Related papers: Dynamics of domain wall networks with junctions
After inflation occurs, a weakly coupled scalar field will in general not be in thermal equilibrium but have a distribution of values determined by the inflationary Hubble parameter. If such a field subsequently undergoes discrete symmetry…
The analysis of domain wall dynamics is often simplified to one dimensional physics. For domain walls in thin films, more realistic approaches require the description as two dimensional objects. This includes the study of vortices and…
This work deals with bifurcation and pattern changing in models described by two real scalar fields. We consider generic models with quartic potentials and show that the number of independent polynomial coefficients affecting the ratios…
Domain walls, optimal droplets and disorder chaos at zero temperature are studied numerically for the solid-on-solid model on a random substrate. It is shown that the ensemble of random curves represented by the domain walls obeys Schramm's…
We study the coevolutionary dynamics of network topology and social complex contagion using a threshold cascade model. Our coevolving threshold model incorporates two mechanisms: the threshold mechanism for the spreading of a minority state…
A certain complexity threshold is proposed which defines the term `complex network' for RSN, e.g. Kauffman networks with s>=2 - more than two equally probable state variants. Such Kauffman networks are no longer Boolean networks. RSN are…
We propose a general class of co-evolving tree network models driven by local exploration where new vertices attach to the current network via randomly sampling a vertex and then exploring the graph for a random number of steps in the…
The cosmological evolution of topological defect networks can broadly be divided into two stages. At early times they are friction-dominated due to particle scattering and therefore non-relativistic, and may either be conformally stretched…
Some fractals -- for instance those associated with the Mandelbrot and quadratic Julia sets -- are computed by iterating a function, and identifying the boundary between hyperparameters for which the resulting series diverges or remains…
Cosmological domain walls can be formed as a result of symmetry breaking at any epoch during the evolution of our universe. We study their interaction with a classical macroscopic object, like Earth or a satellite in Earth's orbit. We set…
We study the kinetic roughening of a driven domain wall between spin-up and spin-down domains for a model with non-conserved order parameter and quenched disorder. To understand the scaling behavior of this interface we construct an…
Many complex systems can be described in terms of networks of interacting units. Recent studies have shown that a wide class of both natural and artificial nets display a surprisingly widespread feature: the presence of highly heterogeneous…
Using a generalized random recurrent neural network model, and by extending our recently developed mean-field approach [J. Aljadeff, M. Stern, T. Sharpee, Phys. Rev. Lett. 114, 088101 (2015)], we study the relationship between the network…
Synchronization problems in complex networks are very often studied by researchers due to its many applications to various fields such as neurobiology, e-commerce and completion of tasks. In particular, Scale Free networks with degree…
The complex configurations of dynamic friction patterns-regarding real time contact areas- are transformed into appropriate networks. With this transformation of a system to network space, many properties can be inferred about the structure…
One of the outstanding problems in complexity science and dynamical system theory is understanding the dynamic behavior of high-dimensional networked systems and their susceptibility to transitions to undesired states. Because of varied…
We discuss several aspects of the loss landscape of regularized neural networks: the structure of stationary points, connectivity of optimal solutions, path with nonincreasing loss to arbitrary global optimum, and the nonuniqueness of…
We study a mean field model of a complex network, focusing on edge and triangle densities. Our first result is the derivation of a variational characterization of the entropy density, compatible with the infinite node limit. We then…
We study the family of network models derived by requiring the expected properties of a graph ensemble to match a given set of measurements of a real-world network, while maximizing the entropy of the ensemble. Models of this type play the…
In many networks such as transportation or communication networks, distance is certainly a relevant parameter. In addition, real-world examples suggest that when long-range links are existing, they usually connect to hubs-the well connected…