Degree distributions of the visibility graphs mapped from fractional Brownian motions and multifractal random walks

The dynamics of a complex system is usually recorded in the form of time series, which can be studied through its visibility graph from a complex network perspective. We investigate the visibility graphs extracted from fractional Brownian motions and multifractal random walks, and find that the degree distributions exhibit power-law behaviors, in which the power-law exponent α is a linear function of the Hurst index H of the time series. We also find that the degree distribution of the visibility graph is mainly determined by the temporal correlation of the original time series with minor influence from the possible multifractal nature. As an example, we study the visibility graphs constructed from three Chinese stock market indexes and unveil that the degree distributions have power-law tails, where the tail exponents of the visibility graphs and the Hurst indexes of the indexes are close to the α∼H linear relationship.     

Quantifying cross-correlations using local and global detrending approaches

In order to quantify the long-range cross-correlations between two time series qualitatively, we introduce a new cross-correlations test Q_CC(m), where m is the number of degrees of freedom. If there are no cross-correlations between two time series, the cross-correlation test agrees well with the χ²(m) distribution. If the cross-correlations test exceeds the critical value of the χ²(m) distribution, then we say that the cross-correlations are significant. We show that if a Fourier phase-randomization procedure is carried out on a power-law cross-correlated time series, the cross-correlations test is substantially reduced compared to the case before Fourier phase randomization. We also study the effect of periodic trends on systems with power-law cross-correlations. We find that periodic trends can severely affect the quantitative analysis of long-range correlations, leading to crossovers and other spurious deviations from power laws, implying both local and global detrending approaches should be applied to properly uncover long-range power-law auto-correlations and cross-correlations in the random part of the underlying stochastic process.     

A new theoretical constraint on the static critical behaviour of the specific heat

We show from a field-theoretical approach that, if we admit that the additive renormalization function of the specific heat C is singular at the fixed point, we obtain a coherent formulation of the critical behaviour of C. Especially we show that the α<0 case, which corresponds to a cusp for C, is dominated by a critical constant B_cr generated by the long-range correlations of the fluctuations. We derive a universal combination between the leading and first correction amplitudes and B_cr, which will have a great importance in the analysis of experimental data.     

Fokker-Planck equation with fractional coordinate derivatives

Using the generalized Kolmogorov-Feller equation with long-range interaction, we obtain kinetic equations with fractional derivatives with respect to coordinates. The method of successive approximations, with averaging with respect to a fast variable, is used. The main assumption is that the correlation function of probability densities of particles to make a step has a power-law dependence. As a result, we obtain a Fokker-Planck equation with fractional coordinate derivative of order 1<α<2.     

Self-affine analysis of protein energy

We study the time series of the total energy of polypeptides and proteins. These time series were generated by molecular dynamics methods and analyzed by applying detrended fluctuation analysis to estimate the long-range power-law correlation, i.e. to measure scaling exponents α. Such exponents were calculated for all systems and their values follow environment conditions, i.e., they are temperature dependent and also, in a continuum medium approach, vary according to the dielectric constants (we simulated ?=2 and ?=80). The procedure was applied to investigate polyalanines, and other realistic models of proteins (Insect Defensin A and Hemoglobin). The present findings exhibit results that are consistent with previous ones obtained by other methodologies.     

Spectral Gap and Exponential Decay of Correlations

We study the relation between the spectral gap above the ground state and the decay of the correlations in the ground state in quantum spin and fermion systems with short-range interactions on a wide class of lattices. We prove that, if two observables anticommute with each other at large distance, then the nonvanishing spectral gap implies exponential decay of the corresponding correlation. When two observables commute with each other at large distance, the connected correlation function decays exponentially under the gap assumption. If the observables behave as a vector under the U(1) rotation of a global symmetry of the system, we use previous results on the large distance decay of the correlation function to show the stronger statement that the correlation function itself, rather than just the connected correlation function, decays exponentially under the gap assumption on a lattice with a certain self-similarity in (fractal) dimensions D < 2. In particular, if the system is translationally invariant in one of the spatial directions, then this self-similarity condition is automatically satisfied. We also treat systems with long-range, power-law decaying interactions.     

Low energy excitations in KMnO4 with 1 eV<=ΔE<=10 eV from electron-energy loss spectroscopy

Electron-energy loss spectra of potassium permanganate (KMnO₄) with primary electron energies 25 eV<=E₀<=500 eV show 7 peaks in the energy-loss range 1 eV<=ΔE<=10eV and are successfully analysed with a superposition of 7 independent Gaussians. The intensity of these lines follow roughly a power-law dependence on the primary energy I∝E ₀ ^-α . There are two groups of lines, the first with an exponent α≈0.5, while the lines in the second group decay much stronger with increasingE ₀ corresponding to a value 0.9<=α<=1.3. The 4 lines in the first group are identified as dipole allowed transitions by comparison to recent first principle molecular-orbital calculations for the (MnO₄) molecule by H. Nakai et al. The dipole-allowed excitation spectrum obtained from this analysis agrees very well with these first principle calculations.     

