Genetic algorithms for discovery of matrix multiplication methods

We present a parallel genetic algorithm for nding matrix multiplication algo-rithms. For 3 x 3 matrices our genetic algorithm successfully discovered algo-rithms requiring 23 multiplications, which are equivalent to the currently best known human-developed algorithms. We also studied the cases with less mul-tiplications and evaluated the suitability of the methods discovered. Although our evolutionary method did not reach the theoretical lower bound it led to an approximate solution for 22 multiplications.

Relaxation of alternating iterative algorithms for the Cauchy problem associated with the modified Helmholtz equation

We propose two algorithms involving the relaxation of either the given Dirichlet data or the prescribed Neumann data on the over-specified boundary, in the case of the alternating iterative algorithm of ` 12 ` 12 `$12 `&12 `#12 `^12 `_12 `%12 `~12 *Kozlov91 applied to Cauchy problems for the modified Helmholtz equation. A convergence proof of these relaxation methods is given, along with a stopping criterion. The numerical results obtained using these procedures, in conjunction with the boundary element method (BEM), show the numerical stability, convergence, consistency and computational efficiency of the proposed methods.

A variational method and approximations of a Cauchy problem for elliptic equations

A Cauchy problem for general elliptic second-order linear partial differential equations in which the Dirichlet data in H½(?1 ? ?3) is assumed available on a larger part of the boundary ? of the bounded domain O than the boundary portion ?1 on which the Neumann data is prescribed, is investigated using a conjugate gradient method. We obtain an approximation to the solution of the Cauchy problem by minimizing a certain discrete functional and interpolating using the finite diference or boundary element method. The minimization involves solving equations obtained by discretising mixed boundary value problems for the same operator and its adjoint. It is proved that the solution of the discretised optimization problem converges to the continuous one, as the mesh size tends to zero. Numerical results are presented and discussed.

Replication-based inference algorithms for hard computational problems

Inference algorithms based on evolving interactions between replicated solutions are introduced and analyzed on a prototypical NP-hard problem: the capacity of the binary Ising perceptron. The efficiency of the algorithm is examined numerically against that of the parallel tempering algorithm, showing improved performance in terms of the results obtained, computing requirements and simplicity of implementation. © 2013 American Physical Society.

Visual data mining using principled projection algorithms and information visualization techniques

We introduce a flexible visual data mining framework which combines advanced projection algorithms from the machine learning domain and visual techniques developed in the information visualization domain. The advantage of such an interface is that the user is directly involved in the data mining process. We integrate principled projection algorithms, such as generative topographic mapping (GTM) and hierarchical GTM (HGTM), with powerful visual techniques, such as magnification factors, directional curvatures, parallel coordinates and billboarding, to provide a visual data mining framework. Results on a real-life chemoinformatics dataset using GTM are promising and have been analytically compared with the results from the traditional projection methods. It is also shown that the HGTM algorithm provides additional value for large datasets. The computational complexity of these algorithms is discussed to demonstrate their suitability for the visual data mining framework. Copyright 2006 ACM.

A critical comparison of ICA algorithms

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Algorithms for solving large random graphs

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Message-passing algorithms for optimal utilization of cognitive radio networks

Cognitive Radio has been proposed as a key technology to significantly improve spectrum usage in wireless networks by enabling unlicensed users to access unused resource. We present new algorithms that are needed for the implementation of opportunistic scheduling policies that maximize the throughput utilization of resources by secondary users, under maximum interference constraints imposed by existing primary users. Our approach is based on the Belief Propagation (BP) algorithm, which is advantageous due to its simplicity and potential for distributed implementation. We examine convergence properties and evaluate the performance of the proposed BP algorithms via simulations and demonstrate that the results compare favorably with a benchmark greedy strategy. © 2013 IEEE.

Combining algorithms to predict bacterial protein sub-cellular location:parallel versus concurrent implementations

We describe a novel and potentially important tool for candidate subunit vaccine selection through in silico reverse-vaccinology. A set of Bayesian networks able to make individual predictions for specific subcellular locations is implemented in three pipelines with different architectures: a parallel implementation with a confidence level-based decision engine and two serial implementations with a hierarchical decision structure, one initially rooted by prediction between membrane types and another rooted by soluble versus membrane prediction. The parallel pipeline outperformed the serial pipeline, but took twice as long to execute. The soluble-rooted serial pipeline outperformed the membrane-rooted predictor. Assessment using genomic test sets was more equivocal, as many more predictions are made by the parallel pipeline, yet the serial pipeline identifies 22 more of the 74 proteins of known location.

Using genetic algorithms for improved discrete sequence prediction

A statistics-based method using genetic algorithms for predicting discrete sequences is presented. The prediction of the next value is based upon a fixed number of previous values and the statistics offered by the training data. According to the statistics, in similar past cases different values occurred next. If these values are considered with the appropriate weights, the forecast is successful. Weights are generated by genetic algorithms.