A spectral formulation of the boundary integral equation method for antiplane problems is presented. The boundary integral equation method relates the slip and the shear stress at an interface between two half-planes. It involves evaluating a space-time convolution of the shear stress or the slip at the interface. In the spectral formulation, the convolution with respect to the spatial coordinate is performed in the spectral domain. This leads to greater numerical efficiency. Prior work on the spectral formulation of the boundary integral equation method has performed the elastodynamic convolution of the slip at the interface. In the present work, the convolution is performed of the shear stress at the interface. The spectral formulation is developed both for an interface between identical solids and for a bi-material interface. It is validated by numerically calculating the response of the interface to harmonic and to impulsive disturbances and comparing with known analytical solutions. To illustrate use of the method, dynamic slip rupture propagation with a slip-weakening friction law is simulated.
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Integration：Integration, the VLSI Journal。
Explanation：集成，VLSI雜志。
Publisher：Elsevier。
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Time series (TS) are present in many fields of knowledge, research, and engineering. The processing and analysis of TS are essential in order to extract knowledge from the data and to tackle forecasting or predictive maintenance tasks among others The modeling of TS is a challenging task, requiring high statistical expertise as well as outstanding knowledge about the application of Data Mining(DM) and Machine Learning (ML) methods. The overall work with TS is not limited to the linear application of several techniques, but is composed of an open workflow of methods and tests. These workflow, developed mainly on programming languages, are complicated to execute and run effectively on different systems, including Cloud Computing (CC) environments. The adoption of CC can facilitate the integration and portability of services allowing to adopt solutions towards services Internet Technologies (IT) industrialization. The definition and description of workflow services for TS open up a new set of possibilities regarding the reduction of complexity in the deployment of this type of issues in CC environments. In this sense, we have designed an effective proposal based on semantic modeling (or vocabulary) that provides the full description of workflow for Time Series modeling as a CC service. Our proposal includes a broad spectrum of the most extended operations, accommodating any workflow applied to classification, regression, or clustering problems for Time Series, as well as including evaluation measures, information, tests, or machine learning algorithms among others.
We propose and explore a new, general-purpose method for the implicit time integration of elastica. Key to our approach is the use of a mixed variational principle. In turn its finite element discretization leads to an efficient alternating projections solver with a superset of the desirable properties of many previous fast solution strategies. This framework fits a range of elastic constitutive models and remains stable across a wide span of timestep sizes, material parameters (including problems that are quasi-static and approximately rigid). It is efficient to evaluate and easily applicable to volume, surface, and rods models. We demonstrate the efficacy of our approach on a number of simulated examples across all three codomains.
Casting nonlocal problems in variational form and discretizing them with the finite element (FE) method facilitates the use of nonlocal vector calculus to prove well-posedeness, convergence, and stability of such schemes. Employing an FE method also facilitates meshing of complicated domain geometries and coupling with FE methods for local problems. However, nonlocal weak problems involve the computation of a double-integral, which is computationally expensive and presents several challenges. In particular, the inner integral of the variational form associated with the stiffness matrix is defined over the intersections of FE mesh elements with a ball of radius $\delta$, where $\delta$ is the range of nonlocal interaction. Identifying and parameterizing these intersections is a nontrivial computational geometry problem. In this work, we propose a quadrature technique where the inner integration is performed using quadrature points distributed over the full ball, without regard for how it intersects elements, and weights are computed based on the generalized moving least squares method. Thus, as opposed to all previously employed methods, our technique does not require element-by-element integration and fully circumvents the computation of element-ball intersections. This paper considers one- and two-dimensional implementations of piecewise linear continuous FE approximations, focusing on the case where the element size h and the nonlocal radius $\delta$ are proportional, as is typical of practical computations. When boundary conditions are treated carefully and the outer integral of the variational form is computed accurately, the proposed method is asymptotically compatible in the limit of $h \sim \delta \to 0$, featuring at least first-order convergence in L^2 for all dimensions, using both uniform and nonuniform grids.
M\"{o}bius transformations play an important role in both geometry and spherical image processing -- they are the group of conformal automorphisms of 2D surfaces and the spherical equivalent of homographies. Here we present a novel, M\"{o}bius-equivariant spherical convolution operator which we call M\"{o}bius convolution, and with it, develop the foundations for M\"{o}bius-equivariant spherical CNNs. Our approach is based on a simple observation: to achieve equivariance, we only need to consider the lower-dimensional subgroup which transforms the positions of points as seen in the frames of their neighbors. To efficiently compute M\"{o}bius convolutions at scale we derive an approximation of the action of the transformations on spherical filters, allowing us to compute our convolutions in the spectral domain with the fast Spherical Harmonic Transform. The resulting framework is both flexible and descriptive, and we demonstrate its utility by achieving promising results in both shape classification and image segmentation tasks.
