Rotating clusters in phase-lagged Kuramoto oscillators with higher-order interactions.

The effect of phase-lag in pairwise interactions has been a topic of great interest for a while. However, real-world systems often have interactions that are beyond pairwise and can be modeled using simplicial complexes. We show that the inclusion of higher-order interactions in phase-lagged coupled Kuramoto oscillators shifts the critical point at which first-order transition from a cluster synchronized state to an incoherent state takes place. Considering the polar coordinates, we obtain the rotation frequency of the clusters, which turns out to be a function of the phase-lag parameter. In turn, the phase- lag can be used as a control parameter to achieve a desired cluster frequency. Moreover, in the thermodynamic limit, by employing the Ott-Antonsen approach we derive a reduced equation for the order parameter measuring cluster synchronization and progress further through the self-consistency method to obtain a closed form of the order parameter measuring global synchronization which was lacking in the Ott-Antonsen approach.

Prolonged hysteresis in the Kuramoto model with inertia and higher-order interactions.

The inclusion of inertia in the Kuramoto model has long been reported to change the nature of a phase transition, providing a fertile ground to model the dynamical behaviors of interacting units. More recently, higher-order interactions have been realized as essential for the functioning of real-world complex systems ranging from the brain to disease spreading. Yet analytical insights to decipher the role of inertia with higher-order interactions remain challenging. Here, we study the Kuramoto model with inertia on simplicial complexes, merging two research domains. We develop an analytical framework in a mean-field setting using self-consistent equations to describe the steady-state behavior, which reveals a prolonged hysteresis in the synchronization profile. Inertia and triadic interaction strength exhibit isolated influence on system dynamics by predominantly governing, respectively, the forward and backward transition points. This paper sets a paradigm to deepen our understanding of real-world complex systems such as power grids modeled as the Kuramoto model with inertia.

First-order transition to oscillation death in coupled oscillators with higher-order interactions.

We investigate the dynamical evolution of Stuart-Landau oscillators globally coupled through conjugate or dissimilar variables on simplicial complexes. We report a first-order explosive phase transition from an oscillatory state to oscillation death, with higher-order (2-simplex triadic) interactions, as opposed to the second-order transition with only pairwise (1-simplex) interactions. Moreover, the system displays four distinct homogeneous steady states in the presence of triadic interactions, in contrast to the two homogeneous steady states observed with dyadic interactions. We calculate the backward transition point analytically, confirming the numerical results and providing the origin of the dynamical states in the transition region. The results are robust against the application of noise. The study will be useful in understanding complex systems, such as ecological and epidemiological, having higher-order interactions and coupling through conjugate variables.

Synchronization onset for contrarians with higher-order interactions in multilayer systems.

We investigate the impact of contrarians (via negative coupling) in multilayer networks of phase oscillators having higher-order interactions. We report that the multilayer framework facilitates synchronization onset in the negative pairwise coupling regime. The multilayering strength governs the onset of synchronization and the nature of the phase transition, whereas the higher-order interactions dictate the backward critical coupling. Specifically, the system does not synchronize below a critical value of the multilayering strength. The analytical calculations using the mean-field Ott-Antonsen approach agree with the simulations. The results presented here may be useful for understanding emergent behaviors in real-world complex systems with contrarians and higher-order interactions, such as the brain and social system.

Tiered synchronization in Kuramoto oscillators with adaptive higher-order interactions.

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.

Eigenvector localization in hypergraphs: Pairwise versus higher-order links.

Localization behaviors of Laplacian eigenvectors of complex networks furnish an explanation to various dynamical phenomena of the corresponding complex systems. We numerically examine roles of higher-order and pairwise links in driving eigenvector localization of hypergraphs Laplacians. We find that pairwise interactions can engender localization of eigenvectors corresponding to small eigenvalues for some cases, whereas higher-order interactions, even being much much less than the pairwise links, keep steering localization of the eigenvectors corresponding to larger eigenvalues for all the cases considered here. These results will be advantageous to comprehend dynamical phenomena, such as diffusion, and random walks on a range of real-world complex systems having higher-order interactions in better manner.

Solitary death in coupled limit cycle oscillators with higher-order interactions.

Coupled limit cycle oscillators with pairwise interactions are known to depict phase transitions from an oscillatory state to amplitude or oscillation death. This Research Letter introduces a scheme to incorporate higher-order interactions which cannot be decomposed into pairwise interactions and investigates the dynamical evolution of Stuart-Landau oscillators under the impression of such a coupling. We discover an oscillator death state through a first-order (explosive) phase transition in which a single, coupling-dependent stable death state away from the origin exists in isolation without being accompanied by any other stable state usually existing for pairwise couplings. We call such a state a solitary death state. Contrary to widespread subcritical Hopf bifurcation, here we report homoclinic bifurcation as an origin of the explosive death state. Moreover, this explosive transition to the death state is preceded by a surge in amplitude and followed by a revival of the oscillations. The analytical value of the critical coupling strength for the solitary death state agrees with the simulation results. Finally, we point out the resemblance of the results with different dynamical states associated with epileptic seizures.

