Fast Monte Carlo Algorithms for Permutation Groups

Fast Monte Carlo Algorithms for Tensor Operations

We consider scalable randomized algorithms for many common tensor operations, including tensor multiplication, low-rank decomposition and nuclear norm minimization. Such operations arise in a number of modern day applications of tensors in machine learning and signal processing. Specifically, we introduce polynomial time algorithms that employ a small number of lateral and/or horizontal slices ...

Monte-Carlo Permutation Tests

The distribution of running time could be anything at all. We didnt even say whether it is continuous or discrete. Even so, the null hypothesis does induce a probability distribution on the test statistic without any other information. Specifically, it implies that the samples are indistinguishable and exchangeable. Our test statistic is a mean of 6 values (algorithm B running times) minus the ...

Fast Monte-Carlo Algorithms for Approximate Matrix Multipli ation

Fast Monte Carlo Algorithms for Matrices I: Approximating Matrix Multiplication

Motivated by applications in which the data may be formulated as a matrix, we consider algorithms for several common linear algebra problems. These algorithms make more efficient use of computational resources, such as the computation time, random access memory (RAM), and the number of passes over the data, than do previously known algorithms for these problems. In this paper, we devise two alg...

Evaluating Performance of Algorithms in Lung IMRT: A Comparison of Monte Carlo, Pencil Beam, Superposition, Fast Superposition and Convolution Algorithms

Background: Inclusion of inhomogeneity corrections in intensity modulated small fields always makes conformal irradiation of lung tumor very complicated in accurate dose delivery.Objective: In the present study, the performance of five algorithms via Monte Carlo, Pencil Beam, Convolution, Fast Superposition and Superposition were evaluated in lung cancer Intensity Modulated Radiotherapy plannin...