for stocks are not well described by a normal probability density function (pdf). Student’s t-distributions, which have fat tails, are known to fit the distributions of the returns. We present pricing of European call or put options using a log Student’s t-distribution, which we call a Gosset approach in honour of W.S. Gosset, the author behind the nom de plume Student. The approach that we present can be used to price European options using other distributions and yields the Black-Scholes formula for returns described by a normal pdf.     

Josephson effect in supercondutor/ferromagnetic semiconductor/superconductor junctions

Using a general expression for dc Josephson current, we study the Josephson effect in ballistic superconductor (SC)/ferromagnetic semiconductor (FS)/SC junctions, in which the mismatches of the effective mass and Fermi velocity between the FS and SC, spin polarization P in the FS, as well as strengths of potential scattering Z at the interfaces are included. It is shown that in the coherent regime, the oscillatory dependences of the maximum Josephson current on the FS layer thickness L and Josephson current on the macroscopic phase difference φ for the heavy and light holes, resulting from the spin splitting energy gained or lost by a quasiparticle Andreev-reflected at the FS/SC interface, are much different due to the different mismatches in the effective mass and Fermi velocity between the FS and the SC, which is related to the crossovers between positive (0) and negative (π) couplings or equivalently 0 and π junctions. Also, we find that, for the same reason, Z and P are required not to surpass different critical values for the Josephson currents of the heavy and light holes. Furthermore, it is found that, for the dependence of the Josephson current on φ, regardless of how L,Z, and P change, the Josephson junctions do not transit between 0 and π junctions for the light hole.     

Point-contact study of the heavy-fermion superconductor CeCoIn5

We have investigated the differential conductance spectra of the point contacts between the heavy-fermion superconductor CeCoIn₅ and Pt. Many of them show a double-maximum structure that indicates the superconducting energy gap Δ. The Δ values derived using Blonder-Tinkham-Klapwijk model, however, varies from 0.47 to 0.77 meV, and yet they are within the scatter of the reported values. The evolution of Δ below T_c is slow as compared with that of BCS gap probably reflecting the unconventional superconductivity in CeCoIn₅.     

Information theoretic description of networks

We present a new information theoretic approach for network characterizations. It is developed to describe the general type of networks with n nodes and L directed and weighted links, i.e., it also works for the simpler undirected and unweighted networks. The new information theoretic measures for network characterizations are based on a transmitter-receiver analogy of effluxes and influxes. Based on these measures, we classify networks as either complex or non-complex and as either democracy or dictatorship networks. Directed networks, in particular, are furthermore classified as either information spreading and information collecting networks.The complexity classification is based on the information theoretic network complexity measure medium articulation (MA). It is proven that special networks with a medium number of links (L∼n^1.5) show the theoretical maximum complexity . A network is complex if its MA is larger than the average MA of appropriately randomized networks: MA>MA_r. A network is of the democracy type if its redundancy R<R_r, otherwise it is a dictatorship network. In democracy networks all nodes are, on average, of similar importance, whereas in dictatorship networks some nodes play distinguished roles in network functioning. In other words, democracy networks are characterized by cycling of information (or mass, or energy), while in dictatorship networks there is a straight through-flow from sources to sinks. The classification of directed networks into information spreading and information collecting networks is based on the conditional entropies of the considered networks (H(A/B)=uncertainty of sender node if receiver node is known, H(B/A)=uncertainty of receiver node if sender node is known): if H(A/B)>H(B/A), it is an information collecting network, otherwise an information spreading network.Finally, different real networks (directed and undirected, weighted and unweighted) are classified according to our general scheme.     

Frequency-dependent linear and non-linear response properties of single carrier quantum dots: Role of effective mass and anharmonicity in the confinement potential

We explore the pattern of frequency-dependent linear and non-linear optical (NLO) response of one electron quantum dots harmonically confined in two dimensions. For some fixed values of transverse magnetic field strength (ω_c), and harmonic confinement potential (ω₀), the influence of effective mass (m^*) of the system and the symmetry breaking anharmonic interaction on the frequency-dependent linear (α), and the first (β), and second (γ) NLO responses of the dot is computed through linear variational route. The investigation reveals interesting roles played by the anharmonic interaction and effective mass in modulating the response properties.     