Multiple first-order transitions in simplicial complexes on multilayer systems.

The presence of higher-order interactions (simplicial complexes) on globally coupled systems yield abrupt first-order transitions to synchronization. We discover that simplicial complexes on multilayer systems can yield multiple basins of attraction, leading to multiple abrupt first-order transitions to (de)synchronization for associated coupled dynamics. Using the Ott-Antonsen approach, we develop an analytical framework for simplicial complexes on multilayer systems, reducing the high-dimensional evolution equation to a low-dimensional manifold, which thoroughly explains the origin and stability of all possible dynamical states, including multiple synchronization transitions. The study illustrating rich dynamical behaviors could be pivotal in comprehending the impacts of higher-order interactions on dynamics of complex real-world networks, such as brain, social, and technological, which have inherent multilayer architectures.

Nucleotide-based genetic networks: Methods and applications.

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.

First-order route to antiphase clustering in adaptive simplicial complexes.

This Letter investigates the transition to synchronization of oscillator ensembles encoded by simplicial complexes in which pairwise and higher-order coupling weights alter with time through a rate-based adaptive mechanism inspired by the Hebbian learning rule. These simultaneously evolving disparate adaptive coupling weights lead to a phenomenon in that the in-phase synchronization is completely obliterated; instead, the antiphase synchronization is originated. In addition, the onsets of antiphase synchronization and desynchronization are manageable through both dyadic and triadic learning rates. The theoretical validation of these numerical assessments is delineated thoroughly by employing Ott-Antonsen dimensionality reduction. The framework and results of the Letter would help understand the underlying synchronization behavior of a range of real-world systems, such as the brain functions and social systems where interactions evolve with time.

Eigenvalue ratio statistics of complex networks: Disorder versus randomness.

The distribution of the ratios of consecutive eigenvalue spacings of random matrices has emerged as an important tool to study spectral properties of many-body systems. This article numerically investigates the eigenvalue ratios distribution of various model networks, namely, small-world, Erdos-Rényi random, and (dis)assortative random having a diagonal disorder in the corresponding adjacency matrices. Without any diagonal disorder, the eigenvalues ratio distribution of these model networks depict Gaussian orthogonal ensemble (GOE) statistics. Upon adding diagonal disorder, there exists a gradual transition from the GOE to Poisson statistics depending upon the strength of the disorder. The critical disorder (w_{c}) required to procure the Poisson statistics increases with the randomness in the network architecture. We relate w_{c} with the time taken by maximum entropy random walker to reach the steady state. These analyses will be helpful to understand the role of eigenvalues other than the principal one for various network dynamics such as transient behavior.

Role of mitochondrial genetic interactions in determining adaptation to high altitude human population.

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.

Synchronization in multiplex models of neuron-glial systems: Small-world topology and inhibitory coupling.

In this work, we investigate the impact of mixed coupling on synchronization in a multiplex oscillatory network. The network mimics the neural-glial systems by incorporating interacting slow ("glial") and fast ("neural") oscillatory layers. Connections between the "glial" elements form a regular periodic structure, in which each element is connected to the eight other neighbor elements, whereas connections among "neural" elements are represented by Watts-Strogatz networks (from regular and small-world to random Erdös-Rényi graph) with a matching mean node degree. We find that the random rewiring toward small-world topology readily yields the dynamics close to that exhibited for a completely random graph, in particular, leading to coarse-graining of dynamics, suppressing multi-stability of synchronization regimes, and the onset of Kuramoto-type synchrony in both layers. The duration of transient dynamics in the system measured by relaxation times is minimized with the increase of random connections in the neural layer, remaining substantial only close to synchronization-desynchronization transitions. "Inhibitory" interactions in the "neural" subnetwork layer undermine synchronization; however, the strong coupling with the "glial" layer overcomes this effect.

Explosive synchronization and chimera in interpinned multilayer networks.

This Letter investigates the nature of synchronization in multilayered and multiplexed populations in which the interlayer interactions are randomly pinned. First, we show that a multilayer network constructed by setting up all-to-all interlayer connections between the two populations leads to explosive synchronization in the two populations successively, leading to the coexistence of coherent and incoherent populations forming chimera states. Second, a multiplex formation of the two populations in which only the mirror nodes are interconnected espouses explosive transitions in the two populations concurrently. The occurrence of both explosive synchronization and chimera are substantiated with rigorous theoretical mean-field analysis. The random pinning in the interlayer interactions concerns the practical problems where the impact of dynamics of one network on that of other interconnected networks remains elusive, as is the case for many real-world systems.

Explosive synchronization in interlayer phase-shifted Kuramoto oscillators on multiplex networks.

