Random walks and diameter of finite scale-free networks

Dynamical scalings for the end-to-end distance R_ee and the number of distinct visited nodes N_v of random walks (RWs) on finite scale-free networks (SFNs) are studied numerically. 〈R_ee〉 shows the dynamical scaling behavior , where is the average minimum distance between all possible pairs of nodes in the network, N is the number of nodes, γ is the degree exponent of the SFN and t is the step number of RWs. Especially, in the limit t→∞ satisfies the relation , where d is the diameter of network with for γ≥3 or for γ<3. Based on the scaling relation 〈R_ee〉, we also find that the scaling behavior of the diameter of networks can be measured very efficiently by using RWs.     

Emergence of scale-free behavior in networks from limited-horizon linking and cost trade-offs

We study network growth from a fixed set of initially isolated nodes placed at random on the surface of a sphere. The growth mechanism we use adds edges to the network depending on strictly local gain and cost criteria. Only nodes that are not too far apart on the sphere may be considered for being joined by an edge. Given two such nodes, the joining occurs only if the gain of doing it surpasses the cost. Our model is based on a multiplicative parameter λ that regulates, in a function of node degrees, the maximum geodesic distance that is allowed between nodes for them to be considered for joining. For n nodes distributed uniformly on the sphere, and for within limits that depend on cost-related parameters, we have found that our growth mechanism gives rise to power-law distributions of node degree that are invariant for constant . We also study connectivity- and distance-related properties of the networks.     

Effects of epidemic threshold definition on disease spread statistics

We study the statistical properties of SIR epidemics in random networks, when an epidemic is defined as only those SIR propagations that reach or exceed a minimum size s_c. Using percolation theory to calculate the average fractional size of an epidemic, we find that the strength of the spanning link percolation cluster P_∞ is an upper bound to . For small values of s_c, P_∞ is no longer a good approximation, and the average fractional size has to be computed directly. We find that the choice of s_c is generally (but not always) guided by the network structure and the value of T of the disease in question. If the goal is to always obtain P_∞ as the average epidemic size, one should choose s_c to be the typical size of the largest percolation cluster at the critical percolation threshold for the transmissibility. We also study Q, the probability that an SIR propagation reaches the epidemic mass s_c, and find that it is well characterized by percolation theory. We apply our results to real networks (DIMES and Tracerouter) to measure the consequences of the choice s_c on predictions of average outcome sizes of computer failure epidemics.     

Node similarity within subgraphs of protein interaction networks

We propose a biologically motivated quantity, twinness, to evaluate local similarity between nodes in a network. The twinness of a pair of nodes is the number of connected, labeled subgraphs of size n in which the two nodes possess identical neighbours. The graph animal algorithm is used to estimate twinness for each pair of nodes (for subgraph sizes n=4 to n=12) in four different protein interaction networks (PINs). These include an Escherichia coli PIN and three Saccharomyces cerevisiae PINs — each obtained using state-of-the-art high-throughput methods. In almost all cases, the average twinness of node pairs is vastly higher than that expected from a null model obtained by switching links. For all n, we observe a difference in the ratio of type twins (which are unlinked pairs) to type twins (which are linked pairs) distinguishing the prokaryote E. coli from the eukaryote S. cerevisiae. Interaction similarity is expected due to gene duplication, and whole genome duplication paralogues in S. cerevisiae have been reported to co-cluster into the same complexes. Indeed, we find that these paralogous proteins are over-represented as twins compared to pairs chosen at random. These results indicate that twinness can detect ancestral relationships from currently available PIN data.     

4-benzyl pyridinium dihydrogenmonophosphate C6H5CH2C5H4NHH2PO4 : Single-crystal structure and its conductivity in polycrystalline form

The salt 4-benzyl pyridinium dihydrogenmonophosphate is monoclinic P2₁/c with the following unit cell dimensions: ; ; ; and β=97.328(11). Also, , D_x=1.403, , F(000)=560; ; and R=0.0495 and R_w=0.0964 for 3733 independent reflections. The structure consists of infinite parallel two-dimensional planes built of H₂PO₄⁻ anions and C₆H₅CH₂C₅H₄NH⁺ cations mutually connected by strong O-H ?O and N-H ?O hydrogen bonding. There are no contacts other than the normal Van der Waals interactions between the layers. The conductivity relaxation parameters associated with some H⁺ conduction have been determined from an analysis of the spectrum measured in a wide temperature range.     

