Fractal and multifractal descriptors restore ergodicity broken by non-Gaussianity in time series

Ergodicity breaking is a challenge for biological and psychological sciences. Ergodicity is a necessary condition for linear causal modeling. Long-range correlations and non-Gaussianity characterizing various biological and psychological measurements break ergodicity routinely, threatening our capacity for causal modeling. Long-range correlations (e.g., in fractional Gaussian noise, a.k.a. "pink noise") break ergodicity--in raw Gaussian series, as well as in some but not all standard descriptors of variability, i.e., in coefficient of variation (CV) and root mean square (RMS) but not standard deviation (SD) for longer series. The present work demonstrates that progressive increases in non-Gaussianity conspire with long-range correlations to break ergodicity in SD for all series lengths. Meanwhile, explicitly encoding the cascade dynamics that can generate temporally correlated non-Gaussian noise offers a way to restore ergodicity to our causal models. Specifically, fractal and multifractal properties encode both scale-invariant power-law correlations and their variety, respectively, both of which features index the underlying cascade parameters. Fractal and multifractal descriptors of long-range correlated non-Gaussian processes show no ergodicity breaking and hence, provide a more stable explanation for the long-range correlated non-Gaussian form of biological and psychological processes. Fractal and multifractal descriptors offer a path to restoring ergodicity to causal modeling in these fields.Comment: 33 pages, 11 figures. arXiv admin note: text overlap with arXiv:2202.0109

Exploring & Identifying Predictors That Affect Asian American College Students' Sense of Belonging: "How Do I Fit In?"

The purpose of this study was to explore the relationship among various college environment factors, specifically living on campus, on-campus employment, mentorship, involvement in college organizations and student groups, socio-cultural discussions, and perception of nondiscriminatory climate and how these relationships potentially affect Asian American college students' sense of belonging. Data came from the 2009 Multi-Institutional Study of Leadership, which had a robust Asian American sample that included 6,786 Asian American college student participants. Descriptive analysis was conducted to provide an overview of the sample under study in terms of gender, parents' education, high school involvement, major, institutional characteristics, live on-campus, work on-campus, have a mentor, involvement in college organizations and the type of college organization involvement. Through mean comparisons, distribution of sense of belonging was analyzed between all Asian Americans and the three subpopulations being investigated which were Chinese Americans, Filipino Americans, and Asian Indian Americans. A one-way ANOVA was used to determine if there were differences in perception of sense of belonging between the ethnic subpopulations as well as from the overall Asian Americans college students and a random sample of non-Asian college students. Astin's (1993) college impact I-E-O model was used to design blocked hierarchical multiple regression models to test and identify significant predictors of sense of belonging for all Asian Americans and the three subpopulations. T-tests were conducted and significant differences between standardized and unstandardized beta coefficients were evaluated. Several key findings emerged from this study to include the most significant predictors of Asian Americans' sense of belonging were the perception of a nondiscriminatory climate on campus and participation in socio-cultural discussions with peers. Other significant predictors include having a mentor and being involved in a college organization particularly student governance and campus wide programming types of student groups. Scholars and practitioners within the field of higher education can continue the work from this study in disaggregating the data on the many Asian American ethnic groups to better understand their respective needs, and in turn, improve services and programs that strengthen this growing constituency's sense of belonging and collegiate success

On the psychological origins of tool use

The ubiquity of tool use in human life has generated multiple lines of scientific and philosophical investigation to understand the development and expression of humans' engagement with tools and its relation to other dimensions of human experience. However, existing literature on tool use faces several epistemological challenges in which the same set of questions generate many different answers. At least four critical questions can be identified, which are intimately intertwined-(1) What constitutes tool use? (2) What psychological processes underlie tool use in humans and nonhuman animals? (3) Which of these psychological processes are exclusive to tool use? (4) Which psychological processes involved in tool use are exclusive to Homo sapiens? To help advance a multidisciplinary scientific understanding of tool use, six author groups representing different academic disciplines (e.g., anthropology, psychology, neuroscience) and different theoretical perspectives respond to each of these questions, and then point to the direction of future work on tool use. We find that while there are marked differences among the responses of the respective author groups to each question, there is a surprising degree of agreement about many essential concepts and questions. We believe that this interdisciplinary and intertheoretical discussion will foster a more comprehensive understanding of tool use than any one of these perspectives (or any one of these author groups) would (or could) on their own

Multifractal test for nonlinearity of interactions across scales in time series

The creativity and emergence of biological and psychological behavior tend to be nonlinear, and correspondingly, biological and psychological measures contain degrees of irregularity. The linear model might fail to reduce these measurements to a sum of independent random factors (yielding a stable mean for the measurement), implying nonlinear changes over time. The present work reviews some of the concepts implicated in nonlinear changes over time and details the mathematical steps involved in their identification. It introduces multifractality as a mathematical framework helpful in determining whether and to what degree the measured series exhibits nonlinear changes over time. These mathematical steps include multifractal analysis and surrogate data production for resolving when multifractality entails nonlinear changes over time. Ultimately, when measurements fail to fit the structures of the traditional linear model, multifractal modeling allows making those nonlinear excursions explicit, that is, to come up with a quantitative estimate of how strongly events may interact across timescales. This estimate may serve some interests as merely a potentially statistically significant indicator of independence failing to hold, but we suspect that this estimate might serve more generally as a predictor of perceptuomotor or cognitive performance

Multifractal test for nonlinearity of interactions across scales in time series

The creativity and emergence of biological and psychological behavior tend to be nonlinear—biological and psychological measures contain degrees of irregularity. The linear model might fail to reduce these measurements to a sum of independent random factors (yielding a stable mean for the measurement), implying nonlinear changes over time. The present work reviews some of the concepts implicated in nonlinear changes over time and details the mathematical steps involved in their identification. It introduces multifractality as a mathematical framework helpful in determining whether and to what degree the measured series exhibits nonlinear changes over time. These mathematical steps include multifractal analysis and surrogate data production for resolving when multifractality entails nonlinear changes over time. Ultimately, when measurements fail to fit the structures of the traditional linear model, multifractal modeling allows making those nonlinear excursions explicit, that is, to come up with a quantitative estimate of how strongly events may interact across timescales. This estimate may serve some interests as merely a potentially statistically significant indicator, but we suspect that this estimate might serve more generally as a predictor of perceptuomotor or cognitive performance