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A tensor-based formulation of hetero-functional graph theory.

ABSTRACT: Recently, hetero-functional graph theory (HFGT) has developed as a means to mathematically model the structure of large-scale complex flexible engineering systems. It does so by fusing concepts from network science and model-based systems engineering (MBSE). For the former, it utilizes multiple graph-based data structures to support a matrix-based quantitative analysis. For the latter, HFGT inherits the heterogeneity of conceptual and ontological constructs found in model-based systems engineering including system form, system function, and system concept. These diverse conceptual constructs indicate multi-dimensional rather than two-dimensional relationships. This paper provides the first tensor-based treatment of hetero-functional graph theory. In particular, it addresses the "system concept" and the hetero-functional adjacency matrix from the perspective of tensors and introduces the hetero-functional incidence tensor as a new data structure. The tensor-based formulation described in this work makes a stronger tie between HFGT and its ontological foundations in MBSE. Finally, the tensor-based formulation facilitates several analytical results that provide an understanding of the relationships between HFGT and multi-layer networks.

SUBMITTER: Farid AM

PROVIDER: S-EPMC9637230 | biostudies-literature | 2022 Nov

REPOSITORIES: biostudies-literature

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A tensor-based formulation of hetero-functional graph theory.

Farid Amro M AM Thompson Dakota J DJ Schoonenberg Wester W

Scientific reports 20221105 1

Recently, hetero-functional graph theory (HFGT) has developed as a means to mathematically model the structure of large-scale complex flexible engineering systems. It does so by fusing concepts from network science and model-based systems engineering (MBSE). For the former, it utilizes multiple graph-based data structures to support a matrix-based quantitative analysis. For the latter, HFGT inherits the heterogeneity of conceptual and ontological constructs found in model-based systems engineeri ...[more]

PMID: 36335143

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Project description:The assessment of task-independent functional connectivity (FC) after a lesion causing hemianopia remains an uncovered topic and represents a crucial point to better understand the neural basis of blindsight (i.e. unconscious visually triggered behavior) and visual awareness. In this light, we evaluated functional connectivity (FC) in 10 hemianopic patients and 10 healthy controls in a resting state paradigm. The main aim of this study is twofold: first of all we focused on the description and assessment of density and intensity of functional connectivity and network topology with and without a lesion affecting the visual pathway, and then we extracted and statistically compared network metrics, focusing on functional segregation, integration and specialization. Moreover, a study of 3-cycle triangles with prominent connectivity was conducted to analyze functional segregation calculated as the area of each triangle created connecting three neighboring nodes. To achieve these purposes we applied a graph theory-based approach, starting from Pearson correlation coefficients extracted from pairs of regions of interest. In these analyses we focused on the FC extracted by the whole brain as well as by four resting state networks: The Visual (VN), Salience (SN), Attention (AN) and Default Mode Network (DMN), to assess brain functional reorganization following the injury. The results showed a general decrease in density and intensity of functional connections, that leads to a less compact structure characterized by decrease in functional integration, segregation and in the number of interconnected hubs in both the Visual Network and the whole brain, despite an increase in long-range inter-modules connections (occipito-frontal connections). Indeed, the VN was the most affected network, characterized by a decrease in intra- and inter-network connections and by a less compact topology, with less interconnected nodes. Surprisingly, we observed a higher functional integration in the DMN and in the AN regardless of the lesion extent, that may indicate a functional reorganization of the brain following the injury, trying to compensate for the general reduced connectivity. Finally we observed an increase in functional specialization (lower between-network connectivity) and in inter-networks functional segregation, which is reflected in a less compact network topology, highly organized in functional clusters. These descriptive findings provide new insight on the spontaneous brain activity in hemianopic patients by showing an alteration in the intrinsic architecture of a large-scale brain system that goes beyond the impairment of a single RSN.

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A tensor-based formulation of hetero-functional graph theory.

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A tensor-based formulation of hetero-functional graph theory.

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