Scale invariance analysis of the premature ECG signals

The multifractal detrended fluctuation analysis and detrending moving average algorithm were introduced in detail and applied to the study of the multifractal characteristics of the normal signals, the atrial premature beat (APB) signals and the premature ventricular contraction (PVC) signals. By analyzing the generalized Hurst exponents, Renyi exponents and multifractal spectrum and comparing the relation of h∼h(q)$h\sim h\left(q\right)$ for original signals and their shuffled time series, the result indicated that the three signals have multifractality and present long-range correlation in a certain range. According to the mean value of Δα$\Delta \alpha$, we found that the strength of the multifractality is varying. The PVC signals is the strongest, and the Normal signals is the weakest. It is useful for clinical practice of medicine to distinguish APB signals with PVC signals.     

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.     

On the scaling ranges of detrended fluctuation analysis for long-term memory correlated short series of data

We examine the scaling regime for the detrended fluctuation analysis (DFA)—the most popular method used to detect the presence of long-term memory in data and the fractal structure of time series. First, the scaling range for DFA is studied for uncorrelated data as a function of time series length L$L$ and the correlation coefficient of the linear regression R²$R^2$ at various confidence levels. Next, a similar analysis for artificial short series of data with long-term memory is performed. In both cases the scaling range λ$\lambda$ is found to change linearly—both with L$L$ and R²$R^2$. We show how this dependence can be generalized to a simple unified model describing the relation λ=λ(L,R²,H)$\lambda =\lambda (L,R^2,H)$ where H$H$ (1/2≤H≤1$1/2\le H\le 1$) stands for the Hurst exponent of the long range autocorrelated signal. Our findings should be useful in all applications of DFA technique, particularly for instantaneous (local) DFA where a huge number of short time series has to be analyzed at the same time, without possibility of checking the scaling range in each of them separately.     

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.     

Primordial perturbation in Hořava–Lifshitz cosmology

Recently, Ho?ava has proposed a renormalizable theory of gravity with critical exponent z=3$z=3$ in the UV. This proposal might imply that the scale invariant primordial perturbation can be generated in any expansion of early universe with a∼tn$a\sim t^n$ and n>1/3$n>1/3$, which, in this Letter, will be confirmed by solving the motion equation of perturbation mode on super sound horizon scale for any background evolution of early universe. It is found that if enough efolding number of primordial perturbation suitable for observable universe is required, then n?1$n?1$ needs to be satisfied, unless the scale of UV regime is quite low. However, the possible UV completeness of HL gravity helps to relax this bound.     

Empirical study of the scaling behavior of the amplitude–frequency distribution of the Hilbert–Huang transform and its application in sunspot time series analysis

Investigating long-range correlation by the Hurst exponent, H$H$, is crucial in the study of time series. Recently, empirical-mode-decomposition-based arbitrary-order Hilbert spectral analysis (EMD-HSA) has been proposed to numerically obtain without proof a scaling relationship, generated from the amplitude–frequency distribution, related to H$H$. We propose a formalism to empirically study EMD-HSA, to deduce its scaling exponent ξ(q)$\xi \left(q\right)$ from the perspective of EMD-based arbitrary-order Hilbert marginal spectrum (EMD-HMS), and to numerically compare the results with the expected H$H$. EMD-HSA and EMD-HMS experiments show that, by incompletely removing (quasi-)periodic trends, the sunspot series should have an H$H$ value around 0.12.     

About the fastest growth of the Order Parameter in models of percolation

The growth of the average size 〈_smax〉$〈s_{max}〉$ of the largest component at the percolation threshold _pc(N)$p_c\left(N\right)$ on a graph of size N$N$ has been defined as 〈_smax(_pc(N),N)〉∼N^χ$〈s_{max}(p_c\left(N\right),N)〉\sim N^{\chi }$. Here we argue that the precise value of the ‘growth exponent’ χ$\chi$ indicates the nature of percolation transition; χ<1$\chi <1$ or χ=1$\chi =1$ determines if the transition is continuous or discontinuous. We show that a related exponent η=1−χ$\eta =1-\chi$ which describes how the average maximal jump sizes in the Order Parameter decays on increasing the system size, is the single exponent that describes the finite-size scaling of a number of distributions related to the fastest growth of the Order Parameter in these problems. Excellent quality scaling analysis are presented for the two single peak distributions corresponding to the Order Parameters at the two ends of the maximal jump, the bimodal distribution constructed by the weighted average of these distributions and for the distribution of the maximal jump in the Order Parameter.     

Geometrically-frustrated pseudogap phase of Coulomb liquids

We study a class of models with long-range repulsive interactions of the generalized Coulomb form V(r)∼1/r^α$V(r)\sim 1/r^{\alpha }$. We show that decreasing the interaction exponent in the regime α<d$\alpha <d$ dramatically depresses the charge ordering temperature T_c in any dimension d≥2$d\ge 2$, reflecting the strong geometric frustration produced by long-range interactions. A nearly frozen Coulomb liquid then survives in a broad pseudogap phase found at T>T_c$T>T_c$, which is characterized by an unusual temperature dependence of all quantities. In contrast, the leading critical behavior very close to the charge-ordering temperature remains identical as in models with short-range interactions.     

