Feigenbaum graphs: a complex network perspective of chaos

The recently formulated theory of horizontal visibility graphs transforms time series into graphs and allows the possibility of studying dynamical systems through the characterization of their associated networks. This method leads to a natural graph-theoretical description of nonlinear systems with qualities in the spirit of symbolic dynamics. We support our claim via the case study of the period-doubling and band-splitting attractor cascades that characterize unimodal maps. We provide a universal analytical description of this classic scenario in terms of the horizontal visibility graphs associated with the dynamics within the attractors, that we call Feigenbaum graphs, independent of map nonlinearity or other particulars. We derive exact results for their degree distribution and related quantities, recast them in the context of the renormalization group and find that its fixed points coincide with those of network entropy optimization. Furthermore, we show that the network entropy mimics the Lyapunov exponent of the map independently of its sign, hinting at a Pesin-like relation equally valid out of chaos.Comment: Published in PLoS ONE (Sep 2011

Table Detection in Invoice Documents by Graph Neural Networks

This is the author accepted manuscript. The final version is available from IEEE via the DOI in this record.Tabular structures in documents offer a complementary dimension to the raw textual data, representing logical or quantitative relationships among pieces of information. In digital mail room applications, where a large amount of administrative documents must be processed with reasonable accuracy, the detection and interpretation of tables is crucial. Table recognition has gained interest in document image analysis, in particular in unconstrained formats (absence of rule lines, unknown information of rows and columns). In this work, we propose a graph-based approach for detecting tables in document images. Instead of using the raw content (recognized text), we make use of the location, context and content type, thus it is purely a structure perception approach, not dependent on the language and the quality of the text reading. Our framework makes use of Graph Neural Networks (GNNs) in order to describe the local repetitive structural information of tables in invoice documents. Our proposed model has been experimentally validated in two invoice datasets and achieved encouraging results. Additionally, due to the scarcity of benchmark datasets for this task, we have contributed to the community a novel dataset derived from the RVL-CDIP invoice data. It will be publicly released to facilitate future research.European Unio

A combinatorial framework to quantify peak/pit asymmetries in complex dynamics

LL’s acknowledges funding from an EPSRC Early Career Fellowship EP/P01660X/1

Time reversibility from visibility graphs of nonstationary processes

Visibility algorithms are a family of methods to map time series into networks, with the aim of describing the structure of time series and their underlying dynamical properties in graph-theoretical terms. Here we explore some properties of both natural and horizontal visibility graphs associated to several non-stationary processes, and we pay particular attention to their capacity to assess time irreversibility. Non-stationary signals are (infinitely) irreversible by definition (independently of whether the process is Markovian or producing entropy at a positive rate), and thus the link between entropy production and time series irreversibility has only been explored in non-equilibrium stationary states. Here we show that the visibility formalism naturally induces a new working definition of time irreversibility, which allows to quantify several degrees of irreversibility for stationary and non-stationary series, yielding finite values that can be used to efficiently assess the presence of memory and off-equilibrium dynamics in non-stationary processes without needs to differentiate or detrend them. We provide rigorous results complemented by extensive numerical simulations on several classes of stochastic processes

Effectiveness of dismantling strategies on moderated vs. unmoderated online social platforms

Online social networks are the perfect test bed to better understand large-scale human behavior in interacting contexts. Although they are broadly used and studied, little is known about how their terms of service and posting rules affect the way users interact and information spreads. Acknowledging the relation between network connectivity and functionality, we compare the robustness of two different online social platforms, Twitter and Gab, with respect to dismantling strategies based on the recursive censor of users characterized by social prominence (degree) or intensity of inflammatory content (sentiment). We find that the moderated (Twitter) vs unmoderated (Gab) character of the network is not a discriminating factor for intervention effectiveness. We find, however, that more complex strategies based upon the combination of topological and content features may be effective for network dismantling. Our results provide useful indications to design better strategies for countervailing the production and dissemination of anti-social content in online social platforms

Post-OCR Paragraph Recognition by Graph Convolutional Networks

Paragraphs are an important class of document entities. We propose a new approach for paragraph identification by spatial graph convolutional neural networks (GCN) applied on OCR text boxes. Two steps, namely line splitting and line clustering, are performed to extract paragraphs from the lines in OCR results. Each step uses a beta-skeleton graph constructed from bounding boxes, where the graph edges provide efficient support for graph convolution operations. With only pure layout input features, the GCN model size is 3~4 orders of magnitude smaller compared to R-CNN based models, while achieving comparable or better accuracies on PubLayNet and other datasets. Furthermore, the GCN models show good generalization from synthetic training data to real-world images, and good adaptivity for variable document styles