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Phase transitions widely occur in natural systems. Incorporation of higher-order interactions in coupled dynamics is known to cause first-order phase transition to synchronization in an otherwise smooth second-order in the presence of only pairwise interactions. Here, we discover that adaptation in higher-order interactions restores the second-order phase transition in the former setup and notably produces additional bifurcation referred as tiered synchronization as a consequence of combination of super-critical pitchfork and two saddle node bifurcations. The Ott–Antonsen manifold underlines the interplay of higher-order interactions and adaptation in instigating tiered synchronization, as well as provides complete description of all (un)stable states. These results would be important in comprehending dynamics of real-world systems with inherent higher-order interactions and adaptation through feedback coupling. [ABSTRACT FROM AUTHOR]

Abstract: We study the mechanism of formation of synchronized clusters in coupled maps on networks with various connection architectures. The nodes in a cluster are self-synchronized or driven-synchronized, based on the coupling strength and underlying network structures. A smaller coupling strength region shows driven clusters independent of the network rewiring strategies, whereas a larger coupling strength region shows the transition from the self-organized cluster to the driven cluster as network connections are rewired to the bi-partite type. Lyapunov function analysis is performed to understand the dynamical origin of cluster formation. The results provide insights into the relationship between the topological clusters which are based on the direct connections between the nodes, and the dynamical clusters which are based on the functional behavior of these nodes. [Copyright &y& Elsevier]

We investigate the spectra of adjacency matrices of multiplex networks under random matrix theory (RMT) framework. Through extensive numerical experiments, we demonstrate that upon multiplexing two random networks, the spectra of the combined multiplex network exhibit superposition of two Gaussian orthogonal ensemble (GOE)s for very small multiplexing strength followed by a smooth transition to the GOE statistics with an increase in the multiplexing strength. Interestingly, randomness in the connection architecture, introduced by random rewiring to 1D lattice, of at least one layer may govern nearest neighbor spacing distribution (NNSD) of the entire multiplex network, and in fact, can drive to a transition from the Poisson to the GOE statistics or vice versa. Notably, this transition transpires for a very small number of the random rewiring corresponding to the small-world transition. Ergo, only one layer being represented by the small-world network is enough to yield GOE statistics for the entire multiplex network. Spectra of adjacency matrices of underlying interaction networks have been contemplated to be related with dynamical behavior of the corresponding complex systems, the investigations presented here have implications in achieving better structural and dynamical control to the systems represented by multiplex networks against structural perturbation in only one of the layers. • Impact of structural randomness on the spectra of an entire multiplex network. • The interplay of spectra, interlayer coupling, and structural randomness in multiplex networks. • Poisson-GOE transition is observed in the course of SW transition in one of the layers. • Results are consistent with different kind of randomness and 3-layer multiplex networks. [ABSTRACT FROM AUTHOR]

Genomic variations have been acclaimed as among the key players in understanding the biological mechanisms behind migration, evolution, and adaptation to extreme conditions. Due to stochastic evolutionary forces, the frequency of polymorphisms is affected by changes in the frequency of nearby polymorphisms in the same DNA sample, making them connected in terms of evolution. This article presents all the ingredients to understand the cumulative effects and complex behaviors of genetic variations in the human mitochondrial genome by analyzing co-occurrence networks of nucleotides, and shows key results obtained from such analyses. The article emphasizes recent investigations of these co-occurrence networks, describing the role of interactions between nucleotides in fundamental processes of human migration and viral evolution. The corresponding co-mutation-based genetic networks revealed genetic signatures of human adaptation in extreme environments. This article provides the methods of constructing such networks in detail, along with their graph-theoretical properties, and applications of the genomic networks in understanding the role of nucleotide co-evolution in evolution of the whole genome. [ABSTRACT FROM AUTHOR]

The Ethereum blockchain and its ERC20 token standard have revolutionized the landscape of digital assets and decentralized applications. ERC20 tokens are programmable and interoperable tokens, enabling various applications and token economies. Transaction graphs, representing the flow of the value between wallets within the Ethereum network, have played a crucial role in understanding the system's dynamics, such as token transfers and the behavior of traders. Here, we explore the evolution of daily transaction graphs of ERC20 token transactions, which sheds light on the trader's behavior during the Black Swan Events – 2018 crypto crash and the COVID-19 pandemic. By using the tools from network science and differential geometry, we analyze 0.98 billion of ERC20 token transaction data from November 2015 to January 2023. Our analysis reveals an increase in diverse interaction among the traders and a greater adoption of ERC20 tokens in a maturing Ethereum ERC20 financial ecosystem after the Crypto Crash 2018 and the COVID-19 pandemic. Before the crash and the COVID-19 pandemic, most traders interacted with other traders in an isolated or restricted manner, with each trader focusing solely on either buying or selling activities. However, after the crash and during the pandemic, most traders diversely interacted among themselves by participating in both buying and selling activities. In addition, we observe no significant negative impact of the COVID-19 pandemic on user behavior in the financial ecosystem. • Explore the evolution of daily transaction graphs of ERC20 token transactions • Shed light on the trader's behavior during the Black Swan Events • Analyze 0.98 billion of ERC20 token transaction data • Before the black swan events, each trader focused solely on either buying or selling activities • After the crash and during the pandemic, most traders diversely participating in both buying and selling activities • No significant negative impact of the COVID-19 pandemic on user behavior in the financial ecosystem. [ABSTRACT FROM AUTHOR]

