新世代3D浏览器space time DETA

随着技术的发展，现在的电脑普遍采用了海量内存，而软件的发展趋势就是更充分地利用那些内存。由于电脑的运算能力随着处理器的更新换代而稳步增强，因此软件设计师们可以设计出更加生动活泼的应用软件。在图形处理技术一日千里的世界，还有很多人不能像游戏发烧友那样享受到这种进步带来的好处，因为桌面应用和视频编解码要么用不到这么强的功能，要么要用的功能它没提供。以前我们上网游戏网页，显示的都是平面的网页；在3D技术不断成熟的时期，浏览器也有3D的了。任何用过微软最新操作系统Vista的用户都知道，在电脑上观看三维内容并不是什么新鲜事儿。在Vista系统中，窗口都是以三维模式进行排列，用户可以翻阅那些窗口，然后选择想看的窗口。苹果公司推出的OSX操作系统也将采用类似的三维效果即“时间机器”，它可以展示和保存电脑创建文件的所有版本。SpaceTime与它们的三维概念是相同的，而且它不需要嵌入操作系统，它的导航机制更为灵活有为。SpaceTime就是一个另类的3D浏览器，它试图打破常规二维分页式浏览模式，充分发挥现代先进电脑的强大图形功能，将我们的网络冲浪浏览进行了3D时代！下面我们就来一起体验一下吧。[编者按]     

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.     

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.     

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.     

Characterizing implications of two-dimensional space–time orientations for principal component analysis of geographic time series

This article introduces four new modes of principal component analysis (PCA) to investigate space–time variability in an image time series. Using the concept of tensors, an image time series can be understood as a space–time cube and can be analysed using six different orientations by grouping the basic elements (voxels) of the cube across different dimensions. Voxels grouped across columns or rows of the cube to produce vectors result in profiles. Voxels grouped across different planes to produce matrices result in slices. The traditional S-mode and T-mode PCA are thus the profile modes and slice modes across time and across space, respectively. This research introduces two profile-mode orientations across longitude and latitude and two slice-mode orientations across longitude–time and latitude–time. The research shows that a more complete understanding of the spatio-temporal variability in the data set can be achieved by investigating these different orientation modes, as individual modes have the capability of capturing variability in a particular dimension of a spatio-temporal data set. A case study was carried out using weekly anomalies of the AVISO (Archiving, Validation and Interpretation of Satellite Oceanographic data) sea surface height product filtered for tropical instability waves (TIWs) for a three-year time period from 1997 to 1999 in the tropical Pacific region. The results show that PCA with longitude as the dimension of variability and latitude–time as the dimension of variability were able to capture the TIW and barotropic Rossby wave propagation across the equatorial Pacific. The other two orientation modes were able to detect dominant latitudinal locations for TIW.     

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.     

Quantum algorithm to solve function inversion with time–space trade-off

In general, it is a difficult problem to solve the inverse of any function. With the inverse implication operation, we present a quantum algorithm for solving the inversion of function via using time–space trade-off in this paper. The details are as follows. Let function \(f(x)=y\) have k solutions, where \(x\in \{0, 1\}^{n}, y\in \{0, 1\}^{m}\) for any integers n, m. We show that an iterative algorithm can be used to solve the inverse of function f(x) with successful probability \(1-\left( 1-\frac{k}{2^{n}}\right) ^{L}\) for \(L\in Z^{+}\). The space complexity of proposed quantum iterative algorithm is O(Ln), where L is the number of iterations. The paper concludes that, via using time–space trade-off strategy, we improve the successful probability of algorithm.     

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 fast algorithm for solving the space–time fractional diffusion equation

In this paper, we propose a fast algorithm for efficient and accurate solution of the space–time fractional diffusion equations defined in a rectangular domain. The spatial discretization is done by using the central finite difference scheme and matrix transfer technique. Due to its nonlocality, numerical discretization of the spectral fractional Laplacian ${(?\Delta )}_s^{\alpha /2}$ results in a large dense matrix. This causes considerable challenges not only for storing the matrix but also for computing matrix–vector products in practice. By utilizing the compact structure of the discrete system and the discrete sine transform, our algorithm avoids to store the large matrix from discretizing the nonlocal operator and also significantly reduces the computational costs. We then use the Laplace transform method for time integration of the semi-discretized system and a weighted trapezoidal method to numerically compute the convolutions needed in the resulting scheme. Various experiments are presented to demonstrate the efficiency and accuracy of our method.     

A stable space–time finite element method for parabolic evolution problems

This paper is concerned with the analysis of a new stable space–time finite element method (FEM) for the numerical solution of parabolic evolution problems in moving spatial computational domains. The discrete bilinear form is elliptic on the FEM space with respect to a discrete energy norm. This property together with a corresponding boundedness property, consistency and approximation results for the FEM spaces yield an a priori discretization error estimate with respect to the discrete norm. Finally, we confirm the theoretical results with numerical experiments in spatial moving domains.     

