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Hierarchical networks actually have many applications in the real world. Firstly, we propose a new class of hierarchical networks with scale-free and fractal structure, which are the networks with triangles compared to traditional…

In real-world applications, observations are often constrained to a small fraction of a system. Such spatial subsampling can be caused by the inaccessibility or the sheer size of the system, and cannot be overcome by longer sampling.…

We analyze all individual cosmic strings of various lengths in a large ensemble of the global cosmic string networks in the post-inflationary scenario, obtained from numerical simulations on a discrete lattice with $N^3 = 4096^3$. A strong…

We constructs a new network by superposition of hexahedron , which are scale-free, highly sparse,disassortative ,and maximal planar graphs. The network degree distribution, agglomeration coefficient and degree of correlation are computed…

A class of random graph models is considered, combining features of exponential-family models and latent structure models, with the goal of retaining the strengths of both of them while reducing the weaknesses of each of them. An open…

Real world complex networks are scale free and possess meso-scale properties like core-periphery and community structure. We study evolution of the core over time in real world networks. This paper proposes evolving models for both…

In an ego-network, an individual (ego) organizes its friends (alters) in different groups (social circles). This social network can be efficiently analyzed after learning representations of the ego and its alters in a low-dimensional, real…

In this paper we present the results of numerical simulations intended to study the behavior of non-Abelian cosmic strings networks. In particular we are interested in discussing the variations in the asymptotic behavior of the system as we…

The spectral evolution model aims to characterize the growth of large networks (i.e., how they evolve as new edges are established) in terms of the eigenvalue decomposition of the adjacency matrices. It assumes that, while eigenvectors…

Deep neural networks are widely used prediction algorithms whose performance often improves as the number of weights increases, leading to over-parametrization. We consider a two-layered neural network whose first layer is frozen while the…

The push to train ever larger neural networks has motivated the study of initialization and training at large network width. A key challenge is to scale training so that a network's internal representations evolve nontrivially at all…

Preferential attachment is often suggested to be the underlying mechanism of the growth of a network, largely due to that many real networks are, to a certain extent, scale-free. However, such attribution is usually made under debatable…

Complex network theory has been used to study complex systems. However, many real-life systems involve multiple kinds of objects . They can't be described by simple graphs. In order to provide complete information of these systems, we…

In studying network growth, the conventional approach is to devise a growth mechanism, quantify the evolution of a statistic or distribution (such as the degree distribution), and then solve the equations in the steady state (the…

Many biological, ecological and economic systems are best described by weighted networks, as the nodes interact with each other with varying strength. However, most network models studied so far are binary, the link strength being either 0…

Neural fields have emerged as a new data representation paradigm and have shown remarkable success in various signal representations. Since they preserve signals in their network parameters, the data transfer by sending and receiving the…

Existing models of network growth typically have one or two parameters or strategies which are fixed for all times. We introduce a general framework where feedback on the current state of a network is used to dynamically alter the values of…

We describe the detailed study and results of high-resolution numerical simulations of string-induced structure formation in open universes and those with a non-zero cosmological constant. The effect from small loops generated from the…

We introduce a growing network model in which a new node attaches to a randomly-selected node, as well as to all ancestors of the target node. This mechanism produces a sparse, ultra-small network where the average node degree grows…

Random Boolean networks, originally invented as models of genetic regulatory networks, are simple models for a broad class of complex systems that show rich dynamical structures. From a biological perspective, the most interesting networks…