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Connectivity functions and polymatroids
Advances in Applied Mathematics, 2016 A {\em connectivity function on} a set $E$ is a function $λ:2^E\rightarrow \mathbb R$ such that $λ(\emptyset)=0$, that $λ(X)=λ(E-X)$ for all $X\subseteq E$ and that $λ(X\cap Y)+λ(X\cup Y)\leq λ(X)+λ(Y)$ for all $X,Y \subseteq E$. Graphs, matroids and, more generally, polymatroids have associated connectivity functions.
Susan Jowett, Songbao Mo, Geoff Whittle
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Frontiers in Neuroanatomy, 2018 The heterogeneity and complexity of white matter (WM) pathways of the human brain were discretely described by pioneers such as Willis, Stenon, Malpighi, Vieussens and Vicq d’Azyr up to the beginning of the 19th century. Subsequently, novel approaches to
Emmanuel Mandonnet +2 more
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Connectivity of submodular functions
Discrete Mathematics, 1992 This paper relates the connectivity of submodular functions \(f\) to that of certain submodular functions which are derived from \(f\). Here the function \(f\) on \(S\) is submodular if \(f(A)+f(B)\geq f(A\cup B)+f(A\cap B)\) for all subsets \(A\) and \(B\) of \(S\).
James G. Oxley, Geoff Whittle
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Structural Brain Connectivity Constrains within-a-Day Variability of Direct Functional Connectivity
Frontiers in Human Neuroscience, 2017 The idea that structural white matter connectivity constrains functional connectivity (interactions among brain regions) has widely been explored in studies of brain networks; studies have mostly focused on the “average” strength of functional ...
Bumhee Park +6 more
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Insula Functional Connectivity in Schizophrenia [PDF]
Schizophrenia Research, 2019 Abstract The insula is structurally abnormal in schizophrenia, demonstrating robust reductions in gray matter volume, cortical thickness, and altered gyrification during prodromal, early and chronic stages of the illness. Despite compelling structural alterations, less is known about its functional connectivity, limited by studies ...
Julia M. Sheffield +4 more
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Positive Connectivity Predicts the Dynamic Intrinsic Topology of the Human Brain Network
Frontiers in Systems Neuroscience, 2018 Functional connectivity MRI (fcMRI) has become instrumental in facilitating research of human brain network organization in terms of coincident interactions between positive and negative synchronizations of large-scale neuronal systems. Although there is
Jingyu Qian +11 more
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Functional Connectivity in Aging [PDF]
, 2019 A large body of research shows that aging is accompanied by localized changes in brain structure and function. However, over the past decade the neuroimaging community has begun to recognize the importance of investigating the brain as a network.
Franziskus Liem +3 more
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Biophysical Modulations of Functional Connectivity [PDF]
Brain Connectivity, 2011 Resting-state low frequency oscillations have been detected in many functional magnetic resonance imaging (MRI) studies and appear to be synchronized between functionally related areas. Converging evidence from MRI and other imaging modalities suggest that this activity has an intrinsic neuronal origin.
Peltier, Scott J., Shah, Yash
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The Functional Relevance of Task-State Functional Connectivity [PDF]
The Journal of Neuroscience, 2020 Resting-state functional connectivity has provided substantial insight into intrinsic brain network organization, yet the functional importance of task-related change from that intrinsic network organization remains unclear. Indeed, such task-related changes are known to be small, suggesting they may have only minimal functional relevance ...
Michael W. Cole +3 more
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The impact of ischemic stroke on connectivity gradients
NeuroImage: Clinical, 2019 The functional organization of the brain can be represented as a low-dimensional space that reflects its macroscale hierarchy. The dimensions of this space, described as connectivity gradients, capture the similarity of areas' connections along a ...
Şeyma Bayrak +6 more
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