Related papers: Complex Network Approach to Number Theory
We revisit the elegant observation of T. Cover '65 which, perhaps, is not as well-known to the broader community as it should be. The first goal of the tutorial is to explain---through the prism of this elementary result---how to solve…
Simple algebraic rules can produce complex networks with rich structures. These graphs are obtained when looking at a monoid operating on a ring. There are relations to dynamical systems theory and number theory. This document illustrates…
The dominating set problem has many practical applications but is well-known to be NP-hard. Therefore, there is a need for efficient approximation algorithms, especially in applications such as ad hoc wireless networks. Most distributed…
Social studies researchers use graphs to model group activities in social networks. An important property in this context is the centrality of a vertex: the inverse of the average distance to each other vertex. We describe a randomized…
Network Science provides a universal formalism for modelling and studying complex systems based on pairwise interactions between agents. However, many real networks in the social, biological or computer sciences involve interactions among…
We develop a new framework for generalizing approximation algorithms from the structural graph algorithm literature so that they apply to graphs somewhat close to that class (a scenario we expect is common when working with real-world…
Motivated by economic dispatch and linearly-constrained resource allocation problems, this paper proposes a novel Distributed Approx-Newton algorithm that approximates the standard Newton optimization method. A main property of this…
Algorithmic statistics considers the following problem: given a binary string $x$ (e.g., some experimental data), find a "good" explanation of this data. It uses algorithmic information theory to define formally what is a good explanation.…
This paper proposes a new algorithm for solving maximal cliques for simple undirected graphs using the theory of prime numbers. A novel approach using prime numbers is used to find cliques and ends with a discussion of the algorithm.
We propose a novel approach to perform approximate Bayesian inference in complex models such as Bayesian neural networks. The approach is more scalable to large data than Markov Chain Monte Carlo, it embraces more expressive models than…
A novel graph-to-tree conversion mechanism called the deep-tree generation (DTG) algorithm is first proposed to predict text data represented by graphs. The DTG method can generate a richer and more accurate representation for nodes (or…
The application of the network approach to the urban case poses several questions in terms of how to deal with metric distances, what kind of graph representation to use, what kind of measures to investigate, how to deepen the correlation…
We study the problem of generating graphs with prescribed degree sequences for bipartite, directed, and undirected networks. We first propose a sequential method for bipartite graph generation and establish a necessary and sufficient…
We consider the problem of training a machine learning model over a network of nodes in a fully decentralized framework. The nodes take a Bayesian-like approach via the introduction of a belief over the model parameter space. We propose a…
This chapter aims at reviewing complex networks models and methods that were either developed for or applied to socioeconomic issues, and pertinent to the theme of New Economic Geography. After an introduction to the foundations of the…
This paper presents a new approach for computing posterior probabilities in Bayesian nets, which sidesteps the triangulation problem. The current state of art is the clique tree propagation approach. When the underlying graph of a Bayesian…
Bayesian network is a complete model for the variables and their relationships, it can be used to answer probabilistic queries about them. A Bayesian network can thus be considered a mechanism for automatically applying Bayes' theorem to…
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…
The unique prime factorization theorem is used to show the existence of a function on a countable set $\mathcal{X}$ so that the sum aggregator function is injective on all multisets of $\mathcal{X}$ of finite size.
In the last 15 years, statistical physics has been a very successful framework to model complex networks. On the theoretical side, this approach has brought novel insights into a variety of physical phenomena, such as self-organisation,…