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      Can local-community-paradigm and epitopological learning enhance our understanding of how local brain connectivity is able to process, learn and memorize chronic pain?

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          Abstract

          The mystery behind the origin of the pain and the difficulty to propose methodologies for its quantitative characterization fascinated philosophers (and then scientists) from the dawn of our modern society. Nowadays, studying patterns of information flow in mesoscale activity of brain networks is a valuable strategy to offer answers in computational neuroscience. In this paper, complex network analysis was performed on the time-varying brain functional connectomes of a rat model of persistent peripheral neuropathic pain, obtained by means of local field potential and spike train analysis. A wide range of topological network measures (14 in total, the code is publicly released at: https://github.com/biomedical-cybernetics/topological_measures_wide_analysis) was employed to quantitatively investigate the rewiring mechanisms of the brain regions responsible for development and upkeep of pain along time, from three hours to 16 days after nerve injury. The time trend (across the days) of each network measure was correlated with a behavioural test for rat pain, and surprisingly we found that the rewiring mechanisms associated with two local topological measure, the local-community-paradigm and the power-lawness, showed very high statistical correlations (higher than 0.9, being the maximum value 1) with the behavioural test. We also disclosed clear functional connectivity patterns that emerged in association with chronic pain in the primary somatosensory cortex (S1) and ventral posterolateral (VPL) nuclei of thalamus. This study represents a pioneering attempt to exploit network science models in order to elucidate the mechanisms of brain region re-wiring and engram formations that are associated with chronic pain in mammalians. We conclude that the local-community-paradigm is a model of complex network organization that triggers a local learning rule, which seems associated to processing, learning and memorization of chronic pain in the brain functional connectivity. This rule is based exclusively on the network topology, hence was named epitopological learning.

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          The online version of this article (doi:10.1007/s41109-017-0048-x) contains supplementary material, which is available to authorized users.

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          Modularity and community structure in networks

          M. Newman (2006)
          Many networks of interest in the sciences, including a variety of social and biological networks, are found to divide naturally into communities or modules. The problem of detecting and characterizing this community structure has attracted considerable recent attention. One of the most sensitive detection methods is optimization of the quality function known as "modularity" over the possible divisions of a network, but direct application of this method using, for instance, simulated annealing is computationally costly. Here we show that the modularity can be reformulated in terms of the eigenvectors of a new characteristic matrix for the network, which we call the modularity matrix, and that this reformulation leads to a spectral algorithm for community detection that returns results of better quality than competing methods in noticeably shorter running times. We demonstrate the algorithm with applications to several network data sets.
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            Power-law distributions in empirical data

            Power-law distributions occur in many situations of scientific interest and have significant consequences for our understanding of natural and man-made phenomena. Unfortunately, the detection and characterization of power laws is complicated by the large fluctuations that occur in the tail of the distribution -- the part of the distribution representing large but rare events -- and by the difficulty of identifying the range over which power-law behavior holds. Commonly used methods for analyzing power-law data, such as least-squares fitting, can produce substantially inaccurate estimates of parameters for power-law distributions, and even in cases where such methods return accurate answers they are still unsatisfactory because they give no indication of whether the data obey a power law at all. Here we present a principled statistical framework for discerning and quantifying power-law behavior in empirical data. Our approach combines maximum-likelihood fitting methods with goodness-of-fit tests based on the Kolmogorov-Smirnov statistic and likelihood ratios. We evaluate the effectiveness of the approach with tests on synthetic data and give critical comparisons to previous approaches. We also apply the proposed methods to twenty-four real-world data sets from a range of different disciplines, each of which has been conjectured to follow a power-law distribution. In some cases we find these conjectures to be consistent with the data while in others the power law is ruled out.
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              What is principal component analysis?

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                Author and article information

                Contributors
                kalokagathos.agon@gmail.com
                Journal
                Appl Netw Sci
                Appl Netw Sci
                Applied Network Science
                Springer International Publishing (Cham )
                2364-8228
                30 August 2017
                30 August 2017
                2017
                : 2
                : 1
                : 28
                Affiliations
                [1 ]ISNI 0000 0001 2111 7257, GRID grid.4488.0, Biomedical Cybernetics Group, Biotechnology Center (BIOTEC), Center for Molecular and Cellular Bioengineering (CMCB), Center for Systems Biology Dresden (CSBD), Department of Physics, , Technische Universität Dresden, ; Dresden, Germany
                [2 ]GRID grid.419419.0, Brain bio-inspired computatiing (BBC) lab, IRCCS Centro Neurolesi “Bonino Pulejo”, ; Messina, Italy
                [3 ]ISNI 0000 0004 1789 9809, GRID grid.428490.3, Institute of Molecular Bioimaging and Physiology, Consiglio Nazionale delle Ricerche, ; Segrate, Milan, Italy
                Article
                48
                10.1007/s41109-017-0048-x
                6214247
                038e18f0-2b2d-48a6-9ec1-045d300e521a
                © The Author(s) 2017

                Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License ( http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

                History
                : 17 February 2017
                : 7 August 2017
                Categories
                Research
                Custom metadata
                © The Author(s) 2017

                network topology,topological measures,local-community-paradigm,brain connectivity,pain markers,computational neuroscience,learning,memory

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