空间网络上的随机游走

本文以一维均匀环为基础, 通过添加有限数量的长程连接构造出了一维有限能量约束下的空间网络, 环上任意节点i与j之间存在一条长程连接的概率满足p_ijα d_ij^-α (α≥ 0),其中d_ij为节点i与j之间的网格距离, 并且所有长程连接长度总和受到总能量∧=cN(c≥ 0)的约束, N为网络节点总数.通过研究该空间网络上的随机游走过程,存在最优幂指数α₀ 使得陷阱问题的平均首达时间最短.进一步研究发现,平均首达时间与网络规模N之间存在着幂律关系, 随着网络规模N和总能量∧的增加,最优幂指数α₀单调增加,并趋近最优值1.5.     

Long-range dependence in tree-ring width time series of Austrocedrus Chilensis revealed by means of the detrended fluctuation analysis

By using the detrended fluctuation analysis and detrended moving average method, 823 time series of tree-ring widths in Austrocedrus Chilensis in Patagonia were analyzed. The tree-ring widths of A. Chilensis have been widely used for climatological studies. The results point out to the presence of significant scaling in the temporal fluctuations of tree-ring, which is not due to singular probability density function of the widths but due to the presence of long-range correlations. Such results are in good agreement with those concerning the evidence of long-range dependencies in weather time series.     

One-Dimensional Ising Models with Long Range Interactions: Cluster Expansion,Phase-Separating Point

We consider the phase separation problem for the one-dimensional ferromagnetic Ising model with long-range two-body interaction, J(n) = n ^?2+α , where ${n\in {\rm {I\!N}}}$ denotes the distance of the two spins and ${\alpha \in [0,\alpha_+[}$ with α ₊ = (log 3)/(log 2) ?1. We prove that when α = 0 the localization of the phase separation fluctuates macroscopically with a non-uniform explicit limiting law, while when 0 < α < α ₊ the macroscopic fluctuations disappear and mesoscopic ones appear with a gaussian behavior when conveniently scaled. The mean magnetization profile is also given.     

Statistical properties of visibility graph of energy dissipation rates in three-dimensional fully developed turbulence

We study the statistical properties of complex networks constructed from time series of energy dissipation rates in three-dimensional fully developed turbulence using the visibility algorithm. The degree distribution is found to have a power-law tail with the tail exponent α=3.0. The exponential relation between the number of the boxes N_B and the box size l_B based on the edge-covering box-counting method illustrates that the network is not self-similar, which is also confirmed by the hub-hub attraction according to the visibility algorithm. In addition, it is found that the skeleton of the visibility network exhibits excellent allometric scaling with the scaling exponent η=1.163±0.005.     

Subnanosecond transient photocurrents in a-Si:H: A probe of thermalization within shallow band-tail states

The measurement of transient photocurrents in amorphous semiconductors has been shown to be a powerful way of exploring the thermalization of excess carriers within the manifold of localized states adjacent to the band edges. The extent to which thermalization within the shallowest states can be resolved in controlled by the experimental observation time. Reported here are measurements of transient photocurrents, using high-speed stripline techniques, in glow-discharge a-Si:H carried out in the time regime (0.6 ? 100 nsec) and the temperature range 150 ? 320K. We find an effective electron drift mobility of <μ_D(t)> = 1–3 cm²/Vsec at t=0.6 nsec and T=300K and a time-dependent activation energy, _?(t), for the photocurrent magnitude. The initial photocurrent decay (t < 100 nsec) can be fit to a power-law, t^?n, and the temperature dependence of the dispersion parameter, α=1?n, is given by α=α₀+βT. In view of these results the nature of the band-tail near the conduction band edge is discussed.     

Magnetic properties of MnxMg1-xS solid solutions

The static magnetic properties of the polycrystalline solid solutions Mn_xMg_1-xS(0<x?1) are reported. The experimental data reveal the appearance of a critical concentration x_c=0.13±0.01 for long-range magnetic ordering, which is in good agreement with the result of a series expansion of the mean cluster size for a face-centered cubic lattice with exchange interactions up to 12 nearest neighbours and 6 next-nearest neighbours. At concentrations far below x_c the existence of long-range exchange interactions is demonstrated.     

