Related papers: Short survey about combinatorics on words and algo…
We develop a new tool, namely polynomial and linear algebraic methods, for studying systems of word equations. We illustrate its usefulness by giving essentially simpler proofs of several hard problems. At the same time we prove extensions…
We seek random versions of some classical theorems on complex approximation by polynomials and rational functions, as well as investigate properties of random compact sets in connection to complex approximation.
The twenty-first century is a data-driven era where human activities and behavior, physical phenomena, scientific discoveries, technology advancements, and almost everything that happens in the world resulting in massive generation,…
The study of iterations of functions over a finite field and the corresponding functional graphs is a growing area of research with connections to cryptography. The behaviour of such iterations is frequently approximated by what is know as…
This dissertation explores the linguistic and computational aspects of the meaning relations that can hold between two or more complex linguistic expressions (phrases, clauses, sentences, paragraphs). In particular, it focuses on…
In 20th century mathematics, the field of topology, which concerns the properties of geometric objects under continuous transformation, has proved surprisingly useful in application to the study of discrete mathematics, such as…
We present an algorithm that takes an unannotated corpus as its input, and returns a ranked list of probable morphologically related pairs as its output. The algorithm tries to discover morphologically related pairs by looking for pairs…
Hypergraphs are structures that can be decomposed or described; in other words they are recursively countable. Here, we get exact and asymptotic enumeration results on hypergraphs by means of exponential generating functions. The number of…
In this article we consider combinatorial maps approach to graphs on surfaces, and how between them can be establish terminological uniformity in favor of combinatorial maps in way rotations are set as base structural elements and all other…
The authors describe their approach to teaching a course on finite fields and combinatorial applications, including block designs and error-correcting codes, using a hybrid of lectures and active learning. Under the discussed classroom…
The proposed algorithmic approach deals with finding the sense of a word in an electronic data. Now a day,in different communication mediums like internet, mobile services etc. people use few words, which are slang in nature. This approach…
Although much effort has recently been devoted to training high-quality sentence embeddings, we still have a poor understanding of what they are capturing. "Downstream" tasks, often based on sentence classification, are commonly used to…
Learning word embeddings has received a significant amount of attention recently. Often, word embeddings are learned in an unsupervised manner from a large collection of text. The genre of the text typically plays an important role in the…
This paper studies a subset of the free semi-group $F_k$ with letters in a field $k$ which has some interesting arithmetic and combinatorial properties.
In this paper we give a detailed analysis of deterministic and randomized algorithms that enumerate any number of irreducible polynomials of degree $n$ over a finite field and their roots in the extension field in quasilinear where $N=n^2$…
Distilling knowledge from a well-trained cumbersome network to a small one has recently become a new research topic, as lightweight neural networks with high performance are particularly in need in various resource-restricted systems. This…
The concept of a universal algorithm is discussed. Examples of this kind of algorithms are presented. Software implementations of such algorithms in C++ type languages are discussed together with means that provide for computations with an…
Falmagne recently introduced the concept of a medium, a combinatorial object encompassing hyperplane arrangements, topological orderings, acyclic orientations, and many other familiar structures. We find efficient solutions for several…
We consider sigma-words, which are words used by Evdokimov in the construction of the sigma-sequence. We then find the number of occurrences of certain patterns and subwords in these words.
Nonparametric estimation of a mixing density based on observations from the corresponding mixture is a challenging statistical problem. This paper surveys the literature on a fast, recursive estimator based on the predictive recursion…