Modeling innovation by a kinetic description of the patent citation system

This paper reports results of a network theory approach to the study of the United States patent system. We model the patent citation network as a discrete time, discrete space stochastic dynamic system. From patent data we extract an attractiveness function, A(k,l)$A(k,l)$, which determines the likelihood that a patent will be cited. A(k,l)$A(k,l)$ shows power law aging and preferential attachment. The exponent of the latter is increasing since 1993, suggesting that patent citations are increasingly concentrated on a relatively small number of patents. In particular, our results appear consistent with an increasing patent “thicket”, in which more and more patents are issued on minor technical advances.     

First observation of electronic structure of the even parity boron acceptor states in diamond

We use electronic Raman scattering for studying the band structure of the ns$\mathrm{n}s$ boron acceptor states in diamond. For the first time, the spin–orbit splitting of these acceptor states and the 1s→ns$1s\to \mathrm{n}s$ Lyman series of transitions are observed. The spin–orbit splitting linearly increases with n number. Lyman series exhibit fine structure consisting of four bands each. The energy spacing between series is equal to ∼13 meV$\sim 13\text{meV}$. Evolution of Raman spectra of the boron-doped diamond with increasing boron concentration is shown. Mott transition is revealed in Raman spectrum. Correct values of Luttinger parameters for diamond are specified.     

Coincidence problem in YM field dark energy model

The coincidence problem is studied in the effective Yang–Mills condensate dark energy model. As the effective YM Lagrangian is completely determined by quantum field theory, there is no adjustable parameter in this model except the energy scale, and the cosmic evolution only depends on the initial conditions. For generic initial conditions with the YM condensate subdominant to the radiation and matter, the model always has a tracking solution, the Universe transits from matter-dominated into the dark energy dominated stage only recently z∼0.3$z\sim 0.3$, and evolve to the present state with Ωy∼0.73${\Omega }_y\sim 0.73$ and Ωm∼0.27${\Omega }_m\sim 0.27$.     

Efficiency of star-like graphs and the Atlanta subway network

The distance d(i,j)$d(i,j)$ between any two vertices i$i$ and j$j$ in a graph is the number of edges in a shortest path between i$i$ and j$j$. If there is no path connecting i$i$ and j$j$, then d(i,j)=∞$d(i,j)=\infty$. In 2001, Latora and Marchiori introduced the measure of efficiency between vertices in a graph (Latora and Marchiori, 2001) [1]. The efficiency between two vertices i$i$ and j$j$ is defined to be _∈i,j=j${\in }_{i,j}=j$. In this paper, we investigate the efficiency of star-like networks, and show that networks of this type have a high level of efficiency. We apply these ideas to an analysis of the Metropolitan Atlanta Rapid Transit Authority (MARTA) Subway system, and show this network is 82% as efficient as a network where there is a direct line between every pair of stations.     

Implications of neutrino mass generation from QCD confinement

We consider the possibility that the quark condensate formed by QCD confinement generates Majorana neutrino masses mν$m_{\nu }$ via dimension seven operators. No degrees of freedom beyond the Standard Model are necessary, below the electroweak scale. Obtaining experimentally acceptable neutrino masses requires the new physics scale Λ∼TeV$\Lambda \sim \text{TeV}$, providing a new motivation for weak-scale discoveries at the LHC. We implement this mechanism using a Z₃$Z_3$ symmetry which leads to a massless up quark above the QCD chiral condensate scale. We use non-helicity-suppressed light meson rare decay data to constrain Λ. Experimental constraints place a mild hierarchy on the flavor structure of dimension seven operators and the resulting neutrino mass matrix.     

Quantum criticality and Yang–Mills gauge theory

We present a family of nonrelativistic Yang–Mills gauge theories in D+1$D+1$ dimensions whose free-field limit exhibits quantum critical behavior with gapless excitations and dynamical critical exponent z=2$z=2$. The ground state wavefunction is intimately related to the partition function of relativistic Yang–Mills in D   dimensions. The gauge couplings exhibit logarithmic scaling and asymptotic freedom in the upper critical spacetime dimension, equal to 4+1$4+1$. The theories can be deformed in the infrared by a relevant operator that restores Poincaré invariance as an accidental symmetry. In the large-N limit, our nonrelativistic gauge theories can be expected to have weakly curved gravity duals.     

Worm Monte Carlo study of the honeycomb-lattice loop model

We present a Markov-chain Monte Carlo algorithm of worm   type that correctly simulates the O(n)$O(n)$ loop model on any (finite and connected) bipartite cubic graph, for any real n>0$n>0$, and any edge weight, including the fully-packed limit of infinite edge weight. Furthermore, we prove rigorously that the algorithm is ergodic and has the correct stationary distribution. We emphasize that by using known exact mappings when n=2$n=2$, this algorithm can be used to simulate a number of zero-temperature Potts antiferromagnets for which the Wang–Swendsen–Kotecký cluster algorithm is non-ergodic, including the 3-state model on the kagome lattice and the 4-state model on the triangular lattice. We then use this worm algorithm to perform a systematic study of the honeycomb-lattice loop model as a function of n?2$n?2$, on the critical line and in the densely-packed and fully-packed phases. By comparing our numerical results with Coulomb gas theory, we identify a set of exact expressions for scaling exponents governing some fundamental geometric and dynamic observables. In particular, we show that for all n?2$n?2$, the scaling of a certain return time in the worm dynamics is governed by the magnetic dimension of the loop model, thus providing a concrete dynamical interpretation of this exponent. The case n>2$n>2$ is also considered, and we confirm the existence of a phase transition in the 3-state Potts universality class that was recently observed via numerical transfer matrix calculations.