Sarika Jalan

Indian Institute of Technology Indore | IITI

Finite-size systems of a Kuramoto model display intricate dynamics, especially in the presence of multi-stability where both coherent and incoherent states coexist. We investigate such a scenario in globally coupled populations of Kuramoto phase oscillators with higher-order interactions and observe that fluctuations inherent to finite-size systems...

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 ass...

Reservoir computing is a useful framework for predicting critical transitions of a dynamical system if the bifurcation parameter is also provided as an input. This work shows how the dynamical system theory provides the underlying mechanism behind the prediction. Using numerical methods, by considering dynamical systems which show Hopf bifurcation,...

Coupled oscillators models help us in understanding the origin of synchronization phenomenon prevalent in both natural and artificial systems. Here, we study the coupled Kuramoto oscillator model having phase lag and adaptation in higher-order interactions. We find that the type of transition to synchronization changes from the first-order to secon...

Reservoir computing has been shown to be a useful framework for predicting critical transitions of a dynamical system if the bifurcation parameter is also provided as an input. Its utility is significant because in real-world scenarios, the exact model equations are unknown. This Letter shows how the theory of dynamical system provides the underlyi...

Impact of noise in coupled oscillators with pairwise interactions has been extensively explored. Here, we study stochastic second-order coupled Kuramoto oscillators with higher-order interactions, and show that as noise strength increases the critical points associated with synchronization transitions shift toward higher coupling values. By employi...

Finite-size systems of Kuramoto model display intricate dynamics, especially in the presence of multi-stability where both coherent and incoherent states coexist. We investigate such scenario in globally coupled populations of Kuramoto phase oscillators with higher-order interactions, and observe that fluctuations inherent to finite-size systems dr...

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...

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 disea...

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-Landa...

Mounting experimental evidence suggests a significant role for glial cells, particularly astrocytes, in shaping neuronal activity in both cell cultures and the brain, driving interest in exploring multi-component network dynamics [1]. These systems are modeled at varying levels of physiological detail, ranging from the Hodgkin-Huxley and Ullah mode...

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...

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...

Most real-world networks are endowed with the small-world property, by means of which the maximal distance between any two of their nodes scales logarithmically rather than linearly with their size. The evidence sparkled a wealth of studies trying to reveal possible mechanisms through which the pairwise interactions amongst the units of a network a...

Pair-wise co-mutation networks of the mitochondrial genome have already provided ample evidences about the roles of genetic interactions in the manifestation of phenotype under altered environmental conditions. Here, we present a method to construct and analyze higher-order interactions, namely, 3-uniform hypergraphs of the mitochondrial genome for...

Coupled limit cycle oscillators with pairwise interactions depict phase transitions to amplitude or oscillation death. This Letter introduces a scheme for higher-order interactions, which can not be decomposed into pairwise interactions. We investigate Stuart Landau oscillators' dynamical evolution under the impression of such a coupling scheme and...

The effect of phase-lag parameter in pairwise interactions has been a topic of great interest for long. However, real-world systems often have interactions that are beyond pairwise and can be modeled using simplicial complexes. We investigate the effect of the inclusion of phase-lag in coupled Kuramoto oscillators with simplicial interactions and f...

The Ethereum blockchain and its ERC20 token standard have revolutionized the landscape of digital assets and decentralized applications. ERC20 tokens developed on the Ethereum blockchain have gained significant attention since their introduction. They are programmable and interoperable tokens, enabling various applications and token economies. Tran...

We investigate the dynamical evolution of globally connected Stuart-Landau oscillators coupled through conjugate or dis-similar variables on simplicial complexes. We report a first-order explosive phase transition from oscillatory state to death state, with 2-simplex (triadic) interactions, as opposed to the second-order transition with only 1-simp...

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-orde...

Eigenvalues statistics of various many-body systems have been widely studied using the nearest neighbor spacing distribution under the random matrix theory framework. Here, we numerically analyze eigenvalue ratio statistics of multiplex networks consisting of directed Erd ̋os-R ́enyi random networks layers represented as, first, weighted non-Hermit...

We show how multiplexing influences propagating fronts in multilayer networks of coupled bistable oscillators. Using numerical simulation, we investigate both deterministic and noise-sustained propagation. In particular, we demonstrate that the multiplexing allows to reduce the intra-layer dynamics to a common regime where the front propagation spe...

Most real-world networks are endowed with the small-world property, by means of which the maximal distance between any two of their nodes scales logarithmically rather than linearly with their size. The evidence sparkled a wealth of studies trying to reveal possible mechanisms through which the pairwise interactions amongst the units of a network a...

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 o...

The inclusion of inertia in the Kuramoto model has been long reported to change the nature of 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...

