In this work, we use a symbolic algebra package to derive a family of finite difference approximations for the biharmonic equation on a 9-point compact stencil. The solution and its first derivatives are carried as unknowns at the grid points. Dirichlet boundary conditions are thus incorporated naturally. Since the approximations use the 9-point compact stencil, no special formulas are needed near the boundaries. Both second-order and fourth-order discretizations are derived.The fourth-order approximations produce more accurate results than the 13-point classical stencil or the commonly used system of two second-order equations coupled with the boundary condition.The method suffers from slow convergence when classical iteration methods such as Gauss-Seidel or SOR are employed. In order to alleviate this problem we propose several multigrid techniques that exhibit grid-independent convergence and solve the biharmonic equation in a small amount of computer time. Test results from three different problems, including Stokes flow in a driven cavity, are reported.
In this correspondence, we present a variational approach to the problem of finding suitable radiometric image transformations that optimize desirable characteristics of the output image histogram. This variational approach can be interpreted as the minimization of the cumulative spacing between histogram bars in the least squares sense subject to some weight function. Most of the common histogram transformation procedures used in remote sensing applications can be deduced from this general variational approach with an appropriate choice of the weight function.
Malware, which is a malevolent software, mostly programmed by attackers for either disrupting the normal computer operation or gaining access to private computer systems. A malware detector determines the malicious intent of a program and thereafter, stops executing the program if the program is malicious. While a substantial number of various malware detection techniques based on static and dynamic analysis has been studied for decades, malware detection based on mining program graph features has attracted recent attention. It is commonly believed that graph based representation of a program is a natural way to understand its semantics and thereby, unveil its execution intent. This paper presents a state of the art survey on mining program-graph features for malware detection. We have also outlined the challenges of malware detection based on mining program graph features for its successful deployment, and opportunities that can be explored in the future.
This paper presents scalable parallel algorithms for high dimensional surface fitting and predictive modelling which are used in data mining applications. These algorithms are based on techniques like finite elements, thin plate splines, wavelets and additive models. They all consist of two steps: First, data is read from secondary storage and a linear system is assembled. Secondly, the linear system is solved. The assembly can be done with almost no communication and the size of the linear system is independent of the data size. Thus the presented algorithms are both scalable with the data size and the number of processors.
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