Related papers: Scaling limit for subsystems and Doplicher-Roberts…
Scale-free networks are ubiquitous in social, biological and technological networked systems. Dynamic Scale-free networks and their synchronizations are important to understand and predict the behavior of social, biological and…
Many CFTs can be extended to lines of nonlocal CFTs parametrised by the scaling dimension $\Delta$ of the fundamental field appearing in the action. $\Delta=\frac{d}{2}-\zeta$ is set by the exponent of the kinetic term…
Fixed points for scalar theories in $4-\varepsilon$, $6-\varepsilon$ and $3-\varepsilon$ dimensions are discussed. It is shown how a large range of known fixed points for the four dimensional case can be obtained by using a general…
We describe the results of the largest and most accurate three-dimensional field theory simulations of domain wall networks with junctions. We consider a previously introduced class of models which, in the limit of large number $N$ of…
Geometric constraints impact the formation of a broad range of spatial networks, from amino acid chains folding to proteins structures to rearranging particle aggregates. How the network of interactions dynamically self-organizes in such…
We first rephrase and unify known bijections between bipartite plane maps and labelled trees with the formalism of looptrees, which we argue to be both more relevant and technically simpler since the geometry of a looptree is explicitly…
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…
This work is concerned with fractional Gaussian fields, i.e. Gaussian fields whose covariance operator is given by the inverse fractional Laplacian $(-\Delta)^{-s}$ (where, in particular, we include the case $s >1$). We define a lattice…
We consider an infinite spatial inhomogeneous random graph model with an integrable connection kernel that interpolates nicely between existing spatial random graph models. Key examples are versions of the weight-dependent random connection…
Contrary to many recent models of growing networks, we present a model with fixed number of nodes and links, where it is introduced a dynamics favoring the formation of links between nodes with degree of connectivity as different as…
In many interesting situations the size of epsilon-nets depends only on $\epsilon$ together with different complexity measures. The aim of this paper is to give a systematic treatment of such complexity measures arising in Discrete and…
In a recursive way and by including a parameter, we introduce a family of deterministic scale-free networks. The resulting networks exhibit small-world effects. We calculate the exact results for the degree exponent, the clustering…
We present a rigorous renormalization group scheme for lattice quantum field theories in terms of operator algebras. The renormalization group is considered as an inductive system of scaling maps between lattice field algebras. We construct…
Scalar field theories regularized on a $D$ dimensional lattice are found to exhibit double scaling for a class of critical behaviors labeled by an integer $m\geq 2$. The continuum theory reached in the double scaling limit defines a…
Scale-free percolation is a percolation model on $\mathbb{Z}^d$ which can be used to model real-world networks. We prove bounds for the graph distance in the regime where vertices have infinite degrees. We fully characterize transience vs.…
We introduce a simple one-parameter network growth algorithm which is able to reproduce a wide variety of realistic network structures but without having to invoke any global information about node degrees such as preferential-attachment…
We use the embedding formalism to construct conformal fields in $D$ dimensions, by restricting Lorentz-invariant ensembles of homogeneous neural networks in $(D+2)$ dimensions to the projective null cone. Conformal correlators may be…
In this paper, we show that one can naturally associate a limiting dynamical system $F: T\longrightarrow T$ on an $\R$-tree to any degenerating sequence of rational maps $f_n: \hat\C \longrightarrow \hat\C$ of fixed degree. The construction…
Correlation between nodes is found to be a common and important property in many complex networks. Here we investigate degree correlations of the Barabasi-Albert (BA) Scale-Free model with both analytical results and simulations, and find…
We study operators with large internal charge in boundary conformal field theories (BCFTs) with internal symmetries. Using the state-operator correspondence and the existence of a macroscopic limit, we find a non-trivial relation between…