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In reservoir computing, the coupling strength of the initial untrained recurrent neural network (the reservoir) is an important hyperparameter that can be varied for accurate training. A common heuristic is to set this parameter near the…

Research in network science has shown that many naturally occurring and technologically constructed networks are scale free, that means a power law degree distribution emerges from a growth model in which each new node attaches to the…

We derive the sampling properties of random networks based on weights whose pairwise products parameterize independent Bernoulli trials. This enables an understanding of many degree-based network models, in which the structure of realized…

An intuitive overview of the scalability of a variety of types of wireless networks is presented. Simple heuris- tic arguments are demonstrated here for scaling laws presented in other works, as well as for conditions not previously…

The universal fractality of river networks is very well known, however understanding of the underlying mechanisms for them is still lacking in terms of stochastic processes. By introducing probability changing dynamically, we have described…

Stochastic network design is a general framework for optimizing network connectivity. It has several applications in computational sustainability including spatial conservation planning, pre-disaster network preparation, and river network…

In this paper we investigate networks whose evolution is governed by the interaction of a random assembly process and an optimization process. In the first process, new nodes are added one at a time and form connections to randomly selected…

The shoaling of surface gravity waves has been acknowledged as a mechanism of rogue wave formation. This problem is generally reduced to water waves passing over a step, but non-equilibrium physics allows finite slopes to be considered.…

Decaying turbulence is studied numerically using as initial condition a random flow whose shell-integrated energy spectrum increases with wavenumber k like k^q. Alternatively, initial conditions are generated from a driven turbulence…

Electric power-systems are one of the most important critical infrastructures. In recent years, they have been exposed to extreme stress due to the increasing demand, the introduction of distributed renewable energy sources, and the…

We propose a dynamical model for cascading failures in single-commodity network flows. In the proposed model, the network state consists of flows and activation status of the links. Network dynamics is determined by a, possibly…

The scaling properties of the roughness of surfaces grown by two different processes randomly alternating in time, are addressed. The duration of each application of the two primary processes is assumed to be independently drawn from given…

Porous sediments in geological systems are exposed to stress by the above-laying mass and consequent compaction, which may be significantly nonuniform across the massif. We derive scaling laws for the compaction of sediments of similar…

What is the best way to divide a rugged landscape? Since ancient times, watersheds separating adjacent water systems that flow, for example, toward different seas, have been used to delimit boundaries. Interestingly, serious and even tense…

Two node variables determine the evolution of cascades in random networks: a node's degree and threshold. Correlations between both fundamentally change the robustness of a network, yet, they are disregarded in standard analytic methods as…

In this paper, we consider a system of partial differential equations modeling the evolution of a landscape. A ground surface is eroded by the flow of water over it, either by sedimentation or dilution. The system is composed by three…

We define a dynamic model of random networks, where new vertices are connected to old ones with a probability proportional to a sublinear function of their degree. We first give a strong limit law for the empirical degree distribution, and…

Turbulent flows within and over sparse canopies are investigated using direct numerical simulations. We focus on the effect of the canopy on the background turbulence, the part of the flow that remains once the element-induced flow is…

We review the recent fast progress in statistical physics of evolving networks. Interest has focused mainly on the structural properties of random complex networks in communications, biology, social sciences and economics. A number of giant…

We formulate a general model for the growth of scale-free networks under filtering information conditions--that is, when the nodes can process information about only a subset of the existing nodes in the network. We find that the…