Abstract Cascades over networks (e.g., neuronal avalanches, social contagions, and system failures) often involve higher-order dependencies, yet theory development has largely focused on pairwise-interaction models. Here, we develop a ‘simplicial threshold model’ (STM) for cascades simplicial complexes that encode dyadic, triadic interactions. Focusing small-world models containing both short- ...

Cascades are a network phenomenon in which small local shocks can result in wide-spread fads, strikes, innovations, or power failures. Determining which initial shocks will result in the largest cascades is of interest to marketing, epidemiology, and computer networking. This paper surveys work in maximizing the size of cascades in social networks.

Period-doubling cascades for the quadratic family are familiar to every student of elementary dynamical systems. Cascades are also often observed in both numerical and scientific experiments. Yet in all but the simplest cases, very little is known about why they exist. When there is one cascade, there are almost always infinitely many. Further, there has been no systematic way of distinguishing...

We report the discovery of a discrete hierarchy of microtransitions occurring in models of continuous and discontinuous percolation. The precursory microtransitions allow us to target almost deterministically the location of the transition point to global connectivity. This extends to the class of intrinsically stochastic processes the possibility to use warning signals anticipating phase trans...

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. We formulate and develop the Structured Prediction Cascade architecture: a sequence of increasingly complex models that progressively filter the space of pos...

Development of numerical methods for internal flows such as the flow in gas turbines or compressors has generally met with less success than that for external flows, due to the complexity of the flow pattern. Potential flow methods had been the major approach in cascade flow calculations until fairly recently, when solution of the Euler equations became practically feasible. The most widely use...

Mandelbrot multiplicative cascades provide a construction of a dynamical system on a set of probability measures defined by inequalities on moments. To be more specific, beyond the first iteration, the trajectories take values in the set of fixed points of smoothing transformations (i.e., some generalized stable laws). Studying this system leads to a central limit theorem and to its functional ...