Conducting to non-conducting transition in dual transmission lines using a ternary model with long-range correlated disorder

In this work we study the behavior of the allowed and forbidden frequencies in disordered classical dual transmission lines when the values of capacitances {Cj} are distributed according to a ternary model with long-range correlated disorder. We introduce the disorder from a random sequence with a power spectrum S(k)∝k−(2α−1), where α?0.5 is the correlation exponent. From this sequence we generate an asymmetric ternary map using two map parameters b₁ and b₂, which adjust the occupancy probability of each possible value of the capacitances Cj={CA,CB,CC,}. If the sequence of capacitance values is totally at random α=0.5 (white noise), the electrical transmission line is in the non-conducting state for every frequency ω. When we introduce long-range correlations in the distribution of capacitances, the electrical transmission lines can change their conducting properties and we can find a transition from the non-conducting to conducting state for a fixed system size. This implies the existence of critical values of the map parameters for each correlation exponent α. By performing finite-size scaling we obtain the asymptotic value of the map parameters in the thermodynamic limit for any α. With these data we obtain a phase diagram for the symmetric ternary model, which separates the non-conducting state from the conducting one. This is the fundamental result of this Letter. In addition, introducing one or more impurities in random places of the long-range correlated distribution of capacitances, we observe a dramatic change in the conducting properties of the electrical transmission lines, in such a way that the system jumps from conducting to non-conducting states. We think that this behavior can be considered as a possible mechanism to secure communication.     

Multifractal properties of the Indian financial market

We investigate the multifractal properties of the logarithmic returns of the Indian financial indices (BSE & NSE) by applying the multifractal detrended fluctuation analysis. The results are compared with that of the US S&P 500 index. Numerically we find that qth-order generalized Hurst exponents h(q) and τ(q) change with the moments q. The nonlinear dependence of these scaling exponents and the singularity spectrum f(α) show that the returns possess multifractality. By comparing the MF-DFA results of the original series to those for the shuffled series, we find that the multifractality is due to the contributions of long-range correlations as well as the broad probability density function. The financial markets studied here are compared with the Binomial Multifractal Model (BMFM) and have a smaller multifractal strength than the BMFM.     

Impact of initial lattice structures on networks generated by traces of random walks

We show that the platform stage of network evolution plays a principal role in the topology of resulting networks generated by short-cuts stimulated by the movements of a random walker, the mechanism of which tends to produce power-law degree distributions. To examine the numerical results, we have developed a statistical method which relates the power-law exponent γ to random properties of the subgraph developed in the platform stage. As a result, we find that an important exponent in the network evolution is α, which characterizes the size of the subgraph in the form V∼t^α, where V and t denote the number of vertices in the subgraph and the time variable, respectively. 2D lattices can impose specific limitations on the walker’s diffusion, which keeps the value of α within a moderate range and provides typical properties of complex networks. 1D and 3D cases correspond to different ends of the spectrum for α, with 2D cases in between. Especially for 2D square lattices, a discontinuous change of the network structure is observed, which varies according to whether γ is greater or less than 2. For 1D cases, we show that emergence of nearly complete subgraphs is guaranteed by α<1/2, although the transient power-law is permitted at low increase rates of edges. Additionally, the model exhibits a spontaneous emergence of highly clustered structures regardless of its initial structure.     

Alpha-heavy-ion angular correlations from 28Si + 12C

Alpha particles have been measured in coincidence with heavy recoil nuclei from the ²⁸Si + ¹²C reaction. At E_lab = 87 MeV angular correlations for alphas between 15° and 55° and heavy ions at angles ?9°, ?12° and ?15° have been taken. An excitation function of coincidence events with θ_α = 30° and θ_HI = ?12° has been measured for 84 MeV < E_lab < 91.5 MeV. The results are well described by a statistical-model calculation for compound nucleus decay. No evidence is found for additional processes.     

CMS ridge effect at LHC as a manifestation of bremsstrahlung of gluons off quarks accelerated in a strong color field

The recently reported effect of long-range near-side angular correlations at LHC occurs for large multiplicities of particles with 1 GeV<p _T <3 GeV. To understand the effect several possibilities have been discussed. In the letter we propose a simple qualitative mechanism which corresponds to gluon bremsstrahlung of quarks moving with acceleration defined by the string tension. The smallness of azimuthal angle difference Δφ along with large Δη at large multiplicities in this interval of p _T are natural in this mechanism. The mechanism predicts also bremsstrahlung photons with mean values of p _T ≈2.9 and 0.72 GeV.     

Transition on the relationship between fractal dimension and Hurst exponent in the long-range connective sandpile models

The relationships between the Hurst exponent H and the power-law scaling exponent B in a new modification of sandpile models, i.e. the long-range connective sandpile (LRCS) models, exhibit a strong dependence upon the system size L. As L decreases, the LRCS model can demonstrate a transition from the negative to positive correlations between H- and B-values. While the negative and null correlations are associated with the fractional Gaussian noise and generalized Cauchy processes, respectively, the regime with the positive correlation between the Hurst and power-law scaling exponents may suggest an unknown, interesting class of the stochastic processes.     

Evidence for a spin glass state in the intermetallic compounds Gd3Pd4−xPtx

Magnetic susceptability measurements in static fields have shown that the intermetallic compound Gd₃Pd_4?xPt_x exhibits a transition from antiferromagnetism for x = 3 to a spin glass state for x < 2 below 7.5 K. For x = 3 long-range ordering is established and for x = 2 both long-range ordering and the spin glass state are clearly present.