An incorporation of higher-order interactions is known to lead an abrupt first-order transition to synchronization in otherwise smooth second-order one for pair-wise coupled systems. Here, we show that adaptation in higher-order coupling strength may yield completely different phenomena, notably, second-order transition to synchronization and tiere...

Eigenvalues statistics of various many-body systems have been widely studied using the nearest neighbor spacing distribution under the random matrix theory framework. Here, we numerically analyze eigenvalue ratio statistics of multiplex networks consisting of directed Erdos-Renyi random networks layers represented as, first, weighted non-Hermitian...

Studies of pair-wise co-mutation of mitochondrial genome have already provided ample evidences about roles of genetic interactions in manifestation of phenotype under altered environmental conditions. High-altitude is one such condition which causes mitochondrial genome to undergo natural selection. Here, we provide a method to construct and analys...

Quenching of oscillations, namely, amplitude and oscillations death, is an emerging phenomenon exhibited by many real-world complex systems. Here, we introduce a scheme that combines dissimilar couplings and repulsive feedback links for the interactions of Stuart-Landau oscillators and analytically derive the conditions required for the amplitude d...

Quenching of oscillations, namely amplitude and oscillations death, is an emerging phenomenon exhibited by many real-world complex systems. Here, we introduce a scheme that combines dissimilar couplings and repulsive feedback links for the interactions of Stuart Landau oscillators and analytically derives the conditions required for the amplitude d...

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 dy...

Prediction of correlation matrices from given time series data has several applications for a range of problems, such as inferring neuronal connections from spiking data, deducing causal dependencies between genes from expression data, and discovering long spatial range influences in climate variations. Traditional methods of predicting correlation...

Localization behaviours of Laplacian eigenvectors of complex networks provide understanding to various dynamical phenomena on the corresponding complex systems. We numerically investigate role of hyperedges in driving eigenvector localization of hypergraphs Laplacians. By defining a single parameter \gamma which measures the relative strengths of p...

From predicting the epidemic threshold of a disease outbreak to anticipating the stability of a complex system, analysis of spectra of the adjacency matrices of the underlying networks play a pivotal role. Despite spectra of networks considered as fingerprints of the corresponding complex systems, most works and review articles have circumscribed a...

This Letter investigates the transition to synchronization of oscillator ensembles encoded by simplicial complexes in which pairwise and higher-order coupling weights adapt with time through the Hebbian learning mechanism. These concurrently evolving disparate adaptive coupling weights lead to a novel phenomenon in that the in-phase synchronization...

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, Erdős-Rényi random, and (dis)assortative random having a dia...

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, Erd\H{o}s-R\'enyi random, and (dis)assortative random having...

This Letter investigates the upshots of adaptive development of pure 2- and 3- simplicial complexes (triad and tetrad) on the nature of the transition to desynchrony of the oscillator ensembles. The adaptation exercised in the pure simplicial coupling takes a cue from the Hebbian learning rule, i.e., the coupling weight of a triad (tetrad) is prone...

This Letter investigates the upshots of adaptive development of pure 2- and 3- simplicial complexes (triad and tetrad) on the nature of the transition to desynchrony of the oscillator ensembles. The adaptation exercised in the pure simplicial coupling takes a cue from the Hebbian learning rule, i.e., the coupling weight of a triad (tetrad) is prone...

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 evolu...

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...

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 connecte...

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 succes...

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 multiplex...

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 multiplex...

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 nearby polymorphism on the same DNA sample making them connected in terms of evolut...

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 succes...

Chimera and Solitary states have captivated scientists and engineers due to their peculiar dynamical states corresponding to co-existence of coherent and incoherent dynamical evolution in coupled units in various natural and artificial systems. It has been further demonstrated that such states can be engineered in systems of coupled oscillators by...

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 oscilla-tors can also instigate ES in the layers. As α → π/2, ES emerges along wit...

Many real-world complex systems have small-world topology characterized by the high clustering of nodes and short path lengths. It is well-known that higher clustering drives localization while shorter path length supports delocalization of the eigenvectors of networks. Using multifractals technique, we investigate localization properties of the ei...

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...

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...

We show that an introduction of a phase parameter ($\alpha$), with $0 \le \alpha \le \pi/2$, in the interlayer coupling terms of multiplex networks of Kuramoto oscillators can induce explosive synchronization (ES) in the multiplexed layers. Along with the {\alpha} values, the hysteresis width is determined by the interlayer coupling strength and th...

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. Mitoch...

Adaptation plays a pivotal role in the evolution of natural and artificial complex systems, and in the determination of their functionality. Here, we investigate the impact of adaptive interlayer processes on intra-layer synchronization in multiplex networks. The considered adaptation mechanism is governed by a Hebbian learning rule, i.e., the link...