Robust μ -stability for uncertain stochastic neural networks with unbounded time-varying delays

In this paper, we investigate the global robust stability for uncertain stochastic neural networks with unbounded time-varying delays and norm-bounded parameter uncertainties. A new concept of global robust μ-stability in the mean square for neural networks is given first, then by means of the linear matrix inequality (LMI) approach, stability criteria are presented. Several corollaries are also derived. A simple example is presented to demonstrate the effectiveness of the main result.     

Tsallis’ statistics in the variability of El Niño/Southern Oscillation during the Holocene epoch

Analysis of the Tsallis q-triplet for the variability of El Niño Southern Oscillation (ENSO) index during the Holocene epoch (last 11,000 years) is presented. Three periods are analyzed, 0-7000, 7000-9700, 9700-11,000 years before the present. During the first and the third periods, the q-index values have the expected usual relations between them (q_sens<1<q_stat<q_rel), and in the second one there is an inversion between q_stat and q_rel (q_stat>q_rel).     

Pairing enhancement in Betts lattices with next nearest neighbor couplings: Exact results

Electron instabilities in the Hubbard model with the next nearest neighbor coupling are calculated by exact diagonalization in finite, two-dimensional Betts cells (lattices). A viable spin and charge coherent pairing, signaled by quantum critical points and a negative charge gap region, is found in 8- and 10-site Betts lattices at small and moderate U regions consistent with our exact results in elementary bipartite geometries [Phys. Rev. B 78 (2008) 075431]. The contour isolines for continuous temperature driven-crossover between the Mott-Hubbard insulating and coherent pairing phases are demonstrated. The criteria for smooth and abrupt phase transitions are found for systematic enhancement of coherent pairing by optimization of the next nearest neighbor coupling parameter.     

Anti-persistence in levels of Lake Naivasha: Assessing effect of human intervention through time-series analysis

Lake Naivasha in Kenya is an important natural fresh water reserve, supporting surrounding wildlife as well as agriculture and industry. Uncontrolled use of the lake water for the past few decades is causing concern for environmentalists. In the present paper, fluctuations in the lake level for the last half century are analysed using standard tools for time-series analysis. The intervals 1951-1980 (period I) and 1981-2000 (period II) are treated separately, to look for any difference in their statistical patterns. From period II onwards, increased human consumption is believed to affect the level significantly. We analyse the data using three different approaches: (i) rescaled range analysis (R/S), (ii) roughness scaling analysis and (iii) a Lomb periodogram. R/S analysis shows no difference between the behavior in periods I and II, but the other methods reveal different fluctuation patterns for the two periods. The water level shows stronger fluctuations in period I compared to II. R/S analysis, however, shows an interesting anti-persistence with a Hurst exponent 0.44, which is not usually observed in natural time series.     

Proximity effects in a superconductor/ferromagnet junction

A proximity effect in an s-wave superconductor/ferromagnet (SC/F) junction is theoretically studied using the second order perturbation theory for the tunneling Hamiltonian and Green's function method. We calculate a pair amplitude induced by the proximity effect in a weak ferromagnetic metal (FM) and a half-metal (HM). In the SC/FM junction, it is found that a spin-singlet pair amplitude (Ψ_s) and spin-triplet pair amplitude (Ψ_t) are induced in FM and both amplitudes depend on the frequency in the Matsubara representation. Ψ_s is an even function and Ψ_t is an odd function with respect to the Matsubara frequency (ω_n). In the SC/HM junction, we examine the proximity effects by taking account of magnon excitations in HM. It is found that the triplet-pair correlation is induced in HM. The induced pair amplitude in HM shows a damped oscillation as a function of the position and contains the terms of even and odd functions of ω_n as in the case of the SC/FM junction. We discuss that in our tunneling model the pair amplitude of even function of ω_n only contributes to a Josephson current.     

Mean wind: Its velocity and temperature fluctuation in low-Prandtl-number thermal convection

Large-scale circulation in the confined thermal turbulence of mercury is studied experimentally. The instantaneous velocity profile at 128 points is directly measured using ultrasonic velocimetry and the temperature fluctuation is simultaneously obtained by a small thermistor at the cell center. The periodic velocity oscillation is observed for aspect ratios Γ=1,2, but for Γ=0.5. The temperature oscillation is confirmed only in the Γ=2 cell. It is found that the flow patterns depending on the aspect ratio are characterized sufficiently by the joint probability density function up to Ra=4×10⁸.     

