Related papers: Parallel Random Apollonian Networks
The exact formula for the average path length of Apollonian networks is found. With the help of recursion relations derived from the self-similar structure, we obtain the exact solution of average path length, $\bar{d}_t$, for Apollonian…
We propose a novel paradigm for modeling real-world scale-free networks, where the integration of new nodes is driven by the combined attractiveness of degree and betweenness centralities, the competition of which (expressed by a parameter…
We present a family of scale-free network model consisting of cliques, which is established by a simple recursive algorithm. We investigate the networks both analytically and numerically. The obtained analytical solutions show that the…
In this paper, we studied the research areas of Chinese natural science basic research from a point view of complex network. Two research areas are considered to be connected if they appear in one fund proposal. The explicit network of such…
The parallel computational complexity of the quadratic map is studied. A parallel algorithm is described that generates typical pseudotrajectories of length t in a time that scales as log t and increases slowly in the accuracy demanded of…
In this note we make some specific observations on the distribution of the degree of a given vertex in certain model of randomly growing networks. The rule for network growth is the following. Starting with an initial graph of minimum…
Generative Adversarial Networks (GANs) are modern methods to learn the underlying distribution of a data set. GANs have been widely used in sample synthesis, de-noising, domain transfer, etc. GANs, however, are designed in a model-free…
K-means Fast Learning Artificial Neural Network (K-FLANN) is an unsupervised neural network requires two parameters: tolerance and vigilance. Best Clustering results are feasible only by finest parameters specified to the neural network.…
Convolutional neural network (CNN) architectures utilize downsampling layers, which restrict the subsequent layers to learn spatially invariant features while reducing computational costs. However, such a downsampling operation makes it…
Graphons offer a powerful framework for modeling large-scale networks, yet estimation remains challenging. We propose a novel approach that leverages a low-rank additive representation, yielding both a low-rank connection probability matrix…
A growing random graph is constructed by successively sampling without replacement an element from the pool of virtual vertices and edges. At start of the process the pool contains $N$ virtual vertices and no edges. Each time a vertex is…
Graph neural networks have become a staple in problems addressing learning and analysis of data defined over graphs. However, several results suggest an inherent difficulty in extracting better performance by increasing the number of…
The organizational development of growing random networks is investigated. These growing networks are built by adding nodes successively and linking each to an earlier node of degree k with attachment probability A_k. When A_k grows slower…
In this paper, we tackle the challenge of radio access network (RAN) slicing within an open RAN (O-RAN) architecture. Our focus centers on a network that includes multiple mobile virtual network operators (MVNOs) competing for physical…
Real-world road networks have an approximate scale-invariance property; can one devise mathematical models of random networks whose distributions are {\em exactly} invariant under Euclidean scaling? This requires working in the continuum…
We study a general model of random dynamical simplicial complexes and derive a formula for the asymptotic degree distribution. This asymptotic formula encompasses results for a number of existing models, including random Apollonian networks…
Real-world networks evolve over time via additions or removals of vertices and edges. In current network evolution models, vertex degree varies or grows arbitrarily. A recently introduced degree-preserving network growth (DPG) family of…
We introduce a new embarrassingly parallel parameter learning algorithm for Markov random fields with untied parameters which is efficient for a large class of practical models. Our algorithm parallelizes naturally over cliques and, for…
The interconnection network comprises a significant portion of the cost of large parallel computers, both in economic terms and power consumption. Several previous proposals exploit large-radix routers to build scalable low-distance…
Training deep neural networks (DNNs) in large-cluster computing environments is increasingly necessary, as networks grow in size and complexity. Local memory and processing limitations require robust data and model parallelism for crossing…