Related papers: Monte Carlo Methods for the Self-Avoiding Walk

We introduce a model of self-repelling random walks where the short-range interaction between two elements of the chain decreases as a power of the difference in proper time. Analytic results on the exponent $\nu$ are obtained. They are in…

We recently published [J. Phys A: Math. Theor. {\bf 45} 115202 (2012)] a new and more efficient implementation of a transfer-matrix algorithm for exact enumerations of self-avoiding polygons. Here we extend this work to the enumeration of…

We give an introduction to the calculation of path integrals on a lattice, with the quantum harmonic oscillator as an example. In addition to providing an explicit computational setup and corresponding pseudocode, we pay particular…

We describe a new algebraic technique for enumerating self-avoiding walks on the rectangular lattice. The computational complexity of enumerating walks of $N$ steps is of order $3^{N/4}$ times a polynomial in $N$, and so the approach is…

Advanced algorithms are necessary to obtain faster-than-real-time dynamic simulations in a number of different physical problems that are characterized by widely disparate time scales. Recent advanced dynamic Monte Carlo algorithms that…

A class of Monte Carlo algorithms which incorporate absorbing Markov chains is presented. In a particular limit, the lowest-order of these algorithms reduces to the $n$-fold way algorithm. These algorithms are applied to study the escape…

We link the large-scale dynamics of non-reversible Monte Carlo algorithms as well as a lifted TASEP to an exactly soluble model of self-repelling motion. We present arguments for the connection between the problems and perform simulations,…

We present new, more efficient algorithms for estimating random walk scores such as Personalized PageRank from a given source node to one or several target nodes. These scores are useful for personalized search and recommendations on…

We reduce the problem of counting self-avoiding walks in the square lattice to a problem of counting the number of integral points in multidimensional domains. We obtain an asymptotic estimate of the number of self-avoiding walks of length…

We study the correction-to-scaling exponents for the two-dimensional self-avoiding walk, using a combination of series-extrapolation and Monte Carlo methods. We enumerate all self-avoiding walks up to 59 steps on the square lattice, and up…

Monte Carlo simulation is an unbiased numerical tool for studying classical and quantum many-body systems. One of its bottlenecks is the lack of general and efficient update algorithm for large size systems close to phase transition or with…

This paper explores how far the scientific discovery process can be automated. Using the identification of causally significant flow structures in two-dimensional turbulence as an example, it probes how far the usual procedure of planning…

We introduce a new Monte Carlo method by incorporating a guided distribution function to the conventional Monte Carlo method. In this way, the efficiency of Monte Carlo methods is drastically improved. To further speed up the algorithm, we…

We give a brief discussion of the recently developed Constrained-Path Monte Carlo Method. This method is a quantum Monte Carlo technique that eliminates the fermion sign problem plaguing simulations of systems of interacting electrons. The…

In this review we discuss, from a unified point of view, a variety of Monte Carlo methods used to solve eigenvalue problems in statistical mechanics and quantum mechanics. Although the applications of these methods differ widely, the…

We compute the exponent gamma for self-avoiding walks in three dimensions. We get gamma = 1.1575 +- 0.0006 in agreement with renormalization-group predictions. Earlier Monte Carlo and exact-enumeration determinations are now seen to be…

We formulate an irreversible Markov chain Monte Carlo algorithm for the self-avoiding walk (SAW), which violates the detailed balance condition and satisfies the balance condition. Its performance improves significantly compared to that of…

The pivot algorithm is a Markov Chain Monte Carlo algorithm for simulating the self-avoiding walk. At each iteration a pivot which produces a global change in the walk is proposed. If the resulting walk is self-avoiding, the new walk is…

The EM algorithm is a powerful tool for maximum likelihood estimation with missing data. In practice, the calculations required for the EM algorithm are often intractable. We review numerous methods to circumvent this intractability, all of…

We develop statistical enumeration methods for self-avoiding walks using a powerful sampling technique called the multicanonical Monte Carlo method. Using these methods, we estimate the numbers of the two dimensional N-step self-avoiding…