Different methods have been proposed in the past few years to incite explosive synchronization (ES) in Kuramoto phase oscillators. In this work, we show that the introduction of a phase shift α in interlayer coupling terms of a two-layer multiplex network of Kuramoto oscillators can also instigate ES in the layers. As α→π/2, ES emerges along with hysteresis. The width of hysteresis depends on the phase shift α, interlayer coupling strength, and natural frequency mismatch between mirror nodes. A mean-field analysis is performed to justify the numerical results. Similar to earlier works, the suppression of synchronization is accountable for the occurrence of ES. The robustness of ES against changes in network topology and natural frequency distribution is tested. Finally, taking a suggestion from the synchronized state of the multiplex networks, we extend the results to classical single networks where some specific links are assigned phase-shifted interactions.

Machine learning assisted network classification from symbolic time-series.

Machine learning techniques have been witnessing perpetual success in predicting and understanding behaviors of a diverse range of complex systems. By employing a deep learning method on limited time-series information of a handful of nodes from large-size complex systems, we label the underlying network structures assigned in different classes. We consider two popular models, namely, coupled Kuramoto oscillators and susceptible-infectious-susceptible to demonstrate our results. Importantly, we elucidate that even binary information of the time evolution behavior of a few coupled units (nodes) yields as accurate classification of the underlying network structure as achieved by the actual time-series data. The key of the entire process reckons on feeding the time-series information of the nodes when the system evolves in a partially synchronized state, i.e., neither completely incoherent nor completely synchronized. The two biggest advantages of our method over previous existing methods are its simplicity and the requirement of the time evolution of one largest degree node or a handful of the nodes to predict the classification of large-size networks with remarkable accuracy.

Impact of modular mitochondrial epistatic interactions on the evolution of human subpopulations.

Investigation of human mitochondrial (mt) genome variation has been shown to provide insights to the human history and natural selection. By analyzing 24,167 human mt-genome samples, collected for five continents, we have developed a co-mutation network model to investigate characteristic human evolutionary patterns. The analysis highlighted richer co-mutating regions of the mt-genome, suggesting the presence of epistasis. Specifically, a large portion of COX genes was found to co-mutate in Asian and American populations, whereas, in African, European, and Oceanic populations, there was greater co-mutation bias in hypervariable regions. Interestingly, this study demonstrated hierarchical modularity as a crucial agent for these co-mutation networks. More profoundly, our ancestry-based co-mutation module analyses showed that mutations cluster preferentially in known mitochondrial haplogroups. Contemporary human mt-genome nucleotides most closely resembled the ancestral state, and very few of them were found to be ancestral-variants. Overall, these results demonstrated that subpopulation-based biases may favor mitochondrial gene specific epistasis.

Analysis of human mitochondrial genome co-occurrence networks of Asian population at varying altitudes.

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.

Catalytic feed-forward explosive synchronization in multilayer networks.

Inhibitory couplings are crucial for the normal functioning of many real-world complex systems. Inhibition in one layer has been shown to induce explosive synchronization in another excitatory (or positive) layer of duplex networks. By extending this framework to multiplex networks, this article shows that inhibition in a single layer can act as a catalyst, leading to explosive synchronization transitions in the rest of the layers feed-forwarded through intermediate layer(s). Considering a multiplex network of coupled Kuramoto oscillators, we demonstrate that the characteristics of the transition emergent in a layer can be entirely controlled by the intra-layer coupling of other layers and the multiplexing strengths. The results presented here are essential to fathom the synchronization behavior of coupled dynamical units in multi-layer systems possessing inhibitory coupling in one of its layers, representing the importance of multiplexing.

Investigating Mitonuclear Genetic Interactions Through Machine Learning: A Case Study on Cold Adaptation Genes in Human Populations From Different European Climate Regions.

Cold climates represent one of the major environmental challenges that anatomically modern humans faced during their dispersal out of Africa. The related adaptive traits have been achieved by modulation of thermogenesis and thermoregulation processes where nuclear (nuc) and mitochondrial (mt) genes play a major role. In human populations, mitonuclear genetic interactions are the result of both the peculiar genetic history of each human group and the different environments they have long occupied. This study aims to investigate mitonuclear genetic interactions by considering all the mitochondrial genes and 28 nuclear genes involved in brown adipose tissue metabolism, which have been previously hypothesized to be crucial for cold adaptation. For this purpose, we focused on three human populations (i.e., Finnish, British, and Central Italian people) of European ancestry from different biogeographical and climatic areas, and we used a machine learning approach to identify relevant nucDNA-mtDNA interactions that characterized each population. The obtained results are twofold: (i) at the methodological level, we demonstrated that a machine learning approach is able to detect patterns of genetic structure among human groups from different latitudes both at single genes and by considering combinations of mtDNA and nucDNA loci; (ii) at the biological level, the analysis identified population-specific nuclear genes and variants that likely play a relevant biological role in association with a mitochondrial gene (such as the "obesity gene" FTO in Finnish people). Further studies are needed to fully elucidate the evolutionary dynamics (e.g., migration, admixture, and/or local adaptation) that shaped these nucDNA-mtDNA interactions and their functional role.