Attack vulnerability of scale-free networks due to cascading failures

In this paper, adopting the initial load of a node i to be with k_i being the degree of the node i, we propose a cascading model based on a load local redistribution rule and examine cascading failures on the typical network, i.e., the BA network with the scale-free property. We find that the BA scale-free network reaches the strongest robustness level in the case of α=1 and the robustness of the network has a positive correlation with the average degree 〈k〉, where the robustness is quantified by a transition from normal state to collapse. In addition, we further discuss the effects of two different attacks for the robustness against cascading failures on our cascading model and find an interesting result, i.e., the effects of two different attacks, strongly depending to the value α. These results may be very helpful for real-life networks to avoid cascading-failure-induced disasters.     

Traffic dynamics in scale-free networks with limited packet-delivering capacity

We propose a limited packet-delivering capacity model for traffic dynamics in scale-free networks. In this model, the total node’s packet-delivering capacity is fixed, and the allocation of packet-delivering capacity on node i is proportional to , where k_i is the degree of node i and ? is a adjustable parameter. We have applied this model on the shortest path routing strategy as well as the local routing strategy, and found that there exists an optimal value of parameter ? leading to the maximal network capacity under both routing strategies. We provide some explanations for the emergence of optimal ?.     

Scaling and memory effect in volatility return interval of the Chinese stock market

We investigate the probability distribution of the volatility return intervals τ for the Chinese stock market. We rescale both the probability distribution P_q(τ) and the volatility return intervals τ as to obtain a uniform scaling curve for different threshold value q. The scaling curve can be well fitted by the stretched exponential function , which suggests memory exists in τ. To demonstrate the memory effect, we investigate the conditional probability distribution P_q(τ|τ₀), the mean conditional interval 〈τ|τ₀〉 and the cumulative probability distribution of the cluster size of τ. The results show clear clustering effect. We further investigate the persistence probability distribution P_±(t) and find that P₋(t) decays by a power law with the exponent far different from the value 0.5 for the random walk, which further confirms long memory exists in τ. The scaling and long memory effect of τ for the Chinese stock market are similar to those obtained from the United States and the Japanese financial markets.     

Statistical properties of volatility return intervals of Chinese stocks

The statistical properties of the return intervals τ_q between successive 1-min volatilities of 30 liquid Chinese stocks exceeding a certain threshold q are carefully studied. The Kolmogorov-Smirnov (KS) test shows that 12 stocks exhibit scaling behaviors in the distributions of τ_q for different thresholds q. Furthermore, the KS test and weighted KS test show that the scaled return interval distributions of 6 stocks (out of the 12 stocks) can be nicely fitted by a stretched exponential function with γ≈0.31 under the significance level of 5%, where is the mean return interval. The investigation of the conditional probability distribution P_q(τ|τ₀) and the mean conditional return interval 〈τ|τ₀〉 demonstrates the existence of short-term correlation between successive return interval intervals. We further study the mean return interval 〈τ|τ₀〉 after a cluster of n intervals and the fluctuation F(l) using detrended fluctuation analysis, and find that long-term memory also exists in the volatility return intervals.     

Ordered zinc-vacancy induced Zn0.75Ox nanophase structure

Using transmission electron microscopy, a new nano-phase structure of Zn_0.75O_x induced by Zn-vacancy has been discovered to grow on wurtzite ZnO nanobelts. The superstructure grows epitaxial from the surface of the wurtzite ZnO nanobelts and can be fitted as an orthorhombic structure, with lattice parameters a′=2a, and c′=c, where a and c are the lattice parameters of ZnO. The superstructured phase is resulted from high-density Zn vacancies orderly distributed in the ZnO matrix. This study provides direct observation about the existence of Zn-vacancies in ZnO.     

Anisotropy of the magnetocaloric effect in DyNiAl

We present study of the anisotropic magnetocaloric effect in DyNiAl. This compound crystallizes in the hexagonal ZrNiAl-type structure, orders magnetically below and undergoes a further magnetic phase transition at . The Dy-moments are aligned ferromagnetically along the hexagonal c-axis below T_C, the additional antiferromagnetic component develops within the basal plane below T₁. The magnetocaloric effect was evaluated from the magnetization measurements with field applied along the c-axis and perpendicular to it. Our data reveal a strong anisotropy of the magnetocaloric effect. The large effect occurs for field applied along the c-axis whereas the entropy change is small for the perpendicular field direction.     

Local magnetization study of the first-order superconducting transition in CeCoIn5

We report local magnetization measurements on the heavy fermion superconductor CeCoIn₅ using a micro-Hall probe. Below a critical point T₀ (), the local magnetization shows a clear jump at the superconducting transition temperatures for both H∥a and H∥c, indicating that the phase transition at the upper critical field H_c2 becomes a first-order phase transition. In addition, we observed an undershoot behavior of magnetization jump above (H∥c), which suggests a rapid change of textured superconducting structure with vortices and the nodal planes expected in the Fulde-Ferrell-Larkin-Ovchinnikov state.     