In this work, two fast multipole boundary element formulations for the linear time-harmonic acoustic analysis of finite periodic structures are presented. Finite periodic structures consist of a bounded number of unit cell replications in one or more directions of periodicity. Such structures can be designed to efficiently control and manipulate sound waves and are referred to as acoustic metamaterials or sonic crystals. Our methods subdivide the geometry into boxes which correspond to the unit cell. A boundary element discretization is applied and interactions between well separated boxes are approximated by a fast multipole expansion. Due to the periodicity of the underlying geometry, certain operators of the expansion become block Toeplitz matrices. This allows to express matrix-vector products as circular convolutions which significantly reduces the computational effort and the overall memory requirements. The efficiency of the presented techniques is shown based on an acoustic scattering problem. In addition, a study on the design of sound barriers is presented where the performance of a wall-like sound barrier is compared to the performance of two sonic crystal sound barriers.
The strong interference suffered by users can be a severe problem in cache-enabled networks (CENs) due to the content-centric user association mechanism. To tackle this issue, multi-antenna technology may be employed for interference management. In this paper, we consider a user-centric interference nulling (IN) scheme in two-tier multi-user multi-antenna CEN, with a hybrid most-popular and random caching policy at macro base stations (MBSs) and small base stations (SBSs) to provide file diversity. All the interfering SBSs within the IN range of a user are requested to suppress the interference at this user using zero-forcing beamforming. Using stochastic geometry analysis techniques, we derive a tractable expression for the area spectral efficiency (ASE). A lower bound on the ASE is also obtained, with which we then consider ASE maximization, by optimizing the caching policy and IN coefficient. To solve the resultant mixed integer programming problem, we design an alternating optimization algorithm to minimize the lower bound of the ASE. Our numerical results demonstrate that the proposed caching policy yields performance that is close to the optimum, and it outperforms several existing baselines.
This article presents an algorithm to compute digital images of Voronoi, Johnson-Mehl or Laguerre diagrams of a set of punctual sites, in a domain of a Euclidean space of any dimension. The principle of the algorithm is, in a first step, to investigate the voxels in balls centred around the sites, and, in a second step, to process the voxels remaining outside the balls. The optimal choice of ball radii can be determined analytically or numerically, which allows a performance of the algorithm in $O(N_v \ln N_s$), where $N_v$ is the total number of voxels of the domain and $N_s$ the number of sites of the tessellation. Periodic and non-periodic boundary conditions are considered. A major advantage of the algorithm is its simplicity which makes it very easy to implement. This makes the algorithm suitable for creating high resolution images of microstructures containing a large number of cells, in particular when calculations using FFT-based homogenisation methods are then to be applied to the simulated materials.
Safety and decline of road traffic accidents remain important issues of autonomous driving. Statistics show that unintended lane departure is a leading cause of worldwide motor vehicle collisions, making lane detection the most promising and challenge task for self-driving. Today, numerous groups are combining deep learning techniques with computer vision problems to solve self-driving problems. In this paper, a Global Convolution Networks (GCN) model is used to address both classification and localization issues for semantic segmentation of lane. We are using color-based segmentation is presented and the usability of the model is evaluated. A residual-based boundary refinement and Adam optimization is also used to achieve state-of-art performance. As normal cars could not afford GPUs on the car, and training session for a particular road could be shared by several cars. We propose a framework to get it work in real world. We build a real time video transfer system to get video from the car, get the model trained in edge server (which is equipped with GPUs), and send the trained model back to the car.
We propose a geometric convexity shape prior preservation method for variational level set based image segmentation methods. Our method is built upon the fact that the level set of a convex signed distanced function must be convex. This property enables us to transfer a complicated geometrical convexity prior into a simple inequality constraint on the function. An active set based Gauss-Seidel iteration is used to handle this constrained minimization problem to get an efficient algorithm. We apply our method to region and edge based level set segmentation models including Chan-Vese (CV) model with guarantee that the segmented region will be convex. Experimental results show the effectiveness and quality of the proposed model and algorithm.
In this paper, we study the optimal convergence rate for distributed convex optimization problems in networks. We model the communication restrictions imposed by the network as a set of affine constraints and provide optimal complexity bounds for four different setups, namely: the function $F(\xb) \triangleq \sum_{i=1}^{m}f_i(\xb)$ is strongly convex and smooth, either strongly convex or smooth or just convex. Our results show that Nesterov's accelerated gradient descent on the dual problem can be executed in a distributed manner and obtains the same optimal rates as in the centralized version of the problem (up to constant or logarithmic factors) with an additional cost related to the spectral gap of the interaction matrix. Finally, we discuss some extensions to the proposed setup such as proximal friendly functions, time-varying graphs, improvement of the condition numbers.
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