A sparse parallel hybrid Monte Carlo algorithm for matrix computations

In this paper we introduce a new algorithm, based on the successful work of Fathi and Alexandrov, on hybrid Monte Carlo algorithms for matrix inversion and solving systems of linear algebraic equations. This algorithm consists of two parts, approximate inversion by Monte Carlo and iterative refinement using a deterministic method. Here we present a parallel hybrid Monte Carlo algorithm, which uses Monte Carlo to generate an approximate inverse and that improves the accuracy of the inverse with an iterative refinement. The new algorithm is applied efficiently to sparse non-singular matrices. When we are solving a system of linear algebraic equations, Bx = b, the inverse matrix is used to compute the solution vector x = B(-1)b. We present results that show the efficiency of the parallel hybrid Monte Carlo algorithm in the case of sparse matrices.

Applying semiotic analysis to the design and modeling of distributed multimedia systems

Semiotics is the study of signs. Application of semiotics in information systems design is based on the notion that information systems are organizations within which agents deploy signs in the form of actions according to a set of norms. An analysis of the relationships among the agents, their actions and the norms would give a better specification of the system. Distributed multimedia systems (DMMS) could be viewed as a system consisted of many dynamic, self-controlled normative agents engaging in complex interaction and processing of multimedia information. This paper reports the work of applying the semiotic approach to the design and modeling of DMMS, with emphasis on using semantic analysis under the semiotic framework. A semantic model of DMMS describing various components and their ontological dependencies is presented, which then serves as a design model and implemented in a semantic database. Benefits of using the semantic database are discussed with reference to various design scenarios.

Kernel density construction using orthogonal forward regression

An automatic algorithm is derived for constructing kernel density estimates based on a regression approach that directly optimizes generalization capability. Computational efficiency of the density construction is ensured using an orthogonal forward regression, and the algorithm incrementally minimizes the leave-one-out test score. Local regularization is incorporated into the density construction process to further enforce sparsity. Examples are included to demonstrate the ability of the proposed algorithm to effectively construct a very sparse kernel density estimate with comparable accuracy to that of the full sample Parzen window density estimate.

Orthogonal forward selection for constructing the radial basis function network with tunable nodes

An orthogonal forward selection (OFS) algorithm based on the leave-one-out (LOO) criterion is proposed for the construction of radial basis function (RBF) networks with tunable nodes. This OFS-LOO algorithm is computationally efficient and is capable of identifying parsimonious RBF networks that generalise well. Moreover, the proposed algorithm is fully automatic and the user does not need to specify a termination criterion for the construction process.

Landscape state machines: Tools for evolutionary algorithm performance analyses and landscape/algorithm mapping

Many evolutionary algorithm applications involve either fitness functions with high time complexity or large dimensionality (hence very many fitness evaluations will typically be needed) or both. In such circumstances, there is a dire need to tune various features of the algorithm well so that performance and time savings are optimized. However, these are precisely the circumstances in which prior tuning is very costly in time and resources. There is hence a need for methods which enable fast prior tuning in such cases. We describe a candidate technique for this purpose, in which we model a landscape as a finite state machine, inferred from preliminary sampling runs. In prior algorithm-tuning trials, we can replace the 'real' landscape with the model, enabling extremely fast tuning, saving far more time than was required to infer the model. Preliminary results indicate much promise, though much work needs to be done to establish various aspects of the conditions under which it can be most beneficially used. A main limitation of the method as described here is a restriction to mutation-only algorithms, but there are various ways to address this and other limitations.

Error analysis of a Monte Carlo algorithm for computing bilinear forms of matrix powers

In this paper we present error analysis for a Monte Carlo algorithm for evaluating bilinear forms of matrix powers. An almost Optimal Monte Carlo (MAO) algorithm for solving this problem is formulated. Results for the structure of the probability error are presented and the construction of robust and interpolation Monte Carlo algorithms are discussed. Results are presented comparing the performance of the Monte Carlo algorithm with that of a corresponding deterministic algorithm. The two algorithms are tested on a well balanced matrix and then the effects of perturbing this matrix, by small and large amounts, is studied.

