A space–time spectral collocation method for the two-dimensional variable-order fractional percolation equations

In this article, we introduce a space–time spectral collocation method for solving the two-dimensional variable-order fractional percolation equations. The method is based on a Legendre–Gauss–Lobatto (LGL) spectral collocation method for discretizing spatial and the spectral collocation method for the time integration of the resulting linear first-order system of ordinary differential equation. Optimal priori error estimates in $L^2$ norms for the semi-discrete and full-discrete formulation are derived. The method has spectral accuracy in both space and time. Numerical results confirm the exponential convergence of the proposed method in both space and time.     

Rider motion identification during normal bicycling by means of principal component analysis

Recent observations of a bicyclist riding through town and on a treadmill show that the rider uses the upper body very little when performing normal maneuvers and that the bicyclist may, in fact, primarily use steering input for control. The observations also revealed that other motions such as lateral movement of the knees were used in low speed stabilization. In order to validate the hypothesis that there is little upper body motion during casual cycling, an in-depth motion capture analysis was performed on the bicycle and rider system.     

Assessment of time–frequency representation techniques for thoracic sounds analysis

A step forward in the knowledge about the underlying physiological phenomena of thoracic sounds requires a reliable estimate of their time–frequency behavior that overcomes the disadvantages of the conventional spectrogram. A more detailed time–frequency representation could lead to a better feature extraction for diseases classification and stratification purposes, among others. In this respect, the aim of this study was to look for an omnibus technique to obtain the time–frequency representation (TFR) of thoracic sounds by comparing generic goodness-of-fit criteria in different simulated thoracic sounds scenarios. The performance of ten TFRs for heart, normal tracheal and adventitious lung sounds was assessed using time–frequency patterns obtained by mathematical functions of the thoracic sounds. To find the best TFR performance measures, such as the 2D local (ρ_mean) and global (ρ) central correlation, the normalized root-mean-square error (NRMSE), the cross-correlation coefficient (ρ_IF) and the time–frequency resolution (res_TF) were used. Simulation results pointed out that the Hilbert–Huang spectrum (HHS) had a superior performance as compared with other techniques and then, it can be considered as a reliable TFR for thoracic sounds. Furthermore, the goodness of HHS was assessed using noisy simulated signals. Additionally, HHS was applied to first and second heart sounds taken from a young healthy male subject, to tracheal sound from a middle-age healthy male subject, and to abnormal lung sounds acquired from a male patient with diffuse interstitial pneumonia. It is expected that the results of this research could be used to obtain a better signature of thoracic sounds for pattern recognition purpose, among other tasks.     

Error estimates of the space–time spectral method for parabolic control problems

This work is devoted to investigate the spectral approximation of optimal control of parabolic problems. The space–time method is used to boost high-order accuracy by applying dual Petrov–Galerkin spectral scheme in time and spectral method in space. The optimality conditions are derived, and the a priori error estimates indicate the convergence of the proposed method. Numerical tests confirm the theoretical results, and show the efficiency of the method.     

A BSS-based space–time multi-channel algorithm for complex-jamming suppression

This paper considers the problem of suppressing complex-jamming, which contains sidelobe blanket jammings (SLJs), multiple near-mainlobe blanket jammings (multiple-NMLJs) and self-defensive false target jamming (SDJ). We propose a blind source separation (BSS)-based space–time multi-channel algorithm for complex-jamming suppression. The space–time multi-channel consists of spatial multiple beams and temporal multiple adjacent pulse repetition intervals (PRIs). The source signals can be separated by the BSS, owing to their statistical independence. The real target and SDJ can then be obtained by the pulse compression approach, distinguished by echo identification simultaneously. A remarkable feature of the proposed approach is that it does not require prior knowledge about real target or jammings, and it is easy to implement for engineering applications.     

An optimal time–space algorithm for dense stereo matching

The increasing demand for higher resolution images and higher frame rate videos will always pose a challenge to computational power when real-time performance is required to solve the stereo-matching problem in 3D reconstruction applications. Therefore, the use of asymptotic analysis is necessary to measure the time and space performance of stereo-matching algorithms regardless of the size of the input and of the computational power available. In this paper, we survey several classic stereo-matching algorithms with regard to time–space complexity. We also report running time experiments for several algorithms that are consistent with our complexity analysis. We present a new dense stereo-matching algorithm based on a greedy heuristic path computation in disparity space. A procedure which improves disparity maps in depth discontinuity regions is introduced. This procedure works as a post-processing step for any technique that solves the dense stereo-matching problem. We prove that our algorithm and post-processing procedure have optimal O(n) time–space complexity, where n is the size of a stereo image. Our algorithm performs only a constant number of computations per pixel since it avoids a brute force search over the disparity range. Hence, our algorithm is faster than “real-time” techniques while producing comparable results when evaluated with ground-truth benchmarks. The correctness of our algorithm is demonstrated with experiments in real and synthetic data.     

Non-parametric regression for space–time forecasting under missing data

As more and more real time spatio-temporal datasets become available at increasing spatial and temporal resolutions, the provision of high quality, predictive information about spatio-temporal processes becomes an increasingly feasible goal. However, many sensor networks that collect spatio-temporal information are prone to failure, resulting in missing data. To complicate matters, the missing data is often not missing at random, and is characterised by long periods where no data is observed. The performance of traditional univariate forecasting methods such as ARIMA models decreases with the length of the missing data period because they do not have access to local temporal information. However, if spatio-temporal autocorrelation is present in a space–time series then spatio-temporal approaches have the potential to offer better forecasts. In this paper, a non-parametric spatio-temporal kernel regression model is developed to forecast the future unit journey time values of road links in central London, UK, under the assumption of sensor malfunction. Only the current traffic patterns of the upstream and downstream neighbouring links are used to inform the forecasts. The model performance is compared with another form of non-parametric regression, K-nearest neighbours, which is also effective in forecasting under missing data. The methods show promising forecasting performance, particularly in periods of high congestion.     

