相关论文: Computing generating sets of lattice ideals

We consider a programming language based on the lamplighter group that uses only composition and iteration as control structures. We derive generating functions and counting formulas for this language and special subsets of it, establishing…

Integer partitions may be encoded as either ascending or descending compositions for the purposes of systematic generation. Many algorithms exist to generate all descending compositions, yet none have previously been published to generate…

Generative models, such as the method of normalizing flows, have been suggested as alternatives to the standard algorithms for generating lattice gauge field configurations. Studies with the method of normalizing flows demonstrate the proof…

In this article we continue to develop the theory of generating symmetries for integrable equations. A technique for computation of generating symmetries using Maple is presented. The technique is based on the standard symmetry method. By…

The ensemble methods are meta-algorithms that combine several base machine learning techniques to increase the effectiveness of the classification. Many existing committees of classifiers use the classifier selection process to determine…

An algorithm is presented for generating finite modular, semimodular, graded, and geometric lattices up to isomorphism. Isomorphic copies are avoided using a combination of the general-purpose graph-isomorphism tool nauty and some…

Algorithms for machine learning-guided design, or design algorithms, use machine learning-based predictions to propose novel objects with desired property values. Given a new design task -- for example, to design novel proteins with high…

A Markov chain update scheme using a machine-learned flow-based generative model is proposed for Monte Carlo sampling in lattice field theories. The generative model may be optimized (trained) to produce samples from a distribution…

This work delved into the realm of automatic text generation, exploring a variety of techniques ranging from traditional deterministic approaches to more modern stochastic methods. Through analysis of greedy search, beam search, top-k…

I present a new estimation procedure for production functions with latent group structures. I consider production functions that are heterogeneous across groups but time-homogeneous within groups, and where the group membership of the firms…

In this article, we present a new data type agnostic algorithm calculating a concept lattice from heterogeneous and complex data. Our NextPriorityConcept algorithm is first introduced and proved in the binary case as an extension of…

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…

We show how to obtain a fast component-by-component construction algorithm for higher order polynomial lattice rules. Such rules are useful for multivariate quadrature of high-dimensional smooth functions over the unit cube as they achieve…

This is the second of two articles devoted to an exposition of the generating-function method for computing fusion rules in affine Lie algebras. The present paper focuses on fusion rules, using the machinery developed for tensor products in…

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…

Objective and interpretable metrics to evaluate current artificial intelligent systems are of great importance, not only to analyze the current state of such systems but also to objectively measure progress in the future. In this work, we…

Image editing is a common task across a wide range of domains, from personal use to professional applications. Despite advances in computer vision, current tools still demand significant manual effort for editing tasks that require…

Deep generative models are able to suggest new organic molecules by generating strings, trees, and graphs representing their structure. While such models allow one to generate molecules with desirable properties, they give no guarantees…

The goal of this paper is to explicitly describe a minimal binomial generating set of a class of lattice ideals, namely the ideal of certain Veronese $3$-fold projections. More precisely, for any integer $d\ge 4$ and any $d$-th root $e$ of…

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.…