arXiv subjects

Sarika Jalan

Publications and source records attributed to Sarika Jalan.

At least 55 records · Page 3Linked to original sources

arXiv2021

Machine Learning assisted Chimera and Solitary states in Networks

Chimera and Solitary states have captivated scientists and engineers due to their peculiar dynamical states corresponding to the 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 the suitable implementation of communication delays. Here, using supervised machine learning, we predict (a) the precise value of delay which is sufficient for engineering chimera and solitary states for a given set of system parameters, as well as (b) the intensity of incoherence for such engineered states. The results are demonstrated for two different examples consisting of single layer and multi layer networks. First, the chimera states (solitary states) are engineered by establishing delays in the neighboring links of a node (the interlayer links) in a 2-D lattice (multiplex network) of oscillators. Then, different machine learning classifiers, KNN, SVM and MLP-Neural Network are employed by feeding the data obtained from the network models. Once a machine learning model is trained using a limited amount of data, it makes predictions for a given unknown systems parameter values. Testing accuracy, sensitivity, and specificity analysis reveal that MLP-NN classifier is better suited than Knn or SVM classifier for the predictions of parameters values for engineered chimera and solitary states. The technique provides an easy methodology to predict critical delay values as well as the intensity of incoherence for designing an experimental setup to create solitary and chimera states.

nlin.AO↗

arXiv2021

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

We show that an introduction of a phase parameter ($α$), with $0 \le α\le π/2$, in the interlayer coupling terms of multiplex networks of Kuramoto oscillators can induce explosive synchronization (ES) in the multiplexed layers. Along with the α values, the hysteresis width is determined by the interlayer coupling strength and the frequency mismatch between the mirror (inter-connected) nodes. A mean-field analysis is performed to support the numerical results. Similar to the earlier works, we find that the suppression of synchronization is accountable for the origin of ES. The robustness of ES against changes in the network topology and frequency distribution is tested. Finally, taking a suggestion from the synchronized state of the multiplex networks, we extend the results to the classical concept of the single-layer networks in which some specific links are assigned a phase-shifted coupling. Different methods have been introduced in the past years to incite ES in coupled oscillators; our results indicate that a phase-shifted coupling can also be one such method to achieve ES.

nlin.AO↗

arXiv2020

Interlayer Hebbian Plasticity Induces First-Order Transition in Multiplex Networks

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 link weight between a pair of interconnected nodes is enhanced if the two nodes are in phase. Such adaptive coupling induces an irreversible first-order transition route to synchronization accompanied with a hysteresis. We provide rigorous analytic predictions of the critical coupling strengths for the onset of synchronization and de-synchronization, and verify all our theoretical predictions by means of extensive numerical simulations.

nlin.AO↗

arXiv2020

Multifractal analysis of eigenvectors of smallworld networks

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 eigenvectors of the adjacency matrices of small-world networks constructed using Watts-Strogatz algorithm. We find that the central part of the eigenvalue spectrum is characterized by strong multifractality whereas the tail part of the spectrum have Dq->1. Before the onset of the small-world transition, an increase in the random connections leads to an enhancement in the eigenvectors localization, whereas just after the onset, the eigenvectors show a gradual decrease in the localization. We have verified an existence of sharp change in the correlation dimension at the localization-delocalization transition

cond-mat.dis-nn↗

arXiv2020

From Spectra to Localized Networks: A Reverse Engineering Approach

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 networks parameters that is the number of nodes and the number of interactions. We find that the localization behavior of the principal eigenvector (PEV) of such a network is sensitive against a single edge rewiring. We find evidences for eigenvalue crossing phenomena as a consequence of the single edge rewiring, in turn providing an origin to the sensitive behavior of the PEV localization. These insights were then used to analytically construct the highly localized network for a given set of networks parameters. The analysis provides fundamental insight into relationships between the structural and the spectral properties of networks for PEV localized networks. Further, we substantiate the existence of the eigenvalue crossing phenomenon by considering a linear-dynamical process, namely the ribonucleic acid (RNA) neutral network population dynamical model. The analysis presented here on model networks aids in understanding the steady-state behavior of a broad range of linear-dynamical processes, from epidemic spreading to biochemical dynamics associated with the adjacency matrices.

physics.soc-ph↗

arXiv2020

Explosive Synchronization in Multilayer Dynamically Dissimilar Networks

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 powerful model to understand and predict the properties of a diverse range of real-world complex systems. Recently, a multilayer network has been realized as a better suited framework for the representation of complex systems having multiple types of interactions among the same set of constituents. This article shows that by tuning the properties of one layer (network) of a multilayer network, one can regulate the dynamical behavior of another layer (network). By taking an example of a multiplex network comprising two different types of networked Kuramoto oscillators representing two different layers, this article attempts to provide a glimpse of opportunities and emerging phenomena multiplexing can induce which is otherwise not possible for a network in isolation. Here we consider explosive synchronization to demonstrate the potential of multilayer networks framework. To the end, we discuss several possible extensions of the model considered here by incorporating real-world properties.

