Related papers: Multiple Timescale Dynamics of Network Adaptation …
The process of training an artificial neural network involves iteratively adapting its parameters so as to minimize the error of the network's prediction, when confronted with a learning task. This iterative change can be naturally…
Models of complex networks often incorporate node-intrinsic properties abstracted as hidden variables. The probability of connections in the network is then a function of these variables. Real-world networks evolve over time, and many…
The characterization of the "most connected" nodes in static or slowly evolving complex networks has helped in understanding and predicting the behavior of social, biological, and technological networked systems, including their robustness…
We study the multiscale structure of the Jain-Krishna adaptive network model. This model describes the co-evolution of a set of continuous-time autocatalytic ordinary differential equations and its underlying discrete-time graph structure.…
The control of complex systems is an ongoing challenge of complexity research. Recent advances using concepts of structural control deduce a wide range of control related properties from the network representation of complex systems. Here,…
We consider a class of models describing an ensemble of identical interacting agents subject to multiplicative noise. In the thermodynamic limit, these systems exhibit continuous and discontinuous phase transitions in a, generally,…
In a large variety of systems (biological, physical, social etc.), synchronization occurs when different oscillating objects tune their rhythm when they interact with each other. The different underlying network defining the connectivity…
We investigate the emergence of synchronization in the second-order Kuramoto model with adaptive simplicial interactions on a globally connected network. This inertial Kuramoto framework describes systems, where oscillator frequencies…
Spatio-temporal network dynamics is an emergent property of many complex systems which remains poorly understood. We suggest a new approach to its study based on the analysis of dynamical motifs -- small subnetworks with periodic and…
Human dynamical social networks encode information and are highly adaptive. To characterize the information encoded in the fast dynamics of social interactions, here we introduce the entropy of dynamical social networks. By analysing a…
The recent discovery of universal principles underlying many complex networks occurring across a wide range of length scales in the biological world has spurred physicists in trying to understand such features using techniques from…
Dynamical systems on networks are inherently high-dimensional unless the number of nodes is extremely small. Dimension reduction methods for dynamical systems on networks aim to find a substantially lower-dimensional system that preserves…
The evolution of leadership in migratory populations depends not only on costs and benefits of leadership investments but also on the opportunities for individuals to rely on cues from others through social interactions. We derive an…
We explore both analytically and numerically an ensemble of coupled phase-oscillators governed by a Kuramoto-type system of differential equations. However, we have included the effects of time-delay (due to finite signal-propagation…
A broad range of nonlinear processes over networks are governed by threshold dynamics. So far, existing mathematical theory characterizing the behavior of such systems has largely been concerned with the case where the thresholds are…
Complex dynamical systems are prevalent in various domains, but their analysis and prediction are hindered by their high dimensionality and nonlinearity. Dimensionality reduction techniques can simplify the system dynamics by reducing the…
Cascade models based on dynamical complex networks are proposed as models of turbulent energy cascade. Taking a simple shell model as the initial regular lattice with only nearest neighbor interactions, small world network models are…
Designing high-performing networks requires optimizing for functionality while respecting physical, geometric, or budget constraints. Yet, mathematical and computational tools to design such systems remain limited, particularly for…
Synchronization is a universal phenomenon found in many non-equilibrium systems. Much recent interest in this area has overlapped with the study of complex networks, where a major focus is determining how a system's connectivity patterns…
We study the evolution of a random weighted network with complex nonlinear dynamics at each node, whose activity may cease as a result of interactions with other nodes. Starting from a knowledge of the micro-level behaviour at each node, we…