Related papers: Effects of Biases in Domain Wall Network Evolution
The evolution of complex transport networks is investigated under three strategies of link removal: random, intentional attack and "Pseudo-Darwinian" strategy. At each evolution step and regarding the selected strategy, one removes either a…
The recent discovery of universal principles underlying many complex networks occurring across a wide range of length scales in the biological world has spurred physicists in trying to understand such features using techniques from…
We consider the possibility that current hints of spatial variations of the fine structure constant at high redshift, based on VLT/UVES and Keck/HIRES observations, could be caused by a biased domain wall network described by a scalar field…
The growth of domains of stripes evolving from random initial conditions is studied in numerical simulations of models of systems far from equilibrium such as Rayleigh-Benard convection. The scaling of the size of the domains deduced from…
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…
First steps towards a mathematical theory of deep convolutional neural networks for feature extraction were made---for the continuous-time case---in Mallat, 2012, and Wiatowski and B\"olcskei, 2015. This paper considers the discrete case,…
For large-scale power networks, the failure of particular transmission lines can offload power to other lines and cause self-protection trips to activate, instigating a cascade of line failures. In extreme cases, this can bring down the…
Networks describing the interaction of the elements that constitute a complex system grow and develop via a number of different mechanisms, such as the addition and deletion of nodes, the addition and deletion of edges, as well as the…
Random Boolean networks have been used widely to explore aspects of gene regulatory networks. A modified form of the model through which to systematically explore the effects of increasing the number of gene states has previously been…
The way in which different types of dynamics unfold in complex networks is intrinsically related to the propagation of activation along nodes, which is strongly affected by the network connectivity. In this work we investigate to which…
The concept of Schramm-Loewner evolution provides a unified description of domain boundaries of many lattice spin systems in two dimensions, possibly even including systems with quenched disorder. Here, we study domain walls in the…
We investigate the evolutionary dynamics in directed and/or weighted networks. We study the fixation probability of a mutant in finite populations in stochastic voter-type dynamics for several update rules. The fixation probability is…
This study examines long-term trends and shifting behavior in the collaboration network of mathematics literature, using a subset of data from Mathematical Reviews spanning 1985-2009. Rather than modeling the network cumulatively, this…
We show that to explain the growth of the citation network by preferential attachment (PA), one has to accept that individual nodes exhibit heterogeneous fitness values that decay with time. While previous PA-based models assumed either…
Many real-world social networks constantly change their global properties over time, such as the number of edges, size and density. While temporal and local properties of social networks have been extensively studied, the origin of their…
Renewable and sustainable energy is one of the most important challenges currently facing mankind. Wind has made an increasing contribution to the world's energy supply mix, but still remains a long way from reaching its full potential. In…
We propose new direction to understanding evolutionary dynamics of complex networks using two different types of collaboration networks: academic collaboration networks; and, disaster collaboration networks. The results show that academic…
It has been discovered recently that many social, biological and ecological systems have the so-called small-world and scale-free features, which has provoked new research interest in the studies of various complex networks. Yet, most…
Domain walls (DWs) can be produced when a discrete symmetry is spontaneously broken, and long-lived DWs can dominate the energy density of the universe. In this work, we explore the possibility that a "domain wall dominant (DWD)" phase…
We perform an average case analysis of the generalization dynamics of large neural networks trained using gradient descent. We study the practically-relevant "high-dimensional" regime where the number of free parameters in the network is on…