This paper describes a system for delivering movement information from a dance performance through a multi-sensory approach that includes visual, sonic and haptic information. The work builds on previous research into interpreting dance as haptic information for blind, deaf-blind and vision-impaired audience members. This current work is aimed at a general audience with haptic information being one of a number of sensory experiences of the dance. A prototype haptic device has been developed for use in the dance performance research.
This paper surveys some recent developments in non-central limit theorems for long-range dependent random processes and fields. We describe an increasing domain framework for asymptotic behavior of functionals of random processes and fields. Recent results on the rate of convergence to the Hermite-type distributions in non-central limit theorems are presented. The use of these results is demonstrated through an application to the case of Rosenblatt-type distributions.
Weighted complex networks, especially scale-free networks, which characterize real-life systems better than non-weighted networks, have attracted considerable interest in recent years. Studies on the multifractality of weighted complex networks are still to be undertaken. In this paper, inspired by the concepts of Koch networks and Koch island, we propose a new family of weighted Koch networks, and investigate their multifractal behavior and topological properties. We find some key topological properties of the new networks: their vertex cumulative strength has a power-law distribution; there is a power-law relationship between their topological degree and weight strength; the networks have a high weighted clustering coefficient of 0.41004 (which is independent of the scaling factor c) in the limit of large generation t; the second smallest eigenvalue μ2 and the maximum eigenvalue μn are approximated by quartic polynomials of the scaling factor c for the general Laplacian operator, while μ2 is approximately a…
Using finite element method in spatial direction and classical L1 approximation in temporal direction, a fully-discrete scheme is established for a class of two-dimensional multi-term time fractional diffusion equations with Caputo fractional derivatives. The stability analysis of the approximate scheme is proposed. The spatial global superconvergence and temporal convergence of order O(h2+τ2−α) for the original variable in H1-norm is presented by means of properties of bilinear element and interpolation postprocessing technique, where h and τ are the step sizes in space and time, respectively. Finally, several numerical examples are implemented to evaluate the efficiency of the theoretical results.
Jonathan Mann Memorial Lecture on the broad theme of the Murray and its People. Public lecture at La Trobe University Albury-Wodonga Campus, Victoria, Australia.
In this paper, we consider a type of fractional diffusion equation (FDE) with variable coefficients on a finite domain. Firstly, we utilize a second-order scheme to approximate the Riemann–Liouville fractional derivative and present the finite difference scheme. Specifically, we discuss the Crank–Nicolson scheme and solve it in matrix form. Secondly, we prove the stability and convergence of the scheme and conclude that the scheme is unconditionally stable and convergent with the second-order accuracy of O(τ2+h2). Furthermore, we develop a fast accurate iterative method for the Crank–Nicolson scheme, which only requires storage of O(m) and computational cost of O(mlogm) while retaining the same accuracy and approximation property as Gauss elimination, where m=1/h is the partition number in space direction. Finally, several numerical examples are given to show the effectiveness of the numerical method, and the results are in excellent agreement with the theoretical analysis.
A new method-multifractal temporally weighted detrended cross-correlation analysis (MF-TWXDFA)-is proposed to investigate multifractal cross-correlations in this paper. This new method is based on multifractal temporally weighted detrended fluctuation analysis and multifractal cross-correlation analysis (MFCCA). An innovation of the method is applying geographically weighted regression to estimate local trends in the nonstationary time series. We also take into consideration the sign of the fluctuations in computing the corresponding detrended cross-covariance function. To test the performance of the MF-TWXDFA algorithm, we apply it and the MFCCA method on simulated and actual series. Numerical tests on artificially simulated series demonstrate that our method can accurately detect long-range cross-correlations for two simultaneously recorded series. To further show the utility of MF-TWXDFA, we apply it on time series from stock markets and find that power-law cross-correlation between stock returns is signif…
This paper derives the stochastic solution of a Cauchy problem for the distribution of a fractional diffusion process. The governing equation involves the Bessel-Riesz derivative (in space) to model heavy tails of the distribution, and the Caputo-Djrbashian derivative (in time) to depicts the memory of the diffusion process. The solution is obtained as Brownian motion with time change in terms of the Bessel-Riesz subordinator on the inverse stable subordinator. This stochastic solution, named fractional Bessel-Riesz motion, provides a method to simulate a large class of stochastic motions with memory and heavy tails.
There has been a growing interest in visualization of metagenomic data. The present study focuses on the visualization of metagenomic data using inter-nucleotide distances profile. We first convert the fragment sequences into inter-nucleotide distances profiles. Then we analyze these profiles by principal component analysis. Finally the principal components are used to obtain the 2-D scattered plot according to their source of species. We name our method as inter-nucleotide distances profiles (INP) method. Our method is evaluated on three benchmark data sets used in previous published papers. Our results demonstrate that the INP method is good, alternative and efficient for visualization of metagenomic data.
In this paper, we consider a numerical approach based on the matrix transfer method for numerical solution of multi-term time-fractional diffusion equations (MT-TFDEs). The semi- and fully-discrete schemes are developed by using the classical finite difference method and the matrix transfer technique. The unconditional stability and convergence of these two schemes are discussed and theoretically proved. The technique is then extended to MT-TFDEs with fractional Laplace operator. Numerical examples are given to validate and investigate the efficiency and the accuracy of the developed schemes. The results indicate that the present schemes are very effective for modeling and simulation of the MT-TFDEs with integral or fractional Laplacians.