基于space—time的二叉树表达动态环境中的路径规划

研究具有空间和时间的space-time三维动态环境下的机器人路径规划，分析了四叉树表示二维空间的搜索算法，在此基础上，提出采用二叉树表示二维空间的方法。时间信息中增加加速度，利用二叉树遍历方法和A^*算法，设计一个在动态障碍物环境下进行路径规划的新算法，并在足球机器人系统中进行仿真，实现了较好的路径规划。     

A Galerkin finite element scheme for time–space fractional diffusion equation

In this paper, a Galerkin finite element scheme to approximate the time–space fractional diffusion equation is studied. Firstly, the fractional diffusion equation is transformed into a fractional Volterra integro-differential equation. And a second-order fractional trapezoidal formula is used to approach the time fractional integral. Then a Galerkin finite element method is introduced in space direction, where the semi-discretization scheme and fully discrete scheme are given separately. The stability analysis of semi-discretization scheme is discussed in detail. Furthermore, convergence analysis of semi-discretization scheme and fully discrete scheme are given in details. Finally, two numerical examples are displayed to demonstrate the effectiveness of the proposed method.     

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.     

Finite difference method for time–space linear and nonlinear fractional diffusion equations

ABSTRACT

In this paper a finite difference method is presented to solve time–space linear and nonlinear fractional diffusion equations. Specifically, the centred difference scheme is used to approximate the Riesz fractional derivative in space. A trapezoidal formula is used to solve a system of Volterra integral equations transformed from spatial discretization. Stability and convergence of the proposed scheme is discussed which shows second-order accuracy both in temporal and spatial directions. Finally, examples are presented to show the accuracy and effectiveness of the schemes.     

Refinement of flexible space–time finite element meshes and discontinuous Galerkin methods

In this paper we present an algorithm to refine space–time finite element meshes as needed for the numerical solution of parabolic initial boundary value problems. The approach is based on a decomposition of the space–time cylinder into finite elements, which also allows a rather general and flexible discretization in time. This also includes adaptive finite element meshes which move in time. For the handling of three-dimensional spatial domains, and therefore of a four-dimensional space–time cylinder, we describe a refinement strategy to decompose pentatopes into smaller ones. For the discretization of the initial boundary value problem we use an interior penalty Galerkin approach in space, and an upwind technique in time. A numerical example for the transient heat equation confirms the order of convergence as expected from the theory. First numerical results for the transient Navier–Stokes equations and for an adaptive mesh moving in time underline the applicability and flexibility of the presented approach.     

Compressive sensing based sub-mm accuracy UWB positioning systems: A space–time approach

A key challenge to achieve very high positioning accuracy (such as sub-mm accuracy) in Ultra-Wideband (UWB) positioning systems is how to obtain ultra-high resolution UWB echo pulses, which requires ADCs with a prohibitively high sampling rate. The theory of Compressed Sensing (CS) has been applied to UWB systems to acquire UWB pulses below the Nyquist sampling rate. This paper proposes a front-end optimized scheme for the CS-based UWB positioning system. A Space–Time Bayesian Compressed Sensing (STBCS) algorithm is developed for joint signal reconstruction by transferring mutual a priori information, which can dramatically decrease ADC sampling rate and improve noise tolerance. Moreover, the STBCS and time difference of arrival (TDOA) algorithms are integrated in a pipelined mode for fast tracking of the target through an incremental optimization method. Simulation results show the proposed STBCS algorithm can significantly reduce the number of measurements and has better noise tolerance than the traditional BCS, OMP, and multi-task BCS (MBCS) algorithms. The sub-mm accurate CS-based UWB positioning system using the proposed STBCS–TDOA algorithm requires only 15% of the original sampling rate compared with the UWB positioning system using a sequential sampling method.     

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.     

The EM algorithm in a distributed computing environment for modelling environmental space–time data

Statistical models for spatio-temporal data are increasingly used in environmetrics, climate change, epidemiology, remote sensing and dynamical risk mapping. Due to the complexity of the relationships among the involved variables and dimensionality of the parameter set to be estimated, techniques for model definition and estimation which can be worked out stepwise are welcome. In this context, hierarchical models are a suitable solution since they make it possible to define the joint dynamics and the full likelihood starting from simpler conditional submodels. Moreover, for a large class of hierarchical models, the maximum likelihood estimation procedure can be simplified using the Expectation–Maximization (EM) algorithm.In this paper, we define the EM algorithm for a rather general three-stage spatio-temporal hierarchical model, which includes also spatio-temporal covariates. In particular, we show that most of the parameters are updated using closed forms and this guarantees stability of the algorithm unlike the classical optimization techniques of the Newton–Raphson type for maximizing the full likelihood function. Moreover, we illustrate how the EM algorithm can be combined with a spatio-temporal parametric bootstrap for evaluating the parameter accuracy through standard errors and non-Gaussian confidence intervals.To do this a new software library in form of a standard R package has been developed. Moreover, realistic simulations on a distributed computing environment allow us to discuss the algorithm properties and performance also in terms of convergence iterations and computing times.