Related papers: Abstract Phase-space Networks Describing Reactive …
Key features of biological activity can often be captured by transitions between a finite number of semi-stable states that correspond to behaviors or decisions. We present here a broad class of dynamical systems that are ideal for modeling…
By dividing potential energy landscapes into basins of attractions surrounding minima and linking those basins that are connected by transition state valleys, a network description of energy landscapes naturally arises. These networks are…
We propose an automatable data-driven methodology for robust nonlinear reduced-order modelling from time-resolved snapshot data. In the kinematical coarse-graining, the snapshots are clustered into few centroids representable for the whole…
We study the dynamics of the contact-process, one of the simplest nonequilibrium stochastic processes, taking place on a scale-free network. We consider the network topology as annealed, i.e. all links are rewired at each microscopic time…
Animals survive in dynamic environments changing at arbitrary timescales, but such data distribution shifts are a challenge to neural networks. To adapt to change, neural systems may change a large number of parameters, which is a slow…
A Potts associative memory network has been proposed as a simplified model of macroscopic cortical dynamics, in which each Potts unit stands for a patch of cortex, which can be activated in one of S local attractor states. The internal…
Partial synchronization plays a crucial role in the functioning of neuronal networks: selective, coordinated activation of neurons enables information processing that flexibly adapts to a changing computational context. Since the structure…
Networks are a powerful tool to model the structure and dynamics of complex systems across scales. Direct connections between system components are often represented as edges, while paths and walks capture indirect interactions. This…
Various important and useful quantities or measures that characterize the topological network structure are usually investigated for a network, then they are averaged over the samples. In this paper, we propose an explicit representation by…
We study the co-evolution of network structure and node states in a model of multiple state interacting agents. The system displays two transitions, network recombination and fragmentation, governed by time scales that emerge from the…
Virtually all real-world networks are dynamical entities. In social networks, the propensity of nodes to engage in social interactions (activity) and their chances to be selected by active nodes (attractiveness) are heterogeneously…
Using probabilistic approach, the transient dynamics of sparsely connected Hopfield neural networks is studied for arbitrary degree distributions. A recursive scheme is developed to determine the time evolution of overlap parameters. As…
Energy conversion in nanosized devices is studied in the framework of state-space models. We use a network representation of the underlying master equation to describe the dynamics by a graph. Particular segments of this network represent…
The understanding of neural activity patterns is fundamentally linked to an understanding of how the brain's network architecture shapes dynamical processes. Established approaches rely mostly on deviations of a given network from certain…
An operator algebra implementation of Markov chain Monte Carlo algorithms for simulating Markov random fields is proposed. It allows the dynamics of networks whose nodes have discrete state spaces to be specified by the action of an update…
In the study of dynamical processes on networks, there has been intense focus on network structure -- i.e., the arrangement of edges and their associated weights -- but the effects of the temporal patterns of edges remains poorly…
Modern neuroscience has evolved into a frontier field that draws on numerous disciplines, resulting in the flourishing of novel conceptual frames primarily inspired by physics and complex systems science. Contributing in this direction, we…
The modelling of discrete regulatory networks combines a graph specifying the pairwise influences between the variables of the system, and a parametrisation from which can be derived a discrete transition system. Given the influence graph…
A network as a substrate for dynamic processes may have its own dynamics. We propose a model for networks which evolve together with diffusing particles through a coupled dynamics, and investigate emerging structural property. The model…
Complex contagion models have been developed to understand a wide range of social phenomena such as adoption of cultural fads, the diffusion of belief, norms, and innovations in social networks, and the rise of collective action to join a…