FPGA implementation of time–frequency analysis algorithms for laser welding monitoring

The on-line monitoring and detection of defects in laser welding is a basic manufacturing requirement in several applicative contexts, as vehicle assembly in automotive production. This work presents the FPGA implementation of time–frequency analysis algorithms as an effective solution compared with pure software implementation based on different modern processors. In particular the proposed FPGA based approach not only satisfies the processing constraints of the considered application, but still offers a high degree of flexibility and modularity.     

A unified difference-spectral method for time–space fractional diffusion equations

In this paper we develop a unified difference-spectral method for stably solving time–space fractional sub-diffusion and super-diffusion equations. Based on the equivalence between Volterra integral equations and fractional ordinary differential equations with initial conditions, this proposed method is constructed by combining the spectral Galerkin method in space and the fractional trapezoid formula in time. Numerical experiments are carried out to verify the effectiveness of the method, and demonstrate that the unified method can achieve spectral accuracy in space and second-order accuracy in time for solving two kinds of time–space fractional diffusion equations.     

A space–time adaptation scheme for unsteady shallow water problems

We provide a space–time adaptation procedure for the approximation of the Shallow Water Equations (SWE). This approach relies on a recovery based estimator for the global discretization error, where the space and time contributions are kept separate. In particular we propose an ad hoc procedure for the recovery of the time derivative of the numerical solution and then we employ this reconstruction to define the error estimator in time. Concerning the space adaptation, we move from an anisotropic error estimator able to automatically identify the density, the shape and the orientation of the elements of the computational mesh. The proposed global error estimator turns out to share the good properties of each recovery based error estimator. The whole adaptive procedure is then combined with a suitable stabilized finite element SW solver. Finally the reliability of the coupled solution–adaptation procedure is successfully assessed on two unsteady test cases of interest for hydraulics applications.     

A haar wavelet approximation for two-dimensional time fractional reaction–subdiffusion equation

Engineering with Computers - In this study, we established a wavelet method, based on Haar wavelets and finite difference scheme for two-dimensional time fractional reaction–subdiffusion...     

Robust multi-branch space–time beamforming for OFDM system with interference

Space–time receive beamforming is a promising technique to suppress co-channel multiuser interference for orthogonal frequency division multiplexing (OFDM) systems. However, the performance of existing receive beamforming methods is highly sensitive to the memory length of time–domain equalizer. In this paper, we propose a new robust solution of space–time receive beamforming to combat co-channel multiuser interference for OFDM systems. The proposed method performs subspace analysis for the received space–time snapshots from both the training block and few data blocks, and constrains the space–time beamforming vectors to lie in the corresponding signal subspace. A few beamforming vectors are then carefully designed to suppress interference as well as provide the potential multi-branch diversity gain. The numerical results are provided to corroborate the proposed studies. We show that the proposed method not only can outperform the exiting competitors but also has the advantage of being quite insensitive to the memory length of time–domain equalizer.     

Population shift bias in tests of space–time interaction

Common to all tests of space–time interaction is the assumption that the population underlying the events of interest exhibits a trajectory of growth that is consistent through time and across space. In practice, however, this assumption is often untenable and, when violated, can introduce population shift bias into the results of these tests. While this problem is widely recognized, more work remains to compare its effect across tests and to determine the extent to which it is a problem for study short periods. This paper quantifies and compares the population shift bias present in the results of the Knox, Mantel, and Jacquez tests of space–time interaction. A simulation study is carried out which quantifies the bias present in each test across a variety of population movement scenarios. Results show a positive relationship between population shift bias and the heterogeneity in population growth across all the tests. They also demonstrate variability in the size of the bias across the three tests for space–time interaction considered. Finally, the results illustrate that population shift bias can be a serious problem for short study periods. Collectively, these findings suggest that an unbiased approach to assessing the significance of space–time interaction test results is needed whenever spatially heterogeneous population change is identified within a study area.     

Motion recognition using local auto-correlation of space–time gradients

In this paper, we propose a motion recognition scheme based on a novel method of motion feature extraction. The feature extraction method utilizes auto-correlations of space–time gradients of three-dimensional motion shape in a video sequence. The method effectively exploits the local relationships of the gradients corresponding to the space–time geometric characteristics of the motion. For recognizing motions, we apply the framework of bag-of-frame-features, which, in contrast to the standard bag-of-features framework, enables the motion characteristics to be captured sufficiently and the motions to be quickly recognized. In experiments on various datasets for motion recognition, the proposed method exhibits favorable performances as compared to the other methods, and faster computational time even than real time.     

A hybridization of teaching–learning-based optimization and differential evolution for chaotic time series prediction

Chaotic time series prediction problems have some very interesting properties and their prediction has received increasing interest in the recent years. Prediction of chaotic time series based on the phase space reconstruction theory has been applied in many research fields. It is well known that prediction of a chaotic system is a nonlinear, multivariable and multimodal optimization problem for which global optimization techniques are required in order to avoid local optima. In this paper, a new hybrid algorithm named teaching–learning-based optimization (TLBO)–differential evolution (DE), which integrates TLBO and DE, is proposed to solve chaotic time series prediction. DE is incorporated into update the previous best positions of individuals to force TLBO jump out of stagnation, because of its strong searching ability. The proposed hybrid algorithm speeds up the convergence and improves the algorithm’s performance. To demonstrate the effectiveness of our approaches, ten benchmark functions and three typical chaotic nonlinear time series prediction problems are used for simulating. Conducted experiments indicate that the TLBO–DE performs significantly better than, or at least comparable to, TLBO and some other algorithms.