Subword balance, position indices and power sums

AbstractIn this paper, we investigate various ways of characterizing words, mainly over a binary alphabet, using information about the positions of occurrences of letters in words. We introduce two new measures associated with words, the position index and sum of position indices. We establish some characterizations, connections with Parikh matrices, and connections with power sums. One particular emphasis concerns the effect of morphisms and iterated morphisms on words

Two-Dimensional Digitized Picture Arrays and Parikh Matrices

Parikh matrix mapping or Parikh matrix of a word has been introduced in the literature to count the scattered subwords in the word. Several properties of a Parikh matrix have been extensively investigated. A picture array is a two-dimensional connected digitized rectangular array consisting of a finite number of pixels with each pixel in a cell having a label from a finite alphabet. Here we extend the notion of Parikh matrix of a word to a picture array and associate with it two kinds of Parikh matrices, called row Parikh matrix and column Parikh matrix. Two picture arrays A and B are defined to be M-equivalent if their row Parikh matrices are the same and their column Parikh matrices are the same. This enables to extend the notion of M-ambiguity to a picture array. In the binary and ternary cases, conditions that ensure M-ambiguity are then obtained

Repetitive subwords

The central notionof thisthesisis repetitionsin words. We studyproblemsrelated to contiguous repetitions. More specifically we will consider repeating scattered subwords of non-primitive words, i.e. words which are complete repetitions of other words. We will present inequalities concerning these occurrences as well as giving apartial solutionto an openproblemposedby Salomaaet al. We will characterize languages, whichare closed under the operation ofduplication, thatis repeating any factor of a word. We alsogive newbounds onthe number of occurrencesof certain types of repetitions of words. We give a solution to an open problem posed by Calbrix and Nivat concerning regular languages consisting of non-primitive words. We alsopresentsomeresultsregarding theduplication closureoflanguages,among which a new proof to a problem of Bovet and Varricchio

Relations on words

In the first part of this survey, we present classical notions arising in combinatorics on words: growth function of a language, complexity function of an infinite word, pattern avoidance, periodicity and uniform recurrence. Our presentation tries to set up a unified framework with respect to a given binary relation. In the second part, we mainly focus on abelian equivalence, $k$-abelian equivalence, combinatorial coefficients and associated relations, Parikh matrices and $M$-equivalence. In particular, some new refinements of abelian equivalence are introduced

Explainable clinical coding with in-domain adapted transformers

Background and Objective: Automatic clinical coding is a crucial task in the process of extracting relevant in-formation from unstructured medical documents contained in Electronic Health Records (EHR). However, most of the existing computer-based methods for clinical coding act as “black boxes”, without giving a detailed description of the reasons for the clinical-coding assignments, which greatly limits their applicability to real-world medical scenarios. The objective of this study is to use transformer-based models to effectively tackle explainable clinical-coding. In this way, we require the models to perform the assignments of clinical codes to medical cases, but also to provide the reference in the text that justifies each coding assignment. Methods: We examine the performance of 3 transformer-based architectures on 3 different explainable clinical-coding tasks. For each transformer, we compare the performance of the original general-domain version with an in-domain version of the model adapted to the specificities of the medical domain. We address the explainable clinical-coding problem as a dual medical named entity recognition (MER) and medical named entity normal-ization (MEN) task. For this purpose, we have developed two different approaches, namely a multi-task and a hierarchical-task strategy. Results: For each analyzed transformer, the clinical-domain version significantly outperforms the corresponding general domain model across the 3 explainable clinical-coding tasks analyzed in this study. Furthermore, the hierarchical-task approach yields a significantly superior performance than the multi-task strategy. Specifically, the combination of the hierarchical-task strategy with an ensemble approach leveraging the predictive capa-bilities of the 3 distinct clinical-domain transformersFunding for open access charge: Universidad de Málaga / CBUA. The authors thankfully acknowledge the computer resources, technical expertise and assistance provided by the SCBI (Supercomputing and Bioinformatics) center of the University of Málaga