Persistent topology for natural data analysis - A survey

Natural data offer a hard challenge to data analysis. One set of tools is being developed by several teams to face this difficult task: Persistent topology. After a brief introduction to this theory, some applications to the analysis and classification of cells, lesions, music pieces, gait, oil and gas reservoirs, cyclones, galaxies, bones, brain connections, languages, handwritten and gestured letters are shown

Competitive comparison in music: influences upon self-efficacy beliefs by gender

This study profiles gender differences in instrumental performance self-efficacy perceptions of high school students (N = 87) over the course of a three-day orchestra festival in which students competed against one another for rank-based seating and then rehearsed and performed as a group. Reported self-beliefs rose significantly for the sample over the course of the festival. Self-efficacy beliefs of females were significantly lower than those of males before the seating audition and first rehearsal, but were no longer different by the midpoint of the festival. Survey free-response data were coded according to Bandura's (1997 Bandura, A. 1997. Self-efficacy: The Exercise of Control. New York: W. H. Freeman.) four sources of self-efficacy. A 52% drop in the frequency of student comments regarding competitive comparison appeared at the same point in which female self-efficacy beliefs were no longer different from those of males. Results support past research to suggest that males and females may respond differently to rank-based competition versus social support

Intergenerational ties in Latinx Protestant congregations: sustaining ethnicity through organizational and affective connections

This paper examines the persistence of intergenerational ties within Latinx Protestant Congregations (LPCs) and the implications these ties have for the persistence of LPCs as distinctly ethnic institutions. Though studies of generational transitions within ethnic congregations tend to emphasize intergenerational discontinuity, this paper uncovers ways that Latinx Protestants maintain intergenerational ties through LPC involvement, both within and across institutional settings. Rather than focusing on the content of intergenerational transmission, such as cultural practices, ethnic material, or explicit identity labels, this paper is concerned with a more preliminary matter of ethnic identity maintenance—the persistence of channels of transmission across generations. In particular, this paper examines how LPC organizational structures sustain cross-generational links, and how later generation Latinxs express affective ties to earlier generation Latinxs. Taking a religious ecology approach, findings are based on in-depth qualitative research conducted within six LPCs, and an informal survey of eleven additional LPCs, all located in the city of Santa Ana, California, a Latinx majority city. Findings suggest that LPCs are successfully cultivating intergenerational ties among a select group of later generation Latinxs, and that later generation Latinxs who stay connected to LPCs value these ties.https://www.mdpi.com/2077-1444/10/9/504/htmPublished versio

Why Youth (heart) Social Network Sites: The Role of Networked Publics in Teenage Social Life

Part of the Volume on Youth, Identity, and Digital Media Social network sites like MySpace and Facebook serve as "networked publics." As with unmediated publics like parks and malls, youth use networked publics to gather, socialize with their peers, and make sense of and help build the culture around them. This article examines American youth engagement in networked publics and considers how properties unique to such mediated environments (e.g., persistence, searchability, replicability, and invisible audiences) affect the ways in which youth interact with one another. Ethnographic data is used to analyze how youth recognize these structural properties and find innovative ways of making these systems serve their purposes. Issues like privacy and impression management are explored through the practices of teens and youth participation in social network sites is situated in a historical discussion of youth's freedom and mobility in the United States

Persistent homology of time-dependent functional networks constructed from coupled time series

We use topological data analysis to study "functional networks" that we construct from time-series data from both experimental and synthetic sources. We use persistent homology with a weight rank clique filtration to gain insights into these functional networks, and we use persistence landscapes to interpret our results. Our first example uses time-series output from networks of coupled Kuramoto oscillators. Our second example consists of biological data in the form of functional magnetic resonance imaging (fMRI) data that was acquired from human subjects during a simple motor-learning task in which subjects were monitored on three days in a five-day period. With these examples, we demonstrate that (1) using persistent homology to study functional networks provides fascinating insights into their properties and (2) the position of the features in a filtration can sometimes play a more vital role than persistence in the interpretation of topological features, even though conventionally the latter is used to distinguish between signal and noise. We find that persistent homology can detect differences in synchronization patterns in our data sets over time, giving insight both on changes in community structure in the networks and on increased synchronization between brain regions that form loops in a functional network during motor learning. For the motor-learning data, persistence landscapes also reveal that on average the majority of changes in the network loops take place on the second of the three days of the learning process.Comment: 17 pages (+3 pages in Supplementary Information), 11 figures in many text (many with multiple parts) + others in SI, submitte

An Alternative Postulate to see Melody as “Language”

The paper proposes a way to see melodic features in music/songs in the terms of “letters” constituting “words”, while in return investigating the fulfillment of Zipf-Mandelbrot Law in them. Some interesting findings are reported including some possible conjectures for classification of melodic and musical artifacts considering several aspects of culture. The paper ends with some discussions related to further directions, be it enrichment in musicology and the possible plan for musical generative art

Topological Data Analysis of Task-Based fMRI Data from Experiments on Schizophrenia

We use methods from computational algebraic topology to study functional brain networks, in which nodes represent brain regions and weighted edges encode the similarity of fMRI time series from each region. With these tools, which allow one to characterize topological invariants such as loops in high-dimensional data, we are able to gain understanding into low-dimensional structures in networks in a way that complements traditional approaches that are based on pairwise interactions. In the present paper, we use persistent homology to analyze networks that we construct from task-based fMRI data from schizophrenia patients, healthy controls, and healthy siblings of schizophrenia patients. We thereby explore the persistence of topological structures such as loops at different scales in these networks. We use persistence landscapes and persistence images to create output summaries from our persistent-homology calculations, and we study the persistence landscapes and images using $k$-means clustering and community detection. Based on our analysis of persistence landscapes, we find that the members of the sibling cohort have topological features (specifically, their 1-dimensional loops) that are distinct from the other two cohorts. From the persistence images, we are able to distinguish all three subject groups and to determine the brain regions in the loops (with four or more edges) that allow us to make these distinctions