Related papers: Complex Network Approach to Number Theory
Daily internet communication relies heavily on tree-structured graphs, embodied by popular data formats such as XML and JSON. However, many recent generative (probabilistic) models utilize neural networks to learn a probability distribution…
Motivated by the increasing need for fast processing of large-scale graphs, we study a number of fundamental graph problems in a message-passing model for distributed computing, called $k$-machine model, where we have $k$ machines that…
Modern machine learning techniques are successfully being adapted to data modeled as graphs. However, many real-world graphs are typically very large and do not fit in memory, often making the problem of training machine learning models on…
Designing scalable estimation algorithms is a core challenge in modern statistics. Here we introduce a framework to address this challenge based on parallel approximants, which yields estimators with provable properties that operate on the…
Complex networks are universal, arising in fields as disparate as sociology, physics, and biology. In the past decade, extensive research into the properties and behaviors of complex systems has uncovered surprising commonalities among the…
Probabilistic graphical models allow us to encode a large probability distribution as a composition of smaller ones. It is oftentimes the case that we are interested in incorporating in the model the idea that some of these smaller…
Lifted probabilistic inference algorithms have been successfully applied to a large number of symmetric graphical models. Unfortunately, the majority of real-world graphical models is asymmetric. This is even the case for relational…
This document is an informal bibliography of the papers dealing with distributed approximation algorithms. A classic setting for such algorithms is bounded degree graphs, but there is a whole set of techniques that have been developed for…
Within the last fifteen years, network theory has been successfully applied both to natural sciences and to socioeconomic disciplines. In particular, bipartite networks have been recognized to provide a particularly insightful…
Since the mathematicians of ancient Greece until Fermat, since Gauss until today; the way how the primes along the numerical straight line are distributed has become perhaps the most difficult math problem; many people believe that their…
It is commonly believed that real networks are scale-free and fraction of nodes $P(k)$ with degree $k$ satisfies the power law $P(k) \propto k^{-\gamma} \text{ for } k > k_{min} > 0$. Preferential attachment is the mechanism that has been…
In this paper we present a new version of a network growth model, generalized in order to describe the behavior of social networks. The case of study considered is the preprint archive at cul.arxiv.org. Each node corresponds to a scientist,…
It has been proposed that random wide neural networks near Gaussian process are quantum field theories around Gaussian fixed points. In this paper, we provide a novel map with which a wide class of quantum mechanical systems can be cast…
Neural networks are popular state-of-the-art models for many different tasks.They are often trained via back-propagation to find a value of the weights that correctly predicts the observed data. Although back-propagation has shown good…
We have proposed a model based upon flocking on a complex network, and then developed two clustering algorithms on the basis of it. In the algorithms, firstly a \textit{k}-nearest neighbor (knn) graph as a weighted and directed graph is…
We present new algorithms for inference in credal networks --- directed acyclic graphs associated with sets of probabilities. Credal networks are here interpreted as encoding strong independence relations among variables. We first present a…
The emergence of massive graph data sets requires fast mining algorithms. Centrality measures to identify important vertices belong to the most popular analysis methods in graph mining. A measure that is gaining attention is forest…
We introduce the Iterated Global model as a deterministic graph process that simulates several properties of complex networks. In this model, for every set $S$ of nodes of a prescribed cardinality, we add a new node that is adjacent to…
We define and study the link prediction problem in bipartite networks, specializing general link prediction algorithms to the bipartite case. In a graph, a link prediction function of two vertices denotes the similarity or proximity of the…
The traditional approach of hand-crafting priors (such as sparsity) for solving inverse problems is slowly being replaced by the use of richer learned priors (such as those modeled by deep generative networks). In this work, we study the…