Related papers: Complex Network Approach to Number Theory
Combinatorial optimization problems are notoriously challenging for neural networks, especially in the absence of labeled instances. This work proposes an unsupervised learning framework for CO problems on graphs that can provide integral…
We study the statistical properties of large random networks with specified degree distributions. New techniques are presented for analyzing the structure of social networks. Specifically, we address the question of how many nodes exist at…
We will see that key concepts of number theory can be defined for arbitrary operations. We give a generalized distributivity for hyperoperations (usual arithmetic operations and operations going beyond exponentiation) and a generalization…
Network datasets appear across a wide range of scientific fields, including biology, physics, and the social sciences. To enable data-driven discoveries from these networks, statistical inference techniques like estimation and hypothesis…
A drawback of the classic approach for complexity analysis of distributed graph problems is that it mostly informs about the complexity of notorious classes of ``worst case'' graphs. Algorithms that are used to prove a tight (existential)…
Many real-world networks are theorized to have core-periphery structure consisting of a densely-connected core and a loosely-connected periphery. While this phenomenon has been extensively studied in a range of scientific disciplines, it…
We present the pattern underlying some of the properties of natural numbers, using the framework of complex networks. The network used is a divisibility network in which each node has a fixed identity as one of the natural numbers and the…
Exponential random graph models are an important tool in the statistical analysis of data. However, Bayesian parameter estimation for these models is extremely challenging, since evaluation of the posterior distribution typically involves…
This paper presents a novel meta algorithm, Partition-Merge (PM), which takes existing centralized algorithms for graph computation and makes them distributed and faster. In a nutshell, PM divides the graph into small subgraphs using our…
In this work, we propose a novel representation of complex multi-relational networks, which is compact and allows very efficient network analysis. Multi-relational networks capture complex data relationships and have a variety of…
Networks are a popular tool for representing elements in a system and their interconnectedness. Many observed networks can be viewed as only samples of some true underlying network. Such is frequently the case, for example, in the…
In this paper, a new measurement to compare two large-scale graphs based on the theory of quantum probability is proposed. An explicit form for the spectral distribution of the corresponding adjacency matrix of a graph is established. Our…
Complex networks of real-world systems are believed to be controlled by common phenomena, producing structures far from regular or random. These include scale-free degree distributions, small-world structure and assortative mixing by…
Within network analysis, the analytical maximum entropy framework has been very successful for different tasks as network reconstruction and filtering. In a recent paper, the same framework was used for link-prediction for monopartite…
Motivated by the increasing need to understand the distributed algorithmic foundations of large-scale graph computations, we study some fundamental graph problems in a message-passing model for distributed computing where $k \geq 2$…
We have a set of processors (or agents) and a set of graph networks defined over some vertex set. Each processor can access a subset of the graph networks. Each processor has a demand specified as a pair of vertices $<u, v>$, along with a…
We characterize probabilities in Bayesian networks in terms of algebraic expressions called quasi-probabilities. These are arrived at by casting Bayesian networks as noisy AND-OR-NOT networks, and viewing the subnetworks that lead to a node…
In this paper, we develop a two-stage distributed algorithm that enables nodes in a graph to cooperatively estimate the spectrum of a matrix $W$ associated with the graph, which includes the adjacency and Laplacian matrices as special…
We consider distributed networks, such as peer-to-peer networks, whose structure can be manipulated by adjusting the rules by which vertices enter and leave the network. We focus in particular on degree distributions and show that, with…
This work theoretically investigates the performance of a composite neural network. A composite neural network is a rooted directed acyclic graph combining a set of pre-trained and non-instantiated neural network models, where a pre-trained…