Network-centric Indicators for fragility in global financial indices

Over the last 2 decades, financial systems have been studied and analyzed from the perspective of complex networks, where the nodes and edges in the network represent the various financial components and the strengths of correlations between them. Here, we adopt a similar network-based approach to analyze the daily closing prices of 69 global financial market indices across 65 countries over a period of 2000 2014. We study the correlations among the indices by constructing threshold networks superimposed over minimum spanning trees at different time frames. We investigate the effect of critical events in financial markets (crashes and bubbles) on the interaction among the indices by performing both static and dynamic analyses of the correlations. We compare and contrast the structures of these networks during periods of crashes and bubbles, with respect to the normal periods in the market. In addition, we study the temporal evolution of traditional market indicators, various global network measures, and the recently developed edge-based curvature measures. We show that network-centric measures can be extremely useful in monitoring the fragility in the global financial market indices

Discrete Ricci curvatures capture age-related changes in human brain functional connectivity networks

IntroductionGeometry-inspired notions of discrete Ricci curvature have been successfully used as markers of disrupted brain connectivity in neuropsychiatric disorders, but their ability to characterize age-related changes in functional connectivity is unexplored.MethodsWe apply Forman-Ricci curvature and Ollivier-Ricci curvature to compare functional connectivity networks of healthy young and older subjects from the Max Planck Institute Leipzig Study for Mind-Body-Emotion Interactions (MPI-LEMON) dataset (N = 225).ResultsWe found that both Forman-Ricci curvature and Ollivier-Ricci curvature can capture whole-brain and region-level age-related differences in functional connectivity. Meta-analysis decoding demonstrated that those brain regions with age-related curvature differences were associated with cognitive domains known to manifest age-related changes—movement, affective processing, and somatosensory processing. Moreover, the curvature values of some brain regions showing age-related differences exhibited correlations with behavioral scores of affective processing. Finally, we found an overlap between brain regions showing age-related curvature differences and those brain regions whose non-invasive stimulation resulted in improved movement performance in older adults.DiscussionOur results suggest that both Forman-Ricci curvature and Ollivier-Ricci curvature correctly identify brain regions that are known to be functionally or clinically relevant. Our results add to a growing body of evidence demonstrating the sensitivity of discrete Ricci curvature measures to changes in the organization of functional connectivity networks, both in health and disease

Graph Ricci curvatures reveal atypical functional connectivity in autism spectrum disorder

Publisher Copyright: © 2022, The Author(s).While standard graph-theoretic measures have been widely used to characterize atypical resting-state functional connectivity in autism spectrum disorder (ASD), geometry-inspired network measures have not been applied. In this study, we apply Forman–Ricci and Ollivier–Ricci curvatures to compare networks of ASD and typically developing individuals (N = 1112) from the Autism Brain Imaging Data Exchange I (ABIDE-I) dataset. We find brain-wide and region-specific ASD-related differences for both Forman–Ricci and Ollivier–Ricci curvatures, with region-specific differences concentrated in Default Mode, Somatomotor and Ventral Attention networks for Forman–Ricci curvature. We use meta-analysis decoding to demonstrate that brain regions with curvature differences are associated to those cognitive domains known to be impaired in ASD. Further, we show that brain regions with curvature differences overlap with those brain regions whose non-invasive stimulation improves ASD-related symptoms. These results suggest the utility of graph Ricci curvatures in characterizing atypical connectivity of clinically relevant regions in ASD and other neurodevelopmental disorders.Peer reviewe

A Poset-Based Approach to Curvature of Hypergraphs

In this contribution, we represent hypergraphs as partially ordered sets or posets, and provide a geometric framework based on posets to compute the Forman–Ricci curvature of vertices as well as hyperedges in hypergraphs. Specifically, we first provide a canonical method to construct a two-dimensional simplicial complex associated with a hypergraph, such that the vertices of the simplicial complex represent the vertices and hyperedges of the original hypergraph. We then define the Forman–Ricci curvature of the vertices and the hyperedges as the scalar curvature of the associated vertices in the simplicial complex. Remarkably, Forman–Ricci curvature has a simple combinatorial expression and it can effectively capture the variation in symmetry or asymmetry over a hypergraph. Finally, we perform an empirical study involving computation and analysis of the Forman–Ricci curvature of hyperedges in several real-world hypergraphs. We find that Forman–Ricci curvature shows a moderate to high absolute correlation with standard hypergraph measures such as eigenvector centrality and cardinality. Our results suggest that the notion of Forman–Ricci curvature extended to hypergraphs in this work can be used to gain novel insights on the organization of higher-order interactions in real-world hypernetworks

A Poset-Based Approach to Curvature of Hypergraphs

In this contribution, we represent hypergraphs as partially ordered sets or posets, and provide a geometric framework based on posets to compute the Forman–Ricci curvature of vertices as well as hyperedges in hypergraphs. Specifically, we first provide a canonical method to construct a two-dimensional simplicial complex associated with a hypergraph, such that the vertices of the simplicial complex represent the vertices and hyperedges of the original hypergraph. We then define the Forman–Ricci curvature of the vertices and the hyperedges as the scalar curvature of the associated vertices in the simplicial complex. Remarkably, Forman–Ricci curvature has a simple combinatorial expression and it can effectively capture the variation in symmetry or asymmetry over a hypergraph. Finally, we perform an empirical study involving computation and analysis of the Forman–Ricci curvature of hyperedges in several real-world hypergraphs. We find that Forman–Ricci curvature shows a moderate to high absolute correlation with standard hypergraph measures such as eigenvector centrality and cardinality. Our results suggest that the notion of Forman–Ricci curvature extended to hypergraphs in this work can be used to gain novel insights on the organization of higher-order interactions in real-world hypernetworks.</jats:p

