Irfan Altas

Multigrid Solution of Automatically Generated High-Order Discretizations for the Biharmonic Equation

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 approximation 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.

A variational approach to the radiometric enhancement of digital imagery

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.

Approximation of a Thin Plate Spline Smoother Using Continuous Piecewise Polynomial Functions

A new smoothing method is proposed which can be viewed as a finite element thin plate spline. This approach combines the favorable properties of finite element surface fitting with those of thin plate splines. The method is based on first order techniques similar to mixed finite element techniques for the biharmonic equation. The existence of a solution to our smoothing problem is demonstrated, and the approximation theory for uniformly spread data is presented in the case of both exact and noisy data. This convergence analysis seems to be the first for a discrete smoothing spline with data perturbed by white noise. Numerical results are presented which verify our theoretical results and demonstrate our method on a large real life data set.

High accuracy solution of three-dimensional biharmonic equations

In this paper, we consider several finite-difference approximations for the three-dimensional biharmonic equation. A symbolic algebra package is utilized to derive a family of finite-difference approximations for the biharmonic equation on a 27 point compact stencil. The unknown solution and its first derivatives are carried as unknowns at selected grid points. This formulation allows us to incorporate the Dirichlet boundary conditions automatically and there is no need to define special formulas near the boundaries, as is the case with the standard discretizations of biharmonic equations. We exhibit the standard second-order, finite-difference approximation that requires 25 grid points. We also exhibit two compact formulations of the 3D biharmonic equations; these compact formulas are defined on a 27 point cubic grid. The fourth-order approximations are used to solve a set of test problems and produce high accuracy numerical solutions. The system of linear equations is solved using a variety of iterative methods. We employ multigrid and preconditioned Krylov iterative methods to solve the system of equations. Test results from two test problems are reported. In these experiments, the multigrid method gives excellent results. The multigrid preconditioning also gives good results using Krylov methods.

Scalable parallel algorithms for surface fitting and data mining

Abstract 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.

The Integrated Delivery of Large-Scale Data Mining: The ACSys Data Mining Project

Data Mining draws on many technologies to deliver novel and actionable discoveries from very large collections of data. The Australian Governments Cooperative Research Centre for Advanced Computational Systems (ACSys) is a link between industry and research focusing on the deployment of high performance computers for data mining. We present an overview of the work of the ACSys Data Mining projects where the use of large-scale, high performance computers plays a key role. We highlight the use of large-scale computing within three complimentary areas: the development of parallel algorithms for data analysis, the deployment of virtual environments for data mining, and issues in data management for data mining. We also introduce the Data Miners Arcade which provides simple abstractions to integrate these components providing high performance data access for a variety of data mining tools communicating through XML.

A parallel finite element surface fitting algorithm for data mining

A major task in data mining is to develop automatic techniques to process and to detect patterns in very large data sets. Multivariate regression techniques form the core of many data mining applications. A common assumption is that the multivariate data is well approximated by an additive model involving only first and second order interaction terms. In this case high-dimensional nonparametric regression is reduced to the determination of a couple set of first and second order interaction terms, that is the determination of a coupled set of curves and surfaces. Thin plate splines provide a very good method to determine an approximating surface. Obtaining standard thin plate splines requires the solution of a dense linear system of equations of order n, where n is the number of observations. For data mining applications the number of observations is often in the millions, so standard thin plate splines may not be practical. We have developed a finite element approximation of a spline that can handle data sizes with millions of records. The resolution of the finite element method can independently be chosen from the number of observations. The observation data can be read from a secondary storage once, and does not need to be stored in memory. In this paper, we discuss the parallel implementation of this method in an MPI environment.

A comparative study of malware family classification

In this paper, we present a comparative study of conventional malware family classification techniques and identifiy their limitations. In our study, we investigate three different feature set, function length frequency and printable string information as static features and Application Programming Interface (API) calls and API parameters as dynamic features. In our classification process, we used some of well-known machine-learning algorithms by invoking WEKA libraries. We made a comparative analysis and conclude that the independent features are not good enough to defence against current as well as future malware.

An Implementation of a Remote Virtual Networking Laboratory for Educational Purposes

In this paper, we describe a remote networking lab (RNL) which we find useful for teaching networking subjects in distance education (DE) mode. The RNL enables students to work in a networking laboratory (via the Internet) as if physically located next to the equipment. We discuss the architecture and operational features of the RNL and the educational value it provides. We also describe some of the difficulties encountered when establishing this resource, and how these were overcome with the help of student feedback. The RNL has enabled distance students to gain experience using specialised equipment. The cost benefits of this approach are substantial, since a single set of networking devices can service a large cohort

Information Flow Control Using the Java Virtual Machine Tool Interface (JVMTI)

e present an information flow control (IFC) Early attempts at preserving confidentiality in a computer system which monitors information leakage in single-threaded system relied on the use of an access control matrix to Java programs. Our implementation uses the Java Virtual identify the access rights an individual (or subject) had over Machine Tool Interface (JVMTI) and adapts the algorithms of a particular resource. But there is a problem with this Le Guernic et al. [1] for this purpose. We also offer a generic approach. The access rights that appear in the matrix only rule set for enforcing IFC. One advantage of our approach is control initial access to the resource. Once the resource is that it is dynamic, so that we are only concerned with the released from its access container there are no restrictions on security of the current execution of a program, not all possible its use. The mandatory access control (MAC) model was executions. Our system tracks flow at the level of primitive designed to prevent this type of abuse by removing the Java fields, allowing precise control over the information that ability of an arbitrary user to pass on permissions from the is monitored. Further, no modifications to the Java Virtual Machine (JVM) are needed for our system to work.