Reconstructing Cortical Networks: Case of Directed Graphs with High Level of Reciprocity

Nepusz, Tamás; Négyessy, László; Tusnády, Gábor; Bazsó, Fülöp

doi:10.1007/978-3-540-69395-6_8

Cited by 17 publications

(19 citation statements)

References 55 publications

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“…To the best of our knowledge, the earliest link prediction effort in the context of brain neuronal networks goes back to a 1998 paper by Jouve et al (Jouve et al, 1998), which uses the frequency of directed transitive triples to predict missing links at the binary level (existing or not), in an early dataset on the macaque visual system (Felleman and Van Essen, 1991). The next brain link prediction papers appear almost a decade later, which incorporate additional topological and spatial features (Costa et al, 2007;Nepusz et al, 2008), both based on the CoCoMac database (Kötter, 2004), with the latter using a stochastic graph fitting method to handle the uncertainties in the data. Several other publications followed these papers (Hoff, 2009;Cannistraci et al, 2013;Hinne et al, 2017;Røge et al, 2017;Chen et al, 2020;Shen et al, 2019), but all (including the earliest three) are based on preconceived network models whose parameters are fitted to the data, and then used to make predictions (usually at a binary level) on missing links.…”

Section: Discussionmentioning

confidence: 99%

Predictability of cortico-cortical connections in the mammalian brain

Molnár

Horvát

Gomes

et al. 2020

Preprint

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Despite a five-order magnitude range in size, the mammalian brain exhibits many shared anatomical and functional characteristics that should translate into cortical network commonalities. Here we develop a framework employing machine learning to quantify the degree of predictability of the weighted interareal cortical matrix. Data were obtained with retrograde tract-tracing experiments supplemented by projection length measurements. Using this framework with consistent and edge-complete empirical datasets in the macaque and mouse cortex, we show that there is significant amount of predictability embedded in the interareal cortical networks of both species. At the binary level, links are predictable with an Area Under the ROC curve of at least 0.8 for the macaque. At the weighted level, strengths of the medium and strong links are predictable with at least 85-90% accuracy in mouse and 70-80% in macaque, whereas weak links are not predictable in either species. These observations suggest that the formation and evolution of the cortical network at the mesoscale is to a large extent, rule-based, motivating further research on the architectural invariants of the cortical connectome.

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Section: Discussionmentioning

confidence: 99%

Predictability of cortico-cortical connections in the mammalian brain

Molnár

Horvát

Gomes

et al. 2020

Preprint

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“…We note that link probability matrices similar to the previous examples can be also used for community detection as pointed out by Nepusz et al in [28,29]. In their approach (inspired by Szemerédi's regularity lemma [30]) the diagonal elements of the matrix give the the link density inside the corresponding communities, whereas the off-diagonal elements correspond to the link probabilities between the groups.…”

Section: Introductionmentioning

confidence: 91%

Multifractal network generator

Palla

Lovász

Vicsek

2010

Proc. Natl. Acad. Sci. U.S.A.

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We introduce a new approach to constructing networks with realistic features. Our method, in spite of its conceptual simplicity (it has only two parameters) is capable of generating a wide variety of network types with prescribed statistical properties, e.g., with degree or clustering coefficient distributions of various, very different forms. In turn, these graphs can be used to test hypotheses or as models of actual data. The method is based on a mapping between suitably chosen singular measures defined on the unit square and sparse infinite networks. Such a mapping has the great potential of allowing for graph theoretical results for a variety of network topologies. The main idea of our approach is to go to the infinite limit of the singular measure and the size of the corresponding graph simultaneously. A very unique feature of this construction is that with the increasing system size the generated graphs become topologically more structured. We present analytic expressions derived from the parameters of the-to be iteratedinitial generating measure for such major characteristics of graphs as their degree, clustering coefficient, and assortativity coefficient distributions. The optimal parameters of the generating measure are determined from a simple simulated annealing process. Thus, the present work provides a tool for researchers from a variety of fields (such as biology, computer science, biology, or complex systems) enabling them to create a versatile model of their network data.complex networks | sparse graphs | singular measures A s our methods of studying the features of our environment are becoming more and more sophisticated, we also learn to appreciate the complexity of the world surrounding us. The corresponding systems (including natural, social, and technological phenomena) are made of many units, each having an important role from the suitable functioning of the whole. An increasingly popular way of grabbing the intricate structure behind such complex systems is a network or graph representation in which the nodes correspond to the units and the edges to the connections between the units of the original system (1-3). It has turned out that networks corresponding to realistic systems can be highly nontrivial, characterized by a low average distance combined with a high average clustering coefficient (4), anomalous degree distributions (5, 6), and an intricate modular structure (7-9). A better understanding of these graphs is expected and, in many cases has been shown, to be efficient in designing and controlling complex systems ranging from power lines to disease networks (10).As increasingly complex graphs are considered, a need for a better representation of the graphs themselves has arisen as well. Sophisticated visualization techniques emerged (11), and a series of parameters have been introduced over the years (1-3). Very recently one of us (L.L.) proved that, in the infinite network size limit, a dense graph's adjacency matrix can be well represented by a continuous function W ðx; yÞ on th...

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“…The proposed system for the automatic inference of graph models works only with undirected networks, and while cortical networks are thought to be directed networks, it has been shown that an undirected approximation is a reasonable relaxation because the majority of connections are reciprocal [22,36]. The cat cortical network dataset [28] in its undirected form contains 52 cortical nodes and 515 edges.…”

Section: Cortical Networkmentioning

confidence: 99%

Automatic inference of hierarchical graph models using genetic programming with an application to cortical networks

Bailey

Ombuki-Berman

Ventresca

2013

Proceedings of the 15th Annual Conference on Genetic and Evolutionary Computation

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The pathways that relay sensory information within the brain form a network of connections, the precise organization of which is unknown. Communities of neurons can be discerned within this tangled structure, with inhomogeneously distributed connections existing between cortical areas. Classification and modelling of these networks has led to advancements in the identification of unhealthy or injured brains, however, the current models used are known to have major deficiencies. Specifically, the community structure of the cortex is not accounted for in existing algorithms, and it is unclear how to properly design a more representative graph model. It has recently been demonstrated that genetic programming may be useful for inferring accurate graph models, although no study to date has investigated the ability to replicate community structure. In this paper we propose the first GP system for the automatic inference of algorithms capable of generating, to a high accuracy, networks with community structure. We utilize a common cat cortex data set to highlight the efficacy of our approach. Our experiments clearly show that the inferred graph model generates a more representative network than those currently used in scientific literature.

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Reconstructing Cortical Networks: Case of Directed Graphs with High Level of Reciprocity

Cited by 17 publications

References 55 publications

Predictability of cortico-cortical connections in the mammalian brain

Predictability of cortico-cortical connections in the mammalian brain

Multifractal network generator

Automatic inference of hierarchical graph models using genetic programming with an application to cortical networks

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