An Efficient Iteration Method for Toeplitz-Plus-Band Triangular Systems Generated from Fractional Ordinary Differential Equation

It is time consuming to numerically solve fractional differential equations. The fractional ordinary differential equations may produce Toeplitz-plus-band triangular systems. An efficient iteration method for Toeplitz-plus-band triangular systems is presented with OMlogM computational complexity and OM memory complexity in this paper, compared with the regular solution with OM2 computational complexity and OM2 memory complexity. M is the discrete grid points. Some methods such as matrix splitting, FFT, compress memory storage and adjustable matrix bandwidth are used in the presented solution. The experimental results show that the presented method compares well with the exact solution and is 4.25 times faster than the regular solution

Succinct Representations in Collaborative Filtering: A Case Study using Wavelet Tree on 1,000 Cores

User-Item (U-I) matrix has been used as the dominant data infrastructure of Collaborative Filtering (CF). To reduce space consumption in runtime and storage, caused by data sparsity and growing need to accommodate side information in CF design, one needs to go beyond the UI Matrix. In this paper, we took a case study of Succinct Representations in Collaborative Filtering, rather than using a U-I Matrix. Our key insight is to introduce Succinct Data Structures as a new infrastructure of CF. Towards this, we implemented a User-based K-Nearest-Neighbor CF prototype via Wavelet Tree, by first designing a Accessible Compressed Documents (ACD) to compress U-I data in Wavelet Tree, which is efficient in both storage and runtime. Then, we showed that ACD can be applied to develop an efficient intersection algorithm without decompression, by taking advantage of ACD’s characteristics. We evaluated our design on 1,000 cores of Tianhe-II supercomputer, with one of the largest public data set ml-20m. The results showed that our prototype could achieve 3.7 minutes on average to deliver the results

Comparative analysis of simulated in-situ colonization and degradation by Lentinula edodes on oak wafer and corn stalk

IntroductionThe depolymerization of lignocellulose biomass by white-rot fungi has been an important research topic. However, few simulated in-situ analyses have been conducted to uncover the decay.MethodsIn this study, the white-rot Lentinula edodes was used to colonize the wood and non-wood substrates, and then hyphal transcriptional response and substrate degradation were analyzed during the spatial-temporal colonization on different type substrates to better understand the depolymerization of lignocellulose.Results and discussionFaster growth and thicker mat of hyphae on corn stalk were observed in comparison to oak wafer. Coincide with the higher levels of gene transcripts related to protein synthesis on corn stalk. The higher lignin oxidase activity of hyphae was detected on oak wafer, and the higher cellulase activity was observed on corn stalk containing a much higher content of soluble sugars. A large number of carbohydrate-binding module (CBM1 and CBM20)-containing enzyme genes, including lytic polysaccharide monooxygenase (AA9), cellobiohydrolase (GH6 and GH7), glucanase (GH5), xylanase (GH10 and GH11), glucoamylase (GH15), and alpha-amylase (GH13), were significantly upregulated in the back-distal hyphae colonized on corn stalk. The hyphae tended to colonize and degrade the secondary cell wall, and the deposited oxalate crystal suggested that oxalate may play an important role during lignocellulose degradation. In addition, lignin was degraded in priority in oak wafer. Of note, three lignin monomers were degraded simultaneously in oak wafer but sequentially in corn stalk. This growth Our results indicated that the white-rot degradation pattern of lignocellulose is determined by the chemical composition and structure of the colonized biomass

A Domain Decomposition Method for Time Fractional Reaction-Diffusion Equation

The computational complexity of one-dimensional time fractional reaction-diffusion equation is O(N2M) compared with O(NM) for classical integer reaction-diffusion equation. Parallel computing is used to overcome this challenge. Domain decomposition method (DDM) embodies large potential for parallelization of the numerical solution for fractional equations and serves as a basis for distributed, parallel computations. A domain decomposition algorithm for time fractional reaction-diffusion equation with implicit finite difference method is proposed. The domain decomposition algorithm keeps the same parallelism but needs much fewer iterations, compared with Jacobi iteration in each time step. Numerical experiments are used to verify the efficiency of the obtained algorithm