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, mitonucle...

Chimera and Solitary states have captivated scientists and engineers due to their peculiar dynamical states corresponding to co-existence of coherent and incoherent dynamical evolution in coupled units in various natural and artificial systems. It has been further demonstrated that such states can be engineered in systems of coupled oscillators by...

Adaptation plays a pivotal role in the evolution of natural and artificial complex systems, and in the determination of their functionality. Here, we investigate the impact of adaptive inter-layer processes on intra-layer synchronization in multiplex networks. The considered adaptation mechanism is governed by a Hebbian learning rule, i.e., the lin...

Many real-world complex systems have small-world topology characterized by the high clustering of nodes and short path lengths.It is well-known that higher clustering drives localization while shorter path length supports delocalization of the eigenvectors of networks. Using multifractals technique, we investigate localization properties of the eig...

Understanding the localization properties of eigenvectors of complex networks is important to get insight into various structural and dynamical properties of the corresponding systems. Here, we analytically develop a scheme to construct a highly localized network for a given set of parameters that is the number of nodes and interactions. We find th...

The phenomenon of explosive synchronization, which originates from hypersensitivity to small perturbation caused by some form of frustration prevailed in various physical and biological systems, has been shown to lead events of cascading failure of the power grid to chronic pain or epileptic seizure in the brain. Furthermore, networks provide a pow...

It is known that intralayer adaptive coupling among connected oscillators instigates explosive synchronization (ES) in multilayer networks. Taking an altogether different cue in the present work, we consider interlayer adaptive coupling in a two-layer multiplex network of phase oscillators and show that the scheme gives rise to ES with an associate...

Chimera state refers to the coexistence of coherent and non-coherent phases in identically coupled dynamical units found in various complex dynamical systems. Identification of chimera, on one hand, is essential due to its applicability in various areas including neuroscience and, on the other hand, is challenging due to its widely varied appearanc...

The phenomenon of explosive synchronization, which originates from hypersensitivity to small perturbation caused by some form of frustration prevailed in various physical and biological systems, has been shown to lead events of cascading failure of the power grid to chronic pain or epileptic seizure in the brain. Furthermore, networks provide a pow...

Biological aging is a complex process involving multiple biological processes. These can be understood theoretically though considering them as individual networks—e.g., epigenetic networks, cell-cell networks (such as astroglial networks), and population genetics. Mathematical modeling allows the combination of such networks so that they may be st...

Investigation of eigenvector localization properties of complex networks is not only important for gaining insight into fundamental network problems such as network centrality measure, spectral partitioning, development of approximation algorithms, but is also crucial for understanding many real-world phenomena such as disease spreading, criticalit...

Investigation of eigenvector localization properties of complex networks is not only important for gaining insight into fundamental network problems such as network centrality measure, spectral partitioning, development of approximation algorithms, but also is crucial for understanding many real-world phenomena such as disease spreading, criticalit...

Coupled dynamics on the network models have been tremendously helpful in getting insight into complex spatiotemporal dynamical patterns of a wide variety of large-scale real-world complex systems. Chimera, a state of coexistence of incoherence and coherence, is one of such patterns arising in identically coupled oscillators, which has recently draw...

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 popul...

Finding mechanisms behind high altitude adaptation in humans at the Tibetan plateau has been a subject of evolutionary research. Mitochondrial DNA (mt-DNA) variations have been established as one of the key players in understanding the biological mechanisms at the basis of adaptation to these extreme conditions. To explore cumulative effects and dy...

One of the most challenging problems in biomedicine and genomics is the identification of disease biomarkers. In this study, proteomics data from seven major cancers were used to construct two weighted protein–protein interaction networks, i.e., one for the normal and another for the cancer conditions. We developed rigorous, yet mathematically simp...

We present a technique to engineer solitary states by means of delayed links in a network of neural oscillators and in coupled chaotic maps. Solitary states are intriguing partial synchronization patterns, where a synchronized cluster coexists with solitary nodes displaced from this cluster and distributed randomly over the network. We induce solit...

It is known that intra-layer adaptive coupling among connected oscillators instigates explosive synchronization (ES) in multilayer networks. Taking an altogether different cue in the present work, we consider inter-layer adaptive coupling in a multiplex network of phase oscillators and show that the scheme gives rise to ES with an associated hyster...

One of the most challenging problems in biomedicine and genomics is the identification of disease biomarkers. In this study, proteomics data from seven major cancers were used to construct two weighted protein-protein interaction (PPI) networks i.e., one for the normal and another for the cancer conditions. We developed rigorous, yet mathematically...