相关论文: 2D Lyndon Words and Applications

The circular dictionary matching problem is an extension of the classical dictionary matching problem where every string in the dictionary is interpreted as a circular string: after reading the last character of a string, we can move back…

We evaluate the influence of different alphabet orderings on the Lyndon factorization of a string. Experiments with Pizza & Chili datasets show that for most alphabet reorderings, the number of Lyndon factors is usually small, and the…

The aim of this paper is to introduce a novel dictionary learning algorithm for sparse representation of signals defined over combinatorial topological spaces, specifically, regular cell complexes. Leveraging Hodge theory, we embed topology…

We present Grammar-Based Grounded Lexicon Learning (G2L2), a lexicalist approach toward learning a compositional and grounded meaning representation of language from grounded data, such as paired images and texts. At the core of G2L2 is a…

Word embeddings have become the basic building blocks for several natural language processing and information retrieval tasks. Pre-trained word embeddings are used in several downstream applications as well as for constructing…

We propose a novel sparse dictionary learning method for planar shapes in the sense of Kendall, namely configurations of landmarks in the plane considered up to similitudes. Our shape dictionary method provides a good trade-off between…

We consider the dictionary learning problem, where the aim is to model the given data as a linear combination of a few columns of a matrix known as a dictionary, where the sparse weights forming the linear combination are known as…

The concepts of pseudocodeword and pseudoweight play a fundamental role in the finite-length analysis of LDPC codes. The pseudoredundancy of a binary linear code is defined as the minimum number of rows in a parity-check matrix such that…

Reverse Dictionary (RD) is the task of obtaining the most relevant word or set of words given a textual description or dictionary definition. Effective RD methods have applications in accessibility, translation or writing support systems.…

Matrix factorization is a key tool in data analysis; its applications include recommender systems, correlation analysis, signal processing, among others. Binary matrices are a particular case which has received significant attention for…

The Whitehead minimization problem consists in finding a minimum size element in the automorphic orbit of a word, a cyclic word or a finitely generated subgroup in a finite rank free group. We give the first fully polynomial algorithm to…

Piecewise testable languages are a subclass of the regular languages. There are many equivalent ways of defining them; Simon's congruence $\sim_k$ is one of the most classical approaches. Two words are $\sim_k$-equivalent if they have the…

This paper describes an alternative method of generating fixed points of certain substitution systems. This method centres on taking infinite words consisting of one repeated letter per word. These infinite words are then interlaced to form…

We propose different ways of lifting the notion of Dyck language from words to 2-dimensional (2D) pictures, by means of new definitions of increasing comprehensiveness. Two of the proposals are based on alternative definitions of a Dyck…

Lawson's iteration is a classical and effective method for solving the linear (polynomial) minimax approximation problem in the complex plane. Extension of Lawson's iteration for the rational minimax approximation problem with both…

Continuous word representations learned separately on distinct languages can be aligned so that their words become comparable in a common space. Existing works typically solve a least-square regression problem to learn a rotation aligning a…

Learning dictionaries suitable for sparse coding instead of using engineered bases has proven effective in a variety of image processing tasks. This paper studies the optimization of dictionaries on image data where the representation is…

The problem of convex optimization is studied. Usually in convex optimization the minimization is over a d-dimensional domain. Very often the convergence rate of an optimization algorithm depends on the dimension d. The algorithms studied…

We suggest a new algorithm for finding a canonical representative of a given braid, and also for the harder problem of finding a $\sigma_1$-consistent representative. We conjecture that the algorithm is quadratic-time. We present numerical…

Low-latency sliding window algorithms for regular and context-free languages are studied, where latency refers to the worst-case time spent for a single window update or query. For every regular language $L$ it is shown that there exists a…