International Journal of Modern Physics C

We report our experiences with the optimization and parallelization of a discrete element code for convex polyhedra on multi-core machines and introduce a novel variant of the sort-and-sweep neighborhood algorithm. While in theory the whole code in itself parallelizes ideally, in practice the results on different architectures with different compilers and performance measurement tools depend very much on the particle number and optimization of the code. After difficulties with the interpretation of the data for speedup and efficiency are overcome, respectable parallelization speedups could be obtained.

We identify the different styles of texting in Filipino short message service (SMS) texts and analyze the change in unigram and bigram frequencies due to these styles. Style preference vectors for sample texts were calculated and used to identify the style combination used by an average individual. The change in Shannon entropy of the SMS text is explained in light of a coding process.

We introduce a new generation rule for local thresholding in scale-free networks based on the nodes' degree. The resulting networks are disassortative with a hierarchical structure. There is, however, a subnet of the nodes, which we call the active nodes, which is neither disassortative nor has such a structure. It is shown that networks with a wide range of cluster coefficients, ranging from very small to close to unity and with scaling exponent from 2.5 to 4 are generated by the new method, which mimic some important real-world networks.

We extend the technique of using the trapezoidal rule for efficient evaluation of the special functions of mathematical physics given by integral representations. This technique was recently used for Bessel functions, and here we treat incomplete gamma functions and the general confluent hypergeometric function.

The static topology properties of financial networks have been widely investigated since the work done by Mantegna, yet their dynamic evolution with time is little considered. In this paper, we comprehensively study the dynamic evolution of financial network by a sliding window technique. The vertices and edges of financial network are represented by the stocks from S&P500 components and correlations between pairs of daily returns of price fluctuation, respectively. Furthermore, the duration of stock price fluctuation, spanning from January 4, 1985 to September 14, 2009, makes us to carefully observe the relation between the dynamic topological properties and big financial crashes. The empirical results suggest that the financial network has the robust small-world property when the time evolves, and the topological structure drastically changes when the big financial crashes occur. This correspondence between the dynamic evolution of financial network and big financial crashes may provide a novel view to understand the origin of economic crisis.

There has been considerable interest in quantifying the complexity of different time series, such as physiologic time series, traffic time series. However, these traditional approaches fail to account for the multiple time scales inherent in time series, which have yielded contradictory findings when applied to real-world datasets. Then multi-scale entropy analysis (MSE) is introduced to solve this problem which has been widely used for physiologic time series. In this paper, we first apply the MSE method to different correlated series and obtain an interesting relationship between complexity and Hurst exponent. A modified MSE method called multiscale permutation entropy analysis (MSPE) is then introduced, which replaces the sample entropy (SampEn) with permutation entropy (PE) when measuring entropy for coarse-grained series. We employ the traditional MSE method and MSPE method to investigate complexities of different traffic series, and obtain that the complexity of weekend traffic time series differs from that of the workday time series, which helps to classify the series when making predictions.

In this paper, synchronization of complex-variable dynamical networks with complex coupling is investigated. An adaptive feedback control scheme is adopted to design controllers for achieving synchronization of a general network with both complex inner and outer couplings. For a network with only complex inner or outer coupling, pinning control and adaptive coupling strength methods are adopted to achieve synchronization under some assumptions. Several synchronization criteria are derived based on Lyapunov stability theory. Numerical simulations are provided to verify the effectiveness of the theoretical results.

We present a numerical technique for counting and computing the eigenvalues of a complex tridiagonal matrix, lying in a given region of the complex plane. First, we evaluate the integral of the logarithmic derivative p′(λ)/p(λ), where p(λ) is the characteristic polynomial of the tridiagonal matrix, on a simple closed contour, being the closure of that region. The problem of evaluating this integral is transformed into the equivalent problem of numerically solving a complex initial value problem defined on an ordinary first-order differential equation, integrated along this contour, and solved by the Fortran package dcrkf54.f95 (developed recently by the authors). In accordance with the "argument principle," the value of the contour integral, divided by 2πi, counts the eigenvalues lying in the region. Second, a Newton–Raphson (NR) method, fed by random guesses lying in the region, computes the roots one by one. If, however, NR signals that |p′(λ)| converges to zero, i.e. a multiple root probably exists at the current value λ, then counting the roots within an elementary square centered at λ reveals the multiplicity of this root.