Related papers: Simplicial cascades are orchestrated by the multid…
Structured prediction tasks pose a fundamental trade-off between the need for model complexity to increase predictive power and the limited computational resources for inference in the exponentially-sized output spaces such models require.…
Complex dynamical systems are often modeled as networks, with nodes representing dynamical units which interact through the network's links. Gene regulatory networks, responsible for the production of proteins inside a cell, are an example…
The independent cascade model is a widely used framework for simulating the spread of influence in social networks. In this model, activations propagate stochastically through the network, with each edge having a probability of transmitting…
Threshold rules of spreading in binary-state networks lead to cascades. We study persistent cascade-recovery dynamics on quasi-robust networks, i.e., networks which are robust against small trigger but may collapse for larger one. It is…
Cascades on random networks are typically analyzed by assuming they map onto percolation processes and then are solved using generating function formulations. This approach assumes that the network is infinite and weakly connected, yet…
Tipping points are critical thresholds of parameters where tiny perturbations can lead to abrupt and large qualitative changes in the systems. Many real-world systems that exhibit tipping behavior can be represented as networks of…
Over the past few years, research on deep graph learning has shifted from static graphs to temporal graphs in response to real-world complex systems that exhibit dynamic behaviors. In practice, temporal graphs are formalized as an ordered…
Many real-world networks, ranging from subway systems to polymer structures and fungal mycelia, do not form by the incremental addition of individual nodes but instead grow through the successive extension and intersection of lines or…
Higher order networks are able to characterize data as different as functional brain networks, protein interaction networks and social networks beyond the framework of pairwise interactions. Most notably higher order networks include…
In spiking neural networks an action potential could in principle trigger subsequent spikes in the neighbourhood of the initial neuron. A successful spike is that which trigger subsequent spikes giving rise to cascading behaviour within the…
Temporal network data are increasingly available in various domains, and often represent highly complex systems with intricate structural and temporal evolutions. Due to the difficulty of processing such complex data, it may be useful to…
Certain linear matrix operators arise naturally in systems analysis and design problems involving cascade interconnections of linear time-invariant systems, including problems of stabilization, estimation, and model order reduction. We…
We consider a version of the Watts cascade model on directed multiplex configuration model networks, and present a detailed analysis of the cascade size, single-seed cascade probability and cascade condition. We then introduce a smaller…
A cascade model is described based on multiplier distributions determined from 3D direct numerical simulations (DNS) of turbulent particle laden flows, which include two-way coupling between the phases at global mass loadings equal to…
Triadic closure, the formation of a connection between two nodes in a network sharing a common neighbor, is considered a fundamental mechanism determining the clustered nature of many real-world topologies. In this work we define a static…
Recent experiments have highlighted how collective dynamics in networks of brain regions affect behavior and cognitive function. In this paper we show that a simple, homogeneous system of densely connected oscillators representing the…
This article presents a theory for constructing hierarchical networks in such a way that the networks are guaranteed to be provably scale covariant. We first present a general sufficiency argument for obtaining scale covariance, which holds…
Understanding the dynamics of spatially extended systems represents a challenge in diverse scientific disciplines, ranging from physics and mathematics to the earth and climate sciences or the neurosciences. This challenge has stimulated…
Randomly connected networks of excitatory and inhibitory spiking neurons provide a parsimonious model of neural variability, but are notoriously unreliable for performing computations. We show that this difficulty is overcome by…
We investigate the properties of an autoassociative network of threshold-linear units whose synaptic connectivity is spatially structured and asymmetric. Since the methods of equilibrium statistical mechanics cannot be applied to such a…