Are degree distributions of human brain functional connectivity networks heavy-tailed? Initial claims based on least-square fitting suggested that brain functional connectivity networks obey power law scaling in their degree distributions. This interpretation has been challenged on methodological grounds. Subsequently, estimators based on maximum-likelihood and non-parametric tests involving surrogate data have been proposed. No clear consensus has emerged as results especially depended on data resolution. To identify the underlying topological distribution of brain functional connectivity calls for a closer examination of the relationship between resolution and statistics of model fitting. In this study, we analyze high-resolution functional magnetic resonance imaging (fMRI) data from the Human Connectome Project to assess its degree distribution across resolutions. We consider resolutions from one thousand to eighty thousand regions of interest (ROIs) and test whether they follow a heavy or short-tailed distribution. We analyze power law, exponential, truncated power law, log-normal, Weibull and generalized Pareto probability distributions. Notably, the Generalized Pareto distribution is of particular interest since it interpolates between heavy-tailed and short-tailed distributions, and it provides a handle on estimating the tail's heaviness or shortness directly from the data. Our results show that the statistics support the short-tailed limit of the generalized Pareto distribution, rather than a power law or any other heavy-tailed distribution. Working across resolutions of the data and performing cross-model comparisons, we further establish the overall robustness of the generalized Pareto model in explaining the data. Moreover, we account for earlier ambiguities by showing that down-sampling the data systematically affects statistical results. At lower resolutions models cannot easily be differentiated on statistical grounds while their plausibility consistently increases up to an upper bound. Indeed, more power law distributions are reported at low resolutions (5K) than at higher ones (50K or 80K). However, we show that these positive identifications at low resolutions fail cross-model comparisons and that down-sampling data introduces the risk of detecting spurious heavy-tailed distributions. This dependence of the statistics of degree distributions on sampling resolution has broader implications for neuroinformatic methodology, especially, when several analyses rely on down-sampled data, for instance, due to a choice of anatomical parcellations or measurement technique. Our findings that node degrees of human brain functional networks follow a short-tailed distribution have important implications for claims of brain organization and function. Our findings do not support common simplistic representations of the brain as a generic complex system with optimally efficient architecture and function, modeled with simple growth mechanisms. Instead these findings reflect a more nuanced picture of a biological s...
This report presents the organisaton of PBL (Project Based Learning) for a subject included in the IT engineering degree course. It is the result of 10 years of experience of the implantaton and contnuous improvement of the PBL class structure. The latest innovatons include the experience of part-tme monitoring with PBL groups using the Open Meetngs tool in Moodle 2.0, the adopton of actvites that improve learning and interdependence such as the jigsaw classroom, the clear defniton of deliverables that students should present along the semester and the assessment criteria, both on groups and individuals. As a result of this experience, we present PBL student enrolment indexes, student assessment surveys and lecturers' opinions. We conclude with some topics for discussion about the PBL methodology.
Deformation of expressive textures is the gateway to realistic computer synthesis of expressions. By their good mathematical properties and flexible formulation on irregular meshes, most texture mappings rely on solutions to the Laplacian in the cartesian space. In the context of facial expression morphing, this approximation can be seen from the opposite point of view by neglecting the metric. In this paper, we use the properties of the Laplacian in manifolds to present a novel approach to warping expressive facial images in order to generate a morphing between them.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.