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Among the versatile forms of dynamical patterns of activity exhibited by the brain, oscillations are one of the most salient and extensively studied, yet are still far from being well understood. In this paper, we provide various structural…
The model we deal with is the mathematical model for mutually penetrating continua one of which is the carrying medium obeying the wave equation whereas the other one is the oscillating inclusion described by the equation for oscillators.…
Oscillatory activity is ubiquitous in natural and engineered network systems. The interaction scheme underlying interdependent oscillatory components governs the emergence of network-wide patterns of synchrony that regulate and enable…
We introduce an original mathematical model to analyze the diffusion of posts within a generic online social platform. Each user of such a platform has his own Wall and Newsfeed, as well as his own self-posting and re-posting activity. As a…
Functional brain networks can change rapidly as a function of stimuli or cognitive shifts. Tracking dynamic functional connectivity is particularly challenging as it requires estimating the structure of the network at each moment as well as…
Dynamical patterns in complex networks of coupled oscillators are both of theoretical and practical interest, yet to fully reveal and understand the interplay between pattern emergence and network structure remains to be an outstanding…
Understanding complex user behaviour under various conditions, scenarios and journeys can be fundamental to the improvement of the user-experience for a given system. Predictive models of user reactions, responses -- and in particular,…
We study a general set of models of social network evolution and dynamics. The models consist of both a dynamics on the network and evolution of the network. Links are formed preferentially between 'similar' nodes, where the similarity is…
We develop a new closed-form model for the dynamics of an elastic and isotropic sphere and use it to derive new closed-form resonant frequencies.
In this study, we consider users' online communication rhythms (online social rhythms) as coupled oscillators in a complex social network. Users' rhythms may be entrained onto those of their friends, and macro-scale pattern of such rhythms…
Online social networks represent a main source of communication and information exchange in today's life. They facilitate exquisitely news sharing, knowledge elicitation, and forming groups of same interests. Researchers in the last two…
Models of cooperation grounded on social networks and on the ability of individuals to choose actions and partners aim to describe human social behavior. Extensive computer simulations of these models give important insight in the social…
We develop a statistical framework for the dynamical closure of spatiotemporal dynamics governed by partial differential equations. Employing the mathematical framework of quantum mechanics to embed the original classical dynamics into a…
Self-organized network dynamics prevails for systems across physics, biology and engineering. How external signals generate distributed responses in networked systems fundamentally underlies their function, yet is far from fully understood.…
Biological and physical systems that can be classified as oscillatory media give rise to interesting phenomena like target patterns and spiral waves. The existence of these structures has been proven in the case of systems with local…
We introduce and solve a general model of dynamic response under external perturbations. This model captures a wide range of systems out of equilibrium including Ising models of physical systems, social opinions, and population genetics.…
Flaming phenomena represent the divergence in the strength of user dynamics as created by user interactions in online social networks (OSNs). Although it has been known that flaming phenomena occur when the Laplacian matrix of the OSN has…
Internet platforms' traffic defines important characteristics of platforms, such as price of services, advertisements, speed of operations. The traffic is usually estimated with the help of the traditional time series models (ARIMA,…
Modern communication networks are inherently complex in nature. First of all, they have a large number of heterogeneous components. Secondly, their connectivity is extremely dynamic. Nodes can come and go, links can be removed and added…
Individuals modify their opinions towards a topic based on their social interactions. Opinion evolution models conceptualize the change of opinion as a uni-dimensional continuum, and the effect of influence is built by the group size, the…