Fast Monte Carlo algorithms for knotted polymers

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 ...

A fast Monte Carlo algorithm for studying bottle-brush polymers

Obtaining reliable estimates of the statistical properties of complex macromolecules by computer simulation is a task that requires high computational effort as well as the development of highly efficient simulation algorithms. We present here an algorithm combining local moves, the pivot algorithm, and an adjustable simulation lattice box for simulating dilute systems of bottle-brush polymers ...

Monte Carlo Results for Projected Self-Avoiding Polygons: A Two-dimensional Model for Knotted Polymers

We introduce a two-dimensional lattice model for the description of knotted polymer rings. A polymer configuration is modeled by a closed polygon drawn on the square diagonal lattice, with possible crossings describing pairs of strands of polymer passing on top of each other. Each polygon configuration can be viewed as the two-dimensional projection of a particular knot. We study numerically th...

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...