nlin.AO↗

arXiv2020

Identification of Chimera using Machine Learning

Chimera state refers to 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 other hand is challenging due to its widely varied appearance in different systems and the peculiar nature of its profile. Therefore, a simple yet universal method for its identification remains an open problem. Here, we present a very distinctive approach using machine learning techniques to characterize different dynamical phases and identify the chimera state from given spatial profiles generated using various different models. The experimental results show that the performance of the classification algorithms varies for different dynamical models. The machine learning algorithms, namely random forest, oblique random forest based on tikhonov, parallel-axis split and null space regularization achieved more than $96\% $ accuracy for the Kuramoto model. For the logistic-maps, random forest and tikhonov regularization based oblique random forest showed more than $90\%$ accuracy, and for the Hénon-Map model, random forest, null-space and axis-parallel split regularization based oblique random forest achieved more than $80\%$ accuracy. The oblique random forest with null space regularization achieved consistent performance (more than $83\%$ accuracy) across different dynamical models while the auto-encoder based random vector functional link neural network showed relatively lower performance. This work provides a direction for employing machine learning techniques to identify dynamical patterns arising in coupled non-linear units on large-scale, and for characterizing complex spatio-temporal patterns in real-world systems for various applications.

nlin.AO↗

arXiv2020

Wheel graph strategy for PEV localization of networks

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, criticality in brain network dynamics. For a network, an eigenvector is said to be localized when most of its components take value near to zero, with a few components taking very high values. In this article, we devise a methodology to construct a principal eigenvector (PEV) localized network from a given input network. The methodology relies on adding a small component having a wheel graph to the given input network. By extensive numerical simulation and an analytical formulation based on the largest eigenvalue of the input network, we compute the size of the wheel graph required to localize the PEV of the combined network. Using the susceptible-infected-susceptible model, we demonstrate the success of this method for various models and real-world networks consider as input networks. We show that on such PEV localized networks, the disease gets localized within a small region of the network structure before the outbreaks. The study is relevant in controlling spreading processes on complex systems represented by networks.

physics.soc-ph↗

arXiv2020

Principal eigenvector localization and centrality in networks: revisited

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.

physics.soc-ph↗

arXiv2019

Inter-layer adaptation induced explosive synchronization in multiplex networks

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 hysteresis irrespective of the network architecture of individual layers. The hysteresis is shaped by the inter-layer coupling strength and the frequency mismatch between the mirror nodes. We provide rigorous mean-field analytical treatment for the measure of global coherence and manifest they are in a good match with respective numerical assessments. Moreover, the analytical predictions provide a complete insight into how adaptive multiplexing suppresses the formation of a giant cluster, eventually giving birth to ES. The study will help in spotlighting the role of multiplexing in the emergence of ES in real-world systems represented by multilayer architecture. Particularly, it is relevant to those systems which have limitations towards change in intra-layer coupling strength.

nlin.AO↗

arXiv2019

Symmetry in cancer networks identified: Proposal for multi-cancer biomarkers

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 simple, methodology based on the degeneracy at -1 eigenvalues to identify structural symmetry or motif structures in network. Utilising eigenvectors corresponding to degenerate eigenvalues in the weighted adjacency matrix, we identified structural symmetry in underlying weighted PPI networks constructed using seven cancer data. Functional assessment of proteins forming these structural symmetry exhibited the property of cancer hallmarks. Survival analysis refined further this protein list proposing BMI, MAPK11, DDIT4, CDKN2A, and FYN as putative multi-cancer biomarkers. The combined framework of networks and spectral graph theory developed here can be applied to identify symmetrical patterns in other disease networks to predict proteins as potential disease biomarkers.

q-bio.MN↗

arXiv2019

Delay engineered solitary states in complex networks

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 solitary states in the originally synchronized network of identical nodes by introducing delays in the links for a certain number of selected network elements. It is shown that the extent of displacement and the position of solitary elements can be completely controlled by the choice (values) and positions (locations) of the incorporated delays, reshaping the delay engineered solitary states in the network.