Multiple superconducting gap and anisotropic spin fluctuations in iron arsenides: Comparison with nickel analog

We present extensive ⁷⁵As NMR and NQR data on the superconducting arsenides PrFeAs_0.89F_0.11, LaFeAsO_0.92F_0.08, LiFeAs and Ba_0.72K_0.28Fe₂As₂ single crystal, and compare with the nickel analog LaNiAsO_0.9F_0.1. In contrast to LaNiAsO_0.9F_0.1 where the superconducting gap is shown to be isotropic, the spin lattice relaxation rate 1/T₁ in the Fe-arsenides decreases below T_c with no coherence peak and shows a step-wise variation at low temperatures. The Knight shift decreases below T_c and shows a step-wise T variation as well. These results indicate spin-singlet superconductivity with multiple gaps in the Fe-arsenides. The Fe antiferromagnetic spin fluctuations are anisotropic and weaker compared to underdoped copper-oxides or cobalt-oxide superconductors, while there is no significant electron correlations in LaNiAsO_0.9F_0.1. We will discuss the implications of these results and highlight the importance of the Fermi surface topology.     

Critical current density and flux pinning in an unconventional superconductor

The functional dependence of the critical current density on magnetic field, Jc(H), observed at fixed temperatures in the unconventional type-II superconductor, LaAg1−cMnc (c=0.1,0.2,0.3) alloys, but not the relative magnitude of Jc in different alloy compositions at any given temperature and field, is adequately described by the exponential-decay critical state model. In accordance with the predictions of the Kramer's flux-pinning model, the peak value of the pinning force density with the exponent 1.7?m?2.8 and scales with h=H/Hc₂, where Hc₂ is the upper critical field. Irrespective of sample composition and temperature in the superconducting state, the pinning of the flux line lattice (FLL) dominates over the plastic FLL shear.     

Synthesis and crystal structure of [3,5-(CH3)2C6H3NH3]4P4O12·3H2O

Chemical preparation and crystal structure are given for a new cyclotetraphosphate: [3,5-(CH₃)₂C₆H₃NH₃]₄P₄O₁₂·3H₂O. This compound is triclinic P with the following unit-cell parameters: a=8.298(3), b=8.299(3), c=17.242(7)Å, α=97.13(3), β=102.72(3), γ=64.55(3)°, Z=1 and V=1045.2(8)ų. The crystal structure has been solved and refined to R=0.040 using 6086 independent reflections. The atomic arrangement can be described as layers organization. Layers built by P₄O₁₂ ring anions, ammonium groups and water molecules parallel to the plan (001), between which the organic groups are located. Characterization by X-ray diffraction, IR absorption, and thermal analysis are described.     

Low-temperature magnetic structures in the DySi FeB-type compound 27.03.09

The low-temperature magnetic ordering of the dimorphic DySi compound has been studied at 1.5 K by neutron diffraction on two polycrystalline samples. The samples comprise various amounts of the two orthorhombic modifications: CrB-type (Cmcm Nr. 63, all atoms at 4c site: (0, y, )) and FeB-type (Pnma Nr. 62, all atoms at 4c site: (x, , z)), both order antiferromagnetically (T_N≈38 K). The CrB-type phase orders with a uniaxial structure with the wave vector q₁=(0, 0, ) requiring a doubling of the c-axis. The Dy moments point along the linear chain with the shortest distance c. At 1.5 K, the ordered moment value is 8.57(1) μ_B/Dy atom.Two symmetry independent wave vectors describe the 1.5 K magnetic ordering of the FeB-type phase: q₂=(0, , ) and q₃=(0, 0.484(1), 0.0892(1)), coexisting in form of domains. In both structures the magnetic moments are confined to the (0 0 1) plane at an angle of 2(2)° and 22(3)° from the shortest axis b, respectively. Both structures correspond to sine wave modulations. The amplitude of the q₂ wave is m_o=7.5(1) μ_B/Dy atom and that of q₃ 8.2(1) μ_B/Dy atom. The wave vector q₂ when referring to the (a, 2b, c) cell and the wave vector q=(0, 0, ) corresponds to a transversal modulation, which by a proper origin choice can be also described as an antiphase domain structure with two amplitudes. The moments point to the b-axis and are stacked in the sequence (+m_o/2, −m_o/2, −m_o, −m_o/2, +m_o/2, +m_o, …) along the c-direction, while t_b acts as an antitranslation. For the q₃ phase, the local moment value depends on the atom position in the wave. We also discuss the case where q₃ and q₂ act simultaneously in physical space.