相关论文: Scaling limit for a drainage network model

We present a numerical study on the dynamics of imbibition fronts in porous media using a pipe network model. This model quantitatively reproduces the anomalous scaling behavior found in imbibition experiments [Phys. Rev. E {\bf 52}, 5166…

Transport is an important function in many network systems and understanding its behavior on biological, social, and technological networks is crucial for a wide range of applications. However, it is a property that is not well-understood…

Despite their diverse origin, networks of large real-world systems reveal a number of common properties including small-world phenomena, scale-free degree distributions and modularity. Recently, network self-similarity as a natural outcome…

This work will appear as a chapter in a forthcoming volume titled "Topics in Probabilistic Graph Theory". A theory of scaling limits for random graphs has been developed in recent years. This theory gives access to the large-scale geometric…

We explore and calculate the rich scaling behavior of copolymer networks in solution by renormalization group methods. We establish a field theoretic description in terms of composite operators. Our 3rd order resummation of the spectrum of…

We consider inhomogeneous branching diffusions on an infinite domain of $\mathbb{R}^d$. The first aim of this article is to derive a general criterium under which the size process (number of particles) and the genealogy of the particle…

Quantification of symmetries in complex networks is typically done globally in terms of automorphisms. Extending previous methods to locally assess the symmetry of nodes is not straightforward. Here we present a new framework to quantify…

We study the renormalization group flow of $\mathbb{Z}_2$-invariant supersymmetric and non-supersymmetric scalar models in the local potential approximation using functional renormalization group methods. We focus our attention to the fixed…

Recently, Hammond and Sheffield introduced a model of correlated random walks that scale to fractional Brownian motions with long-range dependence. In this paper, we consider a natural generalization of this model to dimension $d\geq 2$. We…

Universal scaling of distances between vertices of Erdos-Renyi random graphs, scale-free Barabasi-Albert models, science collaboration networks, biological networks, Internet Autonomous Systems and public transport networks are observed. A…

Capacity scaling laws are analyzed in an underwater acoustic network with $n$ regularly located nodes on a square. A narrow-band model is assumed where the carrier frequency is allowed to scale as a function of $n$. In the network, we…

We consider a multihop wireless system. There are multiple source-destination pairs. The data from a source may have to pass through multiple nodes. We obtain a channel scheduling policy which can guarantee end-to-end mean delay for the…

In their recent work "Scale-free networks are rare", Broido and Clauset address the problem of the analysis of degree distributions in networks to classify them as scale-free at different strengths of "scale-freeness." Over the last two…

Standard field theoretic renormalization group is applied to the model of landscape erosion introduced by R. Pastor-Satorras and D. H. Rothman [Phys. Rev. Lett. 80: 4349 (1998); J. Stat. Phys. 93: 477 (1998)] yielding unexpected results:…

Tensor models provide a way to access the path-integral for discretized quantum gravity in d dimensions. As in the case of matrix models for two-dimensional quantum gravity, the continuum limit can be related to a Renormalization Group…

We conclude a sequence of work by giving near-optimal sketching and streaming algorithms for estimating Shannon entropy in the most general streaming model, with arbitrary insertions and deletions. This improves on prior results that obtain…

Many existing statistical and machine learning tools for social network analysis focus on a single level of analysis. Methods designed for clustering optimize a global partition of the graph, whereas projection based approaches (e.g. the…

The use of network Newton methods for the decentralized optimization of a sum cost distributed through agents of a network is considered. Network Newton methods reinterpret distributed gradient descent as a penalty method, observe that the…

The double scaling limit of a new class of the multi-matrix models proposed in \cite{MMM91}, which possess the $W$-symmetry at the discrete level, is investigated in details. These models are demonstrated to fall into the same universality…

As a function of connectivity, spring networks exhibit a critical transition between floppy and rigid phases at an isostatic threshold. For connectivity below this threshold, fiber networks were recently shown theoretically to exhibit a…