The Characteristics of Cloud Computing

Abstract—Cloud computing emerges as one of the hottest topic in field of information technology. Cloud computing is based on several other computing research areas such as HPC, virtualization, utility computing and grid computing. In order to make clear the essential of cloud computing, we propose the characteristics of this area which make cloud computing being cloud computing and distinguish it from other research areas. The cloud computing has its own conceptional, technical, economic and user experience characteristics. The service oriented, loose coupling, strong fault tolerant, business model and ease use are main characteristics of cloud computing. Clear insights into cloud computing will help the development and adoption of this evolving technology both for academe and industry. Keywords- cloud computing; serviec oriented; loose coupling; strong fault tolerant; business pattern; ease use I

Computational Challenge of Fractional Differential Equations and the Potential Solutions: A Survey

We present a survey of fractional differential equations and in particular of the computational cost for their numerical solutions from the view of computer science. The computational complexities of time fractional, space fractional, and space-time fractional equations are O(N2M), O(NM2), and O(NM(M + N)) compared with O(MN) for the classical partial differential equations with finite difference methods, where M, N are the number of space grid points and time steps. The potential solutions for this challenge include, but are not limited to, parallel computing, memory access optimization (fractional precomputing operator), short memory principle, fast Fourier transform (FFT) based solutions, alternating direction implicit method, multigrid method, and preconditioner technology. The relationships of these solutions for both space fractional derivative and time fractional derivative are discussed. The authors pointed out that the technologies of parallel computing should be regarded as a basic method to overcome this challenge, and some attention should be paid to the fractional killer applications, high performance iteration methods, high order schemes, and Monte Carlo methods. Since the computation of fractional equations with high dimension and variable order is even heavier, the researchers from the area of mathematics and computer science have opportunity to invent cornerstones in the area of fractional calculus

A Parallel Algorithm for the Two-Dimensional Time Fractional Diffusion Equation with Implicit Difference Method

It is very time consuming to solve fractional differential equations. The computational complexity of two-dimensional fractional differential equation (2D-TFDE) with iterative implicit finite difference method is O(MxMyN2). In this paper, we present a parallel algorithm for 2D-TFDE and give an in-depth discussion about this algorithm. A task distribution model and data layout with virtual boundary are designed for this parallel algorithm. The experimental results show that the parallel algorithm compares well with the exact solution. The parallel algorithm on single Intel Xeon X5540 CPU runs 3.16–4.17 times faster than the serial algorithm on single CPU core. The parallel efficiency of 81 processes is up to 88.24% compared with 9 processes on a distributed memory cluster system. We do think that the parallel computing technology will become a very basic method for the computational intensive fractional applications in the near future

A Neural Network-Based Mesh Quality Indicator for Three-Dimensional Cylinder Modelling

Evaluating mesh quality prior to performing the computational fluid dynamics (CFD) simulation is an essential step to ensure the acceptable accuracy of cylinder modelling. However, traditional mesh quality indicators are often insufficient since they only check geometric information on individual distorted elements. To yield more accurate results, the current evaluation process usually requires careful manual re-evaluation for quality properties such as mesh distribution and local refinement, which heavily increase the meshing overhead. In this paper, we introduce an efficient quality indicator for varisized cylinder meshes, consisting of a mesh pre-processing method and a neural network-based indicator, Mesh-Net. We also publish a cylinder mesh benchmark dataset. The proposed indicator is trained to study the role of CFD meshes on the accuracy of numerical simulations. It considers both the effect of element geometry (e.g., orthogonality) and quality properties (e.g., smoothness and distribution). Thereafter, the well-trained indicator is used as a black-box to predict the overall quality of the input mesh automatically. Experimental results demonstrate that the proposed indicator is accurate and can be applied in the mesh quality evaluation process without manual interactions

ISpliter: an intelligent and automatic surface mesh generator using neural networks and splitting lines

Abstract In this paper, we present a novel surface mesh generation approach that splits B-rep geometry models into isotropic triangular meshes based on neural networks and splitting lines. In the first stage, a recursive method is designed to generate plentiful data to train the neural network model offline. In the second stage, the implemented mesh generator, ISpliter, maps each surface patch into the parameter plane, and then the trained neural network model is applied to select the optimal splitting line to divide the patch into subdomains continuously until they are all triangles. In the third stage, ISpliter remaps the 2D mesh back to the physical space and further optimizes it. Several typical cases are evaluated to compare the mesh quality generated by ISpliter and two baselines, Gmsh and NNW-GridStar. The results show that ISpliter can generate isotropic triangular meshes with high average quality, and the generated meshes are comparable to those generated by the other two software under the same configuration