nlin.AO↗

arXiv2019

Taming Chimeras in Networks through Multiplexing Delays

Chimera referring to a coexistence of coherent and incoherent states, is traditionally very difficult to control due to its peculiar nature. Here, we provide a recipe to construct chimera states in the multiplex networks with the aid of multiplexing-delays. The chimera state in multiplex networks is produced by introducing heterogeneous delays in a fraction of inter-layer links, referred as multiplexing-delay, in a sequence. Additionally, the emergence of the incoherence in the chimera state can be regulated by making appropriate choice of both inter- and intra-layer coupling strengths, whereas the extent and the position of the incoherence regime can be regulated by appropriate placing and {strength} of the multiplexing delays. The proposed technique to construct such {engineered} chimera equips us with multiplex network's structural parameters as tools in gaining both qualitative- and quantitative-control over the incoherent section of the chimera states and, in turn, the chimera. Our investigation can be of worth in controlling dynamics of multi-level delayed systems and attain desired chimeric patterns.

nlin.AO↗

arXiv2019

Inhibition induced explosive synchronization in multiplex networks

To date, explosive synchronization (ES) is shown to be originated from either degree-frequency correlation or inertia of phase oscillators. Of late, it has been shown that ES can be induced in a network by adaptively controlled phase oscillators. Here we show that ES is a generic phenomenon and can occur in any network by appropriately multiplexing it with another layer. We devise an approach which leads to the occurrence of ES with hysteresis loop in a network upon its multiplexing with a negatively coupled (or inhibitory) layer. We discuss the impact of various structural properties of positively coupled (or excitatory) and inhibitory layer along with the strength of multiplexing in gaining control over the induced ES transition. This investigation is a step forward in highlighting the importance of multiplex framework not only in bringing novel phenomena which are not possible in an isolated network but also in providing more structural control over the induced phenomena.

nlin.AO↗

arXiv2018

Spectral properties of complex networks

This review presents an account of the major works done on spectra of adjacency matrices drawn on networks and the basic understanding attained so far. We have divided the review under three sections: (a) extremal eigenvalues, (b) bulk part of the spectrum and (c) degenerate eigenvalues, based on the intrinsic properties of eigenvalues and the phenomena they capture. We have reviewed the works done for spectra of various popular model networks, such as the Erdős-Rényi random networks, scale-free networks, 1-d lattice, small-world networks, and various different real-world networks. Additionally, potential applications of spectral properties for natural processes have been reviewed.

cond-mat.dis-nn↗

arXiv2018

Delay Regulated Explosive Synchronization in Multiplex Networks

It is known that explosive synchronization (ES) in an isolated network of Kuramoto oscillators with inertia is significantly enhanced by the presence of time delay. Here we show that time delay in one layer of the multiplex network governs the transition to synchronization and ES in the other layers. We found that a single layer with time-delayed intra-layer coupling, depending on the values of time delay, experiences a different type of transition to synchronization, e.g., ES or continuous, and the same type of transition is incorporated simultaneously in other layer(s) as well. Hence, a suitable choice of time-delay in only one layer can lead to a desired (either ES or continuous) transition simultaneously in the delayed and other undelayed layers of multiplexed network. These results offer a platform for a better understanding of the dynamics of those complex systems which are represented by multilayered framework and contain time delays in the communication processes.

nlin.AO↗

arXiv2018

Weak multiplexing in neural networks: Switching between chimera and solitary states

We investigate spatio-temporal patterns occurring in a two-layer multiplex network of oscillatory FitzHugh-Nagumo neurons, where each layer is represented by a nonlocally coupled ring. We show that weak multiplexing, i.e., when the coupling between the layers is smaller than that within the layers, can have a significant impact on the dynamics of the neural network. We develop control strategies based on weak multiplexing and demonstrate how the desired state in one layer can be achieved without manipulating its parameters, but only by adjusting the other layer. We find that for coupling range mismatch weak multiplexing leads to the appearance of chimera states with different shapes of the mean velocity profile for parameter ranges where they do not exist in isolation. Moreover, we show that introducing a coupling strength mismatch between the layers can suppress chimera states with one incoherent domain (one-headed chimeras) and induce various other regimes such as in-phase synchronization or two-headed chimeras. Interestingly, small intra-layer coupling strength mismatch allows to achieve solitary states throughout the whole network.

nlin.CD↗

arXiv2018

Astrocyte-induced positive integrated information in neuroglial ensembles

The Integrated Information is a quantitative measure from information theory how tightly all parts of a system are interconnected in terms of information exchange. In this study we show that astrocyte, playing an important role in regulation of information transmission between neurons, may contribute to a generation of positive Integrated Information in neuronal ensembles. Analytically and numerically we show that the presence of astrocyte may be essential for this information attribute in neuro-astrocytic ensembles. Moreover, the proposed "spiking-bursting" mechanism of generating positive Integrated Information is shown to be generic and not limited to neuroglial networks, and is given a complete analytic description.

q-bio.NC↗