Network-centric Indicators for Fragility in Global Financial Indices

Over the last 2 decades, financial systems have been studied and analyzed from the perspective of complex networks, where the nodes and edges in the network represent the various financial components and the strengths of correlations between them. Here, we adopt a similar network-based approach to analyze the daily closing prices of 69 global financial market indices across 65 countries over a period of 2000–2014. We study the correlations among the indices by constructing threshold networks superimposed over minimum spanning trees at different time frames. We investigate the effect of critical events in financial markets (crashes and bubbles) on the interactions among the indices by performing both static and dynamic analyses of the correlations. We compare and contrast the structures of these networks during periods of crashes and bubbles, with respect to the normal periods in the market. In addition, we study the temporal evolution of traditional market indicators, various global network measures, and the recently developed edge-based curvature measures. We show that network-centric measures can be extremely useful in monitoring the fragility in the global financial market indices.</jats:p

Relative importance of composition structures and biologically meaningful logics in bipartite Boolean models of gene regulation

International audienceAbstract Boolean networks have been widely used to model gene networks. However, such models are coarse-grained to an extent that they abstract away molecular specificities of gene regulation. Alternatively, bipartite Boolean network models of gene regulation explicitly distinguish genes from transcription factors (TFs). In such bipartite models, multiple TFs may simultaneously contribute to gene regulation by forming heteromeric complexes, thus giving rise to composition structures . Since bipartite Boolean models are relatively recent, an empirical investigation of their biological plausibility is lacking. Here, we estimate the prevalence of composition structures arising through heteromeric complexes. Moreover, we present an additional mechanism where composition structures may arise as a result of multiple TFs binding to cis -regulatory regions and provide empirical support for this mechanism. Next, we compare the restriction in BFs imposed by composition structures and by biologically meaningful properties. We find that though composition structures can severely restrict the number of Boolean functions (BFs) driving a gene, the two types of minimally complex BFs, namely nested canalyzing functions (NCFs) and read-once functions (RoFs), are comparatively more restrictive. Finally, we find that composition structures are highly enriched in real networks, but this enrichment most likely comes from NCFs and RoFs

Composition structures and biologically meaningful logics: plausibility and relevance in bipartite models of gene regulation

Boolean network models have widely been used to study the dynamics of gene regulatory networks. However, such models are coarse-grained to an extent that they abstract away molecular specificities of gene regulation. In contrast, bipartite Boolean network models of gene regulation explicitly distinguish genes from transcription factors (TFs). In such models, multiple TFs may simultaneously contribute to the regulation of a gene by forming heteromeric complexes. The formation of heteromeric complexes gives rise to composition structures in the corresponding bipartite network. Remarkably, composition structures can severely restrict the number of Boolean functions (BFs) that can be assigned to a gene. The introduction of bipartite Boolean network models is relatively recent, and so far an empirical investigation of their biological plausibility is lacking. Here, we estimate the prevalence of composition structures arising through heteromeric complexes in Homo sapiens. Moreover, we present an additional mechanism by which composition structures arise as a result of multiple TFs binding to the cis-regulatory regions of a gene and we provide empirical support for this mechanism. Next, we compare the restriction in BFs imposed by composition structures and by biologically meaningful properties. We find that two types of minimally complex BFs, namely nested canalyzing functions (NCFs) and read-once functions (RoFs), are more restrictive than composition structures. Finally, using a compiled dataset of 2687 BFs from published models, we find that composition structures are highly enriched in real biological networks, but that this enrichment is most likely driven by NCFs and RoFs.</jats:p

Discrete Ricci curvatures capture age-related changes in human brain functional connectivity networks

Funding Information: AS would like to acknowledge research support from the Max Planck Society, Germany via a Max Planck Partner Group in Mathematical Biology and the Department of Atomic Energy (DAE), Government of India. JJ acknowledges support from the German-Israeli Foundation (GIF) grant number I-1514-304.6/2019. Publisher Copyright: Copyright © 2023 Yadav, Elumalai, Williams, Jost and Samal.Introduction: Geometry-inspired notions of discrete Ricci curvature have been successfully used as markers of disrupted brain connectivity in neuropsychiatric disorders, but their ability to characterize age-related changes in functional connectivity is unexplored. Methods: We apply Forman-Ricci curvature and Ollivier-Ricci curvature to compare functional connectivity networks of healthy young and older subjects from the Max Planck Institute Leipzig Study for Mind-Body-Emotion Interactions (MPI-LEMON) dataset (N = 225). Results: We found that both Forman-Ricci curvature and Ollivier-Ricci curvature can capture whole-brain and region-level age-related differences in functional connectivity. Meta-analysis decoding demonstrated that those brain regions with age-related curvature differences were associated with cognitive domains known to manifest age-related changes—movement, affective processing, and somatosensory processing. Moreover, the curvature values of some brain regions showing age-related differences exhibited correlations with behavioral scores of affective processing. Finally, we found an overlap between brain regions showing age-related curvature differences and those brain regions whose non-invasive stimulation resulted in improved movement performance in older adults. Discussion: Our results suggest that both Forman-Ricci curvature and Ollivier-Ricci curvature correctly identify brain regions that are known to be functionally or clinically relevant. Our results add to a growing body of evidence demonstrating the sensitivity of discrete Ricci curvature measures to changes in the organization of functional connectivity networks, both in health and disease.Peer reviewe