Inácio de Sousa Fadigas

Mathematics education semantic networks

Abstract Continuous technological advances have resulted in analysis techniques that can be used in network theory. Topological characterisation, study of cohesion, and analysis of prominence are relevant techniques through which vertices (e.g., words) and their relationships are considered. The goal of this paper is to produce a comparative study on semantic networks based on titles of scientific papers in the field of mathematics education in Portuguese (Brazil) and English to ascertain the topological structure of these semantic networks and to present reflections thereafter concerning the diffusion of mathematics education. The vertices of proposed semantic networks are words with intrinsic meaning belonging to the titles of scientific papers and two words are connected if both belong to the same title. Methods and metrics from social and complex network analysis have been used to develop a diagnosis of the characterisation of this type of semantic network. Within this context, this study could be used to offer support to facilitate the process of diffusing knowledge in specific areas.

Community detection in visibility networks: an approach to categorize percussive influence on audio musical signals

The feature extraction is a very important step in the music audio classification. This task has been performed by renowned descriptors using, in most cases, the time-frequency approach. In this article we propose a descriptor that performs the feature extraction in a set of music audio files labeled in symphonic and percussive music, using parameters calculated within the Euclidean domain. First we calculate the variance fluctuation series of music signal, after we map this series into visibility graphs [13]. At the end each audio track will correspond to a network, where the links are defined by the visibility of variance fluctuations of their respective audio signal. Then, we measure the strength of the partitions of each network in clusters, using calculation of modularity. The results of computation of this parameter in sixty networks showed that percussive and symphonic music can be distinguished and hierarchized on a growing rang, following a direct correlation with modularity.

Categorisation of polyphonic musical signals by using modularity community detection in audio-associated visibility network

This article proposes a method to numerically characterise the homogeneity of polyphonic musical signals through community detection in audio-associated visibility networks and to detect patterns that allow the categorisation of these signals into two types of grouping based on this numerical characterization. To implement this methodology, we first calculate the variance fluctuation series in fixed-size windows of an audio stretch. Next we map this series onto a visibility graph, where the nodes are the points of the series, and the edges are defined by the visibility between each pair of points. Then, we measure the quality of the partitions of the network using the modularity and Louvain optimisation. We observed that a greater or lesser homogeneity of the magnitudes of the signal transients is related to a higher or lower modularity of the audio-associated visibility network. We also note that these differences are related to musical choices that can establish important differences between musical styles. In this article, we show that the modularity is able to give relevant information to allow the categorisation of 120 musical signs labelled in percussive and symphonic music.