Related papers: A new transfer-matrix algorithm for exact enumerat…
A new algorithm is developed allowing the Monte Carlo study of a 1 + 1 dimensional theory in real time. The main algorithmic development is to avoid the explicit calculation of the Jacobian matrix and its determinant in the update process.…
In practical applications, lattice quantizers leverage discrete lattice points to approximate arbitrary points in the lattice. An effective lattice quantizer significantly enhances both the accuracy and efficiency of these approximations.…
We present a lattice algorithm specifically designed for some classical applications of lattice reduction. The applications are for lattice bases with a generalized knapsack-type structure, where the target vectors are boundably short. For…
The purpose of this text is to provide an accessible introduction to a set of recently developed algorithms for factorizing matrices. These new algorithms attain high practical speed by reducing the dimensionality of intermediate…
Lattices are an efficient and effective method to encode ambiguity of upstream systems in natural language processing tasks, for example to compactly capture multiple speech recognition hypotheses, or to represent multiple linguistic…
We show how to construct highly symmetric algorithms for matrix multiplication. In particular, we consider algorithms which decompose the matrix multiplication tensor into a sum of rank-1 tensors, where the decomposition itself consists of…
We present an implementation of Redelemeier's algorithm for the enumeration of lattice animals in high dimensional lattices. The implementation is lean and fast enough to allow us to extend the existing tables of animal counts, perimeter…
We have calculated long series expansions for self-avoiding walks and polygons on the honeycomb lattice, including series for metric properties such as mean-squared radius of gyration as well as series for moments of the area-distribution…
We use the finite lattice method to calculate the radius of gyration, the first and second area-weighted moments of self-avoiding polygons on the square lattice. The series have been calculated for polygons up to perimeter 82. Analysis of…
We present a complete algorithm for finding an exact minimal polynomial from its approximate value by using an improved parameterized integer relation construction method. Our result is superior to the existence of error controlling on…
In this paper, we propose an efficient and scalable low rank matrix completion algorithm. The key idea is to extend orthogonal matching pursuit method from the vector case to the matrix case. We further propose an economic version of our…
Optimal packing of objects in containers is a critical problem in various real-life and industrial applications. This paper investigates the two-dimensional packing of convex polygons without rotations, where only translations are allowed.…
Bridging algorithms are global Monte Carlo moves which allow for an efficient sampling of single polymer chains. In this manuscript we discuss the adaptation of three bridging algorithms from lattice to continuum models, and give details on…
We present an $(1+\varepsilon)$-approximation algorithm with quasi-polynomial running time for computing the maximum weight independent set of polygons out of a given set of polygons in the plane (specifically, the running time is $n^{O(…
The behavior of a Lattice Monte Carlo algorithm (if it is designed correctly) must approach that of the continuum system that it is designed to simulate as the time step and the mesh step tend to zero. However, we show for an algorithm for…
We propose a new exact method for shortest-path distance queries on large-scale networks. Our method precomputes distance labels for vertices by performing a breadth-first search from every vertex. Seemingly too obvious and too inefficient…
The implicit trace estimation problem asks for an approximation of the trace of a square matrix, accessed via matrix-vector products (matvecs). This paper designs new randomized algorithms, XTrace and XNysTrace, for the trace estimation…
Efficient learning from demonstration for long-horizon tasks remains an open challenge in robotics. While significant effort has been directed toward learning trajectories, a recent resurgence of object-centric approaches has demonstrated…
Lattice rules and polynomial lattice rules are quadrature rules for approximating integrals over the $s$-dimensional unit cube. Since no explicit constructions of such quadrature methods are known for dimensions $s > 2$, one usually has to…
We study a class of rearrangement problems under a novel pick-n-swap prehensile manipulation model, in which a robotic manipulator, capable of carrying an item and making item swaps, is tasked to sort items stored in lattices of variable…