In stock markets, nonlinear interdependencies between various companies result in nontrivial time-varying patterns in stock prices. A network representation of these interdependencies has been successful in identifying and understanding hidden signals before major events like stock market crashes. However, these studies have revolved around the assumption that correlations are mediated in a pairwise manner, whereas, in a system as intricate as this, the interactions need not be limited to pairwise only. Here, we introduce a general methodology using information-theoretic tools to construct a higher-order representation of the stock market data, which we call functional hypergraphs. This framework enables us to examine stock market events by analyzing the following functional hypergraph quantities: Forman–Ricci curvature, von Neumann entropy, and eigenvector centrality. We compare the corresponding quantities of networks and hypergraphs to analyze the evolution of both structures and observe features like robustness towards events like crashes during the course of a time period. [ABSTRACT FROM AUTHOR]

Physiological and haplogroup studies performed to understand high-altitude adaptation in humans are limited to individual genes and polymorphic sites. Due to stochastic evolutionary forces, the frequency of a polymorphism is affected by changes in the frequency of a near-by polymorphism on the same DNA sample making them connected in terms of evolution. Here, first, we provide a method to model these mitochondrial polymorphisms as "co-mutation networks" for three high-altitude populations, Tibetan, Ethiopian and Andean. Then, by transforming these co-mutation networks into weighted and undirected gene–gene interaction (GGI) networks, we were able to identify functionally enriched genetic interactions of CYB and CO3 genes in Tibetan and Andean populations, while NADH dehydrogenase genes in the Ethiopian population playing a significant role in high altitude adaptation. These co-mutation based genetic networks provide insights into the role of different set of genes in high-altitude adaptation in human sub-populations. [ABSTRACT FROM AUTHOR]

Networks have been established as an extremely powerful framework to understand and predict the behavior of many large-scale complex systems. We studied network motifs, the basic structural elements of networks, to describe the possible role of co-occurrence of genomic variations behind high altitude adaptation in the Asian human population. Mitochondrial DNA (mtDNA) variations have been acclaimed as one of the key players in understanding the biological mechanisms behind adaptation to extreme conditions. To explore the cumulative effects of variations in the mitochondrial genome with the variation in the altitude, we investigated human mt-DNA sequences from the NCBI database at different altitudes under the co-occurrence motifs framework. Analysis of the co-occurrence motifs using similarity clustering revealed a clear distinction between lower and higher altitude regions. In addition, the previously known high altitude markers 3394 and 7697 (which are definitive sites of haplogroup M9a1a1c1b) were found to co-occur within their own gene complexes indicating the impact of intra-genic constraint on co-evolution of nucleotides. Furthermore, an ancestral 'RSRS50' variant 10,398 was found to co-occur only at higher altitudes supporting the fact that a separate route of colonization at these altitudes might have taken place. Overall, our analysis revealed the presence of co-occurrence interactions specific to high altitude at a whole mitochondrial genome level. This study, combined with the classical haplogroups analysis is useful in understanding the role of co-occurrence of mitochondrial variations in high altitude adaptation. [ABSTRACT FROM AUTHOR]

Complex networks or graphs provide a powerful framework to understand importance of individuals and their interactions in real-world complex systems. Several graph theoretical measures have been introduced to access importance of the individual in systems represented by networks. Particularly, eigenvector centrality (EC) measure has been very popular due to its ability in measuring importance of the nodes based on not only number of interactions they acquire but also particular structural positions they have in the networks. Furthermore, the presence of certain structural features, such as the existence of high degree nodes in a network is recognized to induce localization transition of the principal eigenvector (PEV) of the network's adjacency matrix. Localization of PEV has been shown to cause difficulties in assigning centrality weights to the nodes based on the EC. We revisit PEV localization and its relation with failure of EC problem, and by using simple model networks demonstrate that in addition to the localization of the PEV, the delocalization of PEV may also create difficulties for using EC as a measure to rank the nodes. Our investigation while providing fundamental insight to the relation between PEV localization and centrality of nodes in networks, suggests that for the networks having delocalized PEVs, it is better to use degree centrality measure to rank the nodes. [ABSTRACT FROM AUTHOR]

More than 300 000 new cases worldwide are being diagnosed with oral cancer annually. Complexity of oral cancer renders designing drug targets very difficult. We analyse protein-protein interaction network for the normal and oral cancer tissue and detect crucial changes in the structural properties of the networks in terms of the interactions of the hub proteins and the degree-degree correlations. Further analysis of the spectra of both the networks, while exhibiting universal statistical behaviour, manifest distinction in terms of the zero degeneracy, providing insight to the complexity of the underlying system. [ABSTRACT FROM AUTHOR]

Abstract: We analyze protein–protein interaction networks for six different species under the framework of random matrix theory. Nearest neighbor spacing distribution of the eigenvalues of adjacency matrices of the largest connected part of these networks emulate universal Gaussian orthogonal statistics of random matrix theory. We demonstrate that spectral rigidity, which quantifies long range correlations in eigenvalues, for all protein–protein interaction networks follow random matrix prediction up to certain ranges indicating randomness in interactions. After this range, deviation from the universality evinces underlying structural features in network. [Copyright &y& Elsevier]

Tipping phenomena in complex systems represent abrupt transitions in the system behavior due to incremental changes in parameters. Here, we report the emergence of an abrupt transition from an oscillatory to a death state in coupled limit cycle oscillators with higher-order repulsive interactions. This transition contrasts with the typical continuous transitions observed with pairwise repulsive links. It is notable that higher-order interactions introduce more complexity to the system dynamics, thereby leading to the transition to the death state at lower coupling strengths compared to pairwise coupled systems. Importantly, there exists a sudden revival of the oscillation from the death state with increasing the pairwise coupling strength despite the detrimental effect of pairwise couplings. The results are also robust for nonidentical systems. Furthermore, the analytical determination of the critical coupling strength for the tipping point aligns closely with the results obtained from numerical simulations.