Related papers: A Fractal Space-filling Complex Network
We introduce a growing network model---the copying model---in which a new node attaches to a randomly selected target node and, in addition, independently to each of the neighbors of the target with copying probability $p$. When…
The scaling properties of spectra of real world complex networks are studied by using the wavelet transform. It is found that the spectra of networks are multifractal. According to the values of the long-range correlation exponent, the Hust…
We introduce a design strategy for neural network macro-architecture based on self-similarity. Repeated application of a simple expansion rule generates deep networks whose structural layouts are precisely truncated fractals. These networks…
Deep connections are known to exist between scale-free networks and non-Gibbsian statistics. For example, typical degree distributions at the thermodynamical limit are of the form $P(k) \propto e_q^{-k/\kappa}$, where the $q$-exponential…
We propose a general geometric growth model for pseudofractal scale-free web, which is controlled by two tunable parameters. We derive exactly the main characteristics of the networks: degree distribution, second moment of degree…
We analyse properties of contact networks formed in packings of soft frictionless disks near the unjamming transition. We construct polygonal tilings and triangulations of the contact network that partitions space into convex regions which…
Complex networks have abundant and extensive applications in real life. Recently, researchers have proposed a number of complex networks, in which some are deterministic and others are random. Compared with deterministic networks, random…
A model for the generation of fractal growth networks in Euclidean spaces of arbitrary dimension is presented. These networks are considered as the spatial support of reaction-diffusion and pattern formation processes. The local dynamics at…
Geometry of networks endowed with a causal structure is discussed using the conventional framework of equilibrium statistical mechanics. The popular growing network models appear as particular causal models. We focus on a class of tree…
Two dimensional space-filling bearings are dense packings of disks that can rotate without slip. We consider the entire first family of bearings for loops of size four and propose a hierarchical construction of their contact network. We…
In this paper, we introduce the foundation of a fractal topological space constructed via a family of nested topological spaces endowed with subspace topologies, where the number of topological spaces involved in this family is related to…
The decimation map $\mathcal{D}$ for a network of admittances on an $n$-simplex lattice fractal is studied. The asymptotic behaviour of $\mathcal{D}$ for large-size fractals is examined. It is found that in the vicinity of the isotropic…
We propose a systematic approach to constructing microscopic models with fractional excitations in three-dimensional (3D) space. Building blocks are quantum wires described by the (1+1)-dimensional conformal field theory (CFT) associated…
The piecewise linearity condition on the total energy with respect to the total magnetization of finite quantum systems is derived, using the infinite-separation-limit technique. This generalizes the well-known constancy condition, related…
We consider a family of deep neural networks consisting of two groups of convolutional layers, a downsampling operator, and a fully connected layer. The network structure depends on two structural parameters which determine the numbers of…
We show that an M X N user MIMO X network with A antennas at each node has AMN/(M+N-1) degrees of freedom (DoF), thus resolving in this case a discrepancy between the spatial scale invariance conjecture (scaling the number of antennas at…
Recently, a framework for analyzing time series by constructing an associated complex network has attracted significant research interest. One of the advantages of the complex network method for studying time series is that complex network…
Power-law sensitivity to initial conditions at the edge of chaos provides a natural relation between the scaling properties of the dynamics attractor and its degree of nonextensivity as prescribed in the generalized statistics recently…
Complex networks are characterized by several topological properties: degree distribution, clustering coefficient, average shortest path length, etc. Using a simple model to generate scale-free networks embedded on geographical space, we…
We generalize a tensor-network algorithm to study thermodynamic properties of self-similar spin lattices constructed on a square-lattice frame with two types of couplings, $J_{1}^{}$ and $J_{2}^{}$, chosen to transform a regular square…