Monte Carlo numerical treatment of large linear algebra problems

In this paper we deal with performance analysis of Monte Carlo algorithm for large linear algebra problems. We consider applicability and efficiency of the Markov chain Monte Carlo for large problems, i.e., problems involving matrices with a number of non-zero elements ranging between one million and one billion. We are concentrating on analysis of the almost Optimal Monte Carlo (MAO) algorithm for evaluating bilinear forms of matrix powers since they form the so-called Krylov subspaces. Results are presented comparing the performance of the Robust and Non-robust Monte Carlo algorithms. The algorithms are tested on large dense matrices as well as on large unstructured sparse matrices.

Complexity of Monte Carlo algorithms for a class of integral equations

In this work we study the computational complexity of a class of grid Monte Carlo algorithms for integral equations. The idea of the algorithms consists in an approximation of the integral equation by a system of algebraic equations. Then the Markov chain iterative Monte Carlo is used to solve the system. The assumption here is that the corresponding Neumann series for the iterative matrix does not necessarily converge or converges slowly. We use a special technique to accelerate the convergence. An estimate of the computational complexity of Monte Carlo algorithm using the considered approach is obtained. The estimate of the complexity is compared with the corresponding quantity for the complexity of the grid-free Monte Carlo algorithm. The conditions under which the class of grid Monte Carlo algorithms is more efficient are given.

A Monte Carlo Approach for the Cook -Torrance Model

In this work we consider the rendering equation derived from the illumination model called Cook-Torrance model. A Monte Carlo (MC) estimator for numerical treatment of the this equation, which is the Fredholm integral equation of second kind, is constructed and studied.

The effects of web logs and the semantic web on autonomous web agents

Search engines exploit the Web's hyperlink structure to help infer information content. The new phenomenon of personal Web logs, or 'blogs', encourage more extensive annotation of Web content. If their resulting link structures bias the Web crawling applications that search engines depend upon, there are implications for another form of annotation rapidly on the rise, the Semantic Web. We conducted a Web crawl of 160 000 pages in which the link structure of the Web is compared with that of several thousand blogs. Results show that the two link structures are significantly different. We analyse the differences and infer the likely effect upon the performance of existing and future Web agents. The Semantic Web offers new opportunities to navigate the Web, but Web agents should be designed to take advantage of the emerging link structures, or their effectiveness will diminish.

Femtosecond evolution of spatially inhomogeneous carrier excitations: part 2: stochastic approach and GRID implementation

We present a stochastic approach for solving the quantum-kinetic equation introduced in Part I. A Monte Carlo method based on backward time evolution of the numerical trajectories is developed. The computational complexity and the stochastic error are investigated numerically. Variance reduction techniques are applied, which demonstrate a clear advantage with respect to the approaches based on symmetry transformation. Parallel implementation is realized on a GRID infrastructure.

Eye tracking and gaze based interaction within immersive virtual environments

Our eyes are input sensors which Provide our brains with streams of visual data. They have evolved to be extremely efficient, and they will constantly dart to-and-fro to rapidly build up a picture of the salient entities in a viewed scene. These actions are almost subconscious. However, they can provide telling signs of how the brain is decoding the visuals and call indicate emotional responses, prior to the viewer becoming aware of them. In this paper we discuss a method of tracking a user's eye movements, and Use these to calculate their gaze within an immersive virtual environment. We investigate how these gaze patterns can be captured and used to identify viewed virtual objects, and discuss how this can be used as a, natural method of interacting with the Virtual Environment. We describe a flexible tool that has been developed to achieve this, and detail initial validating applications that prove the concept.

Fast kernel classifier construction using orthogonal forward selection to minimise leave-one-out misclassification rate

We propose a simple yet computationally efficient construction algorithm for two-class kernel classifiers. In order to optimise classifier's generalisation capability, an orthogonal forward selection procedure is used to select kernels one by one by minimising the leave-one-out (LOO) misclassification rate directly. It is shown that the computation of the LOO misclassification rate is very efficient owing to orthogonalisation. Examples are used to demonstrate that the proposed algorithm is a viable alternative to construct sparse two-class kernel classifiers in terms of performance and computational efficiency.