The static and dynamic properties of PuCoGa5 and NpCoGa5 investigated by neutron scattering experiments

Neutron scattering results on single crystals shed light on the static and dynamic properties of the superconductor () PuCoGa₅ and its isostructural but antiferromagnetic () homologue NpCoGa₅. By polarized neutron diffraction the magnetization density in the paramagnetic state of both compounds has been inferred. The microscopic magnetization of NpCoGa₅ is consistent with the orbital and spin components of a localized Np³⁺ magnetic moment. In the case of PuCoGa₅ the microscopic magnetization is small, temperature-independent and cannot be described as a localized Pu³⁺ magnetic moment. For NpCoGa₅ a dynamic magnetic signal has been observed by three-axis spectroscopy in the antiferromagnetically ordered state. The magnetic signal is strongest at the antiferromagnetic zone center and an energy transfer of about 5 meV. Magnetic fluctuations persist at this position in the paramagnetic state. The dynamic response is similar to the dynamic response observed in other actinide intermetallic compounds. This supports the possibility that magnetic fluctuations could also be present in the paramagnetic superconductor PuCoGa₅.     

Soft x-ray PHA measurement of the long pulse discharge in HT-7 tokamak

By analyzing the soft x-ray energy spectrum measured by the soft x-ray pulse height analysis (PHA) system, the electron temperature (Te) and the effective charge number (Zeff) of the ultra-long pulse discharge driven by lower hybrid wave (LHW) were obtained in the HT-7 tokamak. Moreover, the information of medium-Z impurities such as Ti, Cr, Fe, and Ni intrinsic to HT-7 tokamak can also be inspected. The accuracy of the electron temperature derived from the soft x-ray energy spectrum measurements is verified by comparing with the temperature measured by the Thomson scattering system for various plasmas and electron cyclotron emission diagnostic system for ohmic plasmas. The bulk electron temperature of about 1 keV and Zeff≈2 were achieved for long pulse plasma. The appreciable Kα lines of Ti, Cr, Fe and Ni metallic impurities released from the antennas of radio frequency wave and/or the first wall and Ar injected into plasma can be observed, and they kept stable during the long duration discharges. As a result, the longest pulse discharge with relatively high temperature of Te(0)∼1 keV, and ne(0)∼0.5×¹⁰¹⁹ m−3 has been achieved with a duration of 400 s in the HT-7 experimental campaign in 2008.     

The active role played by nonmagnetic Sr in magnetostructural coupling in SrTcO3 from first principles

The total energies and structural parameters of SrTcO₃ are calculated by means of the generalized gradient approximation (GGA) plus on-site Coulomb interaction corrections (GGA+U) method. G-type antiferromagnetic (G-AFM) is found to be ground state, in consistence with the previous experimental result. The distortions around Sr and Tc upon magnetic transition are compared and the change of distortion for SrO bond upon magnetic transition is found to be 25.83 times of the change for TcO bond. Our results point to an active role played by Sr in magnetostructural coupling in SrTcO₃.     

Magnetization and characteristic fields in Nd0.8Ba0.2FeAsO0.6F0.4 with binary doping

In the present work, the iron oxypnictide superconductor of the namely Nd_0.8Ba_0.2FeAsO_0.6F_0.4 is prepared with respect to the observation of distinct magnetization characteristics arising from both electron and hole doping. A magnetothermal phase diagram is given for the present iron oxypnictide system, based on the irreversibility fields (H_irr) and the upper critical fields (H_c2) obtained from magnetotransport measurements, as well as the lower critical fields (H_c1) evaluated by magnetization loops at various temperatures. High H_c2(0) are revealed at low temperature range, which is in consistent with the observations of comparatively high critical current (J_c) and the temperature dependent peak effect in the J_c vs H curves.     

Description of the transport critical current density behavior of polycrystalline superconductors as a function of the applied magnetic field

A model to describe the critical current density behavior of high-T_c polycrystalline superconductors is proposed for all magnetic field values. The main features of the model are as follows: the transport critical current density is controlled by the weak-link network at grain boundaries. The size distribution of weak links is well represented by a Gamma-type distribution. Finally, the tunneling critical current between grains follows a Fraunhofer diffraction pattern or a modified pattern if the applied magnetic field is lower or higher than the first critical field H_c1.