相关论文: Faster Algorithms for Constructing a Concept (Galo…
We address the inverse problem of designing isotropic pairwise particle interaction potentials that lead to the formation of a desired lattice when a system of particles is cooled. The design problem is motivated by the desire to produce…
The (fast) component-by-component (CBC) algorithm is an efficient tool for the construction of generating vectors for quasi-Monte Carlo rank-1 lattice rules in weighted reproducing kernel Hilbert spaces. We consider product weights, which…
We present a continuous-time quantum search algorithm on a graphene lattice. This provides the sought-after implementation of an efficient continuous-time quantum search on a two-dimensional lattice. The search uses the linearity of the…
We present the LATE algorithm, an asynchronous variant of the Earley algorithm for parsing context-free grammars. The Earley algorithm is naturally task-based, but is difficult to parallelize because of dependencies between the tasks. We…
We discuss the possibility of the existence of finite algorithms that may give distinct knot classes. In particular we present two attempts for such algorithms which seem promising, one based on knot projections on a plane, the other on…
Computing a basis for the exponent lattice of algebraic numbers is a basic problem in the field of computational number theory with applications to many other areas. The main cost of a well-known algorithm…
We construct an algorithm to decide whether two given Legendrian or transverse links are equivalent. In general, the complexity of the algorithm is too high for practical implementation. However, in many cases, when the symmetry group of…
Graphlet analysis is an approach to network analysis that is particularly popular in bioinformatics. We show how to set up a system of linear equations that relate the orbit counts and can be used in an algorithm that is significantly…
We restate a process presented by Stanley as a technique to prove that there exists exactly one $d$-differential distributive lattice for any positive integer $d$. This process can be trivially extended to apply to distributive finitary…
Polynomial reconstruction on Cartesian grids is fundamental in many scientific and engineering applications, yet it is still an open problem how to construct for a finite subset $K$ of $\mathbb{Z}^{\textsf{D}}$ a lattice $\mathcal{T}\subset…
Constructing a similarity graph from a set $X$ of data points in $\mathbb{R}^d$ is the first step of many modern clustering algorithms. However, typical constructions of a similarity graph have high time complexity, and a quadratic space…
A lattice reduction is an algorithm that transforms the given basis of the lattice to another lattice basis such that problems like finding a shortest vector and closest vector become easier to solve. Some of the famous lattice reduction…
It has been shown that the parallel Lattice Linear Predicate (LLP) algorithm solves many combinatorial optimization problems such as the shortest path problem, the stable marriage problem and the market clearing price problem. In this…
These notes are an exposition of Galois Theory from the original Lagrangian and Galoisian point of view. A particular effort was made here to better understand the connection between Lagrange's purely combinatorial approach and Galois…
Finding the Lie-algebraic closure of a handful of matrices has important applications in quantum computing and quantum control. For most realistic cases, the closure cannot be determined analytically, necessitating an explicit numerical…
We introduce the use of Fourier analysis on lattices as an integral part of a lattice based construction. The tools we develop provide an elegant description of certain Gaussian distributions around lattice points. Our results include two…
A simple fast algorithm of the conodes calculation in binary systems is proposed. The method is based on exact solution of the problem on common tangent to pair of approximating parabolas. Sequence of approximating parabolas pairs having…
Lattices with minimal normalized second moments are designed using a new numerical optimization algorithm. Starting from a random lower-triangular generator matrix and applying stochastic gradient descent, all elements are updated towards…
A method of fast linear transform algorithm synthesis for an arbitrary tensor, matrix, or vector is proposed. The method is based on factorization of a tensor and using the factors for building computational structures performing fast…
We present a fast algorithm for the design of smooth paths (or trajectories) that are constrained to lie in a collection of axis-aligned boxes. We consider the case where the number of these safe boxes is large, and basic preprocessing of…